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# Net present values, investment requirements, discount rates.

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1. You just won the lottery and want to put some money away for your child's college education. College will cost \$65,000 in 18 years. You can earn 8% compounded annually. How much do you need to invest?
2. You just won the lottery. You and your heirs will receive \$25,000 per year forever, beginning one year from now. What is the present value of your winnings at an 8% discount rate? Answer:
3. You are suppose to receive \$2,000 five years from now. At an interest rate of 6%, what is that \$2,000 worth today? Answer: =
4. What is the future value in 10 years of \$1,000 payments received at the beginning of each year for the next 10 years? Assume an interest rate of 5.625%. Answer: =
5. In order to help you through college, your parents just deposited \$25,000 into a back account paying 8% interest. Starting next year, you plan to withdraw equal amounts for the account at the end of each of the next four years. What is the most you can withdraw annually? Answer: =
6. What is the market value of a bond that will pay a total of forty semiannual coupons of \$50 each over the remainder of its life? Assume the bond has a \$1,000 face value and an 8% yield to maturity (YTM).
Price of the Bond
7. J&J, Inc. just issued a bond with a \$1,000 face value and a coupon rate of 7%. If the bond has a life of 30 years, pays annual coupons and the YTM is 6.8%, what will the bond sell for? =
8. What would you pay for a bond that pays an annual coupon of \$35, has a face value of \$1,000, matures in 7 years, and has a yield to maturity (YTM) of 8%?
Price of Bond =
9. What would you pay for a share of ABC Corporation stock today if the next dividend will be \$2 per share, your required return on equity investments is 12%, and the stock is expected to be worth \$110 one year from now?
10. What would you pay today for a stock that is expected to make a \$1.50 dividend in one year if the expected dividend growth rate is 3% and you require a 16% return on your investment? Answer:
11. A project costs \$475 and has cash flows of \$100 for the first three years and \$75 in each of the project's last five years. What is the payback period of the project?
12 What is the NPV of a project that is expected to pay \$10,000 a year for 7 years if the initial investment is \$40,000 and the required return is 15%?
13. Calculate the NPV of the following project using a discount rate of 12%.
YR0 = -\$500; YR1 = -\$50; YR2 = \$50; YR3 = \$200; YR4 = \$400; YR5 = \$400
14. A project has an initial investment of \$10,000, with \$3,500 annual inflows for each of the subsequent four (4) years. If the required return is 15%, what is the Net Present Value (NPV)? Answer:
15. What is the IRR of an investment that costs \$77,700 and pays \$27,500 a year for 4 years? ?

16. Suppose a project costs \$300 and produces cash flow of \$100 over each of the following six years. What is the IRR of this project?
17. A firm's stock has a required return of 10%. The stock's dividend yield is 6%. What dividend did the firm just pay if the current stock price is \$40?
18. Topstone Industries' preferred stock pays an annual dividend of \$4.00 per share. When issued, the shares sold for their par value of \$100 per share. What is the cost of preferred stock if the current price is \$125.00?
19. Why do you think debt offerings are more common than equity offerings and typically much larger as well?
20. A number of publicly traded firms pay no dividends yet investors are willing to buy shares in these firms? Does this violate our basic principle of stock valuation? Explain.

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#### Solution Preview

19 Why do you think debt offerings are more common than equity offerings and typically much larger as well?
This decision is related to long term financing decision. Long term financing decision is about determining firm's optimum capital structure. A firm's optimal capital structure is that mixture of debt and equity than minimizes its weighted average cost of capital (WACC).

Since the after-tax cost of debt is lower than equity for many corporations,iIt turns out that, debt reduces a company's tax liability because interest payments are deductible expenses. Hence debt offerings are more than the equity offerings as they are cheaper.

One caution:
Higher amounts of debt raise the ...

#### Solution Summary

The solution answers many questions on investments, discount rates, present values, and bond pricing.

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