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# Time Value of Money

1. Find the present value of a payment stream of \$100 per year for the first fifteen years and \$200 per year for the next five years, given a 12% discount rate.

2.A company stock was priced at \$15 per share two years ago. The stock sold for \$13 last year and now it sells for \$18. What was the total return for owning this company stock during the most recent year? Assume that no dividends were paid and round to the nearest percent.

3.Stock A has a required return of 18% and a beta of 1.4. The expected market return is 14%. What is the risk-free rate?

4.A company is putting out a new product. The product will pay out \$25,000 in the first year, and after that the payouts will grow by an annual rate of 2.5 percent forever. If you can invest the cash flows at 7.5 percent, how much will you be willing to pay for this perpetuity?

5. To pay for school a student need \$12,000 at the end of four years. She can invest a certain amount at the beginning of each of the next four years in a bank account that will pay her 6.8 percent annually. How much will she have to invest annually to reach her target?

6. I plan to start saving for retirement. I will invest \$5,000 at the end of each year for the next 45 years in a fund that will earn a return of 10 percent. How much will I have at the end of 45 years?

7.A renter will be making lease payments of \$3,895.50 for a 10-year period, starting at the end of this year. If the renter uses a 9 percent discount rate, what is the present value of this annuity?

8.A company has generated a net income of \$161,424 this year. The firm expects to see an annual growth of 30 percent for the next five years, followed by a growth rate of 15 percent for each of the next three years. What will be the firm's expected net income in eight years?

#### Solution Preview

1. Find the present value of a payment stream of \$100 per year for the first fifteen years and \$200 per year for the next five years, given a 12% discount rate.

There are two streams of cash flow - \$100 and \$200. We find the present value separately for the two and then add them up. Both the streams are an annuity and so we use the PVIFA table to get the PV factor and find the present value.
a. \$100 for 15 years. This starts at the beginning and so
PV = 100 X PVIFA (15,12%) = 100 X 6.8109 = \$681.09
b. We get \$200 each year from year 16 onwards for 5 years. We first find the PV in year 15 and then again discount to now
PV in year 15 = 200 X PVIFA (5,12%) = 200 X 3.6048 = 720.96
Now this is a lump sum which we can discount to get the PV today
PV today = 720.96/(1+12%)^15 = 131.72
Total PV = 681.09+131.72 = \$812.80

2.A company stock was priced at \$15 per share two years ago. The stock sold for \$13 last year and now it sells for \$18. What was the total return for owning this company stock ...

#### Solution Summary

The solution explains some questions relating to time value of money

\$2.19