# Calculating the Rate of Return for Annuities

Your insurance agent is trying to sell you an annuity that costs $230,000 today. By buying this annuity, your agent promises that you will receive payments of $1,225 a month for the next 30 years. What is the rate of return on this investment?

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#### Solution Preview

230,000 = 1,225 * (1- [1/30*12/ (1+r/12) / r/12

30 * 12 / 12 - 230,000 = 1,225

Calculator function = PMT FV 1,225 = 4.93%.

We must use a combination of ...

#### Solution Summary

This solution calculates the rate of return on the investment.

Economics Questions

1. What is the Future Value at the end of 17 years of depositing $1,750 into a

Mutual Fund today, assuming the fund is expected to earn 12% a year?

2. You are considering the purchase of a bond with a semiannual coupon of $40,

Ten years to maturity, a face value of $1,000, and a current market price of

$1,000.

a. At what price will the bond sell in the market in 6 months, immediately after

the first coupon payment, if the stated annual yield on the bond (in six mos.)

is 4%?

b. If you were to buy the bond now and sell it after six mos., what holding period rate of return would be earned over the six month period?

3. Calculate the expected return on the portfolio [E ( R )] of the following assets

if you invest 20% in asset 1, 30% in asset 2, and 50% in asset 3. How and why

will your answer change if you shift 20% of invested funds from the least risky

(asset 3) to the most risky (asset 1) asset?

Asset Return

1 10%

2 7%

3 6%

4. You are considering an investment in a project with a life of eight years, an

initial outlay $120,000, and annual after-tax cash flows of $52,000. The project also requires an increase in inventories of $22,000. This $22,000 investment in

inventory is required at the outset of the project and will be released when the project is completed. The appropriate discount rate for this project is 10%.

a. Calculate the payback period for this project.

b. Calculate the NPV for this project.

c. Should this project be accepted? Explain.

5. Calculate the IRR for the following cash flows. Is the project acceptable if the

firm's cost of capital is 12%?

End of Year Cash Flow ($)

0 - $400,000

1 100,000

2 200,000

3 300,000

6. You have been asked to assist your friends with some personal financial

planning. Following their current budget they find they are able to save

approximately $10,000 per year. They expect their investments to grow at a

nominal rate of 8% and you expect inflation to remain at approximately

4% per year. Your friends expect to retire in 30 years.

a. How much money will they have available at their retirement date?

b. What will that amount be worth in today's dollars?

7. Your corporation has the following stockholders equity.

Common Stock at par $ 750,000

Paid in capital in excess of par 1,250,000

Retained earnings 2,500,000

Total $ 4,500,000

a. What is the maximum amount of dividends the corporation can pay

in states where the firm's legal capital is defined as the par value

of its common stock?

b. How does your answer change if the firm is in a state where legal

capital includes all paid-in capital?

8. What is the expected inflation rate in the U.S. and Japan if the real rate

rate of interest in the U.S. is 5% and in Japan 2%, while the nominal

interest rate in the U.S. is 7% and in Japan 5%?

9. Suppose the annual risk-free rate in the U.S. is 3%. The annual risk-free

rate in Pounds Sterling is 5%. The spot rate of exchange is .625pounds/$.

What should the one-year forward rate be between pounds and dollars?

10. Acme offers its customers a cash discount of 4% if payment is made within

15 days, rather than its current net 45 policy. Assuming a 365-day year,

what is the annual rate Acme is charging its customers who do not take the discount?

11. Calculate the present value of an annuity due of $3,600 at 9% for 16 years

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