Chapter 2, Problem 37PS

Growing perpetuities and annuities Your firm’s geologists have discovered a small oil field in New York’s Westchester County. The field is forecasted to produce a cash flow of C₁ = $2 million in the first year. You estimate that you could earn a return of r = 12% from investing in stocks with a similar degree of risk to your oil field. Therefore, 12% is the opportunity cost of capital. What is the present value? The answer, of course, depends on what happens to the cash flows after the first year. Calculate present value for the following cases: a. The cash flows are forecasted to continue forever, with no expected growth or decline. b. The cash flows are forecasted to continue for 20 years only, with no expected growth or decline during that period. c. The cash flows are forecasted to continue forever, increasing by 3% per year because of inflation. d. The cash flows are forecasted to continue for 20 years only, increasing by 3% per year because of inflation.