Chapter Review Problems

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1 Chapter Review Problems Unit 11.1 Present value 1. Suzie s rich aunt promises to give Suzie $100,000 on her 30th birthday, 12 years from now. If money is worth 8.5% compounded annually, what is today s value of her aunt s promise? , , You win the lottery and will collect $5,000 at the end of each month for the next 25 years. Assuming that money is worth 9% compounded monthly, what is the value of your prize in today s dollars? = = , , You own a manufacturing business and are thinking about purchasing a labor-saving device at a cost of $150,000. The device will last 15 years and save you $1,400 per month in labor costs (assume that savings are realized at the end of each month). You need to earn 11.5% compounded monthly on your money. What is the value of the device? = = , , Refer to Problem 3. On the basis of your answer, should you buy the device? No; the device is worth about $120,000 to you, considerably less than its $150,000 cost. 5. You rent an office for $850 per month and offer to prepay 12 months rent. If the landlord can earn 10% compounded monthly, what amount should he accept? = , Begin 6. You leased retail space 5 years ago for $22,000 per month, payable at the beginning of each month. Your lease is for 25 years and allows you to sublease the space. You have outgrown the space and sublease to Smith Furniture Company for the remaining 20 years. Smith will pay you $27,500 per month. What is the value of your leasehold interest, assuming that money is worth 9.5% compounded monthly? = = , ,500 Begin* *Note: Don t forget to put back in end mode. For Problems 7 and 8, we will help Cicily Montague, an author from Paris, figure out the present value of movie rights to her book. Cicily sells the movie rights and will receive payments at the end of each quarter for the next 4 years. The first four payments will be 600,000 euros each, the next four 700,000 euros each, the next four 800,000 euros each, and the final four 900,000 euros each. 7. What is the total amount Cicily will receive? (4 600,000) + (4 700,000) + (4 800,000) + (4 900,000) = 12,000,000 euros 8. Assuming that money is worth 6% compounded quarterly, what is the present value of the movie rights? 0 CFj ,000 CFj 4 _ Nj ,000 CFj 4 _ Nj ,000 CFj 4 _ Nj ,000 CFj 4 _ Nj = I/YR 1.50 _ NPV 10,493, ENTER CFo= ,000 ENTER 4 ENTER F01= ,000 ENTER 4 ENTER F02= ,000 ENTER 4 ENTER F03= ,000 ENTER 4 ENTER F04=4.00 NPV 6 4 = ENTER I=1.50 NPV=10,493, Chapter Review Problems 259

2 For Problems 9 11, we will help Brian Earl solve a business problem. Brian wants to retire from his sporting goods business. Darby McGregor has offered to buy the business for $320,000 cash. Hannah Page has also offered to buy the business; she will pay $5,000 at the end of each month for 48 months, after which she will pay $6,500 for an additional 24 months. 9. What is the total amount Hannah will pay? (48 $5,000) + (24 $6,500) = $396, Assuming that Brian can earn 8.5% compounded monthly, what is the equivalent cash price (present value) of Hannah s offer? *Note: The cash flow at the beginning of the first period is zero. 11. Which price (Darby s or Hannah s) is the greater? Darby s. Hannah will pay a total of $396,000 (see Problem 9); Darby will pay only $320,000. However, Darby s price of $320,000 is greater than the equivalent cash price of Hannah s offer ($304,756.40). Unit 11.2 Rate of return 0 CFj * ,000 CFj 48 _ Nj ,500 CFj 24 _ Nj = I/YR 0.71 _ NPV 304, Refer to the newspaper article. What is the average annual rate of return? 0 ENTER * CFo=0.00 5,000 ENTER 48 ENTER F01= ,500 ENTER 24 ENTER F02=24.00 NPV = ENTER I=0.71 NPV=304, , ,000 For Problems 13-16, you loan a friend $ You are repaid $52 at the end of each month for 4 months. What rate do you earn? Instead, assume your friend repays you $25 at the end of each month for the first 3 months and $133 at the end of the fourth month. What rate do you earn? 200 +/- CFj CFj 3 _ Nj CFj _ IRR/YR = /- ENTER CFo= ENTER 3 ENTER F01= ENTER C02= IRR CPT IRR= = Chapter 11 Present Value and Rate of Return

3 15. Instead, assume your friend repays you $133 at the end of the first month and $25 at the end of the second, third, and fourth months. What rate do you earn? 200 +/- CFj CFj CFj 3 _ Nj 3.00 _ IRR/YR = /- ENTER CFo= ENTER C01= ENTER 3 ENTER F02=3.00 IRR CPT IRR= = In Problem 13, you receive a total of $208 (4 $52); in Problem 14, you receive a total of $208 (3 $25 + $133); in Problem 15, you receive a total of $208 ($ $25). Why, then, are the rates (19.05%, 14.47%, and 27.88%) different? (essay answer) The time-value-of-money affects the rate. In Problem 13, you receive the same amount each month; in Problem 14, you receive most of the money at the end of the loan; in Problem 15, you receive most of the money at the first part of the loan. 17. (True Story) Clara Patterson and Bill Mayne got married in A year later, they bought a home in Salt Lake City, Utah, for $2,450. In 2003, they were still in romantic bliss living in the home; the home was worth $165,000. At what average annual rate has the home increased in value? , ,000 Challenge problems 18. An accomplished pianist lost his right hand in an accident. He successfully sued the party responsible. You, as a member of the jury, are trying to decide what amount the pianist should receive as a settlement. You have determined that the pianist was able to earn $25,000 net income from concerts each month and would have been able to continue earning this amount for another 28 years. Assuming that money is worth 11.5% compounded monthly and that the $25,000 was received at the end of each month, what is a fair settlement? = = ,502, , Ali purchased some corporate stock 3 years ago for $8,000. She received quarterly dividends of $100 at the end of each quarter for the first year and a half, no dividends for the next two quarters, and quarterly dividends of $150 each for the last year. Immediately after receiving her last quarterly dividend check, she sold the stock for $17,500. What interest rate, compounded quarterly, did Ali earn? 8,000 +/- CFj -8, CFj 6 _ Nj CFj 2 _ Nj CFj 3 _ Nj 3.00* ,500 = CFj 17, IRR/YR = ,000 +/- ENTER CFo=-8, ENTER 6 ENTER F01= ENTER 2 ENTER F02= ENTER 3 ENTER F03=3.00* ,500 = ENTER C04=17, IRR CPT IRR= = *Note: The last $150 dividend happened at the same time as the sale, so the two cash flows are combined. Chapter Review Problems 261

4 20. You have the chance to buy a promissory note in which you will receive 157 monthly payments of $550, starting a month from now. What is the total amount you will receive. $ = $86, Refer to Problem 20. If you want to earn 6.5% compounded monthly, what price should you pay for the note? = , You have the chance to buy a promissory note in which you will receive 42 monthly payments of $700 (starting a month from now), followed by 180 monthly payments of $800. What is the total amount you will receive? ($700 42) + ($ ) = $173, Refer to Problem 22. If you want to earn 8.75% compounded monthly, what price should you pay for the note? 0 CFj * CFj 42 _ Nj CFj 99 _ Nj CFj 81 Nj = I/YR 0.73 NPV 84, ENTER * CFo= ENTER 42 ENTER F01= ENTER 180 ENTER F02= NPV = ENTER I=0.73 NPV=84, *Note: Because we do not know the amount, we enter a zero cash flow at the beginning of the first period. 24. A recent graph is shown on the right, showing what $4,000 deposited at the beginning of each year has grown to over a 20-year period. Confirm the average annual returns ,000 Begin 191, , , , * * 325,222 *Note: Don t forget to put back in end mode. 262 Chapter 11 Present Value and Rate of Return

5 Practice Test 1. What is the present value of $25,000 to be received in 5 years, assuming money is worth 8% compounded annually? , , John Pappas is a real estate agent. John has earned a commission in which the owner of the property has agreed to pay John 5% of the rent collected during the next 15 years. The owner will pay John at the end of each 6-month period. The monthly rent is $10,000 for the first 5 years, $12,500 for the second 5 years, and $15,000 for the last 5 years. If money is worth 9.5% compounded semiannually, what is the present value of John s commission agreement? Semiannual commissions First 5 years: $10,000 6 months 5% = $3,000 Second 5 years: $12,500 6 months 5% = $3,750 Third 5 years: $15,000 6 months 5% = $4,500 0 CFj 0.00* 3,000 CFj 10 _ Nj ,750 CFj 10 _ Nj ,500 CFj 10 _ Nj = I/YR 4.75 NPV 55, ENTER CFo=0.00* 3,000 ENTER 10 ENTER F01= ,750 ENTER 10 ENTER F02= ,500 ENTER 10 ENTER F03=10.00 NPV = ENTER I=4.75 NPV=55, *Note: Because we do not know the amount, we enter a zero cash flow at the beginning of the first period. 3. Norma Wilder purchased some corporate stock 8 years ago for $12,000. She sold the stock today for $17,300. What interest rate, compounded annually, did Norma earn? ,000 17, Junko Fujimoto purchased some corporate stock 8 years ago for $12,000. Junko received quarterly dividends of $200 at the end of each quarter for the first 5 years, nothing for the sixth year, and $250 at the end of each quarter for the last 2 years. Immediately after receiving the last quarterly dividend, Junko sold the stock for $17,300. What interest rate, compounded quarterly, did Junko earn? 12,000 +/- CFj -12, CFj 20 _ Nj CFj 4 _ Nj CFj 7 _ Nj 7.00* ,300 = CFj 17, _ IRR/YR = ,000 +/- ENTER CFo=-12, ENTER 20 ENTER F01= ENTER 4 ENTER F02= ENTER 7 ENTER F03=7.00* ,300 = ENTER C04=17, IRR CPT IRR= = 9.95 IRR 2nd QUIT *Note: The last $250 dividend happened at the same time as the sale, so the two cash flows are combined. Practice Test 263

Chapter Review Problems

Chapter Review Problems State all stock and bond prices in dollars and cents. Unit 14.1 Stocks 1. When a corporation earns a profit, the board of directors is obligated by law to immediately distribute