benefit-cost (B/C) ratio analysis
Present value of marginal social benefits per dollar of marginal social cost before discounting are a misleading measure of the attractiveness of each project because they do not reflect differences in the time frame over which program benefits and costs are generated.
A relevant measure of the attractiveness of each respective program is the social net present value of each program, where each dollar of marginal social benefits and marginal social costs is converted into a common current-dollar basis. The social rate of discount used to convert nominal dollar values into present-value terms is 8 percent for program A, 10 percent for program B, and 12 percent for program C. Each respective social discount rate plays the role of a present-value interest factor that can be used to convert nominal dollar costs and benefits to a common present-value basis. If a 5 percent yield to maturity on short-term Treasury bills is taken as a proxy for the risk-free rate, program A involves a 3 percent risk premium, program B entails a 5 percent risk premium, and program C employs a 7 percent risk premium.
Because social benefits received in the future are worth less than social costs incurred at the beginning of the program, the SNPV for any public program tends to be much less than the nominal dollar amount of social benefits. Using a program-specific social rate of discount, the present value of marginal social benefits is $4,609,087.90 for program A, $4,256,781.86 for program B, and $6,364,117.84 for program C. After considering the present value of marginal social cost for each program, the SNPV for program A is SNPVA = -$390,912.10, calculated as follows:
SNPVa = PV of MSB - PV of MSC = $4,609,087.90 - $5,000,000 = -$390,912.10
The SNPVa = -$390,912.10 means that the present value of marginal social costs for this program exceeds the present value of marginal social benefits. Funding program A would represent an unwise use of public resources. Whenever SNPV < 0, program funding is unwise on an economic basis. A judicious use of social resources requires that SNPV > 0 for every public program or public investment project.
Again using an appropriate program-specific social rate of discount, the present value of marginal social benefits is $4,256,781.86 for program B and $6,364,117.84 for program C. After considering the present value of marginal social cost for each program, the SNPV for program B is $1,256,781.86 and for program C is $1,364,117.84. Both programs B and C represent a wise use of public resources because SNPVB > 0 and SNPVC > 0. if public funding is sufficient to fund both projects at the same time, both should be underwritten. If public funding is scarce and both programs cannot be funded, program C is preferred to program B since SNPVC > SNPVB.
As discussed in Chapter 15, large projects tend to be favored through the use of net present-value criterion because large net present values usually require the commitment of significant capital resources. In a similar fashion, the SNPV can result in a bias toward larger projects because a large social net present value typically requires the commitment of significant marginal social costs. This has the potential to result in a bias toward larger as opposed to smaller social programs and public-sector investment projects when the SNPV criterion is employed. To avoid such a bias, it becomes necessary to introduce two additional public-sector capital budgeting decision rules.
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