{"paper_id":"27ceef39-7341-4be3-9c5c-d41a9bc51519","body_text":"Intertemporal economic valuation and depletion pathways of metallic mineral resources in La Libertad, Peru: Implications for sustainable management under Hotelling’s rule | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Intertemporal economic valuation and depletion pathways of metallic mineral resources in La Libertad, Peru: Implications for sustainable management under Hotelling’s rule Neyder P. Araujo-Avila, Jairo J. Marquina-Araujo, Marco A. Cotrina-Teatino This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9087323/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The exploitation of metallic mineral resources in territories highly dependent on mining poses a central sustainability challenge, as increases in production and current revenues do not necessarily guarantee the sustainable economic valuation of mineral stock in the long term. In this context, the aim of the study was to evaluate the intertemporal economic valuation and depletion pathways of gold and silver resources in La Libertad, Peru, and to examine their implications for sustainable management under Hotelling’s rule. A quantitative, applied, and non-experimental study was conducted based on official data on reserves, production, prices, and interest rates. Price, revenue, and net present value trajectories were projected for the 2025–2040 period, extraction pathways were simulated until reserve exhaustion, and a sensitivity analysis was performed under variations in prices and interest rates. The results showed that gold reserves would be exhausted in approximately eight years, whereas silver would reach a depletion horizon of nearly sixty-four years. Although projected nominal revenues increased steadily, net present value remained nearly stable, ranging from USD 3.49 to 3.54 billion for gold and from USD 28.69 to 29.26 million for silver. It is concluded that extractive sustainability depends not only on reserves and prices, but also on the rate of extraction, the economic lifespan of the stock, and the financial conditions under which the resource is valued. Hotelling’s rule intertemporal valuation mineral resource depletion sustainable mining governance Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Introduction The exploitation of metallic mineral resources poses a fundamental challenge to the economic sustainability of extractive territories: each unit extracted generates revenue in the present while simultaneously reducing the future availability of natural stock. This intertemporal dilemma was classically formulated by Hotelling ( 1931 ), who demonstrated that the efficient allocation of an exhaustible resource depends on the evolution of its scarcity rent over time, and was later extended by Solow ( 1974 ) and Hartwick ( 1977 ), who linked the depletion of natural capital to intergenerational equity and the need to transform extractive rents into other forms of capital. From this perspective, mining cannot be understood solely as a productive activity, but also as a process through which natural wealth is converted into economic wealth, with implications for future welfare, fiscal sustainability, and territorial development pathways (Cotrina-Teatino et al., 2025 ). From this standpoint, Hotelling’s rule remains one of the most influential analytical frameworks for the study of non-renewable resources. In its basic formulation, it states that, under ideal conditions, the net price of the resource should grow at a rate equal to the interest rate, such that the resource owner is indifferent between extracting today and postponing extraction (Gaitan et al., 2015 ; Hotelling, 1931 ; Livernois, 2009 ; Pfingsten, 1986 ). However, empirical evidence shows that this logic is rarely observed in its pure form due to deposit heterogeneity, changing extraction costs, additional exploration, technological change, and market imperfections (Mlambo, 2022 ). Therefore, rather than being treated as a strict empirical law, the rule is more commonly used as a useful framework for organizing intertemporal valuation exercises, simulating depletion trajectories, and conducting sensitivity analyses under explicit assumptions, as suggested by the reviews of Krautkraemer ( 1990 , 1998 ) and the broader assessments of Ferreira da Cunha and Missemer (2020); Gaudet ( 2007 ); Gaudet and Howitt ( 1989 ); Slade ( 1984 ); Slade and Thille ( 2009 ). The current interest in this approach is not merely theoretical. Mineral resource governance now occupies a central place in the international sustainability agenda, given that minerals and metals underpin critical supply chains while also generating long-term environmental, social, and territorial pressures (Christmann, 2021 ). In this context, the International Resource Panel has emphasized that twenty-first-century mineral governance should be oriented toward transforming extractive wealth into lasting benefits, integrating environmental sustainability into decision-making, and strengthening the institutional capacity of producing territories (Ayuk et al., 2020 ). Complementarily, the IGF’s Mining Policy Framework highlights that a well-governed mining sector must align economic benefits, social legitimacy, long-term planning, and environmental protection (IGF, 2023 ). In the Peruvian case, mining has been one of the main pillars of economic growth, although its territorial outcomes have depended to a large extent on institutional quality, the design of fiscal decentralization, and local capacity to manage rents and conflicts. Arellano-Yanguas ( 2011 ) showed that mining expansion in Peru can intensify territorial tensions when the distribution of benefits and institutional capacities is uneven, while Figueroa B. et al. ( 2010 ) found that the depreciation of natural capital and the degradation associated with metallic mining represent a substantial share of the sector’s economic value. More recently, Orihuela et al. ( 2024 ) demonstrated that incorporating changes in natural capital stock and environmental degradation significantly alters the measurement of mining GDP and NNP in the country, thereby reinforcing the need for assessments that go beyond production indicators or current revenue flows. In this context, the La Libertad region constitutes a particularly relevant case. According to official information from MINEM and the Central Reserve Bank of Peru (BCRP), it has remained one of the country’s main gold-producing territories and continues to hold an important position within mining activity in northern Peru, with gold playing a prominent role and silver maintaining a sustained presence in its recent productive structure (BCRP, 2025 ; MINEM, 2025 ). However, despite the economic importance of these territories, studies that integrate, at the regional scale, the Hotelling framework with reserves, observed production, projected price trajectories, net present value, and depletion pathways for metallic resources remain scarce. Many empirical applications have been developed at the national or highly aggregated level, such as Mlambo ( 2022 ) study on gold in South Africa, whereas in Peru the literature has largely focused on green accounting exercises or macroeconomic adjustments to mining output. This gap is particularly relevant because mining territories differ in mineral composition, resource quality, extraction intensity, and depletion horizon; as such, an exclusively national perspective may obscure critical differences for regional sustainability and the formulation of territorially grounded public policies (Figueroa B. et al., 2010 ). Against this background, the present study addresses the following research question: how do the intertemporal economic valuation and depletion pathways of metallic resources evolve in La Libertad, Peru? In response, the main objective is to evaluate the intertemporal economic valuation and depletion pathways of metallic mineral resources in La Libertad and to examine their implications for sustainable management under Hotelling’s rule. To this end, the study: (i) characterizes the regional mineral base and productive context; (ii) estimates projected trajectories of prices, revenues, and net present value for gold and silver; (iii) simulates intertemporal extraction and depletion pathways under reserve constraints; and (iv) analyses the sensitivity of valuation to changes in prices and interest rates. In doing so, the article seeks to provide useful evidence for linking the economics of exhaustible resources, mineral governance, and territorial sustainability in a strategic region of Peru. The remainder of the article is organized as follows. Section 2 presents the methodology. Section 3 reports the results. Section 4 discusses the findings. Finally, Section 5 summarizes the main conclusions. 2. Methodology 2.1. Research approach and analytical design The study followed a quantitative, applied, and non-experimental approach, with a descriptive-analytical and prospective scope, to estimate the intertemporal economic valuation and depletion pathways of gold and silver in La Libertad, Peru. A regional case-study scale was adopted because it allows reserves, production, prices, and macro-financial conditions to be examined within a specific mining territory, thereby avoiding the aggregation bias of national-level studies and better capturing relevant extractive differences (Cotrina-Teatino & Marquina-Araujo, 2024 ). This choice is consistent with contemporary interpretations of Hotelling’s rule, which emphasize the importance of economic and institutional context in its application (Ferreira da Cunha & Missemer, 2020; Gaudet, 2007 ). Moreover, in contrast to the predominance of national-scale studies, such as Mlambo ( 2022 ) analysis for South Africa, La Libertad constitutes an appropriate unit of analysis because of its importance in Peru’s gold and silver production, in line with the intertemporal allocation problem of exhaustible stock originally posed by Hotelling ( 1931 ). 2.2. Study area and unit of analysis The unit of analysis consisted of the metallic resources of gold and silver in the La Libertad region, selected because of their importance within Peru’s mining dynamics and the territorial concentration of gold and silver operations in provinces with a well-established extractive trajectory. This configuration makes La Libertad an appropriate case for examining the intertemporal valuation of the resource and its depletion pathways within a subnational setting, where reserve conditions, production levels, and operational continuity can be observed more precisely than in a national aggregate (Hotelling, 1931 ). The time horizon was structured at two levels. The 2025–2040 period was used to project prices, revenues, and net present value, while the depletion simulation was extended until the year in which the remaining reserves are reduced to zero. This approach simultaneously considers the economic dimension of the expected flow and the physical dimension of the available stock, in line with the intertemporal problem originally formulated by Hotelling ( 1931 ) and with Krautkraemer ( 1998 ) review, which showed that the valuation of a non-renewable resource depends on the initial size of reserves, the rate of extraction, and the expected trajectory of its value over time. 2.3. Data sources, database construction, and variable definition The database was constructed from official and traceable secondary sources to ensure consistency and comparability across the model parameters. Gold and silver reserves and production were obtained from official records of the Peruvian mining sector, baseline prices were taken from international benchmark series, and the interest rate was based on the BCRP reference rate for 2025. This consistency was essential, as even small variations in prices, reserves, or discount rates can significantly affect economic valuation (see Table 1 ) (Lilford, 2023 ; Lilford et al., 2018 ). Table 1 Sources of information and basic model parameters Variable Symbol Description Unit Source Initial reserves \\({R}_{0}\\) Initial regional stock of gold or silver oz MINEM Observed annual production \\({q}_{0}\\) Observed regional production in the base year oz/year MINEM Base price \\({P}_{0}\\) Reference mineral price USD/oz International precious metals price series Interest rate \\(r\\) Reference rate used for projection and discounting % per year BCRP Note. MINEM = Ministry of Energy and Mines of Peru; BCRP = Central Reserve Bank of Peru. The variables included in the model were \\({R}_{0}\\) , \\({q}_{0}\\) , \\({P}_{0}\\) , \\(r\\) , projected price \\(\\left({P}_{t}\\right)\\) , annual revenue \\(\\left({I}_{t}\\right)\\) , net present value \\(\\left(VPN\\right)\\) , cumulative production \\(\\left({Q}_{t}\\right)\\) and remaining reserves \\(\\left({R}_{t}\\right)\\) . This set of variables reflects the basic structure of intertemporal models of exhaustible resources and discounted cash flow valuation approaches. Among them, the discount rate occupies a central role because it directly determines the magnitude of present value; for this reason, it was treated as an explicit assumption and subsequently evaluated through sensitivity analysis (Kamel et al., 2023 ; Savolainen, 2016 ). 2.4. Characterization of the mineral base and economic context Before modelling, the mineral base of La Libertad was characterized by considering the distribution of operating projects, gold and silver reserves, their regional share, the recent evolution of production, and the observed price trajectory, to establish a realistic baseline for the valuation exercise (Hotelling, 1931 ). In addition, ore-grade heterogeneity was incorporated as a contextual element, given that resource quality influences expected profitability and the economic interpretation of the stock, thereby avoiding an exclusively volumetric reading of reserves (Krautkraemer, 1998 ). 2.5. Economic framework of Hotelling’s rule The economic formulation followed Hotelling’s basic principle for exhaustible resources. In continuous time, the intertemporal condition can be expressed as: $$\\frac{d({P}_{t}-{MC}_{t})}{dt}=r({P}_{t}-{MC}_{t})$$ 1 where \\({P}_{t}\\) represents the resource price at time \\(t\\) , \\({MC}_{t}\\) the marginal cost of extraction, and \\(r\\) the interest rate. This expression indicates that the resource rent should grow at the market rate in order to sustain intertemporal efficiency in extraction. Hotelling originally formulated this principle in his seminal 1931 contribution (Hotelling, 1931 ), and subsequent developments, such as those of Levhari and Liviatan ( 1977 ), clarified several of its analytical assumptions. More recently, Ferreira da Cunha and Missemer (2020) showed that the so-called “Hotelling rule” should be understood as a central foundation of non-renewable resource economics, although its empirical validity depends on more restrictive conditions than those assumed in the canonical model. As the study relied on aggregated regional data rather than on homogeneous marginal-cost series for individual mining operations, the market price was used as an operational proxy for the net resource price. Under this assumption, the price trajectory was estimated using an exponential function of the form: $${P}_{t}={P}_{0}{e}^{rt}$$ 2 where \\({P}_{0}\\) is the base price observed in 2025, \\(r\\) is the annual interest rate, and \\(t\\) is the number of years elapsed since the base year. This simplification is appropriate in regional exercises where marginal costs cannot be observed with sufficient consistency across all productive units, although it should be interpreted as an analytical approximation rather than as an exhaustive measure of effective mineral rent. For this reason, the study states this assumption explicitly and limits its use to the construction of intertemporal valuation and depletion scenarios (Ferreira da Cunha & Missemer, 2020). 2.6. Revenue projection and estimation of net present value Once the price trajectory had been estimated, annual gross revenues were calculated for each mineral under an initial constant-production scenario equivalent to the production observed in 2024. The expression used was: $${I}_{t}={P}_{t}*q$$ 3 where \\({I}_{t}\\) is the projected annual revenue, \\({P}_{t}\\) the estimated price, and \\(q\\) the constant production level. This assumption was adopted to isolate the effect of price growth on the intertemporal valuation of the resource before introducing differentiated extraction trajectories. Thus, in this first stage, variation in economic value derives solely from the projected behaviour of price under the Hotelling framework. NPV was then estimated as: $$VPN=\\sum_{t=0}^{n}\\frac{{I}_{t}}{{(1+r)}^{t}}$$ 4 where \\({I}_{t}\\) represents the projected revenue represents in year \\(t\\) , \\(r\\) is the discount rate, and \\(n\\) is the evaluation horizon. NPV was used because it summarizes the combined effect of time, the magnitude of flows, and the opportunity cost of capital, and it remains a widely accepted tool in intertemporal valuation exercises for extractive resources. Even so, its result depends on explicit financial assumptions, particularly on the discount rate. Krautkraemer ( 1998 ) showed that this parameter plays a decisive role in the valuation of non-renewable resources; therefore, in this study, the stability of present value was not interpreted as a universal verification of the theory, but rather as an internal property of the scenario constructed for La Libertad. 2.7. Simulation of depletion pathways In addition to the valuation based on constant production, depletion pathways were estimated to assess the potential duration of reserves under increasing extraction trajectories. Annual production was projected as: $${q}_{t}={q}_{t-1}(1+g)$$ 5 where \\({q}_{t}\\) is production in year \\(t\\) , \\({q}_{t-1}\\) is production in the previous year, and \\(g\\) is the annual extraction growth rate. For gold, \\(g=0.03\\) was adopted, whereas for silver \\(g=0.05\\) was used, in order to represent differentiated extraction pressures according to the relative magnitude of reserves and the distinct scale of availability of each mineral. Based on this projection, cumulative production was calculated as: $${Q}_{t}=\\sum_{i=0}^{t}{q}_{i}$$ 6 and remaining reserves were obtained as: $${R}_{t}={R}_{0}-{Q}_{t}$$ 7 where \\({R}_{0}\\) corresponds to the initial reserve and \\({R}_{t}\\) to the remaining stock available in year \\(t\\) . Depletion was defined as the first period in which \\({R}_{t}\\le0\\) , with final production adjusted to the effectively remaining stock. This made it possible to integrate the economic dimension of valuation with a physical reading of resource duration, which is particularly important when the analysis is oriented toward long-term extractive sustainability (Levhari & Liviatan, 1977 ). These trajectories do not represent an optimum derived from a complete dynamic control problem with endogenous costs, demand, and exploration. Rather, they are interpreted as extraction scenarios consistent with the intertemporal logic of the model and constrained by the physical availability of the resource. This clarification avoids overstating the scope of the exercise and keeps the analysis within transparent and verifiable assumptions. Levhari and Liviatan ( 1977 ), as well as the contemporary reinterpretation offered by Ferreira da Cunha and Missemer (2020), show that the effective dynamics of non-renewable resources may diverge from the canonical model when other economic or institutional mechanisms come into play. 2.8. Verification of intertemporal consistency and sensitivity analysis To verify the internal consistency of the scenario, the projected price trajectory was compared with the expected growth of the financial factor \\({e}^{rt}\\) ; c when both curves are practically coincident, the scenario is considered consistent with Hotelling’s intertemporal logic. This verification was structural rather than econometric, since it did not seek to empirically validate the rule, but rather to ensure the consistency of the simulation constructed for La Libertad, considering that real markets are influenced by factors such as uncertainty, exploration, regulation, and technological change (Krautkraemer, 1998 ). In addition, a sensitivity analysis was performed on two key parameters, the base price and the interest rate, by applying variations of ± 40% and recalculating net present value in each case. $${P}_{0}^{*}={P}_{0}(1+{\\delta}_{P})$$ 8 $${r}^{*}=r(1+{\\delta}_{r})$$ 9 where \\({\\delta}_{P}\\) and \\({\\delta}_{r}\\) represent the percentage variation applied to price and interest rate, respectively. This procedure made it possible to assess the sensitivity of resource value to plausible changes in market conditions and in the opportunity cost of capital, which is a critical issue in mining evaluation, since even small changes in the discount rate can substantially affect NPV and the perceived economic viability of the resource (Krautkraemer, 1998 ; Ovalle, 2020 ). 3. Results 3.1. Productive context of metallic mineral resources in La Libertad La Libertad constitutes one of Peru’s main metallic mining territories due to the territorial concentration of gold and silver operations and the magnitude of its regional reserves. The distribution of operating projects shows a clear predominance of the province of Pataz, where underground mining operations of companies such as Poderosa, Consorcio Minero Horizonte, and MARSA are concentrated, while in Sánchez Carrión and Otuzco surface operations associated with Summa Gold, La Arena, and Barrick Misquichilca predominate (Table 2 ). This configuration reveals a dual extractive structure in which high-grade underground deposits coexist with lower-grade, larger-scale surface operations, thereby reinforcing the importance of analysing the region not only in terms of production volume, but also considering the technical and economic heterogeneity of its mining units. Table 2 Operating metallic mining projects in the La Libertad region Holder Mining unit Product Province District Type of mining Compañía Minera Caravelí S.A.C. La Estrella Au, Ag Pataz Huaylillas Underground Compañía Minera Poderosa S.A. Santa María Au, Ag Pataz Pataz Underground Marañón Au, Ag Pataz Pataz Underground Consorcio Minero Horizonte S.A. Los Zambos Au Pataz Parcoy Underground Parcoy Au Pataz Parcoy Underground Minera Aurífera Retamas S.A. Retamas Au, Ag Pataz Parcoy Underground Summa Gold Corporation S.A.C. El Toro Au, Ag Sánchez Carrión Huamachuco Open pit La Arena S.A. La Arena Au, Ag Sánchez Carrión Huamachuco Open pit Minera Barrick Misquichilca S.A. Alto Chicama Au, Ag Otuzco Quiruvilca Open pit La Libertad holds approximately 9,645,210 oz of gold and 289,904,000 oz of silver, equivalent to about 12% of national gold reserves and 6.44% of silver reserves, which confirms its strategic relevance in Peru’s metallic mining production. In addition, the resource structure shows marked ore-grade heterogeneity: while operations such as Poderosa (14.3 g/t), Caravelí (12.5 g/t), MARSA (10.68 g/t), and Consorcio Minero Horizonte (10.04 g/t) exhibit high gold grades, others such as Barrick Misquichilca (2.49 g/t), Summa Gold (0.43 g/t), and La Arena (0.33 g/t) report considerably lower values. This indicates that regional valuation depends not only on the volume of reserves, but also on ore quality and the type of mining operation. At the same time, international prices followed an upward trend between 2010 and 2025, reaching an average of USD 3,067/oz for gold and USD 40.97/oz for silver in 2025 (Fig. 1 ). However, silver exhibited greater volatility, whereas gold maintained a more stable trajectory, consolidating its role as the region’s main store of economic value. This was accompanied by the financial context: the BCRP reference rate stood at 4.64% in 2025, after peaking at 7.54% in 2023 (Fig. 2 ), thus shaping a less restrictive environment for the intertemporal valuation of the resource. Between 2023 and 2024, gold production in La Libertad increased from 1,085,509 oz to 1,138,356 oz (+ 4.9%), while silver rose from 687,722 oz to 700,382 oz (+ 1.8%). Taken together, both minerals recorded an aggregate growth of 3.4%, reflecting recent production dynamism. This pattern, combined with the magnitude of reserves, ore-grade heterogeneity, and the favourable price environment, provides a solid basis for analysing the intertemporal economic valuation and depletion pathways of metallic mineral resources in the region. 3.2. Intertemporal economic valuation under Hotelling’s rule Based on regional reserves, the production observed in 2024, the 2025 base prices, and an interest rate of 4.64%, an intertemporal valuation scenario was constructed for gold and silver in La Libertad (Table 3 ). Under this framework, projected prices followed an upward trajectory consistent with Hotelling’s logic. Table 3 Economic and productive inputs for metallic minerals in La Libertad Mineral Reserves (oz) Production (2024, oz) Base price (2025, USD/oz) Interest rate (2025, %) Gold 9’645,210.00 1’138,356.00 3,067.00 4.64% Silver 289’904,000.00 700,382.00 40.97 For gold, the 2025–2040 projection showed an increase in price from USD 3,067.00/oz to USD 6,131.84/oz, while, under a constant production level of 1,138,356 oz/year, projected revenues increased from USD 3.491 billion to USD 6.980 billion (Table 4 ). These results confirm the strong economic weight of gold within the regional metallic mining structure. Table 4 Projected gold price and estimated revenues in the La Libertad region (2025–2040) Year t Projected price (USD/oz) Production (oz) Projected revenue (USD) 2025 0 3,067.00 1,138,356 3,491,337,852.00 2026 1 3,212.39 1,138,356 3,656,843,430.84 2027 2 3,364.97 1,138,356 3,830,533,789.32 2028 3 3,524.97 1,138,356 4,012,670,749.32 2029 4 3,692.65 1,138,356 4,203,550,283.40 2030 5 3,868.29 1,138,356 4,403,491,131.24 2031 6 4,052.17 1,138,356 4,612,812,032.52 2032 7 4,244.60 1,138,356 4,831,865,877.60 2033 8 4,445.87 1,138,356 5,060,982,789.72 2034 9 4,656.30 1,138,356 5,300,527,042.80 2035 10 4,876.24 1,138,356 5,550,897,061.44 2036 11 5,106.05 1,138,356 5,812,502,653.80 2037 12 5,346.11 1,138,356 6,085,776,395.16 2038 13 5,596.82 1,138,356 6,371,173,627.92 2039 14 5,858.58 1,138,356 6,669,149,694.48 2040 15 6,131.84 1,138,356 6,980,216,855.04 Note . Annual gold production was kept constant at 1,138,356 oz for simulation purposes. The projected price was estimated using the function \\(\\text{P}\\left(\\text{t}\\right)=3067\\text{*}{e}^{0.0464t}\\) . However, once those future flows were discounted at the same 4.64% rate, the net present value of gold showed only minimal variation over the period analysed. NPV increased from USD 3.491 billion in 2025 to USD 3.535 billion in 2040 (Table 5 ), thus following an almost stable trajectory. This indicates that the strong nominal growth in revenues does not translate into an equivalent increase in the present economic value of the resource, since intertemporal discounting almost entirely offsets the expansion of future flows. Table 5 Net present value of projected gold revenues in the La Libertad region (2025–2040) Year NPV (USD) Year NPV (USD) 2025 3,491,337,852.00 2033 3,520,894,504.38 2026 3,494,689,823.05 2034 3,524,029,017.05 2027 3,498,354,659.29 2035 3,526,840,861.57 2028 3,502,195,076.89 2036 3,529,296,320.90 2029 3,506,108,268.39 2037 3,531,369,970.55 230 3,510,010,948.25 2038 3,533,043,120.06 2031 3,513,818,880.16 2039 3,534,290,406.81 2032 3,517,472,848.79 2040 3,535,110,149.45 Silver exhibited an intertemporal pattern like that of gold, although at a much smaller monetary scale. The projected price increased from USD 40.97/oz in 2025 to USD 82.50/oz in 2040, and estimated revenues, under a constant production level of 700,382 oz/year, rose from USD 28.69 million to USD 57.78 million (Table 6 ). However, once the flows were discounted, NPV remained almost stable, increasing from USD 28.69 million to USD 29.26 million between 2025 and 2040 (Table 7 ), which reflects only a marginal real variation. Table 6 Projected silver price and estimated revenues in the La Libertad region (2025–2040) Year t Projected price (USD/oz) Production (oz) Projected revenue (USD) 2025 0 40.97 700,382 28,694,650.54 2026 1 42.90 700,382 30,046,387.80 2027 2 44.93 700,382 31,468,163.26 2028 3 47.06 700,382 32,959,976.92 2029 4 49.31 700,382 34,535,836.42 2030 5 51.66 700,382 36,181,734.12 2031 6 54.13 700,382 37,911,677.66 2032 7 56.73 700,382 39,732,670.86 2033 8 59.45 700,382 41,637,709.90 2034 9 62.30 700,382 43,633,798.60 2035 10 65.29 700,382 45,727,940.78 2036 11 68.42 700,382 47,920,136.44 2037 12 71.70 700,382 50,217,389.40 2038 13 75.14 700,382 52,626,703.48 2039 14 78.73 700,382 55,141,074.86 2040 15 82.50 700,382 57,781,515.00 Note . Annual silver production was kept constant at 700,382 oz for simulation purposes. The projected price was estimated using the function \\(\\text{P}\\left(\\text{t}\\right)=40.97\\text{*}{e}^{0.0464t}\\) . Table 7 Net present value of projected silver revenues in the La Libertad region (2025–2040) Año VPN (USD) Año VPN (USD) 2025 28,694,650.54 2033 28,967,097.90 2026 28,714,055.62 2034 29,009,713.78 2027 28,739,283.25 2035 29,053,893.14 2028 28,766,942.55 2036 29,096,651.01 2029 28,805,741.21 2037 29,139,450.65 230 28,840,363.04 2038 29,183,384.96 2031 28,879,297.01 2039 29,221,802.00 2032 28,924,352.31 2040 29,263,277.11 Taken together, the comparison between both minerals reveals two main findings (Fig. 3 ): gold overwhelmingly dominates in absolute economic value, and both gold and silver follow a similar intertemporal trajectory, characterized by rising prices, expanding nominal revenues, and relatively stable present values. This suggests internal consistency in the valuation exercise under the Hotelling framework, with the two minerals differing primarily in the economic magnitude of their reserves and productive flows. 3.3. Depletion pathways and intertemporal equilibrium Table 8 shows that gold in La Libertad follows an increasing extraction pathway under Hotelling’s logic, with annual production rising from 1,138,356 oz in 2025 to 1,359,256.60 oz in 2031, while the projected price increases from 3,067.00 USD/oz to 4,052.17 USD/oz. Cumulative extraction reaches 8,722,609.80 oz in 2031, leaving a final balance of 922,600.20 oz for 2032, the year in which reserves are fully exhausted. Taken together, these results indicate a short depletion horizon of approximately eight years, reflecting strong extraction pressure on the regional gold stock. Table 8 Extraction pathway and reserve depletion of gold in the La Libertad region Year t Projected price (USD/oz) Optimal annual extraction (oz) Cumulative extraction (oz) Remaining reserves (oz) 2025 0 3,067.00 1,138,356.00 1,138,356.00 8,506,854.00 2026 1 3,212.39 1,172,506.68 2,310,862.68 7,334,347.32 2027 2 3,364.97 1,207,681.88 3,518,544.56 6,126,665.44 2028 3 3,524.97 1,243,912.34 4,762,456.90 4,882,753.10 2029 4 3,692.65 1,281,229.71 6,043,686.60 3,601,523.40 2030 5 3,868.29 1,319,666.60 7,363,353.20 2,281,856.80 2031 6 4,052.17 1,359,256.60 8,722,609.80 922,600.20 2032 7 4,244.60 922,600.20 9,645,210.00 0 By contrast, Table 9 shows that silver exhibits a much longer depletion pathway because of its larger reserve base. The projected price rises from 40.97 USD/oz in 2025 to 762.07 USD/oz in 2088, while annual extraction increases from 700,382.00 oz to 14,423,528.55 oz in 2087. Cumulative extraction reaches 288,886,459.47 oz, leaving a remaining balance of 1,017,540.53 oz for 2088, when reserves are completely exhausted. Unlike gold, silver displays a much more gradual depletion horizon of around 64 years, suggesting lower relative extraction pressure in the short term. Table 9 Intertemporal extraction pathway and reserve depletion of silver in the La Libertad region Year t Projected price (USD/oz) Optimal annual extraction (oz) Cumulative extraction (oz) Remaining reserves (oz) 2025 0 40.97 700,382.00 700,382.00 289,203,618.00 2026 1 42.9 735,401.10 1,435,783.10 288,468,216.90 2027 2 44.93 772,171.16 2,207,954.26 287,696,045.75 2028 3 47.06 810,779.71 3,018,733.97 286,885,266.03 2029 4 49.31 851,318.70 3,870,052.67 286,033,947.33 2030 5 51.66 893,884.63 4,763,937.30 285,140,062.70 2031 6 54.13 938,578.86 5,702,516.16 284,201,483.84 2032 7 56.73 985,507.81 6,688,023.97 283,215,976.03 2033 8 59.45 1,034,783.20 7,722,807.17 282,181,192.83 2034 9 62.3 1,086,522.36 8,809,329.53 281,094,670.47 2035 10 65.29 1,140,848.48 9,950,178.01 279,953,821.99 … … … … … … 2086 61 694.53 13,736,693.85 274,462,930.93 15,441,069.07 2087 62 727.52 14,423,528.55 288,886,459.47 1,017,540.53 2088 63 762.07 1,017,540.53 289,904,000.00 0 3.4. Sensitivity of valuation to price and interest rate The sensitivity analysis shows that the intertemporal economic valuation of metallic resources in La Libertad depends primarily on the base price and the interest rate. In the case of gold, a 40% increase in price raises NPV from approximately USD 3.5 billion to about USD 4.9–5.0 billion, while a 40% reduction in the interest rate increases it to around USD 5.9 billion. Conversely, an equivalent increase in the interest rate reduces NPV to just over USD 2.3 billion, confirming that discounting exerts a stronger influence than price on the present value of the resource. Silver follows the same pattern, although at a smaller monetary scale. A 40% increase in price raises NPV from approximately USD 29 million to more than USD 40 million, while a 40% reduction in the interest rate increases it to nearly USD 47 million; by contrast, an increase in the interest rate reduces it to slightly above USD 20 million (see Fig. 4 ). Taken together, both minerals respond similarly to changes in market and financial assumptions, but the steeper slope associated with the interest rate confirms that this is the most sensitive parameter in the model. 4. Discussion The findings of this study show that the intertemporal valuation of gold and silver in La Libertad follows a trajectory consistent with the structural logic of Hotelling’s rule: projected prices increase at the pace of the interest rate, nominal revenues grow steadily, and net present value remains virtually stable over the period analysed. This pattern is consistent with the contemporary interpretation of the rule not as a universal empirical law, but as a useful organizing framework for simulating economic trajectories under explicit assumptions, as argued by Ferreira da Cunha and Missemer (2020) in their critical review of Hotelling’s legacy. In this respect, the results differ from those reported by Mlambo ( 2022 ) for gold in South Africa, where no empirical evidence consistent with the rule was found and extraction was concluded not to follow a socially optimal path. This difference may be explained by the fact that the present study does not seek to econometrically test observed market behaviour, but rather to construct a regional intertemporal valuation scenario under controlled assumptions regarding reserves, prices, and discounting. From this perspective, the contribution of the La Libertad case does not lie in “proving” the rule in a strict empirical sense, but in showing how its regional application makes it possible to distinguish between nominal revenue growth and the preservation of the present economic value of the resource, a distinction that is especially relevant in mining territories where production expansion is often mistakenly interpreted as an automatic increase in wealth (Cotrina-Teatino & Marquina-Araujo, 2024 ; Di Maria & Valente, 2008 ; Missemer et al., 2022 ; Uberman, 2023 ). At the same time, the depletion pathways obtained showing a short economic life for gold, close to eight years, and a much longer one for silver, around sixty-four years reinforce the idea that extractive sustainability depends not only on price, but also on the combination of stock size, extraction intensity, and the economic value of mineral. This is consistent with Krautkraemer ( 1998 ), who argued that the scarcity of non-renewable resources must be analysed in relation to quality, costs, and extraction rates, and also with green accounting studies applied to Peruvian mining (Figueroa B. et al., 2010 ). In particular, Figueroa B. et al. ( 2010 ) estimated that the total loss of natural capital in Peruvian metallic mining accounted for between 31% and 51% of mining GDP, and that conventional GDP overstated the sector’s true economic income by 51%–64% over the 1992–2006 period. The results of this study move in the same direction, but from a regional and prospective perspective: rather than retrospectively correcting aggregate accounts, they show how the combination of accelerated gold depletion, present-value stability, and high sensitivity to discounting can be used to anticipate sustainability risks in a specific mining region. In comparison with experiences such as the correction of mining GDP in Chile (Figueroa & Calfucura, 2004 ; Mardones & del Rio, 2019 ), which likewise emphasized the importance of incorporating natural capital depreciation into economic measurement, the case of La Libertad provides evidence that the subnational scale makes it possible to better capture differences between minerals and translate them into more refined criteria for the intertemporal management of the resource. 4.1. Policy implications and sustainable management of metallic resources The results indicate that the sustainability of metallic mining in La Libertad cannot be assessed solely on the basis of reserve volumes or the upward trajectory of prices, but rather on the relationship between present value, extraction pace, and the economic lifespan of the stock. Under the modelled scenario, gold exhausts its reserves in approximately eight years, whereas silver extends its depletion horizon to around sixty-four years; however, even with increasing nominal revenues, the net present value of gold remains around USD 3.49–3.54 billion and that of silver around USD 28.69–29.26 million. This combination suggests that the increase in future flows does not automatically translate into a proportional expansion of regional economic wealth, since a substantial share of that increase is neutralized when expressed in present-value terms. From a public policy perspective, this implies that regional mining planning should not be based solely on extracted volumes or current revenues, but also on indicators that explicitly capture the economic value of the stock and its depletion trajectory, in line with the sustainable-use mandate established by Law No. 26821(Republica del Perú, 2017 ). This interpretation becomes even more relevant when the two minerals analysed are compared. Gold combines greater absolute economic value, accelerated depletion, and high sensitivity to the discount rate, making it a highly profitable asset but also one that is highly vulnerable from an intertemporal perspective. Silver, by contrast, shows much greater availability and a more gradual depletion pathway, thereby opening broader scope for longer-term strategies linked to territorial stability, productive linkages, and economic diversification. Consequently, a uniform mining policy for both minerals would be inefficient. The study’s evidence supports the need for differentiated management by mineral and by depletion horizon: for gold, this implies strengthening stock monitoring, extraction sequencing, and the early transformation of rents into durable assets; for silver, it implies a management strategy that combines economic utilization with a longer-term territorial perspective. This logic is consistent with the Mining Policy Framework, which argues that sound mineral governance should integrate economic benefits, strong institutions, environmental protection, and social legitimacy, rather than reducing mining policy to short-term extractive expansion (Ayuk et al., 2020 ). The sensitivity analysis further reinforces this conclusion. A ± 40% variation in the interest rate generates stronger effects on net present value than an equivalent variation in the base price, for both gold and silver. In the case of gold, a 40% reduction in the interest rate increases NPV to nearly USD 5.9 billion, whereas an equivalent increase reduces it to just over USD 2.3 billion; for silver, the same exercise shifts NPV from around USD 47 million to slightly above USD 20 million. In other words, the apparent profitability of the resource depends not only on the expected behaviour of the mineral market, but also on the macro-financial conditions under which future flows are discounted. The implication is that public and private evaluation of resources and projects should not rely on a single discounting scenario, but should instead incorporate sensitivity bands, stress scenarios, and forward-looking analyses capable of assessing the robustness of decisions under changes in the opportunity cost of capital. In mining territories with high extractive dependence, this precaution is not a minor technical detail, but a necessary condition for avoiding investment, spending, or production-expansion decisions based on overly narrow financial assumptions. The international mineral governance approach itself emphasizes that sustainability requires decisions that are resilient to economic, social, and environmental uncertainty (Onditi, 2022 ). The study also has a direct implication for how mining rent should be understood in a region such as La Libertad. If gold the metallic asset with the highest economic value can be exhausted in less than a decade under the projected extraction scenario, then territorial sustainability depends on the institutional capacity to transform resource rent into other forms of capital before the stock is significantly reduced. This includes infrastructure, non-extractive productive capacities, human capital, institutional strengthening, and environmental restoration. The central issue is therefore no longer only how much income mining generates during the extraction phase, but also what share of that wealth is converted into durable capabilities that compensate for the progressive decline of natural capital. This principle lies at the core of contemporary mineral governance: mining wealth is sustainable only if it is transformed into lasting benefits, rather than being consumed as short-term current income. This conclusion is particularly relevant in the Peruvian context, where the design of rent-distribution and rent-use instruments can only be considered consistent with sustainability if it helps to cushion the gradual loss of an exhaustible natural asset (MINAM, 2005 ). The integration of economic valuation and environmental management constitutes another direct implication of the results. General Environmental Law No. 28611 establishes the basic framework for environmental management in the country, while Law No. 28090 provides that mine closure must be planned and implemented with sufficient environmental guarantees to cover the required investments. In light of the accelerated depletion of gold in La Libertad, these instruments should not be interpreted as peripheral compliance obligations, but rather as central components of the intertemporal management of the resource. The shorter the depletion horizon, the more necessary it becomes to incorporate closure, restoration, monitoring, and territorial recovery costs at an early stage into the economic evaluation of the asset, because sustainability depends not only on the value generated during the productive phase, but also on how liabilities and the post-extractive transition are managed. At this point, intertemporal valuation and environmental policy cease to be separate fields and instead become two dimensions of a single resource-governance strategy (MINAM, 2005 ). Finally, the results show that the sustainable management of metallic resources requires better public information systems on reserves, production, economic value, and depletion. Metrics such as net present value, depletion horizon, and sensitivity to discounting provide a richer reading of sustainability than conventional indicators based on annual production or short-term price movements. Incorporating this type of information into regional and sectoral planning instruments would make it possible to move from a predominantly operational perspective to an intertemporal perspective on the resource, one that is more useful for decisions regarding extraction sequencing, rent use, mine closure, and territorial transition. This approach is consistent with international efforts to strengthen mineral classification, transparency, and governance frameworks oriented toward long-term decision-making, especially in territories where mining constitutes an important foundation of the regional economy (Christmann, 2021 ). Taken together, the study suggests that a mining policy consistent with sustainable management in La Libertad should rest on four main pillars: incorporating the intertemporal valuation of the stock as a decision criterion; differentiating the management of gold and silver according to their depletion pressure and scale of value; evaluating resources and projects under multiple price and discount-rate scenarios; and transforming mining rent into other forms of capital before depletion significantly reduces the regional mineral base. From this perspective, Hotelling’s rule ceases to be merely an abstract formulation of exhaustible resource economics and instead becomes a useful tool for rethinking resource governance through a logic of intertemporal sustainability, in coherence with both the Peruvian legal framework and international mineral governance approaches oriented toward sustainable development (MINAM, 2005 ). 5. Conclusions The study showed that the regional application of Hotelling’s rule makes it possible to interpret, in an integrated manner, the intertemporal economic valuation and depletion pathways of gold and silver in La Libertad. The results revealed rising projected prices and expanding nominal revenues, but relatively stable net present values, indicating that higher future flows do not necessarily imply greater economic wealth in present-value terms. The depletion pathways also revealed important differences between the two minerals: gold exhibited a short economic life of around eight years, whereas silver extended its depletion horizon to approximately sixty-four years. Taken together, these findings suggest that regional extractive sustainability depends not only on reserves and prices, but also on the rate of extraction, the structure of the stock, and the financial conditions under which the resource is valued. Among the main limitations, the model was constructed under explicit assumptions regarding production, price growth, and discounting, without incorporating dynamic marginal costs, uncertainty, additional exploration, technological change, regulation, or socio-environmental externalities. The results should therefore be understood as analytical scenarios rather than exact predictions. Even so, the study provides useful inputs for regional mining planning by highlighting the importance of the present value of the stock, the economic lifespan of reserves, and sensitivity to discounting. Future research could expand this approach by incorporating variable costs, regulatory scenarios, environmental variables, and indicators of mining rent and territorial transformation. References Arellano-Yanguas J (2011) Aggravating the resource curse: Decentralisation, mining and conflict in Peru. 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Resour Policy 98:105342. ttps://doi.org/10.1016/j.resourpol.2024.105342 Cotrina-Teatino MA, Marquina-Araujo JJ, Mamani-Quispe JN, Arango-Retamozo SM, Gonzalez-Vasquez JA (2025) Bibliometric and systematic analysis of the literature on the Hartwick rule in non-renewable resources. Resour Policy 107:105654. ttps://doi.org/10.1016/j.resourpol.2025.105654 Di Maria C, Valente S (2008) Hicks meets Hotelling: The direction of technical change in capital-resource economies. Environ Dev Econ 13(6). ttps://doi.org/10.1017/S1355770X08004567 da Ferreira R, Missemer A (2020) The Hotelling rule in non-renewable resource economics: A reassessment. Can J Econ 53(2). ttps://doi.org/10.1111/caje.12444 Figueroa BE, Calfucura TE (2004) Growth and green income: Evidence from mining in Chile. Resour Policy 29:3–4. ttps://doi.org/10.1016/j.resourpol.2004.08.003 Figueroa B, Orihuela E R., C., Calfucura T, E (2010) Green accounting and sustainability of the Peruvian metal mining sector. 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Hist Polit Econ 54(1). ttps://doi.org/10.1215/00182702-9548337 Mlambo C (2022) Non-Renewable Resources and Sustainable Resource Extraction: An Empirical Test of the Hotelling Rule’s Significance to Gold Extraction in South Africa. Sustain (Switzerland) 14(17). ttps://doi.org/10.3390/su141710619 Onditi F (2022) Mining Policy Frameworks. In Gender Inequalities in Africa’s Mining Policies . ttps://doi.org/10.1007/978-981-16-8252-0_6 Orihuela CE, Añi VCMC, García JYD (2024) Including the change in natural capital stock and environmental degradation in Peruvian mining GDP and NNP. Economia Agrar y Recursos Naturales 24(1). ttps://doi.org/10.7201/earn.2024.01.06 Ovalle A (2020) Analysis of the discount rate for mining projects . ttps://doi.org/10.36487/acg_repo/2063_76 Pfingsten A (1986) A note on Hotelling’s rule. Resour Policy 12(1). ttps://doi.org/10.1016/0301-4207(86)90050-4 Republica del Perú (2017) Ley Orgánica para el aprovechamiento sostenible de los recursos naturales LEY No 26821 Savolainen J (2016) Real options in metal mining project valuation: Review of literature. Resources Policy , 50 . ttps://doi.org/10.1016/j.resourpol.2016.08.007 Slade ME (1984) Tax policy and the supply of exhaustible resources: theory and practice. Land Econ 60(2). ttps://doi.org/10.2307/3145968 Slade ME, Thille H (2009) Whither Hotelling: Tests of the Theory of Exhaustible Resources. Annual Rev Resource Econ 1(1). ttps://doi.org/10.1146/annurev.resource.050708.144223 Solow RM (1974) Intergenerational equity and exhaustible resources. Rev Econ Stud 41(5). ttps://doi.org/10.2307/2296370 Uberman R (2023) The Hotelling’s Rule in practice – analysis of gold mining sector. Gospodarka Surowcami Mineralnymi - Mineral Resour Manage. ttps://doi.org/10.24425/gsm.2021.137568 Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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Introduction\",\"content\":\"\\u003cp\\u003eThe exploitation of metallic mineral resources poses a fundamental challenge to the economic sustainability of extractive territories: each unit extracted generates revenue in the present while simultaneously reducing the future availability of natural stock. This intertemporal dilemma was classically formulated by Hotelling (\\u003cspan citationid=\\\"CR15\\\" class=\\\"CitationRef\\\"\\u003e1931\\u003c/span\\u003e), who demonstrated that the efficient allocation of an exhaustible resource depends on the evolution of its scarcity rent over time, and was later extended by Solow (\\u003cspan citationid=\\\"CR37\\\" class=\\\"CitationRef\\\"\\u003e1974\\u003c/span\\u003e) and Hartwick (\\u003cspan citationid=\\\"CR14\\\" class=\\\"CitationRef\\\"\\u003e1977\\u003c/span\\u003e), who linked the depletion of natural capital to intergenerational equity and the need to transform extractive rents into other forms of capital. From this perspective, mining cannot be understood solely as a productive activity, but also as a process through which natural wealth is converted into economic wealth, with implications for future welfare, fiscal sustainability, and territorial development pathways (Cotrina-Teatino et al., \\u003cspan citationid=\\\"CR6\\\" class=\\\"CitationRef\\\"\\u003e2025\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eFrom this standpoint, Hotelling\\u0026rsquo;s rule remains one of the most influential analytical frameworks for the study of non-renewable resources. In its basic formulation, it states that, under ideal conditions, the net price of the resource should grow at a rate equal to the interest rate, such that the resource owner is indifferent between extracting today and postponing extraction (Gaitan et al., \\u003cspan citationid=\\\"CR11\\\" class=\\\"CitationRef\\\"\\u003e2015\\u003c/span\\u003e; Hotelling, \\u003cspan citationid=\\\"CR15\\\" class=\\\"CitationRef\\\"\\u003e1931\\u003c/span\\u003e; Livernois, \\u003cspan citationid=\\\"CR23\\\" class=\\\"CitationRef\\\"\\u003e2009\\u003c/span\\u003e; Pfingsten, \\u003cspan citationid=\\\"CR32\\\" class=\\\"CitationRef\\\"\\u003e1986\\u003c/span\\u003e). However, empirical evidence shows that this logic is rarely observed in its pure form due to deposit heterogeneity, changing extraction costs, additional exploration, technological change, and market imperfections (Mlambo, \\u003cspan citationid=\\\"CR28\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e). Therefore, rather than being treated as a strict empirical law, the rule is more commonly used as a useful framework for organizing intertemporal valuation exercises, simulating depletion trajectories, and conducting sensitivity analyses under explicit assumptions, as suggested by the reviews of Krautkraemer (\\u003cspan citationid=\\\"CR18\\\" class=\\\"CitationRef\\\"\\u003e1990\\u003c/span\\u003e, \\u003cspan citationid=\\\"CR19\\\" class=\\\"CitationRef\\\"\\u003e1998\\u003c/span\\u003e) and the broader assessments of Ferreira da Cunha and Missemer (2020); Gaudet (\\u003cspan citationid=\\\"CR12\\\" class=\\\"CitationRef\\\"\\u003e2007\\u003c/span\\u003e); Gaudet and Howitt (\\u003cspan citationid=\\\"CR13\\\" class=\\\"CitationRef\\\"\\u003e1989\\u003c/span\\u003e); Slade (\\u003cspan citationid=\\\"CR35\\\" class=\\\"CitationRef\\\"\\u003e1984\\u003c/span\\u003e); Slade and Thille (\\u003cspan citationid=\\\"CR36\\\" class=\\\"CitationRef\\\"\\u003e2009\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eThe current interest in this approach is not merely theoretical. Mineral resource governance now occupies a central place in the international sustainability agenda, given that minerals and metals underpin critical supply chains while also generating long-term environmental, social, and territorial pressures (Christmann, \\u003cspan citationid=\\\"CR4\\\" class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e). In this context, the International Resource Panel has emphasized that twenty-first-century mineral governance should be oriented toward transforming extractive wealth into lasting benefits, integrating environmental sustainability into decision-making, and strengthening the institutional capacity of producing territories (Ayuk et al., \\u003cspan citationid=\\\"CR2\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e). Complementarily, the IGF\\u0026rsquo;s Mining Policy Framework highlights that a well-governed mining sector must align economic benefits, social legitimacy, long-term planning, and environmental protection (IGF, \\u003cspan citationid=\\\"CR16\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eIn the Peruvian case, mining has been one of the main pillars of economic growth, although its territorial outcomes have depended to a large extent on institutional quality, the design of fiscal decentralization, and local capacity to manage rents and conflicts. Arellano-Yanguas (\\u003cspan citationid=\\\"CR1\\\" class=\\\"CitationRef\\\"\\u003e2011\\u003c/span\\u003e) showed that mining expansion in Peru can intensify territorial tensions when the distribution of benefits and institutional capacities is uneven, while Figueroa B. et al. (\\u003cspan citationid=\\\"CR10\\\" class=\\\"CitationRef\\\"\\u003e2010\\u003c/span\\u003e) found that the depreciation of natural capital and the degradation associated with metallic mining represent a substantial share of the sector\\u0026rsquo;s economic value. More recently, Orihuela et al. (\\u003cspan citationid=\\\"CR30\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e) demonstrated that incorporating changes in natural capital stock and environmental degradation significantly alters the measurement of mining GDP and NNP in the country, thereby reinforcing the need for assessments that go beyond production indicators or current revenue flows.\\u003c/p\\u003e \\u003cp\\u003eIn this context, the La Libertad region constitutes a particularly relevant case. According to official information from MINEM and the Central Reserve Bank of Peru (BCRP), it has remained one of the country\\u0026rsquo;s main gold-producing territories and continues to hold an important position within mining activity in northern Peru, with gold playing a prominent role and silver maintaining a sustained presence in its recent productive structure (BCRP, \\u003cspan citationid=\\\"CR3\\\" class=\\\"CitationRef\\\"\\u003e2025\\u003c/span\\u003e; MINEM, \\u003cspan citationid=\\\"CR26\\\" class=\\\"CitationRef\\\"\\u003e2025\\u003c/span\\u003e). However, despite the economic importance of these territories, studies that integrate, at the regional scale, the Hotelling framework with reserves, observed production, projected price trajectories, net present value, and depletion pathways for metallic resources remain scarce. Many empirical applications have been developed at the national or highly aggregated level, such as Mlambo (\\u003cspan citationid=\\\"CR28\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e) study on gold in South Africa, whereas in Peru the literature has largely focused on green accounting exercises or macroeconomic adjustments to mining output. This gap is particularly relevant because mining territories differ in mineral composition, resource quality, extraction intensity, and depletion horizon; as such, an exclusively national perspective may obscure critical differences for regional sustainability and the formulation of territorially grounded public policies (Figueroa B. et al., \\u003cspan citationid=\\\"CR10\\\" class=\\\"CitationRef\\\"\\u003e2010\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eAgainst this background, the present study addresses the following research question: how do the intertemporal economic valuation and depletion pathways of metallic resources evolve in La Libertad, Peru? In response, the main objective is to evaluate the intertemporal economic valuation and depletion pathways of metallic mineral resources in La Libertad and to examine their implications for sustainable management under Hotelling\\u0026rsquo;s rule. To this end, the study: (i) characterizes the regional mineral base and productive context; (ii) estimates projected trajectories of prices, revenues, and net present value for gold and silver; (iii) simulates intertemporal extraction and depletion pathways under reserve constraints; and (iv) analyses the sensitivity of valuation to changes in prices and interest rates. In doing so, the article seeks to provide useful evidence for linking the economics of exhaustible resources, mineral governance, and territorial sustainability in a strategic region of Peru.\\u003c/p\\u003e \\u003cp\\u003eThe remainder of the article is organized as follows. Section 2 presents the methodology. Section 3 reports the results. Section 4 discusses the findings. Finally, Section 5 summarizes the main conclusions.\\u003c/p\\u003e\"},{\"header\":\"2. Methodology\",\"content\":\"\\u003cdiv id=\\\"Sec3\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e2.1. Research approach and analytical design\\u003c/h2\\u003e \\u003cp\\u003eThe study followed a quantitative, applied, and non-experimental approach, with a descriptive-analytical and prospective scope, to estimate the intertemporal economic valuation and depletion pathways of gold and silver in La Libertad, Peru. A regional case-study scale was adopted because it allows reserves, production, prices, and macro-financial conditions to be examined within a specific mining territory, thereby avoiding the aggregation bias of national-level studies and better capturing relevant extractive differences (Cotrina-Teatino \\u0026amp; Marquina-Araujo, \\u003cspan citationid=\\\"CR5\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e). This choice is consistent with contemporary interpretations of Hotelling\\u0026rsquo;s rule, which emphasize the importance of economic and institutional context in its application (Ferreira da Cunha \\u0026amp; Missemer, 2020; Gaudet, \\u003cspan citationid=\\\"CR12\\\" class=\\\"CitationRef\\\"\\u003e2007\\u003c/span\\u003e). Moreover, in contrast to the predominance of national-scale studies, such as Mlambo (\\u003cspan citationid=\\\"CR28\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e) analysis for South Africa, La Libertad constitutes an appropriate unit of analysis because of its importance in Peru\\u0026rsquo;s gold and silver production, in line with the intertemporal allocation problem of exhaustible stock originally posed by Hotelling (\\u003cspan citationid=\\\"CR15\\\" class=\\\"CitationRef\\\"\\u003e1931\\u003c/span\\u003e).\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec4\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e2.2. Study area and unit of analysis\\u003c/h2\\u003e \\u003cp\\u003eThe unit of analysis consisted of the metallic resources of gold and silver in the La Libertad region, selected because of their importance within Peru\\u0026rsquo;s mining dynamics and the territorial concentration of gold and silver operations in provinces with a well-established extractive trajectory. This configuration makes La Libertad an appropriate case for examining the intertemporal valuation of the resource and its depletion pathways within a subnational setting, where reserve conditions, production levels, and operational continuity can be observed more precisely than in a national aggregate (Hotelling, \\u003cspan citationid=\\\"CR15\\\" class=\\\"CitationRef\\\"\\u003e1931\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eThe time horizon was structured at two levels. The 2025\\u0026ndash;2040 period was used to project prices, revenues, and net present value, while the depletion simulation was extended until the year in which the remaining reserves are reduced to zero. This approach simultaneously considers the economic dimension of the expected flow and the physical dimension of the available stock, in line with the intertemporal problem originally formulated by Hotelling (\\u003cspan citationid=\\\"CR15\\\" class=\\\"CitationRef\\\"\\u003e1931\\u003c/span\\u003e) and with Krautkraemer (\\u003cspan citationid=\\\"CR19\\\" class=\\\"CitationRef\\\"\\u003e1998\\u003c/span\\u003e) review, which showed that the valuation of a non-renewable resource depends on the initial size of reserves, the rate of extraction, and the expected trajectory of its value over time.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec5\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e2.3. Data sources, database construction, and variable definition\\u003c/h2\\u003e \\u003cp\\u003eThe database was constructed from official and traceable secondary sources to ensure consistency and comparability across the model parameters. Gold and silver reserves and production were obtained from official records of the Peruvian mining sector, baseline prices were taken from international benchmark series, and the interest rate was based on the BCRP reference rate for 2025. This consistency was essential, as even small variations in prices, reserves, or discount rates can significantly affect economic valuation (see Table\\u0026nbsp;\\u003cspan refid=\\\"Tab1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e) (Lilford, \\u003cspan citationid=\\\"CR21\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e; Lilford et al., \\u003cspan citationid=\\\"CR22\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab1\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 1\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eSources of information and basic model parameters\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"5\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e \\u003cthead\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eVariable\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eSymbol\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eDescription\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eUnit\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eSource\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003c/thead\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eInitial reserves\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({R}_{0}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eInitial regional stock of gold or silver\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eoz\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eMINEM\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eObserved annual production\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({q}_{0}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eObserved regional production in the base year\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eoz/year\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eMINEM\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eBase price\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({P}_{0}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eReference mineral price\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eUSD/oz\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eInternational precious metals price series\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eInterest rate\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e\\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(r\\\\)\\u003c/span\\u003e\\u003c/span\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eReference rate used for projection and discounting\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e% per year\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eBCRP\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003ctfoot\\u003e \\u003ctr\\u003e\\u003ctd colspan=\\\"5\\\"\\u003eNote. MINEM\\u0026thinsp;=\\u0026thinsp;Ministry of Energy and Mines of Peru; BCRP\\u0026thinsp;=\\u0026thinsp;Central Reserve Bank of Peru.\\u003c/td\\u003e\\u003c/tr\\u003e \\u003c/tfoot\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003cp\\u003eThe variables included in the model were \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({R}_{0}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({q}_{0}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({P}_{0}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(r\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, projected price \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\left({P}_{t}\\\\right)\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, annual revenue \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\left({I}_{t}\\\\right)\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, net present value \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\left(VPN\\\\right)\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, cumulative production \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\left({Q}_{t}\\\\right)\\\\)\\u003c/span\\u003e\\u003c/span\\u003e and remaining reserves \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\left({R}_{t}\\\\right)\\\\)\\u003c/span\\u003e\\u003c/span\\u003e. This set of variables reflects the basic structure of intertemporal models of exhaustible resources and discounted cash flow valuation approaches. Among them, the discount rate occupies a central role because it directly determines the magnitude of present value; for this reason, it was treated as an explicit assumption and subsequently evaluated through sensitivity analysis (Kamel et al., \\u003cspan citationid=\\\"CR17\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e; Savolainen, \\u003cspan citationid=\\\"CR34\\\" class=\\\"CitationRef\\\"\\u003e2016\\u003c/span\\u003e).\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec6\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e2.4. Characterization of the mineral base and economic context\\u003c/h2\\u003e \\u003cp\\u003eBefore modelling, the mineral base of La Libertad was characterized by considering the distribution of operating projects, gold and silver reserves, their regional share, the recent evolution of production, and the observed price trajectory, to establish a realistic baseline for the valuation exercise (Hotelling, \\u003cspan citationid=\\\"CR15\\\" class=\\\"CitationRef\\\"\\u003e1931\\u003c/span\\u003e). In addition, ore-grade heterogeneity was incorporated as a contextual element, given that resource quality influences expected profitability and the economic interpretation of the stock, thereby avoiding an exclusively volumetric reading of reserves (Krautkraemer, \\u003cspan citationid=\\\"CR19\\\" class=\\\"CitationRef\\\"\\u003e1998\\u003c/span\\u003e).\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec7\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e2.5. Economic framework of Hotelling\\u0026rsquo;s rule\\u003c/h2\\u003e \\u003cp\\u003eThe economic formulation followed Hotelling\\u0026rsquo;s basic principle for exhaustible resources. In continuous time, the intertemporal condition can be expressed as:\\u003cdiv id=\\\"Equ1\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ1\\\" name=\\\"EquationSource\\\"\\u003e\\n$$\\\\frac{d({P}_{t}-{MC}_{t})}{dt}=r({P}_{t}-{MC}_{t})$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e1\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003ewhere \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({P}_{t}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e represents the resource price at time \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(t\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({MC}_{t}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e the marginal cost of extraction, and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(r\\\\)\\u003c/span\\u003e\\u003c/span\\u003e the interest rate. This expression indicates that the resource rent should grow at the market rate in order to sustain intertemporal efficiency in extraction. Hotelling originally formulated this principle in his seminal 1931 contribution (Hotelling, \\u003cspan citationid=\\\"CR15\\\" class=\\\"CitationRef\\\"\\u003e1931\\u003c/span\\u003e), and subsequent developments, such as those of Levhari and Liviatan (\\u003cspan citationid=\\\"CR20\\\" class=\\\"CitationRef\\\"\\u003e1977\\u003c/span\\u003e), clarified several of its analytical assumptions. More recently, Ferreira da Cunha and Missemer (2020) showed that the so-called \\u0026ldquo;Hotelling rule\\u0026rdquo; should be understood as a central foundation of non-renewable resource economics, although its empirical validity depends on more restrictive conditions than those assumed in the canonical model.\\u003c/p\\u003e \\u003cp\\u003eAs the study relied on aggregated regional data rather than on homogeneous marginal-cost series for individual mining operations, the market price was used as an operational proxy for the net resource price. Under this assumption, the price trajectory was estimated using an exponential function of the form:\\u003cdiv id=\\\"Equ2\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ2\\\" name=\\\"EquationSource\\\"\\u003e\\n$${P}_{t}={P}_{0}{e}^{rt}$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e2\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003ewhere \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({P}_{0}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the base price observed in 2025, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(r\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the annual interest rate, and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(t\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the number of years elapsed since the base year. This simplification is appropriate in regional exercises where marginal costs cannot be observed with sufficient consistency across all productive units, although it should be interpreted as an analytical approximation rather than as an exhaustive measure of effective mineral rent. For this reason, the study states this assumption explicitly and limits its use to the construction of intertemporal valuation and depletion scenarios (Ferreira da Cunha \\u0026amp; Missemer, 2020).\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec8\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e2.6. Revenue projection and estimation of net present value\\u003c/h2\\u003e \\u003cp\\u003eOnce the price trajectory had been estimated, annual gross revenues were calculated for each mineral under an initial constant-production scenario equivalent to the production observed in 2024. The expression used was:\\u003cdiv id=\\\"Equ3\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ3\\\" name=\\\"EquationSource\\\"\\u003e\\n$${I}_{t}={P}_{t}*q$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e3\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003ewhere \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({I}_{t}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the projected annual revenue, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({P}_{t}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e the estimated price, and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(q\\\\)\\u003c/span\\u003e\\u003c/span\\u003e the constant production level. This assumption was adopted to isolate the effect of price growth on the intertemporal valuation of the resource before introducing differentiated extraction trajectories. Thus, in this first stage, variation in economic value derives solely from the projected behaviour of price under the Hotelling framework. NPV was then estimated as:\\u003cdiv id=\\\"Equ4\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ4\\\" name=\\\"EquationSource\\\"\\u003e\\n$$VPN=\\\\sum_{t=0}^{n}\\\\frac{{I}_{t}}{{(1+r)}^{t}}$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e4\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003ewhere \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({I}_{t}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e represents the projected revenue represents in year \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(t\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(r\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the discount rate, and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(n\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the evaluation horizon. NPV was used because it summarizes the combined effect of time, the magnitude of flows, and the opportunity cost of capital, and it remains a widely accepted tool in intertemporal valuation exercises for extractive resources. Even so, its result depends on explicit financial assumptions, particularly on the discount rate. Krautkraemer (\\u003cspan citationid=\\\"CR19\\\" class=\\\"CitationRef\\\"\\u003e1998\\u003c/span\\u003e) showed that this parameter plays a decisive role in the valuation of non-renewable resources; therefore, in this study, the stability of present value was not interpreted as a universal verification of the theory, but rather as an internal property of the scenario constructed for La Libertad.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec9\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e2.7. Simulation of depletion pathways\\u003c/h2\\u003e \\u003cp\\u003eIn addition to the valuation based on constant production, depletion pathways were estimated to assess the potential duration of reserves under increasing extraction trajectories. Annual production was projected as:\\u003cdiv id=\\\"Equ5\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ5\\\" name=\\\"EquationSource\\\"\\u003e\\n$${q}_{t}={q}_{t-1}(1+g)$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e5\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003ewhere \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({q}_{t}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is production in year \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(t\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({q}_{t-1}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is production in the previous year, and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(g\\\\)\\u003c/span\\u003e\\u003c/span\\u003e is the annual extraction growth rate. For gold, \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(g=0.03\\\\)\\u003c/span\\u003e\\u003c/span\\u003ewas adopted, whereas for silver \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(g=0.05\\\\)\\u003c/span\\u003e\\u003c/span\\u003e was used, in order to represent differentiated extraction pressures according to the relative magnitude of reserves and the distinct scale of availability of each mineral. Based on this projection, cumulative production was calculated as:\\u003cdiv id=\\\"Equ6\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ6\\\" name=\\\"EquationSource\\\"\\u003e\\n$${Q}_{t}=\\\\sum_{i=0}^{t}{q}_{i}$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e6\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003eand remaining reserves were obtained as:\\u003cdiv id=\\\"Equ7\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ7\\\" name=\\\"EquationSource\\\"\\u003e\\n$${R}_{t}={R}_{0}-{Q}_{t}$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e7\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003ewhere \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({R}_{0}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e corresponds to the initial reserve and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({R}_{t}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e to the remaining stock available in year \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(t\\\\)\\u003c/span\\u003e\\u003c/span\\u003e. Depletion was defined as the first period in which \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({R}_{t}\\\\le0\\\\)\\u003c/span\\u003e\\u003c/span\\u003e, with final production adjusted to the effectively remaining stock. This made it possible to integrate the economic dimension of valuation with a physical reading of resource duration, which is particularly important when the analysis is oriented toward long-term extractive sustainability (Levhari \\u0026amp; Liviatan, \\u003cspan citationid=\\\"CR20\\\" class=\\\"CitationRef\\\"\\u003e1977\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eThese trajectories do not represent an optimum derived from a complete dynamic control problem with endogenous costs, demand, and exploration. Rather, they are interpreted as extraction scenarios consistent with the intertemporal logic of the model and constrained by the physical availability of the resource. This clarification avoids overstating the scope of the exercise and keeps the analysis within transparent and verifiable assumptions. Levhari and Liviatan (\\u003cspan citationid=\\\"CR20\\\" class=\\\"CitationRef\\\"\\u003e1977\\u003c/span\\u003e), as well as the contemporary reinterpretation offered by Ferreira da Cunha and Missemer (2020), show that the effective dynamics of non-renewable resources may diverge from the canonical model when other economic or institutional mechanisms come into play.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec10\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e2.8. Verification of intertemporal consistency and sensitivity analysis\\u003c/h2\\u003e \\u003cp\\u003eTo verify the internal consistency of the scenario, the projected price trajectory was compared with the expected growth of the financial factor \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({e}^{rt}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e; c when both curves are practically coincident, the scenario is considered consistent with Hotelling\\u0026rsquo;s intertemporal logic. This verification was structural rather than econometric, since it did not seek to empirically validate the rule, but rather to ensure the consistency of the simulation constructed for La Libertad, considering that real markets are influenced by factors such as uncertainty, exploration, regulation, and technological change (Krautkraemer, \\u003cspan citationid=\\\"CR19\\\" class=\\\"CitationRef\\\"\\u003e1998\\u003c/span\\u003e). In addition, a sensitivity analysis was performed on two key parameters, the base price and the interest rate, by applying variations of \\u0026plusmn;\\u0026thinsp;40% and recalculating net present value in each case.\\u003cdiv id=\\\"Equ8\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ8\\\" name=\\\"EquationSource\\\"\\u003e\\n$${P}_{0}^{*}={P}_{0}(1+{\\\\delta}_{P})$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e8\\u003c/div\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Equ9\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equ9\\\" name=\\\"EquationSource\\\"\\u003e\\n$${r}^{*}=r(1+{\\\\delta}_{r})$$\\u003c/div\\u003e\\u003cdiv class=\\\"EquationNumber\\\"\\u003e9\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003ewhere \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({\\\\delta}_{P}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e and \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\({\\\\delta}_{r}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e represent the percentage variation applied to price and interest rate, respectively. This procedure made it possible to assess the sensitivity of resource value to plausible changes in market conditions and in the opportunity cost of capital, which is a critical issue in mining evaluation, since even small changes in the discount rate can substantially affect NPV and the perceived economic viability of the resource (Krautkraemer, \\u003cspan citationid=\\\"CR19\\\" class=\\\"CitationRef\\\"\\u003e1998\\u003c/span\\u003e; Ovalle, \\u003cspan citationid=\\\"CR31\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e).\\u003c/p\\u003e \\u003c/div\\u003e\"},{\"header\":\"3. Results\",\"content\":\"\\u003cdiv id=\\\"Sec12\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e3.1. Productive context of metallic mineral resources in La Libertad\\u003c/h2\\u003e \\u003cp\\u003eLa Libertad constitutes one of Peru\\u0026rsquo;s main metallic mining territories due to the territorial concentration of gold and silver operations and the magnitude of its regional reserves. The distribution of operating projects shows a clear predominance of the province of Pataz, where underground mining operations of companies such as Poderosa, Consorcio Minero Horizonte, and MARSA are concentrated, while in S\\u0026aacute;nchez Carri\\u0026oacute;n and Otuzco surface operations associated with Summa Gold, La Arena, and Barrick Misquichilca predominate (Table\\u0026nbsp;\\u003cspan refid=\\\"Tab2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e). This configuration reveals a dual extractive structure in which high-grade underground deposits coexist with lower-grade, larger-scale surface operations, thereby reinforcing the importance of analysing the region not only in terms of production volume, but also considering the technical and economic heterogeneity of its mining units.\\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab2\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 2\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eOperating metallic mining projects in the La Libertad region\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"6\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c6\\\" colnum=\\\"6\\\"\\u003e\\u003c/div\\u003e \\u003cthead\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eHolder\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eMining unit\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eProduct\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eProvince\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eDistrict\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003eType of mining\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003c/thead\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eCompa\\u0026ntilde;\\u0026iacute;a Minera Caravel\\u0026iacute; S.A.C.\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eLa Estrella\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eAu, Ag\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003ePataz\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eHuaylillas\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003eUnderground\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\" morerows=\\\"1\\\" rowspan=\\\"2\\\"\\u003e \\u003cp\\u003eCompa\\u0026ntilde;\\u0026iacute;a Minera Poderosa S.A.\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eSanta Mar\\u0026iacute;a\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eAu, Ag\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003ePataz\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003ePataz\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003eUnderground\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eMara\\u0026ntilde;\\u0026oacute;n\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eAu, Ag\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003ePataz\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003ePataz\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003eUnderground\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\" morerows=\\\"1\\\" rowspan=\\\"2\\\"\\u003e \\u003cp\\u003eConsorcio Minero Horizonte S.A.\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eLos Zambos\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eAu\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003ePataz\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eParcoy\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003eUnderground\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eParcoy\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eAu\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003ePataz\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eParcoy\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003eUnderground\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eMinera Aur\\u0026iacute;fera Retamas S.A.\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eRetamas\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eAu, Ag\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003ePataz\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eParcoy\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003eUnderground\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eSumma Gold Corporation S.A.C.\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eEl Toro\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eAu, Ag\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eS\\u0026aacute;nchez Carri\\u0026oacute;n\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eHuamachuco\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003eOpen pit\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eLa Arena S.A.\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eLa Arena\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eAu, Ag\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eS\\u0026aacute;nchez Carri\\u0026oacute;n\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eHuamachuco\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003eOpen pit\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eMinera Barrick Misquichilca S.A.\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eAlto Chicama\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eAu, Ag\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eOtuzco\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eQuiruvilca\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003eOpen pit\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003cp\\u003eLa Libertad holds approximately 9,645,210 oz of gold and 289,904,000 oz of silver, equivalent to about 12% of national gold reserves and 6.44% of silver reserves, which confirms its strategic relevance in Peru\\u0026rsquo;s metallic mining production. In addition, the resource structure shows marked ore-grade heterogeneity: while operations such as Poderosa (14.3 g/t), Caravel\\u0026iacute; (12.5 g/t), MARSA (10.68 g/t), and Consorcio Minero Horizonte (10.04 g/t) exhibit high gold grades, others such as Barrick Misquichilca (2.49 g/t), Summa Gold (0.43 g/t), and La Arena (0.33 g/t) report considerably lower values. This indicates that regional valuation depends not only on the volume of reserves, but also on ore quality and the type of mining operation.\\u003c/p\\u003e \\u003cp\\u003eAt the same time, international prices followed an upward trend between 2010 and 2025, reaching an average of USD 3,067/oz for gold and USD 40.97/oz for silver in 2025 (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e). However, silver exhibited greater volatility, whereas gold maintained a more stable trajectory, consolidating its role as the region\\u0026rsquo;s main store of economic value. This was accompanied by the financial context: the BCRP reference rate stood at 4.64% in 2025, after peaking at 7.54% in 2023 (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e), thus shaping a less restrictive environment for the intertemporal valuation of the resource.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003eBetween 2023 and 2024, gold production in La Libertad increased from 1,085,509 oz to 1,138,356 oz (+\\u0026thinsp;4.9%), while silver rose from 687,722 oz to 700,382 oz (+\\u0026thinsp;1.8%). Taken together, both minerals recorded an aggregate growth of 3.4%, reflecting recent production dynamism. This pattern, combined with the magnitude of reserves, ore-grade heterogeneity, and the favourable price environment, provides a solid basis for analysing the intertemporal economic valuation and depletion pathways of metallic mineral resources in the region.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec13\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e3.2. Intertemporal economic valuation under Hotelling\\u0026rsquo;s rule\\u003c/h2\\u003e \\u003cp\\u003eBased on regional reserves, the production observed in 2024, the 2025 base prices, and an interest rate of 4.64%, an intertemporal valuation scenario was constructed for gold and silver in La Libertad (Table\\u0026nbsp;\\u003cspan refid=\\\"Tab3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e). Under this framework, projected prices followed an upward trajectory consistent with Hotelling\\u0026rsquo;s logic.\\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab3\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 3\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eEconomic and productive inputs for metallic minerals in La Libertad\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"5\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e \\u003cthead\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eMineral\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eReserves (oz)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eProduction (2024, oz)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eBase price (2025, USD/oz)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eInterest rate (2025, %)\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003c/thead\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eGold\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e9\\u0026rsquo;645,210.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e1\\u0026rsquo;138,356.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e3,067.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\" morerows=\\\"1\\\" rowspan=\\\"2\\\"\\u003e \\u003cp\\u003e4.64%\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eSilver\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e289\\u0026rsquo;904,000.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e700,382.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e40.97\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003cp\\u003eFor gold, the 2025\\u0026ndash;2040 projection showed an increase in price from USD 3,067.00/oz to USD 6,131.84/oz, while, under a constant production level of 1,138,356 oz/year, projected revenues increased from USD 3.491\\u0026nbsp;billion to USD 6.980\\u0026nbsp;billion (Table\\u0026nbsp;\\u003cspan refid=\\\"Tab4\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e). These results confirm the strong economic weight of gold within the regional metallic mining structure.\\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab4\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 4\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eProjected gold price and estimated revenues in the La Libertad region (2025\\u0026ndash;2040)\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"5\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e \\u003cthead\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eYear\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003et\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eProjected price (USD/oz)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eProduction (oz)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eProjected revenue (USD)\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003c/thead\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2025\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e3,067.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e3,491,337,852.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2026\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e1\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e3,212.39\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e3,656,843,430.84\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2027\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e2\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e3,364.97\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e3,830,533,789.32\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2028\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e3\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e3,524.97\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e4,012,670,749.32\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2029\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e4\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e3,692.65\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e4,203,550,283.40\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2030\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e5\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e3,868.29\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e4,403,491,131.24\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2031\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e6\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e4,052.17\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e4,612,812,032.52\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2032\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e7\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e4,244.60\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e4,831,865,877.60\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2033\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e8\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e4,445.87\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e5,060,982,789.72\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2034\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e9\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e4,656.30\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e5,300,527,042.80\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2035\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e10\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e4,876.24\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e5,550,897,061.44\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2036\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e11\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e5,106.05\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e5,812,502,653.80\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2037\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e12\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e5,346.11\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e6,085,776,395.16\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2038\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e13\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e5,596.82\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e6,371,173,627.92\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2039\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e14\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e5,858.58\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e6,669,149,694.48\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2040\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e15\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e6,131.84\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e6,980,216,855.04\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003ctfoot\\u003e \\u003ctr\\u003e\\u003ctd colspan=\\\"5\\\"\\u003e\\u003cb\\u003eNote\\u003c/b\\u003e. Annual gold production was kept constant at 1,138,356 oz for simulation purposes. The projected price was estimated using the function \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\text{P}\\\\left(\\\\text{t}\\\\right)=3067\\\\text{*}{e}^{0.0464t}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e.\\u003c/td\\u003e\\u003c/tr\\u003e \\u003c/tfoot\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003cp\\u003eHowever, once those future flows were discounted at the same 4.64% rate, the net present value of gold showed only minimal variation over the period analysed. NPV increased from USD 3.491\\u0026nbsp;billion in 2025 to USD 3.535\\u0026nbsp;billion in 2040 (Table\\u0026nbsp;\\u003cspan refid=\\\"Tab5\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e), thus following an almost stable trajectory. This indicates that the strong nominal growth in revenues does not translate into an equivalent increase in the present economic value of the resource, since intertemporal discounting almost entirely offsets the expansion of future flows.\\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab5\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 5\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eNet present value of projected gold revenues in the La Libertad region (2025\\u0026ndash;2040)\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"4\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e \\u003cthead\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eYear\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eNPV (USD)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eYear\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eNPV (USD)\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003c/thead\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2025\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e3,491,337,852.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2033\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e3,520,894,504.38\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2026\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e3,494,689,823.05\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2034\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e3,524,029,017.05\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2027\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e3,498,354,659.29\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2035\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e3,526,840,861.57\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2028\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e3,502,195,076.89\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2036\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e3,529,296,320.90\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2029\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e3,506,108,268.39\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2037\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e3,531,369,970.55\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e230\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e3,510,010,948.25\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2038\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e3,533,043,120.06\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2031\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e3,513,818,880.16\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2039\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e3,534,290,406.81\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2032\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e3,517,472,848.79\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2040\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e3,535,110,149.45\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003cp\\u003eSilver exhibited an intertemporal pattern like that of gold, although at a much smaller monetary scale. The projected price increased from USD 40.97/oz in 2025 to USD 82.50/oz in 2040, and estimated revenues, under a constant production level of 700,382 oz/year, rose from USD 28.69\\u0026nbsp;million to USD 57.78\\u0026nbsp;million (Table\\u0026nbsp;\\u003cspan refid=\\\"Tab6\\\" class=\\\"InternalRef\\\"\\u003e6\\u003c/span\\u003e). However, once the flows were discounted, NPV remained almost stable, increasing from USD 28.69\\u0026nbsp;million to USD 29.26\\u0026nbsp;million between 2025 and 2040 (Table\\u0026nbsp;\\u003cspan refid=\\\"Tab7\\\" class=\\\"InternalRef\\\"\\u003e7\\u003c/span\\u003e), which reflects only a marginal real variation.\\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab6\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 6\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eProjected silver price and estimated revenues in the La Libertad region (2025\\u0026ndash;2040)\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"5\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e \\u003cthead\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eYear\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003et\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eProjected price (USD/oz)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eProduction (oz)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eProjected revenue (USD)\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003c/thead\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2025\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e40.97\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e28,694,650.54\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2026\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e1\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e42.90\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e30,046,387.80\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2027\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e2\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e44.93\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e31,468,163.26\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2028\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e3\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e47.06\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e32,959,976.92\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2029\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e4\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e49.31\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e34,535,836.42\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2030\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e5\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e51.66\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e36,181,734.12\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2031\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e6\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e54.13\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e37,911,677.66\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2032\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e7\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e56.73\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e39,732,670.86\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2033\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e8\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e59.45\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e41,637,709.90\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2034\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e9\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e62.30\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e43,633,798.60\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2035\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e10\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e65.29\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e45,727,940.78\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2036\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e11\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e68.42\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e47,920,136.44\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2037\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e12\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e71.70\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e50,217,389.40\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2038\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e13\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e75.14\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e52,626,703.48\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2039\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e14\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e78.73\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e55,141,074.86\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2040\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e15\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e82.50\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e57,781,515.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003ctfoot\\u003e \\u003ctr\\u003e\\u003ctd colspan=\\\"5\\\"\\u003e\\u003cb\\u003eNote\\u003c/b\\u003e. Annual silver production was kept constant at 700,382 oz for simulation purposes. The projected price was estimated using the function \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\text{P}\\\\left(\\\\text{t}\\\\right)=40.97\\\\text{*}{e}^{0.0464t}\\\\)\\u003c/span\\u003e\\u003c/span\\u003e.\\u003c/td\\u003e\\u003c/tr\\u003e \\u003c/tfoot\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab7\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 7\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eNet present value of projected silver revenues in the La Libertad region (2025\\u0026ndash;2040)\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"4\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e \\u003cthead\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eA\\u0026ntilde;o\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eVPN (USD)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eA\\u0026ntilde;o\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eVPN (USD)\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003c/thead\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2025\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e28,694,650.54\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2033\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e28,967,097.90\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2026\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e28,714,055.62\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2034\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e29,009,713.78\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2027\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e28,739,283.25\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2035\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e29,053,893.14\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2028\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e28,766,942.55\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2036\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e29,096,651.01\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2029\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e28,805,741.21\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2037\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e29,139,450.65\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e230\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e28,840,363.04\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2038\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e29,183,384.96\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2031\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e28,879,297.01\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2039\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e29,221,802.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2032\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e28,924,352.31\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e2040\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e29,263,277.11\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003cp\\u003eTaken together, the comparison between both minerals reveals two main findings (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e): gold overwhelmingly dominates in absolute economic value, and both gold and silver follow a similar intertemporal trajectory, characterized by rising prices, expanding nominal revenues, and relatively stable present values. This suggests internal consistency in the valuation exercise under the Hotelling framework, with the two minerals differing primarily in the economic magnitude of their reserves and productive flows.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec14\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e3.3. Depletion pathways and intertemporal equilibrium\\u003c/h2\\u003e \\u003cp\\u003eTable\\u0026nbsp;\\u003cspan refid=\\\"Tab8\\\" class=\\\"InternalRef\\\"\\u003e8\\u003c/span\\u003e shows that gold in La Libertad follows an increasing extraction pathway under Hotelling\\u0026rsquo;s logic, with annual production rising from 1,138,356 oz in 2025 to 1,359,256.60 oz in 2031, while the projected price increases from 3,067.00 USD/oz to 4,052.17 USD/oz. Cumulative extraction reaches 8,722,609.80 oz in 2031, leaving a final balance of 922,600.20 oz for 2032, the year in which reserves are fully exhausted. Taken together, these results indicate a short depletion horizon of approximately eight years, reflecting strong extraction pressure on the regional gold stock.\\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab8\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 8\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eExtraction pathway and reserve depletion of gold in the La Libertad region\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"6\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c6\\\" colnum=\\\"6\\\"\\u003e\\u003c/div\\u003e \\u003cthead\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eYear\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003et\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eProjected price (USD/oz)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eOptimal annual extraction (oz)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eCumulative extraction (oz)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003eRemaining reserves (oz)\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003c/thead\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2025\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e3,067.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,138,356.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e1,138,356.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e8,506,854.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2026\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e1\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e3,212.39\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,172,506.68\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e2,310,862.68\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e7,334,347.32\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2027\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e2\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e3,364.97\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,207,681.88\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e3,518,544.56\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e6,126,665.44\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2028\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e3\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e3,524.97\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,243,912.34\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e4,762,456.90\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e4,882,753.10\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2029\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e4\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e3,692.65\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,281,229.71\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e6,043,686.60\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e3,601,523.40\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2030\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e5\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e3,868.29\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,319,666.60\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e7,363,353.20\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e2,281,856.80\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2031\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e6\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e4,052.17\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,359,256.60\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e8,722,609.80\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e922,600.20\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2032\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e7\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e4,244.60\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e922,600.20\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e9,645,210.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003cp\\u003eBy contrast, Table\\u0026nbsp;\\u003cspan refid=\\\"Tab9\\\" class=\\\"InternalRef\\\"\\u003e9\\u003c/span\\u003e shows that silver exhibits a much longer depletion pathway because of its larger reserve base. The projected price rises from 40.97 USD/oz in 2025 to 762.07 USD/oz in 2088, while annual extraction increases from 700,382.00 oz to 14,423,528.55 oz in 2087. Cumulative extraction reaches 288,886,459.47 oz, leaving a remaining balance of 1,017,540.53 oz for 2088, when reserves are completely exhausted. Unlike gold, silver displays a much more gradual depletion horizon of around 64 years, suggesting lower relative extraction pressure in the short term.\\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab9\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 9\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eIntertemporal extraction pathway and reserve depletion of silver in the La Libertad region\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"6\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c6\\\" colnum=\\\"6\\\"\\u003e\\u003c/div\\u003e \\u003cthead\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eYear\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003et\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eProjected price (USD/oz)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eOptimal annual extraction (oz)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eCumulative extraction (oz)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003eRemaining reserves (oz)\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003c/thead\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2025\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e40.97\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e700,382.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e700,382.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e289,203,618.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2026\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e1\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e42.9\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e735,401.10\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e1,435,783.10\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e288,468,216.90\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2027\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e2\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e44.93\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e772,171.16\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e2,207,954.26\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e287,696,045.75\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2028\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e3\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e47.06\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e810,779.71\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e3,018,733.97\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e286,885,266.03\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2029\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e4\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e49.31\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e851,318.70\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e3,870,052.67\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e286,033,947.33\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2030\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e5\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e51.66\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e893,884.63\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e4,763,937.30\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e285,140,062.70\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2031\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e6\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e54.13\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e938,578.86\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e5,702,516.16\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e284,201,483.84\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2032\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e7\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e56.73\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e985,507.81\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e6,688,023.97\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e283,215,976.03\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2033\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e8\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e59.45\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,034,783.20\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e7,722,807.17\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e282,181,192.83\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2034\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e9\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e62.3\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,086,522.36\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e8,809,329.53\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e281,094,670.47\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2035\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e10\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e65.29\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,140,848.48\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e9,950,178.01\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e279,953,821.99\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e\\u0026hellip;\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e\\u0026hellip;\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e\\u0026hellip;\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e\\u0026hellip;\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e\\u0026hellip;\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e\\u0026hellip;\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2086\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e61\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e694.53\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e13,736,693.85\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e274,462,930.93\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e15,441,069.07\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2087\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e62\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e727.52\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e14,423,528.55\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e288,886,459.47\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e1,017,540.53\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003e2088\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e63\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e762.07\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e1,017,540.53\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e289,904,000.00\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec15\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e3.4. Sensitivity of valuation to price and interest rate\\u003c/h2\\u003e \\u003cp\\u003eThe sensitivity analysis shows that the intertemporal economic valuation of metallic resources in La Libertad depends primarily on the base price and the interest rate. In the case of gold, a 40% increase in price raises NPV from approximately USD 3.5\\u0026nbsp;billion to about USD 4.9\\u0026ndash;5.0\\u0026nbsp;billion, while a 40% reduction in the interest rate increases it to around USD 5.9\\u0026nbsp;billion. Conversely, an equivalent increase in the interest rate reduces NPV to just over USD 2.3\\u0026nbsp;billion, confirming that discounting exerts a stronger influence than price on the present value of the resource.\\u003c/p\\u003e \\u003cp\\u003eSilver follows the same pattern, although at a smaller monetary scale. A 40% increase in price raises NPV from approximately USD 29\\u0026nbsp;million to more than USD 40\\u0026nbsp;million, while a 40% reduction in the interest rate increases it to nearly USD 47\\u0026nbsp;million; by contrast, an increase in the interest rate reduces it to slightly above USD 20\\u0026nbsp;million (see Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig4\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e). Taken together, both minerals respond similarly to changes in market and financial assumptions, but the steeper slope associated with the interest rate confirms that this is the most sensitive parameter in the model.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003c/div\\u003e\"},{\"header\":\"4. Discussion\",\"content\":\"\\u003cp\\u003eThe findings of this study show that the intertemporal valuation of gold and silver in La Libertad follows a trajectory consistent with the structural logic of Hotelling\\u0026rsquo;s rule: projected prices increase at the pace of the interest rate, nominal revenues grow steadily, and net present value remains virtually stable over the period analysed. This pattern is consistent with the contemporary interpretation of the rule not as a universal empirical law, but as a useful organizing framework for simulating economic trajectories under explicit assumptions, as argued by Ferreira da Cunha and Missemer (2020) in their critical review of Hotelling\\u0026rsquo;s legacy. In this respect, the results differ from those reported by Mlambo (\\u003cspan citationid=\\\"CR28\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e) for gold in South Africa, where no empirical evidence consistent with the rule was found and extraction was concluded not to follow a socially optimal path. This difference may be explained by the fact that the present study does not seek to econometrically test observed market behaviour, but rather to construct a regional intertemporal valuation scenario under controlled assumptions regarding reserves, prices, and discounting. From this perspective, the contribution of the La Libertad case does not lie in \\u0026ldquo;proving\\u0026rdquo; the rule in a strict empirical sense, but in showing how its regional application makes it possible to distinguish between nominal revenue growth and the preservation of the present economic value of the resource, a distinction that is especially relevant in mining territories where production expansion is often mistakenly interpreted as an automatic increase in wealth (Cotrina-Teatino \\u0026amp; Marquina-Araujo, \\u003cspan citationid=\\\"CR5\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e; Di Maria \\u0026amp; Valente, \\u003cspan citationid=\\\"CR7\\\" class=\\\"CitationRef\\\"\\u003e2008\\u003c/span\\u003e; Missemer et al., \\u003cspan citationid=\\\"CR27\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e; Uberman, \\u003cspan citationid=\\\"CR38\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eAt the same time, the depletion pathways obtained showing a short economic life for gold, close to eight years, and a much longer one for silver, around sixty-four years reinforce the idea that extractive sustainability depends not only on price, but also on the combination of stock size, extraction intensity, and the economic value of mineral. This is consistent with Krautkraemer (\\u003cspan citationid=\\\"CR19\\\" class=\\\"CitationRef\\\"\\u003e1998\\u003c/span\\u003e), who argued that the scarcity of non-renewable resources must be analysed in relation to quality, costs, and extraction rates, and also with green accounting studies applied to Peruvian mining (Figueroa B. et al., \\u003cspan citationid=\\\"CR10\\\" class=\\\"CitationRef\\\"\\u003e2010\\u003c/span\\u003e). In particular, Figueroa B. et al. (\\u003cspan citationid=\\\"CR10\\\" class=\\\"CitationRef\\\"\\u003e2010\\u003c/span\\u003e) estimated that the total loss of natural capital in Peruvian metallic mining accounted for between 31% and 51% of mining GDP, and that conventional GDP overstated the sector\\u0026rsquo;s true economic income by 51%\\u0026ndash;64% over the 1992\\u0026ndash;2006 period. The results of this study move in the same direction, but from a regional and prospective perspective: rather than retrospectively correcting aggregate accounts, they show how the combination of accelerated gold depletion, present-value stability, and high sensitivity to discounting can be used to anticipate sustainability risks in a specific mining region. In comparison with experiences such as the correction of mining GDP in Chile (Figueroa \\u0026amp; Calfucura, \\u003cspan citationid=\\\"CR9\\\" class=\\\"CitationRef\\\"\\u003e2004\\u003c/span\\u003e; Mardones \\u0026amp; del Rio, \\u003cspan citationid=\\\"CR24\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e), which likewise emphasized the importance of incorporating natural capital depreciation into economic measurement, the case of La Libertad provides evidence that the subnational scale makes it possible to better capture differences between minerals and translate them into more refined criteria for the intertemporal management of the resource.\\u003c/p\\u003e \\u003cdiv id=\\\"Sec17\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e4.1. Policy implications and sustainable management of metallic resources\\u003c/h2\\u003e \\u003cp\\u003eThe results indicate that the sustainability of metallic mining in La Libertad cannot be assessed solely on the basis of reserve volumes or the upward trajectory of prices, but rather on the relationship between present value, extraction pace, and the economic lifespan of the stock. Under the modelled scenario, gold exhausts its reserves in approximately eight years, whereas silver extends its depletion horizon to around sixty-four years; however, even with increasing nominal revenues, the net present value of gold remains around USD 3.49\\u0026ndash;3.54\\u0026nbsp;billion and that of silver around USD 28.69\\u0026ndash;29.26\\u0026nbsp;million. This combination suggests that the increase in future flows does not automatically translate into a proportional expansion of regional economic wealth, since a substantial share of that increase is neutralized when expressed in present-value terms. From a public policy perspective, this implies that regional mining planning should not be based solely on extracted volumes or current revenues, but also on indicators that explicitly capture the economic value of the stock and its depletion trajectory, in line with the sustainable-use mandate established by Law No. 26821(Republica del Per\\u0026uacute;, \\u003cspan citationid=\\\"CR33\\\" class=\\\"CitationRef\\\"\\u003e2017\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eThis interpretation becomes even more relevant when the two minerals analysed are compared. Gold combines greater absolute economic value, accelerated depletion, and high sensitivity to the discount rate, making it a highly profitable asset but also one that is highly vulnerable from an intertemporal perspective. Silver, by contrast, shows much greater availability and a more gradual depletion pathway, thereby opening broader scope for longer-term strategies linked to territorial stability, productive linkages, and economic diversification. Consequently, a uniform mining policy for both minerals would be inefficient. The study\\u0026rsquo;s evidence supports the need for differentiated management by mineral and by depletion horizon: for gold, this implies strengthening stock monitoring, extraction sequencing, and the early transformation of rents into durable assets; for silver, it implies a management strategy that combines economic utilization with a longer-term territorial perspective. This logic is consistent with the Mining Policy Framework, which argues that sound mineral governance should integrate economic benefits, strong institutions, environmental protection, and social legitimacy, rather than reducing mining policy to short-term extractive expansion (Ayuk et al., \\u003cspan citationid=\\\"CR2\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eThe sensitivity analysis further reinforces this conclusion. A\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;40% variation in the interest rate generates stronger effects on net present value than an equivalent variation in the base price, for both gold and silver. In the case of gold, a 40% reduction in the interest rate increases NPV to nearly USD 5.9\\u0026nbsp;billion, whereas an equivalent increase reduces it to just over USD 2.3\\u0026nbsp;billion; for silver, the same exercise shifts NPV from around USD 47\\u0026nbsp;million to slightly above USD 20\\u0026nbsp;million. In other words, the apparent profitability of the resource depends not only on the expected behaviour of the mineral market, but also on the macro-financial conditions under which future flows are discounted. The implication is that public and private evaluation of resources and projects should not rely on a single discounting scenario, but should instead incorporate sensitivity bands, stress scenarios, and forward-looking analyses capable of assessing the robustness of decisions under changes in the opportunity cost of capital. In mining territories with high extractive dependence, this precaution is not a minor technical detail, but a necessary condition for avoiding investment, spending, or production-expansion decisions based on overly narrow financial assumptions. The international mineral governance approach itself emphasizes that sustainability requires decisions that are resilient to economic, social, and environmental uncertainty (Onditi, \\u003cspan citationid=\\\"CR29\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eThe study also has a direct implication for how mining rent should be understood in a region such as La Libertad. If gold the metallic asset with the highest economic value can be exhausted in less than a decade under the projected extraction scenario, then territorial sustainability depends on the institutional capacity to transform resource rent into other forms of capital before the stock is significantly reduced. This includes infrastructure, non-extractive productive capacities, human capital, institutional strengthening, and environmental restoration. The central issue is therefore no longer only how much income mining generates during the extraction phase, but also what share of that wealth is converted into durable capabilities that compensate for the progressive decline of natural capital. This principle lies at the core of contemporary mineral governance: mining wealth is sustainable only if it is transformed into lasting benefits, rather than being consumed as short-term current income. This conclusion is particularly relevant in the Peruvian context, where the design of rent-distribution and rent-use instruments can only be considered consistent with sustainability if it helps to cushion the gradual loss of an exhaustible natural asset (MINAM, \\u003cspan citationid=\\\"CR25\\\" class=\\\"CitationRef\\\"\\u003e2005\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eThe integration of economic valuation and environmental management constitutes another direct implication of the results. General Environmental Law No. 28611 establishes the basic framework for environmental management in the country, while Law No. 28090 provides that mine closure must be planned and implemented with sufficient environmental guarantees to cover the required investments. In light of the accelerated depletion of gold in La Libertad, these instruments should not be interpreted as peripheral compliance obligations, but rather as central components of the intertemporal management of the resource. The shorter the depletion horizon, the more necessary it becomes to incorporate closure, restoration, monitoring, and territorial recovery costs at an early stage into the economic evaluation of the asset, because sustainability depends not only on the value generated during the productive phase, but also on how liabilities and the post-extractive transition are managed. At this point, intertemporal valuation and environmental policy cease to be separate fields and instead become two dimensions of a single resource-governance strategy (MINAM, \\u003cspan citationid=\\\"CR25\\\" class=\\\"CitationRef\\\"\\u003e2005\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eFinally, the results show that the sustainable management of metallic resources requires better public information systems on reserves, production, economic value, and depletion. Metrics such as net present value, depletion horizon, and sensitivity to discounting provide a richer reading of sustainability than conventional indicators based on annual production or short-term price movements. Incorporating this type of information into regional and sectoral planning instruments would make it possible to move from a predominantly operational perspective to an intertemporal perspective on the resource, one that is more useful for decisions regarding extraction sequencing, rent use, mine closure, and territorial transition. This approach is consistent with international efforts to strengthen mineral classification, transparency, and governance frameworks oriented toward long-term decision-making, especially in territories where mining constitutes an important foundation of the regional economy (Christmann, \\u003cspan citationid=\\\"CR4\\\" class=\\\"CitationRef\\\"\\u003e2021\\u003c/span\\u003e).\\u003c/p\\u003e \\u003cp\\u003eTaken together, the study suggests that a mining policy consistent with sustainable management in La Libertad should rest on four main pillars: incorporating the intertemporal valuation of the stock as a decision criterion; differentiating the management of gold and silver according to their depletion pressure and scale of value; evaluating resources and projects under multiple price and discount-rate scenarios; and transforming mining rent into other forms of capital before depletion significantly reduces the regional mineral base. From this perspective, Hotelling\\u0026rsquo;s rule ceases to be merely an abstract formulation of exhaustible resource economics and instead becomes a useful tool for rethinking resource governance through a logic of intertemporal sustainability, in coherence with both the Peruvian legal framework and international mineral governance approaches oriented toward sustainable development (MINAM, \\u003cspan citationid=\\\"CR25\\\" class=\\\"CitationRef\\\"\\u003e2005\\u003c/span\\u003e).\\u003c/p\\u003e \\u003c/div\\u003e\"},{\"header\":\"5. Conclusions\",\"content\":\"\\u003cp\\u003eThe study showed that the regional application of Hotelling\\u0026rsquo;s rule makes it possible to interpret, in an integrated manner, the intertemporal economic valuation and depletion pathways of gold and silver in La Libertad. The results revealed rising projected prices and expanding nominal revenues, but relatively stable net present values, indicating that higher future flows do not necessarily imply greater economic wealth in present-value terms. The depletion pathways also revealed important differences between the two minerals: gold exhibited a short economic life of around eight years, whereas silver extended its depletion horizon to approximately sixty-four years. Taken together, these findings suggest that regional extractive sustainability depends not only on reserves and prices, but also on the rate of extraction, the structure of the stock, and the financial conditions under which the resource is valued.\\u003c/p\\u003e \\u003cp\\u003eAmong the main limitations, the model was constructed under explicit assumptions regarding production, price growth, and discounting, without incorporating dynamic marginal costs, uncertainty, additional exploration, technological change, regulation, or socio-environmental externalities. The results should therefore be understood as analytical scenarios rather than exact predictions. Even so, the study provides useful inputs for regional mining planning by highlighting the importance of the present value of the stock, the economic lifespan of reserves, and sensitivity to discounting. Future research could expand this approach by incorporating variable costs, regulatory scenarios, environmental variables, and indicators of mining rent and territorial transformation.\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\u003cli\\u003e\\u003cspan\\u003eArellano-Yanguas J (2011) Aggravating the resource curse: Decentralisation, mining and conflict in Peru. 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Mineral Econ 34(2). ttps://doi.org/10.1007/s13563-021-00265-4\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eCotrina-Teatino MA, Marquina-Araujo JJ (2024) Hotelling rule in non-renewable resources: A bibliometric and systematic literature review analysis. Resour Policy 98:105342. ttps://doi.org/10.1016/j.resourpol.2024.105342\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eCotrina-Teatino MA, Marquina-Araujo JJ, Mamani-Quispe JN, Arango-Retamozo SM, Gonzalez-Vasquez JA (2025) Bibliometric and systematic analysis of the literature on the Hartwick rule in non-renewable resources. Resour Policy 107:105654. ttps://doi.org/10.1016/j.resourpol.2025.105654\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eDi Maria C, Valente S (2008) Hicks meets Hotelling: The direction of technical change in capital-resource economies. 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J Polit Econ 39(2). ttps://doi.org/10.1086/254195\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eIGF (2023) \\u003cem\\u003eMining Policy Framework\\u003c/em\\u003e\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eKamel A, Elwageeh M, Bondu\\u0026agrave; S, Elkarmoty M (2023) Evaluation of mining projects subjected to economic uncertainties using the Monte Carlo simulation and the binomial tree method: Case study in a phosphate mine in Egypt. \\u003cem\\u003eResources Policy\\u003c/em\\u003e, \\u003cem\\u003e80\\u003c/em\\u003e. ttps://doi.org/10.1016/j.resourpol.2022.103266\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eKrautkraemer JA (1990) Taxation, ore quality selection, and the depletion of a heterogeneous deposit of a nonrenewable resource. \\u003cem\\u003eJournal of Environmental Economics and Management\\u003c/em\\u003e, \\u003cem\\u003e18\\u003c/em\\u003e(2 PART 1). ttps://doi.org/10.1016/0095-0696(90)90043-X\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eKrautkraemer JA (1998) Nonrenewable Resource Scarcity. J Econ Lit, \\u003cem\\u003e36\\u003c/em\\u003e(4)\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eLevhari D, Liviatan N (1977) Notes on Hotelling\\u0026rsquo;s Economics of Exhaustible Resources. Can J Econ 10(2). ttps://doi.org/10.2307/134437\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eLilford E (2023) Natural resources: Cost of capital and discounting \\u0026ndash; Risk and uncertainty. \\u003cem\\u003eResources Policy\\u003c/em\\u003e, \\u003cem\\u003e80\\u003c/em\\u003e. ttps://doi.org/10.1016/j.resourpol.2022.103242\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eLilford E, Maybee B, Packey D (2018) Cost of capital and discount rates in cash flow valuations for resources projects. \\u003cem\\u003eResources Policy\\u003c/em\\u003e, \\u003cem\\u003e59\\u003c/em\\u003e. ttps://doi.org/10.1016/j.resourpol.2018.09.008\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eLivernois J (2009) On the empirical significance of the hotelling rule. 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Hist Polit Econ 54(1). ttps://doi.org/10.1215/00182702-9548337\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eMlambo C (2022) Non-Renewable Resources and Sustainable Resource Extraction: An Empirical Test of the Hotelling Rule\\u0026rsquo;s Significance to Gold Extraction in South Africa. Sustain (Switzerland) 14(17). ttps://doi.org/10.3390/su141710619\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eOnditi F (2022) Mining Policy Frameworks. In \\u003cem\\u003eGender Inequalities in Africa\\u0026rsquo;s Mining Policies\\u003c/em\\u003e. ttps://doi.org/10.1007/978-981-16-8252-0_6\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eOrihuela CE, A\\u0026ntilde;i VCMC, Garc\\u0026iacute;a JYD (2024) Including the change in natural capital stock and environmental degradation in Peruvian mining GDP and NNP. Economia Agrar y Recursos Naturales 24(1). ttps://doi.org/10.7201/earn.2024.01.06\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eOvalle A (2020) \\u003cem\\u003eAnalysis of the discount rate for mining projects\\u003c/em\\u003e. ttps://doi.org/10.36487/acg_repo/2063_76\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003ePfingsten A (1986) A note on Hotelling\\u0026rsquo;s rule. Resour Policy 12(1). ttps://doi.org/10.1016/0301-4207(86)90050-4\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eRepublica del Per\\u0026uacute; (2017) \\u003cem\\u003eLey Org\\u0026aacute;nica para el aprovechamiento sostenible de los recursos naturales LEY No 26821\\u003c/em\\u003e\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eSavolainen J (2016) Real options in metal mining project valuation: Review of literature. \\u003cem\\u003eResources Policy\\u003c/em\\u003e, \\u003cem\\u003e50\\u003c/em\\u003e. ttps://doi.org/10.1016/j.resourpol.2016.08.007\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eSlade ME (1984) Tax policy and the supply of exhaustible resources: theory and practice. Land Econ 60(2). ttps://doi.org/10.2307/3145968\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eSlade ME, Thille H (2009) Whither Hotelling: Tests of the Theory of Exhaustible Resources. Annual Rev Resource Econ 1(1). ttps://doi.org/10.1146/annurev.resource.050708.144223\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eSolow RM (1974) Intergenerational equity and exhaustible resources. Rev Econ Stud 41(5). ttps://doi.org/10.2307/2296370\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eUberman R (2023) The Hotelling\\u0026rsquo;s Rule in practice \\u0026ndash; analysis of gold mining sector. Gospodarka Surowcami Mineralnymi - Mineral Resour Manage. ttps://doi.org/10.24425/gsm.2021.137568\\u003c/span\\u003e\\u003c/li\\u003e\\u003c/ol\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":true,\"hideJournal\":true,\"highlight\":\"\",\"institution\":\"National University of Trujillo\",\"isAcceptedByJournal\":false,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research Square\",\"twitterHandle\":\"researchsquare\",\"acdcEnabled\":true,\"dfaEnabled\":false,\"editorialSystem\":\"\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":false,\"inReviewRevisionsEnabled\":true},\"keywords\":\"Hotelling’s rule, intertemporal valuation, mineral resource depletion, sustainable mining governance\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-9087323/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-9087323/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eThe exploitation of metallic mineral resources in territories highly dependent on mining poses a central sustainability challenge, as increases in production and current revenues do not necessarily guarantee the sustainable economic valuation of mineral stock in the long term. In this context, the aim of the study was to evaluate the intertemporal economic valuation and depletion pathways of gold and silver resources in La Libertad, Peru, and to examine their implications for sustainable management under Hotelling\\u0026rsquo;s rule. A quantitative, applied, and non-experimental study was conducted based on official data on reserves, production, prices, and interest rates. Price, revenue, and net present value trajectories were projected for the 2025\\u0026ndash;2040 period, extraction pathways were simulated until reserve exhaustion, and a sensitivity analysis was performed under variations in prices and interest rates. The results showed that gold reserves would be exhausted in approximately eight years, whereas silver would reach a depletion horizon of nearly sixty-four years. Although projected nominal revenues increased steadily, net present value remained nearly stable, ranging from USD 3.49 to 3.54\\u0026nbsp;billion for gold and from USD 28.69 to 29.26\\u0026nbsp;million for silver. It is concluded that extractive sustainability depends not only on reserves and prices, but also on the rate of extraction, the economic lifespan of the stock, and the financial conditions under which the resource is valued.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Intertemporal economic valuation and depletion pathways of metallic mineral resources in La Libertad, Peru: Implications for sustainable management under Hotelling’s rule\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2026-03-12 09:06:10\",\"doi\":\"10.21203/rs.3.rs-9087323/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research Square\",\"twitterHandle\":\"researchsquare\",\"acdcEnabled\":true,\"dfaEnabled\":false,\"editorialSystem\":\"\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":false,\"inReviewRevisionsEnabled\":true}}],\"origin\":\"\",\"ownerIdentity\":\"cca839db-91f2-4e7b-8a99-d31aec394a53\",\"owner\":[],\"postedDate\":\"March 12th, 2026\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"posted\",\"subjectAreas\":[],\"tags\":[],\"updatedAt\":\"2026-03-12T09:06:10+00:00\",\"versionOfRecord\":[],\"versionCreatedAt\":\"2026-03-12 09:06:10\",\"video\":\"\",\"vorDoi\":\"\",\"vorDoiUrl\":\"\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-9087323\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-9087323\",\"identity\":\"rs-9087323\",\"version\":[\"v1\"]},\"buildId\":\"XKTyCvWXoU3ODBz1xrDgd\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}