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    The certainty-equivalent approach of capital Budgeting

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    On March 1, 2001, the Australian Coal Exploration Company was investigating the feasibility of two mutually exclusive investment projects. The first prospective investment involved a strip (open-cut) mining operation in western New South Wales. The second investment also involved the extraction of coal, but this expenditure would be an underground site in south-eastern Victoria. Preliminary drilling, sampling and analysis of both sites and consultation with geologists, costing the company $240,000, suggested that both sites have similar coal reserves and useful lives.

    The coal extraction process for the two types of mines and the equipment required for operation of the mines are very different, however, with the underground mining operation expected to be more complex and difficult. The process of drilling underground also increases the dangers faced by employees, although it is more environmentally friendly than the pollution and soil erosion caused by open-cut mining operations.

    For the past several months, John McPhee has been involved in the development of revenue and expense projections for the two projects. In his analysis, sufficient data existed from prior investments to provide relatively accurate cost data. After having drawn upon this information, McPhee made the following projections as to investment costs for each operation:

    Strip Mining Underground Mining
    Equipment $3,000,000 $1,750,000
    Additional working capital requirements 200,000 200,000
    Total $3,200,000 $1,950,000
    With respect to these figures, experience suggests that a 10-year life may be expected on either of the two prospective investments, with the practice being to depreciate the equipment on a prime-cost (straight-line) basis over the life of the projects. Both sites have no alternative productive use for the company, although the land in New South Wales and Victoria could be sold now for $400,000 and $300,000 respectively as grazing land for farming. The projected salvage value for the strip mining operation would be $600,000 at project end, while the equipment for the underground plant could be expected to have a residual value of $150,000. The working capital requirement would arise at the time of the investment, but could be released upon the termination of the project with only a negligible chance of the full amount not being recovered.

    In addition to the cost estimates, the engineers, based upon studies of the subsurface formations, were able to make projections as to the revenues that could be generated from the two fields. As a result of their studies, expected earnings after taxes for the two investments would be as follows:

    Years Annual expected earnings after taxes
    Strip mining 1-4 $400,000
    5-7 $220,000
    8-10 $100,000
    Underground mining 1-4 $360,000
    5-7 $230,000
    8-10 $130,000

    Upon receiving this information, McPhee questioned the reliability of the anticipated earnings. In response, Tony Hughes, head of the engineering staff at the Australian Coal Exploration Company, informed him that both projects would have to be considered to be more risky than the firm's typical investment. The analysis indicated that the expected cash flows from the underground mining operation were subject to considerably more uncertainty than those from the strip mining project. In fact, Hughes considered the extraction of coal through the underground facility to be twice as risky as that of the strip-mining alternative. For this reason, he recommended that the strip-mining project be discounted at a 10 per cent rate, while the underground mining proposal be analysed with a 20 per cent criterion. McPhee questioned Hughes' logic, in that the company's cost of capital had been computed to be 8 per cent. He believed that this figure better reflected the shareholders' required rate of return and for that reason should be used as the discount rate for both projects.

    In support of his position concerning the riskiness of the two proposed investments, Hughes developed some in-depth worksheets for McPhee that suggested other possible returns depending upon the amount of coal actually extracted from the mines. These calculations of the standard deviations from the expected value of earnings are as follows:

    Years Standard deviation of earnings after taxes
    Strip Mining 1-4 $360,000
    5-7 $242,000
    8-10 $190,000
    Underground Mining 1-4 $324,000
    5-7 $276,000
    8-10 $234,000
    In addition to the standard deviation of these reported earnings, engineering personnel estimated the standard deviation relating to the salvage value to be $300,000 for the strip mining facility and $135,000 for the underground mining equipment.

    In reviewing the engineering department's work, John McPhee was quite pleased with the results. However, a question remained in his mind as to the soundness of employing the various discount rates, as suggested by Hughes. As an alternative to adjusting the discount rate for projects with dissimilar risks, he had been conducting informal discussions with top management trying to establish the relationship between the level of risk and the willingness of management to accept such uncertainty, as reflected by 'certainty-equivalent factors'. The results of these meetings are depicted in Exhibit 1 below.

    Exhibit 1: Management's risk-return profile
    Coefficient of variation (CV)* Certainty-equivalent factor
    0.50 0.95
    0.60 0.93
    0.70 0.91
    0.80 0.88
    0.90 0.85
    1.00 0.82
    1.10 0.78
    1.20 0.74
    1.30 0.70
    1.40 0.64
    1.50 0.58
    1.60 0.52
    1.70 0.43
    1.80 0.33
    1.90 0.15

    He felt that a better approach would be to adjust the cash flows by the appropriate certainty-equivalent factor and to discount these adjusted cash flows at the firm's cost of capital. However, Hughes is of the opinion that the risk-free rate, which is currently 6 per cent, would be more appropriate for such analysis.

    At this point, the investigation has been temporarily halted until these outstanding questions have been resolved.


    1) Consider the arguments of John McPhee and Tony Hughes regarding how the risk of these two projects should be measured and incorporated into the investment evaluation process. Are both of them technically correct in the methods they suggest to account for project risk, and which method of risk-adjustment do you think should be applied in evaluating the feasibility of these two projects?

    2) Calculate the net present value for each investment employing (i) the certainty-equivalent approach and (ii) the risk-adjusted rate of return method. Assume that the company faces a marginal corporate tax rate of 30 per cent on earnings and other cash flows. Using these calculations, provide a recommendation to the company as to which project the firm should accept. If an inconsistency between the results of the various capital budgeting techniques does exist, explain the reason(s) Why.

    3) Outline any other factors that you think the Australian Coal Exploration Company should consider prior to making its final decision on these projects, and whether, in your opinion, any of these factors warrant acceptance of one project over another, independent of financial concerns.

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    Solution Preview

    Consider the arguments of John McPhee and Tony Hughes regarding how the risk of these two projects should be measured and incorporated into the investment evaluation process. Are both of them technically correct in the methods they suggest to account for project risk, and which method of risk-adjustment do you think should be applied in evaluating the feasibility of these two projects?

    Risk exists because of the inability of the decision-maker to make perfect forecasts. In formal terms, the risk associated with an investment may be defined as the variability that is likely to occur in the future returns from the investment.
    Three broad categories of the events influencing the investment forecasts:
    General economic conditions
    Industry factors
    Company factors

    The following are the advantages of the certainty equivalent cash flow approach
    Reduce the forecasts of cash flows to some conservative levels.
    The certainty?equivalent coefficient assumes a value between 0 and 1, and varies inversely with risk.
    Decision-maker subjectively or objectively establishes the coefficients.
    The certainty?equivalent coefficient can be determined as a relationship between the certain cash flows and the risky cash flows.

    The following are the advantages of risk-adjusted discount rate method:
    It is simple and can be easily understood.
    It has a great deal of ...

    Solution Summary

    This explains the risk analysis in capital budgeting using the certainty-equivalent approach and the risk-adjusted rate of return method with the help of case study.