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p. 48 of 74 BACK | NEXT I. Introduction II. Background III. The Economic Rationale of A Project IV. Macroeconomic and Sectoral Context V. An Integrated Approach To Economic Analysis VI. Identification and Quantification of Costs and Benefits VII. Valuation of Economic Costs and Benefits VIII. Large Projects, Linkages, and National Affordability IX. Least-Cost and Cost-Effective Analysis X. Investment Criteria: Economic Viability XI. Discount Rate XII. Uncertainty: Sensitivity and Risk Analysis XIII. Sustainability of Project Effects XIV. Distribution of Project Effects XV. Projects and Policies XVI. Appendices Appendix 1: Key Questions For The Economic Analysis of Projects Appendix 2: Project Economic Rationale: Market and Nonmarket Failures Appendix 3: The Project Framework Appendix 4: Identification and Measurement of Consumer Surplus Appendix 5: Treatment of Working Capital Appendix 6: Depletion Premium Appendix 7: The Use of Constant Prices In The Economic Analysis of Projects Appendix 8: General Methodology For Building Up Project Statements Appendix 9: Economic Evaluation of Project Output and Input Appendix 10: Economic Price of Traded Goods and Services Appendix 11: Valuation of Nontraded Outputs and Inputs Appendix 12: Shadow Wage Rate and The Shadow Water Rate Factor Appendix 13: The Economic Price of Land Appendix 14: Treatment of Resettlement Components of Projects Appendix 15: Calculating Economic Prices At The Domestic Market Price Or World Market Price Levels Appendix 16: Estimating The Shadow Exchange Rate Factor and The Standard (Or Average) Conversion Factor Appendix 17: Example of An Economic Rate of Return: An Irrigation Rehabilitation Project Appendix 18: Effect On Net Foreign Exchange and Budget Flows: An Example Appendix 19: Least-Cost Analysis and Choosing Between Alternatives Appendix 20: Estimating The Economic Opportunity Cost of Capital Appendix 21: The Treatment of Uncertainty In The Economic Analysis of Projects: Sensitivity and Risk Analysis Appendix 22: User Charges, Cost Recovery, and Demand Management: An Example For Piped Water Appendix 23: Financial Returns To Project Participants: An Illustration Appendix 24: Economic Evaluation of Environmental Impacts Appendix 25: Distribution of Project Effects Appendix 26: Impact On Poverty Reduction Appendix 27: Difference Between Economic and Financial Prices Appendix 28: Use of Economic Prices In Measuring Effective Protection Appendix 29: Exchange Rate Issues In Project Analysis XVII. Others

Guidelines for the Economic Analysis of Projects : XVI. Appendices

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Appendix 6 : Depletion Premium

1. Many projects involve exploitation of depletable resources, either as an input or an output. The key characteristic of a depletable resource is that it initially exists in a given stock and its use leads to a decline in its stock. Either no process increases the stock in any given deposit, or the rate of use for a given deposit exceeds the rate of replenishment. Normally, mineral and energy deposits are treated as depletable resources. However, environmental goods, such as wilderness, top soil, ozone layers, water aquifers, and endangered species, are also depletable resources. Economic analysis of projects needs to explicitly include the economic cost of depletion.

2. Depletable resources could be either tradable or nontradable goods. Most energy and minerals goods are tradables, whereas most environmental goods are nontradable. Valuation of depletable resources requires the inclusion of an explicit opportunity cost component for depletion, in addition to the normal market value or marginal extraction costs. This opportunity cost is often referred to as a depletion premium. The depletion premium is an additional amount equivalent to the present value of the opportunity cost of extracting the resource at some time in the future, over and above its economic price today. In the following examples, all values are economic values.

3. Two cases of depletion premium are encountered:

• with no stock effect, where the cost of extraction is independent of the remaining stock; and
• with stock effect, where the cost of extraction depends on the remaining stock level.

4. In general, the depletion premium for a particular year can be defined as

DP_t = (PS_T - CS_t ) (1+r)^t (1)
_________________________
(1 + r)^T

where DP_t = depletion premium at time t;
PS_T = price of substitute at the time of complete exhaustion T;
CS_t = extraction cost of present resource, assumed to be constant for all years;
r = discount rate; and
T = time of exhaustion of deposit.

In most projects, the assumption of constant marginal extraction cost is used. However, there are a number of alternative models under different cost conditions.

I. Depletion Premium Without Stock Effect: Natural Gas

5. Natural gas is a depletable resource and many countries have finite stocks. Consider a project that requires natural gas as an input. The calculation of a depletion premium for natural gas requires the basic data outlined in Table 1. Then using equation (1), assuming the price of the fuel substitute in year 15 to be $4.5/mmbtu; using 12 percent as a discount rate; and taking 1995 as the base year for calculations (t=0), we have

Depletion Premium (1995) = (4.5 0.75) x (1.12)⁰ / (1.12)¹⁵ = 0.69
Depletion Premium (1996) = 3.75 x (1.12)¹ / (1.12)¹⁵ = 0.77

and so on. The depletion premium increases as the stock diminishes. For the price to reflect depletion, the project economic analysis will include the economic cost of $0.75 plus the opportunity cost of depletion of $0.69 in 1995, and $0.75 plus the depletion premium of $0.77 in 1996, and so on. The economic value of the natural gas input, therefore, increases over time until the stock is exhausted.

II. Depletion Premium with Stock Effects: Water

6. Some water aquifers also face the phenomenon of depletion when these resources are mined, that is, the natural rate of recharge is less than its consumptive use. This represents a case of depletion with stock effects. In such cases, where significant cost increases take place as the stock depletes, the appropriate valuation of water has to include a depletion premium, irrespective of the time of depletion. The depletion premium here is defined as the present value of future cost increases. The concept is shown very simply in Figure 1. A typical cost function for a constant cost case is a step function:

C_t = C₁ for t < T = C₂ for t > T

where C_t is cost in time period _t, and _T is the time when the present cost increases to a much higher level. C₁ reflects the present low cost, whereas after period _T, the cost will be significantly higher at the C₂ level, as a result of changing to an alternative water source.

7. The depletion premium is defined as the present value at time t of the increase in future costs, that is, the open-ended rectangle area abdg in Figure 1. While the area abdg is infinite, it has a finite present value, that is, if exhaustion can be delayed by one year to T+1, the present value of area abef will be saved. The depletion premium increases each year as the stock of water diminishes. It can be expressed as

DP_t = (C₂ - C₁ ) e^{-r ( T - t)}

where r is the discount rate.

8. Table 2 provides estimates for the depletion premium for water. T is assumed to be 20 years. The cost of desalination of water, the alternative source, is $2.00 per 1,000 gallons, compared to the present economic cost of $0.15 per 1,000 gallons from the existing aquifer. The discount rate used is 12 percent per year. Table 2 shows the depletion premium for each year, and the full economic price of water.

III. Conclusions

9. There are a number of uncertainties inherent in estimating a depletion premium for any resource. The major ones include the present knowledge about the size and life of the deposits, the substitutes to be used, and the level of future prices of both the resource for which the depletion premium is estimated and likely substitutes. It is therefore recommended that analysis of depletion should be carried out in the context of a broader analysis for risk and uncertainty. As far as possible, assumptions about the size or cost of substitutes need to be validated and documented. If there are uncertainties associated with the basic assumptions relating to estimates of a depletion premium, sensitivity analysis should be applied.

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