10. Your grandfather put some money in an account for you on the day you were born. Today is your 18th birthday, and you are allowed to withdraw the money for the first time. The account currently has $3,996 in it and pays interest at 8% per year (annual compounding).
a. How much money would be in your account if you left the money there until your 25th birthday?
b. How much money would be in your account if you left the money there until your 65th birthday?
c. How much money did your grandfather originally put in the account?
11. You are about to deposit $10,000 into one of the following (very special) savings accounts to be left on deposit for 15 years. Each bank offers an account with a different interest rate and compounding period. Assuming you want to maximize your wealth, which of the following bank accounts should you choose? Show how much money would be in each account in 15 years, and the EAR.
BANK A: 9.00 percent rate compounded semi-annually
BANK B: 8.90 percent rate compounded monthly
BANK C: 8.80 percent rate compounded daily
A. FV =_______________; EAR = __________
B. FV =_______________; EAR = __________
C. FV =_______________; EAR = __________
12. You are shopping for a car and read the following advertisement in the paper. “Own a new Swagfire! No money down. Four annual payments of just $10,000.” You have shopped around and know that you can buy a Swagfire for cash for $32,500. What is the interest rate the dealer is advertising (that is, what is the IRR of the loan in the advertisement)? Assume that you must make the annual payments at the end of each year.
13. You are running a biotechnology company. Analysts predict that your firm’s cash flow will remain constant for the next five years while your company is in its product development stage. After that, cash flow growth is expected to be 3% per year forever. The company has just announced that the most recent year’s cash flow was $1,000,000. What is the present value of all future earnings if the interest rate is 8% per year (annual compounding)?
14. You are just starting your MBA, and need to borrow $50,000 to cover tuition and expenses. A lender has offered you two alternatives. The first loan requires you to repay $10,000 per year for six years. The second requires you to repay $5,000 every 6 months, also for 6 years.
a. What is the IRR on each of these loans?
b. Which loan should you choose, and why?
15. Are each of the following statements true or false? Briefly, why?
a. Modigliani and Miller argued that with perfect capital markets (no taxes, transaction costs, etc.), the total value of a firm should not depend on its capital structure.
b. Leverage increases the risk of equity, even when there is no risk that the firm will default.
c. Suppose Firm A has a greater business risk than Firm B. Shareholders, seeing this difference, will generally encourage management of Firm A to take on more debt than Firm B employs.
16. Five years ago (Feb. 2010) you bought a sweet pad on the Cascade River near Marblemount, WA, and financed the purchase with a $440,000, 30-year mortgage (monthly payments) at a 5.03% APR, compounded monthly. You have made 60 monthly payments. Suppose that on your savings, you believe you can currently earn a return of 4.8% APR, compounded monthly.
a. What are your payments on this mortgage?
b. Suppose you plan to stay in your home for 4 more years. A quick search of rates in early February 2015 turns up a 30-year, 3.50% fixed-rate loan for 1.875 points and $1,889 in fixed fees. Given this information, calculate your new payment, and total costs, and render a decision: should you refinance your mortgage? For now, you may ignore future differences in principal.
c. You are concerned that when you sell your home in four years, you might have less equity in the home if you refinance. Show whether this is the case or not. Compute the complete NPV and state whether your answer changes using this additional information.
17. Provide a short answer (2 or 3 sentences) to each of the following questions:
a. Governments sometimes step in to protect large companies that run into financial distress, and bail them out. If this is an accepted practice, what effect would you expect it to have on the debt ratios of firms? Why?
b. Most high-growth firms do not use debt to finance new investments, but some do. What types of high-growth firms are most likely to finance expansion with debt rather than equity?
c. If dividends paid to common stockholders were to become tax deductible, would you predict firms to increase or decrease their proportions of equity relative to debt as a source of capital? Explain.
d. You are comparing two firms in the same business. One firm gets all of its business from 3 large customers, while the other firm has a more diversified customer base, with 300 customers. Assuming that the firms are of similar size and have similar operating income, which firm would you expect to have more bankruptcy risk? Why?
e. Some people argue that the loss in market value of bonds that arises when firms realize increased business risk is not a real loss if lenders are willing to hold on until maturity and collect their cash flows. Do you agree with this argument? Why or why not? Explain.
18. You have a 2 year old daughter. You anticipate that she will attend college. The first annual tuition payment of $35,000 will be due 16 years from today. You expect that tuition payments will increase by 7% per year for the remaining 3 years of college (assume tuition is paid annually).
You plan to save $4,000 per year until then. You will make your first deposit today, and your last deposit one year before the first tuition payment is due. Assume that the discount rate is 10% per year with annual compounding. Will you have saved enough to pay for college? If so, how much extra money will you have? If not, how much more will you need?
19. Underwood Industries expects EBIT next year of $220 million and has a corporate tax rate of 35%. It has $2.9 billion in debt outstanding with an interest rate of 6%.
a. Will Underwood be able to fully realize its interest tax shield next year? Why or why not?
b. What is the annual interest tax shield associated with this debt?
c. What is the present value of the interest tax shield, assuming this debt will be outstanding permanently?
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