Consider an individual with a discount rate of 10 percent who faces the following two possible investments:
Investment 1: Cost in Year 0 = -500 million
Return in Years 1, 2, 3, and 4 = +500 million each year
Investment 2: Cost in Year 0 = -1000 million
Return in Year 2 = +200 million Return in Year 4 = + 3000 million
a) What is the Present Discounted Value of each investment stream? Which investment should the investor choose?
b) Now consider that each investment has “Good” state that is shown in part a) and a “Bad” state that consists of the following:
Investment 1: Cost in Year 0 = -500 million
Return in Years 1-4 = +400 million each year
Investment 2: Cost in Year 0 = -1000 million
Return in Year 2 = +200 million Return in Year 4 = + 2000 million
Each state has a 50 percent chance of occurring. If the investor is interested in maximizing the Expected Present Discounted Value of its investment, which investment should the investor choose?
c) Now consider that the investor has utility U = Ln(PDV of investment) (where Ln is the natural logarithm) and is interested in maximizing expected utility. Which investment should the investor choose? [Note: utility is different in each state]