Finance 3310

Fall 1997

Problem set #2

1. I need some help with my retirement planning. The Social Security Administration sent me my benefits report which indicates the estimated retirement benefits for various ages. I am going to retire at age 60, but I need to decide when to start receiving my social security benefits. If I start receiving benefits at age 62 I will get $1,090 per month. If I wait until age 66 I will get $1,520 per month. Finally, if I wait until age 70 I will get $2,005 per month. If an appropriate discount rate is 6% and I expect to live to age 82, which option should I choose?

2. You have the choice of buying two certificates of deposit (CD's). One CD has a stated annual rate of 8.5% and compounds interest semi-annually; the other has a stated annual rate of 8.4% and compounds interest monthly. Which CD would you choose and why?

3. Compute the cost (value) of the following bonds if such bonds are priced to yield 9%. (assume semi-annual interest payments)

a. 10% coupon, 30 year maturity

b. 0 coupon, 30 year maturity

c. 0 coupon, 15 year maturity

If interest rates change, which of these bonds will be most affected?

4. Suppose you buy a 8% coupon bond maturing in 10 years. Interest payment are made semi-annually. If the price of the bond is $1,175.00,

a) What is the yield to maturity?

b) What assumption does YTM make about the reinvestment rate?

c) If you can reinvest coupons at only 4%, what is your realized return if you hold

the bond to maturity?

5. What is the yield to maturity on a 15 year, 8.5% coupon bond with a par value of $1,000 if the bond is currently selling for: (assume semi-annual payments)

A) $865.00

B) $1,205.00

C) $1,000.00

6. The Consumer Price Index is currently at 110.5. Suppose you buy a 0-coupon bond which matures in 10 years. You pay $245.00 for the bond. If the Consumer Price Index is 150 in 10 years, what is your real rate of return? What is your nominal rate of return?

7. Bang, Inc. is expected to grow at a 35% rate for the next 3 years, after which growth is expected to slow to a long run sustainable rate of 4%. Bang just paid a $1.50 dividend (i.e., D0 = 1.50). If investors require a return of 15% on Bang stock, what should its current price, P0, be?

8. Ancient Items Co. is a manufacturing firm. The company just paid a $5 dividend, but management expects to reduce the payout by 6% per year, indefinitely. If investors require a 12% return on this stock, what will you pay for a share today?

9. Amberjack Corporation stock currently sells for $108 per share. The market requires a 15% return on the firm's stock. If the company maintains a constant 7% growth rate in dividends, what was the most recent dividend per share paid on the stock?

10. Given the following information:

D0 = $2.00

P0 = $30

Expected growth rate = 5%

A) What is the expected return on this stock?

B) Suppose that in actuality D1 = 2.20 and P1 = $35.00. What is the actual return on this stock?

11. The Daloney Bottling Co. is considering the replacement of one of its bottling machines with a newer and more efficient one. The old machine has a current book value of $600,000 and a remaining useful life of 5 years. The firm does not expect to realize any return from scrapping the old machine in 5 yrs, but it can sell it now to another firm in the industry for $265,000. The old machine is being depreciated on a straight-line basis at the rate of $120,000 per year.

The new machine has a purchase price of $1,175,000, no estimated salvage value, and a MACRS life of 5 years. It is expected to economize on electric power usage, labor and repair costs resulting in annual savings of $185,000. It is also expected to reduce the number of defective bottles, resulting in savings of $70,000 per year. The company has a 34% tax rate, and its cost of capital is 12%. MACRS rates for 5 year property are: 20%,32%,19%,12% and 11%. Should the firm purchase the new machine?

12. Gentry Products Co. is considering two mutually exclusive investments. The projects' expected net cash flows are as follows:

The firm's cost of capital is 12%.

A) What is the NPV of each project?

B) Which project would you choose and why?

C) What is the IRR of project B?

D) If these projects were independent, which one(s) would you undertake and why?

13. You have created a bond investment portfolio to fund your child's college. She starts college in 10 years. The weighted average duration of your portfolio is 8 years. What does duration mean? What kind of risk do you face with this portfolio?

14. Reinvest, Inc. currently pays no dividends and doesn't expect to pay any dividends for the next five years. The company intends to pay a $1 dividend after 6 years, and hopes to be able to increase the dividend 5% every year thereafter. If the appropriate discount rate for a stock of Reinvest's risk is 16%, what should its current price be?

15. ABC Co. just paid a $1 dividend. (i.e., D0=1). Such dividend is expected to grow by 35% for the next five years, after which growth is expected to slow to 4% in the long run. Investors require a 12% return on ABC. If DEF Co. also just paid a $1 dividend, what long run growth rate would make it as valuable as ABC. Assume investors require a 12% return on DEF as well. This illustrates that any dividend path can be approximated with a constant growth path.

16. Suppose you observe the following prices for zero-coupon bonds:

Maturity Cost

a. What is the yield to maturity on each bond? Graph the rates as a function of time to maturity. (Note: This graph is called a 'yield curve.')

b. (bonus) Suppose your investment horizon is 2 years. You can buy the two year bond, or you can buy the one year bond, then buy another one year bond in a year. What must the (expected) yield be on the second one-year bond (issued at t=1 and maturing at t=2) in order for you to be indifferent between these two strategies? This rate is called an 'implied forward rate.'

c.(bonus) Now suppose your investment horizon is 3 years. Assume you decide either to buy a three-year bond, or buy a two year bond now, and a one year bond two years from now. What must the expected yield be on the one year bond (issued at t=2 and maturing at t=3) in order for you to be indifferent between these two strategies?


17. Prospective Airlines is considering a four year project to extend airline service to Nirvana. The project requires an initial investment of $90 million to buy new airplanes. The airplanes will be depreciated on a straight-line basis to zero over the project's life. An initial investment in net working capital of $8 million is required to support spare parts inventory. This cost is fully recoverable whenever the project ends. The company believes it can generate $80 million in pretax revenues with $40 million in total pretax operating costs. The tax rate is 38% and the discount rate is 16%. The market value of the airplanes over the life of the project is given below:

a. Assuming Prospective operates this project for four years, what is the NPV?

b. Now compute the project NPV assuming the project is abandoned after only one year, two years, or three years. What economic life of this project maximizes its value to the firm? What does this problem tell you about considering abandonment possibilities when evaluating projects?

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