Question 1: Present Values
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 C 1 = $2 million in the first year. You estimate that you could earn an expected 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:
The cash flows are forecasted to continue forever, with no expected growth or decline.
The cash flows are forecasted to continue for 20 years only, with no expected growth or decline during that period.
The cash flows are forecasted to continue forever, increasing by 3% per year because of inflation.
The cash flows are forecasted to continue for 20 years only, increasing by 3% per year because of inflation.
Question 2: Continuous Compounding
How much will you have at the end of 20 years if you invest $100 today at 15% annually compounded? How much will you have if you invest at 15% continuously compounded?
Question 3: IRR Rule
Cash Flows ($ thousands)
Project
C0
C1
C2
C3
A
-100
+60
+60
0
B
-100
0
0
+140
Calculate the NPV of each project for discount rates of 0%, 10%, and 20%. Plot these on a graph with NPV on the vertical axis and discount rate on the horizontal axis.
What is the approximate IRR for each project?
In what circumstances should the company accept project A?
Calculate the NPV of the incremental investment (B- A) for discount rates of 0%, 10%, and 20%. Plot these on your graph. Show that the circumstances in which you would accept A are also those in which the IRR on the incremental investment is less than the opportunity cost of capital.
Question 4: Capital Rationing
Suppose you have the following investment opportunities, but only $90,000 available for investment. Which projects should you take?
Project
NPV
Investment
1
5,000
10,000
2
5,000
5,000
3
10,000
90,000
4
15,000
60,000
5
15,000
75,000
6
3,000
15,000
Internal
Internal