Rate of return from buying the bond today

Assignment:

It is January 2005, and you observe the following price quote:

BK Corp.    5 1/2s28Dec    Close 92 3/4

Problem 1. Suppose interest rates were to fall by 1.5% over the next year. What would be the rate of return from buying the bond today, holding it for one year, and selling it at its new market price?

Problem 2. You are setting up a scholarship fund for your favorite university by making monthlydeposits into a savings account earning 5.75% compounded monthly. Your first deposit is today, and the last is in 5 years. You expect the perpetual endowment will finance student scholarships of \$7,500 per year, with the first scholarship awardedexactly one year after the final deposit is made. The principal in the account will never be drawn-down (it too earns 5.75% compounded monthly ). According to this scenario, approximately how much must you deposit each month?

The following information pertains to problems 3 & 4:

Eighteen months ago you borrowed \$39,500 to purchase a car. The annual interest rate is 12% and the loan is to be repaid with monthly payments over four years.

Problem 3. How much of the 4th payment will be applied towards interest charges?

Problem 4. How much of the final payment will be applied towards principal reduction?

Problem 5. A share of stock paid its annual dividend of \$1.10 exactly 4 years ago and you expect that next year's dividend will equal \$1.50. Your analyst tells you the stock's expected total return is 12.50%, and that the stock's current price is \$16.25. According to the constant dividend growth model, what is the stock's intrinsic value and, more importantly, should you buy the stock?

For problems 6 & 7:

The total rates of return on equity securities are obviously affected by the business cycle. Business economists for the Genco Co. predict the following outcomes for the economy, and the associated outcomes on their shares:

Growth    Stagnant Recession
Probability    .20    .50    .30
% Return    28%   -3%    24%

Problem 6. What is the expected return AND standard deviation of returns for the Genco shares?

You are looking at investing in shares of either Genco (from problem 5) or Dotcom. The expected returns for Dotcom under the different economic conditions are as follows:

Growth    Stagnant    Recession
Probability    .20    .50    .30
% Return    0%    15%    10%

Problem 7. Suppose you invest 50% of your funds in Genco, and the remainder in Dotcom. What is the expected return AND risk for the portfolio?

Consider the following information:

VK estimates that it can issue debt at a before-tax cost of 12%, and its tax rate is 35%. The company can also issue preferred stock at \$30 per share, which pays a constant dividend of \$5 annually. Floatation costs on the preferred are \$1 per share.

Net income is estimated to be \$200,000, and the firm plans to maintain its policy of paying out 30% as dividends. The company's stock currently sells for \$36 per share. The next dividend is expected to be \$2.35, which is \$.15 higher than the most recent dividend. Furthermore, these dividends are expected to continue to grow at the same rate. Float costs on newly issued common stock are \$3 per share. The company's balance sheet is financed with optimal proportions of debt and equity and is as follows:

PP&E \$250,000    Debt \$250,000
Cash \$100,000    Preferred Stock \$ ?
Inventories \$300,000 Common Equity \$300,000
Total Assets \$650,000    Total Liab.    \$ ?

Problem 8. What is the cost of retained earnings?

Problem 9. What is the relevant cost of debt?

Problem 10. What is VK's current WACC?

Consider the following cash flows for two mutually exclusive investments:

t = 0    t = 1    t = 2    t = 3
A    (\$87)    \$40    \$50    \$29
B    (\$188)    \$51    \$42    \$140

Problem 11. What are the internal rates of return for the projects and which project is best?

For problems 12 - 15:

You have been asked by the president of your company to evaluate the proposed acquisition of a new hydropropolaser for the R&D department. The price for this equipment is \$70,000, and it would cost another \$14,000 to modify it for special use by your firm. The hydropropolaser, which has a MACRS 3-year recovery period (wts. 33%, 45%, 15%, 7%) would be sold after 3 years for \$30,000. Use of this equipment would require an increase in net working capital of \$11,000. The hydropropolaser would have no effect on revenues, but it is expected to save the firm \$20,000 per year in before-tax operating costs, mainly labor. The firm's marginal tax rate is 36%.

Problem 12. What is the initial net investment for the machine (CF0)?

Problem 13. What are the net operating cash flows from this project for years 1 -3?

Problem 14. What are the additional cash flows from this project in year 3?

Problem 15. If the firm's WACC is 14%, should they purchase the hydrpropolaser?

Consider the following information for problems 16 & 17.:

Strike    Calls    Puts
Jul    Aug    Oct    Jul    Aug    Oct
155    10.5    11.75    14    .1875    1.25    2.75
160    6    8.125    11.125    .75    2.75    4.5
165    2.6875    6.45    8.125    2.375    4.75    6.75
170    .8125    3.25    5.50    5.75    7.5    9

It is currently July 6. The stock pays no dividends and is priced at \$162.00. The expirations are July 17, August 21 and October 16.

Problem 16. Suppose you purchased the Oct. 170 calls. What would your return be if the stock price ended at \$185 on Oct. 16 AND how does this rate of return compare to just buying and selling the stock?

Problem 17. Suppose you entered into a straddle with the Aug. 165 calls and puts. What would your rate of return be if the price ended up being \$200?

Problem 18. A currency trader observes that in the spot exchange market, 1 U.S. Dollar can be exchanged for 2.5 Euros or for 106.27 Japanese Yen. If a bank offers to exchange .025 Euro/Yen, what (if any) arbitrage profits could be earned?
(Use \$1,000,000)

Problem 19. 6-month T-bills have a nominal rate of 3.7%, while default-free Japanese bonds that mature in 6 months have a nominal rate of 5.1%. In the spot exchange market, 1 Yen equals \$.0074. If interest rate parity holds, what is the 6 month forward exchange rate?

Problem 20. Your aunt holds the shares of a single company that have been passed down through generations, and have always performed quite well. She also believes (and you agree) that the company will continue to perform well over the foreseeable future. You then proceed to explain why holding just this one company in her portfolio- even though it is not risky, and is providing a nice rate of return - is not a very wise decision. What is your explanation?

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