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PRESENT VALUE OF A PERPETUITY What is the present value of a $600 perpetuity if the interest rate is 5%? If interest rates doubled to 10 %, what would its present value be? 5-16 EFFECTIVE INTEREST RATE You borrow $230,000; the annual loan payments are $20430.31 for 30 years. What interest rate are you being charged? 5-17 5-18 UNEVEN CASH FLOW STREAM a. Find the present values of the following cash flow streams at a 5 % discount rate 0 2 3 4 Stream A $0 $150 $450 $450 $450 $450 $250 Stream B $0 $250 $450 $450 $150 b. What are the PVs of the streams at a 0 % discount rate? 5-19 FUTURE VALUE OF AN ANNUITY retirement, with the first payment to come one year from now. She can save $8,000 per year, and you advise her to invest it in the stock market, which you expect to provide an average return of 10 % in the future. Your client is 26 years old. She wants to begin saving for a. If she follows your advice, how much money will she have at 657 b. How much will she have at 70? c. She expects to live for 20 years if she retires at 65 and for 15 years if she retires at 70. If her investments continue to eam the same rate, how much will she be able to with- draw at the end of each year after retirement at each retirement age? PV OF A CASH FLOW STREAM A rookie quarterback is negotiating his first NFL contract His opportunity cost is 7 %. He has been offered three possible 4-year contracts. Payments are guaranteed, and they would be made at the end of each year. Terms of each contract are as follows: 5-20 3 Contract 1 $3,000,000 $3,000,000 $3,000,000 $3,000,000 Contract 2 $2,000,000 $3,000,000 $4,500,000 $5,500,000 Contract 3 $7,000,000 $1,000,000 $1,000,000 $1,000,000 As his adviser, which contract would you recommend that he accept? Contract 3 $7,000,000 $1,000,000 $1,000,000 $1,000,00U As his adviser, which contract would you recommend that he accept? EVALUATING LUMP SUMS AND ANNUITIES Kristina just won the lottery, and she must choose among three award options. She can elect to receive a lump sum today of $62 million, to receive 10 end-of-year payments of $9.5 million, or to receive 30 end-of-year payments of $5.6 million. 5-21 a. If she thinks she can earn 7% annually, which should she choose? b. If she expects to earn 8% annually, which is the best choice? c. If she expects to earn 9% annually, which option would you recommend? d. Explain how interest rates influence her choice. LOAN AMORTIZATION Jan sold her house on December 31 and took a $10,000 mortgage part of the payment. The 10-year mortgage has a 10% nominal interest rate, but it calls for semiannual payments beginning next June 30. Next year Jan must report on Schedule B of her IRS Form 1040 the amount of interest that was included in the two payments she received during the year. 5-22 as a. What is the dollar amount of each payment Jan receives? b. How much interest was included in the first payment? How much repayment of prin- cipal was included? How do these values change for the second payment? c. How much interest must Jan report on Schedule B for the first year? Will her interest income be the same next year? d. If the payments are constant, why does the amount of interest income change over time? O Cengage Learning. All Rights Reserved, May not be copied scanned or duplicated, in whole or in part. WCN 02-200-203

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