Question

The government is contemplating a project that protects a wilderness area. The project’s initial costs incurred at time t=0 equal $375,000. Starting in year 1, the project is expected to produce annual net benefits of $100,000 into perpetuity.

(a) Calculate the net present value assuming a discount rate of 8%. Do you recommend going forward with this project?

(b) There is some uncertainty about the estimates of initial costs and annual net benefits. Research suggests that there is a 75% chance that the start-up costs are $375,000 and a 25% chance that these costs are $500,000. Similarly, further analysis suggests that there is a 60% chance that annual net benefits are $100,000 into perpetuity but a 40% that these annual net benefits are $65,000. To deal with the uncertainty you undertake

(i) an expected value analysis, and

(ii) a best-case analysis.

Briefly explain how you would proceed in each case and present the results from each. Does this additional analysis support your initial recommendation (from (a) above)?

Answer 1

Solution(s):

Answer 4(a) : The initial cost of the project at time t is = $375,000

                        The discount rate available means the interest rate that is fixed by the US federal reserve for lending of loans to government or other banking institutions. Therefore, to finance the project, the Government can get the money at an interest rate of 8%

                      This means, the per annum interest amount to be paid by the Government would be at least:                     = 8% of $375,000 + portion of principal amount depending on the number of years the loan has been opted for.

                                  = 8/100 x 375,000

                                  = $30,000 + expected amount of the principal amount.

            Since the Government is expected to get annual net benefits of $100,000 , it is recommended that the Government should go ahead with the project.

Answer 2 (b) : The expected value analysis of cost=

                                   = 75% of (0-375000) + 25% of ( 500,000 - 375,000 )

                                   = 0.75 x (-375000) + 0.25 x (125,000)

                                  = $281,250 + $31,250

                                  = $312,500

The expected value analysis of revenue / return=

                                   = 60% of (0-100000) + 40% of ( 65000 - 100000 )

                                   = 0.60 x (-100000) + 0.40 x (35,000)

                                  = $60,000 - $14,000

                                  = $46,000

From the above data calculation, we can sum up that the Government is expected to make an expected net income of $46,000 annually from a total cost of around $ 312,500. The expected revenue is much lesser in comparison to the cost incurred. Therefore, the Government should not continue with this project.