# Finding Future and Present Value of growing annuity

(a) You've inherited $15,000,000 and have decided to use this money to open a shelter for abused women in Aurora one year from today. The annual operating costs are estimated to be $350,000 and are expected to grow at a constant rate of 2% (inflation) starting in year 2. If the interest rate is 4.5%, would you be able to fund this shelter?

(b) Given the above scenario, what would be the maximum amount available for annual operating expenses?

(c) What is the future value of a 20-year growing annuity if the growth rate is 2%, the annual interest rate is 6% and the payment at the end of year 1 is $5,000?

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Solution:

(a) You've inherited $15,000,000 and have decided to use this money to open a shelter for abused women in Aurora one year from today. The annual operating costs are estimated to be $350,000 and are expected to grow at a constant rate of 2% (inflation) starting in year 2. If the interest rate is 4.5%, would you be able to fund this shelter? ...

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Solution describes the steps for finding present and future value of growing annuity.

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.

d. More information is needed to solve this problem.

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.