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# Present Value of Growing Annuity vs Ordinary Annuity

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The city of Cincinnati gave up the right to collect parking fees over a 30-year period in exchange for a lump sum of \$92 million plus a 30-year annuity of \$3 million. Suppose that if the city had not entered into that arrangement, it would have collected parking fees the following year of \$6 million (net of operating costs), and those fees would have grown at a steady 3% for the next 30 years. At an interest rate of 4%, what is the present value of the parking revenue that the city could have collected? Using the same 4% to value the payments that the city was set to receive in their privatization deal, do you think that the city made the correct decision? Why or why not?

#### Solution Summary

The solution explains how to work out the time value of money that the city of Cincinnati might have earned on parking fees over 30yrs had they not accepted a lump sum payment instead. Attached as a Word document.

\$2.19

## Multiple Choice - Time Value of Money

1. What is the value of a share of a firm's stock when the firm is expected to pay \$2.80 per share dividend at the end of each year and the annual discount rate is 7.5 percent?

2. What is the present value of a lease on a warehouse, where the tenants have a lease that goes into perpetuity and have agreed to pay \$300 at the end of each month of the lease with an annual discount rate of 8 percent?

3. Your company signed a 20-year lease for a new office. The lease requirement that your firm pay \$1,000 at the end of each month over the life of the lease. If the current annual rate is a percent, what is the present value of this annuity stream?

4. Suppose you invest \$800 in a mutual fund at the end of each year for the next 30 years and the fund earns an annual rate of return of 10 percent. What will be value of your retirement fund after 30 years?

5. You want to invest \$200 at the end of each month until you have reached your goal of a total balance of \$100,000. You plan to invest in an account that earns an annual rate of 8 percent. How many years will it take to earn the \$100,000?

6. Eleanor Spryzak has endowed her alma matter with a scholarship that is designed to pay out a sum of money to worthy student every year forever. The scholarship amount increase in value by percent every year. Which term most accurately describes this asset?
a. Annuity
b. Perpetuity
c. Growing perpetuity
d. Asset with single cash flow

7. Peter Lord's financial adviser has suggested that he purchases a piece of land in an area of town that is being targeted for development. Peter's plan is to purchase the land and then sell it for a profit when demand in the area increases. Which term most accurately describes this asset?
a. Growing perpetuity
b. Perpetuity
c. Annuity
d. Asset with single cash flow

8. Annuity due is an annuity in which the first payment occurs immediately. Knowing that, which of the following statement is true?
a. The future value of a 10-year ordinary annuity exceeds the future value of a 10-year annuity due.
b. The present value of a 10-year ordinary is equal to that of a 10-year annuity due.
c. The present value of a 10-year annuity due exceeds the present value of a 10-year ordinary annuity.

9. For a perpetuity that is assumed to grow at a constant rate (g), what will the present value of perpetuity approach as g approaches zero?
a. O
b. 1
c. cash flow/r
d. Infinity

10. A bond is issued by the British government pays a coupon of L100 (pound) on January 1 of every for 20 years. Which term most accurately describes this asset?
a. Growing perpetuity
b. Perpetuity
c. Annuity
d. Asset with single flow.

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