This repository has a short literature review regarding social discount rates and individual discount rates. Next, it shows tables containing:
Generation technologies usually have a long useful lifetime (e.g., hydropower, thermal power plants). In terms of expenditures, generation projects face costs in the evaluation process, at the construction phase, in operation/generation, and even during decommissioning. These costs occur at different times during the useful life of such power plants. In this regard, it is crucial to select the proper discount rate if a government or private investor is likely to invest in long life and high capital-intensive energy projects in the supply industry.
Concerning discount rates, one has to differentiate between the financial discount rates and the discount rate to analyze long-term environmental considerations and welfare. The first one, a financial discount, deals from an investment perspective and its financial cash flows. In contrast, the second is used in the evaluation of a social welfare function [1]. The first one is the one that will be used in this paper. Additionally, the discount rate is a term referred to as the cost of capital. Both terms are often interchangeable; yet, these are different. A discount rate is a rate used for discounting cash flows, and a cost of capital is the rate of return from an investment [2].
Studies by Garcia-Gusano et. al. [3] and Goulder et. Al [1] stated the importance of discount rates in optimization models. In this model, we used different discount rates for evaluating combinations of policy decisions, future investments in a series of scenarios to test the sensitivity of generation technologies to discount rates. For instance, we use global or social discount rates (SDR) to assess the total cost from a public perspective. Also, individual or hurdle rates (HR) reflecting a private investor’s expected return.
The private sector is also a way to fund energy projects. As such, from a private investor perspective, the cost of capital is mostly calculated by using the capital asset pricing model (\(CAPM\)) as seen in Eq. 1. \[E[r] = r_f + \beta.(E[r_m]-r_f)\] Where \(E[r]\) is the investor expected rate of return or cost of capital, \(r_f\) is the risk free rate of return and \(E[r_m]\) is the market risk premium. The expression \((E[r_m ]-r_f)\) is the market risk premium modified by β, which is a measure of the systematic risk. In other words, an investor would require a rate of return that considers a risk free rate and compensation due to the risk of taking such investment. As stated earlier, the CAPM model would solve the issue of systematic risk, which is inherent to the market itself; thus, unavoidable. Nevertheless, the investor would solve another issue, the unsystematic risk, which is unique for each project, by diversifying the portfolio.
A second method used in project evaluation and viability is the weighted average cost of capital (\(WACC\)) Eq.2.
\[ WACC = r_e.E + r_d.(1-T_c).D\]
Where the cost of equity and debt are \(r_e\), \(r_d\), and \(T_c\) is the corporate tax. \(E\) and \(D\) are equity and debt ratio, respectively. Both the \(WACC\) and \(CAPM\) generally are methods used to calculate the cost of capital. However, there is high uncertainty, which is the preferred method for countries and private investors. This is due to differences in calculation methods, input data, and mostly in developing countries [12].
According to Khatib [11], the use of the \(WACC\) as a cost of capital is erroneous when comparing projects that have different risks. As such, \(WACC\) is the rate at which a firm is expected to pay to all sources of financing (e.g., equity, debt), not a rate of return. Unlike Khatib, Berk et al. [2] showed that an investor/firm could use the \(WACC\) as the cost of capital under two assumptions. First, the market risk of the project should be similar to the average market risk of the firm’s investments. Second, investor/firm should maintain a constant debt-equity ratio. In a similar study conducted by Villareal et al. [13], it was proposed a modified methodology in which both methods, \(WACC\) and \(CAPM\), showed consistency in results.
Regarding specific rates, Helms et al. [14] found an average cost of capital of 8% in Europe for utility companies; yet, a 5% can be added as a standard practice to obtain a hurdle rate. The most relevant reports showing discount rates or hurdle rates for generation technologies were developed for the Committee on Climate Change and the Department of Energy and Climate Change [15,16]. Both reports used an extended \(CAPM\) framework for determining hurdle rates. Finally, a study in Europe carried out by Steinbach et. Al. [17] for the Building Performance Institute Europe (BPIE) identified SDR and individual hurdle rates for several policies in different countries.
The implemetation of specific discount rates in Osemosys is as follows
The addition of a new parameter for individual discount rates DiscountRateIdv[r,t]. This parameter allows the modeler to enter specific discount rates for each technology. When DiscountRateIdv[r,t] is not stated in the data file, the default discount rate is set to be the DiscountRate[r] or a global discount rate.
param DiscountRateIdv{r in REGION, t in TECHNOLOGY}, default DiscountRate[r];
An extra parameter is added to the code, the Capital Recovery Factor (CRD). The \(CRF\) (Eq. 3) allows calculating a series of equal payments, from the Capital Investment or a lump sum, spread over the operational life of a generation technology. The formula for the CRF is represented as: \[\frac{1-(1+DiscountRateIdv[r,t])^{-1}}{1-(1+DiscountRateIdv[r,t])^{-n}}\] Where \(n\) is operational life of a generation technology.
The representation in Osemosys as GNU MathProg language is:
param CapitalRecoveryFactor{r in REGION, t in TECHNOLOGY} := (1 - (1 + DiscountRateIdv[r,t])^(-1))/(1 - (1 + DiscountRateIdv[r,t])^(-(OperationalLife[r,t])));
The final parameter implemented in the code is the \(PvAnnuity\). This factor allows calculating the present value of the all-individual payments (calculated by the CRF) in the investment year at the global discount rate DiscountRate[r] as seen in Eq.4. \[\frac{(1-(1+DiscountRate[r])^{-n}).(1+DiscountRate[r])}{DiscountRate[r]}\] Where \(n\) is operational life of a generation technology. The representation in Osemosys as GNU MathProg language is:
param PvAnnuity{r in REGION, t in TECHNOLOGY} := (1 - (1 + DiscountRate[r])^(-(OperationalLife[r,t]))) * (1 + DiscountRate[r]) / DiscountRate[r];
Finally, the Capital Investment is updated by the \(CRF\) and the \(PvAnnuity\) factos as follows:
CC1_UndiscountedCapitalInvestment{r in REGION, t in TECHNOLOGY, y in YEAR}: CapitalCost[r,t,y] * NewCapacity[r,t,y] * CapitalRecoveryFactor[r,t] * PvAnnuity[r,t] = CapitalInvestment[r,t,y];
| Technologies | Capital Cost | Fixed Cost | Variable Cost | Life Time | Construction time | Capacity factor | Source |
|---|---|---|---|---|---|---|---|
| (USD/kW) | (USD/kW) | (USD/MWh) | years | years | % | ||
| Biomass 1 | 4400 | 80.0 | 4 | 40 | 3 | varies | [18] |
| CCGT 2 | 1100 | 10.9 | 3.4 | 40 | 2 | varies | [19] |
| Geothermal | 3633 | 35.0 | 2 | 40 | 3 | 80 | [20,21] |
| Hydro_L 3 | 1500 | 31.0 | 2 | 80 | 6 | 50 | [18] |
| Hydro_M 4 | 2000 | 50.0 | 2 | 80 | 4 | 50 | |
| Hydro_S 5 | 3000 | 120.0 | 2 | 80 | 3 | 50 | |
| ICE_biogas | 2175 | 43.5 | 0.005 | 40 | 2 | Varies | [18] |
| ICE_FO (fuel oil) | 1215 | 10.0 | 10 | 40 | 2 | Varies | [22] |
| ICE_res (residue) | 1215 | 10.0 | 10 | 40 | 2 | Varies | [22] |
| Solar PV | 1210 | 21.0 | - | 25 | 1 | 16 | [18,23] |
| Steam_FO | 1021 | 50.0 | 10 | 40 | 2 | varies | [22,24] |
| Wind_pot 6,7 | 1549 | 30.0 | - | 25 | 2 | 25 | [18,23] |
1Fluidized bed (FB) boiler. 2 Combined cycle gas turbine. 3,4,5 Large, medium, and small-scale average capacity factor. 6 Average capacity factor and wind speed higher 7.5 ms-1. 7 Wind potential, adapted from Projected Costs of Generating Electricity 2015 [8]. In the model, we assumed an even expenditure of capital/overnight cost for each year of construction.
| Fuel | Price (USD) | Unit | Model period | Source |
|---|---|---|---|---|
| Diesel | 0.90 | Gallon | 2018-2050 | [26] |
| Fuel oil1 | 0.62 | Gallon | 2018-2050 | |
| Residue2 | 0.41 | Gallon | 2018-2050 | |
| Natural gas3 | 2.75 | MMBTU4 | 2018-2050 | , [27] |
| Natural gas (import) | 3.75 | MMBTU | 2030-2050 | [28] |
1 Average value from two refinery facilities. 2 Residue for electricity generation is a mixture of 80 percent residue and 20 percent solvent (diesel 2). 3 Price for electricity generation. 4 Million Btu
List of future capacity investments for BAU, SDR, and HR scenarios
| year | Power Plant | Capacity (MW) | Annual average energy (GWh) | Type | Source |
|---|---|---|---|---|---|
| 2020 | San Jose de Minas | 6.0 | 40.0 | RoRa | [29,30] |
| Chorillos | 4.0 | 27.4 | RoR | [31,32] | |
| Huascachaca | 50.0 | 122.6 | Wind onshore | [33] | |
| 2021 | Piatua | 30.0 | 172.0 | RoR | [34] |
| Chalpi grande | 7.6 | 33.2 | RoR | [35] | |
| La Magdalena | 20.0 | 114.0 | RoR | [36] | |
| Ibarra Fugua | 30.0 | 207.6 | RoR | [37] | |
| Sabanilla | 30.0 | 194.0 | RoR | [38] | |
| Maravilla | 8.2 | 61.6 | RoR | [39] | |
| 2022 | El Salto | 30.0 | 247.0 | RoR | [40] |
| Quijos | 50.0 | 355.0 | RoR | [41] | |
| Soldados Yanuncay | 7.0 | 30.6 | Storage Hydro | [42] | |
| El Aromo | 200.0 | 280.0 | Solar PV Utility | [43] | |
| CCGT | 400.0 | - | Gas turbine | ||
| 2023 | Yanuncai | 14.6 | 63.9 | Cascade system – Hydro-Soldados | [42] |
| CCb | 600.0 | - | Gas turbine | ||
| Villonaco II y III | 100.0 | - | Wind on-shore | [44] | |
| 2025 | Cardenillo | 596.0 | 3355.8 | Storage Hydro | [45] |
| 2026 | Geothermal | 150.0 | Geothermal | ||
| Santiago I, IIc | 1200.0 | 4966.0 | Storage Hydro | [46,47] | |
| 2027 | Santiago III, IVc | 1200.0 | 4966.0 | Storage Hydro |
a RoR: Run of the river. b Combined cycle gas turbine. c in 2019, the Ministry of Energy announced that the initial project was overestimated, the final capacity should decrease from 3.6 GW to 2.4 GW.
Forked from OSeMOSYS/OSeMOSYS_GNU_MathProg. This repository has the implementation of individual discount rate.
Additional data for residual power plants or installed power plants.
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Social discount rates
Social discount rates (SDR) are used in cost-benefit analysis in long-term government projects by discounting future cash flows to obtain a present value. One of the most challenging factors in a cost-benefit analysis for public investments is selecting the appropriate social discount rate [4,5]. Several authors have analyzed and discussed the advantages and disadvantages of different methods for determining the SDR or developed surveys to collect data from experts in selecting SDR [6]. Yet, there is no consensus on the proper process of how to set a suitable SDR.
This lack of consensus is exemplified in the work undertaken by Zhuang et al. [7]. This study found that there are significant differences in selecting the discount rate in different countries. According to this, developed countries have lower social discount rates from 3% to 7%; however, developing counties were found to apply higher discount rates from 8% to 15%. Another example of such differences is when countries use constant discount rates while others use a declining discount rate [8]. A common practice is that government institutions decide the SDR. For example, the UK set a discount rate at 3.5%, and this rate declines overtime for projects longer than 30 years [9].
Development agencies can also assess the SDR for a specific country. For example, the World Bank often applies discount rates from 10% to 12% for developing countries [10]. The level of the rate depends on factors such as availability of capital, public funds, rate of interest of borrowing, and alternative approaches [11]. A common practice is to undertake projects as long as the rate of return is higher than the cost of borrowing.