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39. Present Value and Interest Rates What is the relationship between the value of an annuity and the level of interest rates? Suppose you just bought a 10-year annuity of \$2,000 per year at the current interest rate of 10 percent per year. What happens to the value of your investment if interest rates suddenly drop to 5 percent? What if interest rates suddenly rise to 15 percent?

40. Calculating the Number of Payments You're prepared to make monthly payments of \$95, beginning at the end of this month, into an account that pays 10 percent interest compounded monthly. How many payments will you have made when your account balance reaches \$18,000?

41. Calculating Annuity Present Values You want to borrow \$40,000 from your local bank to buy a new sailboat. You can afford to make monthly payments of \$825, but no more. Assuming monthly compounding, what is the highest rate you can afford on a 60-month APR loan?

42. Calculating Loan Payments You need a 30-year, fixed-rate mortgage to buy a new home for \$180,000. Your mortgage bank will lend you the money at a 7.5 percent APR for this 360-month loan. However, you can only afford monthly payments of \$1,000, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments at \$1,000?

43. Calculating Present Values In the 1994 NBA draft, no one was surprised when the Milwaukee Bucks took Glenn "Big Dog" Robinson with the first pick, but Robinson wanted big bucks from the Bucks: a 13-year deal worth a total of \$100 million. He had to settle for about \$68 million over 10 years. His contract called for \$2.9 million the first year, with annual raises of \$870,000. So, how big a bite did Big Dog really take? Assume a 10 percent discount rate.

44. Calculating Present Values In our previous question, we looked at the numbers for Big Dog's basketball contract. Now let's take a look at the terms for Shaquille "Shaq" O'Neal, the number one pick in 1992 who was drafted by the Orlando Magic. Shaquille signed a seven-year contract with estimated total payments of about \$40 million. Although the precise terms were not disclosed, it was reported that Shaq would receive a salary of \$3 million the first year, with raises of \$900,000 each year thereafter. If the cash flows are discounted at the same 10 percent discount rate we used for Robinson, does the "Shaq Attack" result in the same kind of numbers? Did Robinson achieve his goal of being paid more than any other rookie in NBA history, including Shaq? Are the different contract lengths a factor? (Hint: yes.)

45. EAR versus APR You have just purchased a new warehouse. To finance the purchase, you've arranged for a 30-year mortgage loan for 80 percent of the \$1,200,000 purchase price. The monthly payment on this loan will be \$9,300. What is the APR on this loan? The EAR?

46. Present Value and Break-Even Interest Consider a firm with a contract to sell an asset for \$95,000 three years from now. The asset costs \$57,000 to produce today. Given a relevant discount rate on this asset of 14 percent per year, will the firm make a profit on this asset? At what rate does the firm just break even?

47. Present Value and Interest Rates You've just won the U.S. Lottery. Lottery officials offer you the choice of two alternative payouts: either \$2 million today, or \$4 million 10 years from now. Which payout will you choose if the relevant discount rate is 0 percent? If it is 10 percent? If it is 20 percent?

Intermediate

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Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

III. Valuation of Future Cash Flows

6. Discounted Cash Flow Valuation