# Question

Consider a project initiated in year 0 and ending in year 2. Investments in year 0 mean that the net benefit in period 0 is NB0 = –180.

a. Assume first that the net benefits are 100 in year 1 and year 2, i.e. NB1 = 100 and NB2 = 100. What is the net present value of the project if the discount rate is 10%?

b. Assume now that the net benefits in year 1 are considered to be uncertain as the market for the product can either be very sluggish or very promising. In specific there is a 50% chance that NB1 = 50 and a 50% chance that NB1 = 150 in period 1. The net benefits in year 2 are assumed to remain certain at NB2 = 100. What is the expected net present value (assuming as before that.

c. Assume now that market conditions are longer lasting so the developments in year 1 are carried over to year 2. Thus, if NB1 is 50, then NB2 is also 50. Likewise, if NB1 is 150, then NB2 is also 150. What is the expected net present value (with the discount rate being 10%)? Calculate the standard deviation of the net present value of the project.

d. Return to the case of certain net benefits, i.e. case a). Now assume instead that there is uncertainty concerning the “correct” discount rate. In specific, 1 / 3 there is a probability that it is 5%, a probability that it is 10% and a probability that it is 15%. Find the expected net present value of the project

a. Assume first that the net benefits are 100 in year 1 and year 2, i.e. NB1 = 100 and NB2 = 100. What is the net present value of the project if the discount rate is 10%?

b. Assume now that the net benefits in year 1 are considered to be uncertain as the market for the product can either be very sluggish or very promising. In specific there is a 50% chance that NB1 = 50 and a 50% chance that NB1 = 150 in period 1. The net benefits in year 2 are assumed to remain certain at NB2 = 100. What is the expected net present value (assuming as before that.

c. Assume now that market conditions are longer lasting so the developments in year 1 are carried over to year 2. Thus, if NB1 is 50, then NB2 is also 50. Likewise, if NB1 is 150, then NB2 is also 150. What is the expected net present value (with the discount rate being 10%)? Calculate the standard deviation of the net present value of the project.

d. Return to the case of certain net benefits, i.e. case a). Now assume instead that there is uncertainty concerning the “correct” discount rate. In specific, 1 / 3 there is a probability that it is 5%, a probability that it is 10% and a probability that it is 15%. Find the expected net present value of the project

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