Chapter 5: The Time Value of Money PDF

CHAPTER 5: THE TIME VALUE OF MONEY 1.​The amount of simple interest is equal to the product of the principal times​ times​. a.​(1 + rate per time period), the number of time periods b.​(1 + rate per time period), (the number of time periods - 1)...

CHAPTER 5: THE TIME VALUE OF MONEY 1.​The amount of simple interest is equal to the product of the principal times​ times​. a.​(1 + rate per time period), the number of time periods b.​(1 + rate per time period), (the number of time periods - 1) c.​rate per time period, the number of time periods d.​rate per time period, (the number of time periods - 1) ANSWER: c 2.​The present value of a single amount can be represented as a.​ PV0 = FVn(PVIFi,n) b.​ PV0 = FVn(PVIFAi,n) c.​ PV0 = FVn[1/(1 + n i) ] d.​a and c ANSWER: d 3.​The basic future value equation is given by a.​ FVn = PV0(PVIFi,n) b.​ FVn = PV0(FVIFAi,n) c.​ FVn = PV0(1/(1 + n i) ) d.​ FVn = PV0(FVIFi,n) ANSWER: d 4.​The process of finding present values is frequently called a.​annualizing b.​compounding c.​discounting d.​leasing ANSWER: c 5.​The values shown in ordinary annuity tables (either present value or compound value) can be adjusted to the annuity due form by​ the ordinary annuity interest factor by​. a.​dividing, (1 + i) © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money n b.​ dividing, (1 + i) c.​multiplying, (1 + i) n d.​ multiplying, (1 + i) ANSWER: c © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter 5: The Time Value of Money 6.​A(n)​ is a financial instrument that agrees to pay an equal amount of money per period into the indefinite future (i.e. forever). a.​annuity b.​annuity due c.​sinking fund d.​perpetuity ANSWER: d 7.​Finding the discounted current value of $1,000 to be received at the end of each of the next 5 years requires calculating the a.​future value of an annuity b.​future value of an annuity due c.​present value of an annuity d.​present value of an annuity due ANSWER: c 8.​Finding the compound sum of $1,000 to be received at the beginning of each of the next 5 years requires calculating the a.​future value of an annuity b.​present value of an annuity c.​future value of an annuity due d.​present value of an annuity due ANSWER: c 9.​When using a present value of an annuity table (e.g., Table IV at the back of the book), a.​payments are assumed to be made at the beginning of each period b.​PVIFA factors decrease with an increase in the interest rate c.​PVIFA factors increase with an increase in the number of periods d.​b and c only ANSWER: d 10.​When using a future value of an annuity table (e.g., Table III at the back of the book), a.​payments are assumed to be made at the end of each period b.​FVIFA factors increase with an increase in the interest rate c.​FVIFA factors increase with an increase in the number of periods d.​all of these ANSWER: d © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter 5: The Time Value of Money 11.​An annuity due is one in which a.​payments or receipts occur at the end of each period. b.​payments or receipts occur at the beginning of each period. c.​payments or receipts occur forever. d.​cash flows occur continuously. ANSWER: b 12.​You have just won a $5 million lottery to be received in twenty annual equal payments of $250,000. What will happen to the present value of your winnings if the interest rate increases during the next 20 years? a.​it will be worth less b.​it will be worth more c.​it will not change d.​it will increase during the first ten years ANSWER: a 13.​You have just calculated the present value of the expected cash flows of a potential investment. Management thinks your figures are too low. Which of the following actions would improve the present value of your cash flows? a.​extend the cash flows over a longer period of time b.​increase the discount rate c.​decrease the discount rate d.​extend the cash flows over a longer period of time, and decrease the discount rate ANSWER: d 14.​If the present value of a given sum is equal to its future value, then a.​the discount rate must be very high b.​there is no inflation c.​the discount rate must be zero d.​none of the answers is correct ANSWER: c 15.​Using the "Rule of 72," about how long will it take a sum of money to double in value if the annual interest rate is 9 percent? a.​9 years b.​7 years c.​8 years d.​10 years ANSWER: c © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter 5: The Time Value of Money 16.​The present value of an ordinary annuity is the a.​sum of the present value of a series of equal periodic payments b.​future value of an equal series of payments c.​receipt of equal cash flows for a specified amount of time d.​sum of the future value of an equal series of payments ANSWER: a 17.​When a loan is amortized over a five year term, the a.​rate of interest is reduced each year b.​amount of interest paid is reduced each year c.​payment is reduced each year d.​balance is paid as a balloon payment in the fifth year ANSWER: b 18.​Annuity due calculations are especially important when dealing with a.​term loans b.​lease contracts c.​capital investments d.​capital recovery problems ANSWER: b 19.​The more frequent the compounding the a.​greater the present value b.​greater the amount deposited c.​greater the effective interest rate d.​lesser the future value ANSWER: c 20.​The effective rate of interest will always be​ the nominal rate. a.​greater than b.​equal to c.​less than d.​equal to or greater than ANSWER: d © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter 5: The Time Value of Money 21.​ ​ is interest that is paid not only on the principal, but also on any interest earned but not withdrawn during earlier periods. a.​basic interest b.​simple interest c.​future interest d.​compound interest ANSWER: d 22.​Which of the following is worth more? a.​Future value of an ordinary annuity of PMT dollars per year for n years discounted at i percent. b.​Future value of an annuity due of PMT dollars per year for n years discounted at i percent. c.​Both are worth the same amount. d.​Cannot be determined from the information given. ANSWER: b 23.​The annual effective rate of interest (ieff ) is a function of: a.​the annual nominal rate of interest (inom) b.​the number of compounding intervals per year (m) c.​the number of years (n) d.​both the nominal rate of interest and the number of compounding periods per year. ANSWER: d 24.​More frequent compounding results in​ future values and​ present values than less frequent compounding at the same interest rate. a.​higher, higher b.​lower, higher c.​higher, lower d.​lower, lower ANSWER: c 25.​The present value of a(n)​ is determined by dividing the annual cash flow by the interest rate. a.​annuity b.​annuity due c.​perpetuity d.​lease ANSWER: c © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter 5: The Time Value of Money 26.​An annuity that begins more than 1 year in the future is referred to as a(n)​. a.​perpetuity b.​annuity due c.​uneven annuity d.​deferred annuity ANSWER: d 27.​The​ of a perpetual stream of equal, annual returns (PMT) discounted at i% per year is equal to​. a.​present value; PMT/i b.​present value; PMT × i c.​future value; PMT/i d.​future value; PMT × i ANSWER: a 28.​Annuity due calculations are most common when dealing with: a.​cash dividends b.​loan repayments c.​lease contracts d.​interest payments ANSWER: c 29.​The payment or receipt of a series of equal cash flows per period, at the end of each period, for a specified amount of time is called a(n): a.​annuity due b.​perpetuity c.​ordinary annuity d.​simple interest ANSWER: c 30.​The difference between an ordinary annuity and an annuity due is: a.​the interest rate b.​the timing of the payments c.​the amount of the payments d.​the number of periods ANSWER: b © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter 5: The Time Value of Money 31.​ ​ is the return earned by someone who has forgone current consumption. a.​the present value b.​principle c.​an annuity d.​interest ANSWER: d 32.​Determine how much $1,000 deposited in a savings account paying 8% (compounded annually) will be worth after 5 years. a.​$5,526 b.​$784 c.​$1,400 d.​$1,469 ANSWER:​ d RATIONALE: All problems use Tables I – IV in the back of the book unless otherwise stated. Solution: FV5 = PV0(FVIF.08,5) = 1,000(1.469) = $1,469 33.​The earnings of Omega Supply Company have grown from $2.00 per share to $4.00 per share over a nine year time period. Determine the compound annual growth rate. a.​11.1% b.​8% c.​22.2% d.​100% ANSWER:​ b RATIONALE: Solution: PVIFi,9 = $2.00/$4.00 = 0.500. i = 8% from Table II. 34.​Mr. Moore is 35 years old today and is beginning to plan for his retirement. He wants to set aside an equal amount at the end of each of the next 25 years so that he can retire at age 60. He expects to live to the maximum age of 80 and wants to be able to withdraw $25,000 per year from the account on his 61st through 80th birthdays. The account is expected to earn 10 percent per annum for the entire period of time. Determine the size of the annual deposits that must be made by Mr. Moore. a.​$212,850 b.​$23,449 c.​$2,164 d.​$8,514 ANSWER:​ c RATIONALE: Solution: PVAN = PMT(PVIFA0.10,20) = $25,000(8.514) = $212,850 needed on 60th birthday $212,850 = PMT(FVIFA0.10,25) = PMT(98.347) PMT = $2,164 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter 5: The Time Value of Money 35.​Comet Powder Company has purchased a piece of equipment costing $100,000. It is expected to generate a ten- year stream of benefits amounting to $16,273 per year. Determine the rate of return Comet expects to earn from this equipment. a.​16.3% b.​62.7% c.​10% d.​20% ANSWER:​ c RATIONALE: Solution: $100,000 = $16,273(PVIFAi,10) PVIFAi,10 = 6.145 Therefore, i = 10% from Table IV 36.​Determine how much you would be willing to pay for a bond that pays $60 annual interest indefinitely and never matures (i.e., a perpetuity), assuming you require an 8 percent rate of return on this investment. a.​$480 b.​$743 c.​$1,000 d.​$750 ANSWER:​ d RATIONALE: Solution: PVPER = PMT/i = $60/.08 = $750 37.​Air Atlantic (AA) has been offered a 3-year old jet airliner under a 12-year lease arrangement. The lease requires AA to make annual lease payments of $500,000 at the beginning of each of the next 12 years. Determine the present value of the lease payments if the opportunity cost of funds is 14 percent. a.​$2,830,000 b.​$13,635,500 c.​$6,000,000 d.​$3,226,200 ANSWER:​ d RATIONALE: Solution: PVAND = PMT[PVIFAi,n(1 + i)]; n = 12; i = 0.14; PMT = $500,000 = $500,000[5.660(1 +.14)] = $3,226,200 38.​If you invest $10,000 in a 4-year certificate of deposit (CD) paying 10 percent interest compounded annually, determine how much the CD will be worth at the end of 4 years. a.​$13,600 b.​$45,730 c.​$14,640 d.​$15,958 ANSWER:​ c © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter 5: The Time Value of Money RATIONALE: Solution: FV4 = PV0(FVIFi,n); PV0 = $10,000; n = 4; i = 0.10 = $10,000(1.464) = $14,640 39.​You sold 100 shares of stock today for $30 per share that you paid $20 for 6 years ago. Determine the average annual rate of return on your investment, assuming the stock paid no dividends. a.​25% b.​8.33% c.​150% d.​7% ANSWER: d RATIONALE: Solution: PV0 = FVn(PVIFi,n); n = 6; PV0 = $20; FV6 = $30 $20 = $30(PVIFi,6) (PVIFi,6) = 0.667; Therefore i = 7% from Table II. 40.​Your grandparents put $1,000 into a savings account for you when you were born 20 years ago. This account has been earning interest at a compound rate of 7 percent. What is its value today? a.​$3,870 b.​$1,967 c.​$3,026 d.​$3,583 ANSWER: a RATIONALE: Solution: FV20 = $1000(3.870) = $3,870 41.​Baggos has seen their EPS increase from $0.30 to $3.16 in seven years. What has been the growth rate of Baggos's EPS? a.​about 30% b.​about 40% c.​about 20% d.​about 10% ANSWER: b RATIONALE: Solution: FVIFi,7 = $3.16/$0.30 = 10.53; or 40 percent from Table I 42.​You have just won a $50,000 bond that pays no interest and matures in 20 years. If the discount rate is 10%, what is the present value of your bond? a.​$7,450 b.​$8,175 c.​$8,900 d.​$1,490 ANSWER: a RATIONALE: Solution: PV = $50,000(0.149) = $7,450 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter 5: The Time Value of Money 43.​BB&C bank has agreed to lend you $30,000 today, but you must repay $42,135 in 3 years. What rate is the bank charging you? a.​10% b.​11% c.​12% d.​13% ANSWER:​ c RATIONALE: Solution: PVIFi,3 = $30,000/$42,135 = 0.712; or 12% from Table II 44.​The Florida lottery agrees to pay the winner $250,000 at the end of each year for the next 20 years. What is the future value of this lottery if you plan to put each payment in an account earning 9 percent? a.​$2.28 million b.​$12.79 million c.​$14.32 million d.​$5.00 million ANSWER:​ b RATIONALE: Solution: FVAN20 = $250,000(51.160) = $12,790,000 45.​Billy Bob has decided to put $2,400 a year (at the end of each year) into an IRA over his 40 year working life and then retire. What will Billy have if the account will earn 10 percent compounded annually? a.​$394,786 b.​$23,470 c.​$1,062,223 d.​$810,917 ANSWER:​ c RATIONALE: Solution: FVAN40 = $2,400(442.593) = $1,062,223 46.​Jane wants to have $200,000 in an account in 20 years. If her account earns 11 percent per annum over the accumulation period, how much must she save per year (end of year) to have the $200,000? a.​$25,116 b.​$3,115 c.​$10,000 d.​$3,492 ANSWER:​ b RATIONALE: Solution: PMT = $200,000/64.203 = $3,115 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter 5: The Time Value of Money 47.​Many IRA fund managers argue that investors should invest at the beginning of the year rather than at the end. What is the difference to an investor who invests $2,000 per year at 11 percent over a 30 year period? a.​$43,785 b.​$36,189 c.​$54,244 d.​There is no difference ANSWER: a RATIONALE: Solution: FVAN30 = $2,000(199.021) = $398,042 FVAND30 = $2,000(199.021)(1.11) = $441,827 Difference = $43,785 48.​An insurance company offers you an end of year annuity of $48,000 per year for the next 20 years. They claim your return on the annuity is 9 percent. What should you be willing to pay today for this annuity? a.​$429,600 b.​$438,144 c.​$408,672 d.​$398,144 ANSWER: b RATIONALE: Solution: PVAN = $48,000(9.128) = $438,144 49.​New Jersey Mutual has offered you a single premium annuity that will pay you $12,000 per year (end of year) for the next 15 years. If you must pay $109,296 today for this annuity, what is your expected rate of return? a.​8% b.​9% c.​7% d.​10% ANSWER: c RATIONALE: Solution: PVIFA = $109,296/$12,000 = 9.108; or 7% from Table IV 50.​Columbia Bank & Trust has just given you a $20,000 term loan to pay for a new concrete mixer. The loan requires five equal annual end of the year payments. If the loan provides the bank with a 12 percent return, what will be your annual payments? a.​$5,548 b.​$3,148.12 c.​$6,000 d.​$1,666.67 ANSWER: a RATIONALE: Solution: PMT = $20,000/3.605 = $5,547.85 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter 5: The Time Value of Money 51.​Idlewild Bank has granted you a seven year loan for $50,000. If your seven annual end of the year payments are $11,660.45, what is the rate of interest Idlewild is charging? a.​14% b.​23% c.​12.6% d.​11% ANSWER: a RATIONALE: Solution: PVIFA = $50,000/$11,660.45 = 4.288; or 14% from Table IV 52.​Your firm, New Sunrise, has just leased a $28,000 BMW for you. The lease requires six beginning of the year payments that will fully amortize the cost of the car. What is the amount of the payments if the interest rate is 12 percent? a.​$6,810.99 b.​$7,766.99 c.​$6,423.74 d.​$6,081.25 ANSWER: d RATIONALE: Solution: PMT = $28,000/(4.111)(1.12) = $6,081.25 53.​The lease on a new office requires an immediate payment of $24,000 plus $24,000 per year at the end of each of the next 10 years. At a discount rate of 14 percent, what is the present value of this stream of lease payments? a.​$130,872 b.​$149,194 c.​$142,710 d.​$264,000 ANSWER: b RATIONALE: Solution: PVAND = $24,000(5.453)(1 + 0.14) = $149,194 54.​Alabama Power has preferred stock that pays an annual dividend of $9.44. If the security has no maturity, what is its value to an investor who wishes to obtain a 9 percent rate of return? a.​$84.96 b.​$104.89 c.​$95.34 d.​$94.40 ANSWER: b RATIONALE: Solution: PVPER = $9.44/0.09 = $104.89 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter 5: The Time Value of Money 55.​Designs Now is opening a showcase office to display and sell its computer designed poster art. Designs expects cash flows to be $120,000 in the first year, $180,000 in the second year, $240,000 in the third year. If Designs uses 11 percent as its discount rate, what is the present value of the cash flows? a.​$429,720 b.​$457,620 c.​$456,000 d.​$424,820 ANSWER: a RATIONALE: Solution: PV = $120,000(0.901) + $180,000(0.812) + $240,000(0.731) = $429,720 56.​In six years, your daughter will be going to college. You wish to have a fund that will provide her $10,000 per year (end of year) for each of her four years in college. How much must you put into that fund today if the fund will earn 10 percent in each of the 10 years? a.​$29,744.65 b.​$29,783.76 c.​$17,878.80 d.​$21,651.10 ANSWER: c RATIONALE: Solution: PVAN = $10,000(3.170) = $31,700 PV = $31,700(0.564) = $17,878.80 57.​What is the future value of a $10,000 college tuition fund if the nominal rate of interest is 12 percent compounded monthly for five years? a.​$17,623.42 b.​$18,170 c.​$16,105.10 d.​$16,122.26 ANSWER: b 12(5) RATIONALE: Solution: FV = $10,000(1 + 0.12/12) = $18,170 (using 1% factor for 60 periods from Table I) 58.​What is the effective rate of interest on a CD that has a nominal rate of 9.5 percent with interest compounded monthly? a.​9.92% b.​9.74% c.​10.02% d.​9.86% ANSWER: a 12 RATIONALE: Solution: ieff = (1 +.095/12) – 1 = 0.0992 or 9.92% © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter 5: The Time Value of Money 59.​John is 25 years old and wishes to retire in 30 years. His plan is to invest in a mutual fund earning a 12 percent annual return and have a $1 million retirement fund at age 55. How much must he invest at the end of each year to achieve this goal? a.​$7,499.96 b.​$5,024.60 c.​$4,143.65 d.​$33,333.33 ANSWER: c RATIONALE: Solution: PMT = $1,000,000/241.333 = $4,143.65 60.​Joe Brady just won a $450,000 lottery in Pennsylvania. Instead of receiving a lump sum, he found that he would receive $22,500 annually (end of year) for 20 years. Joe is 75 years old and wants his money now. He has been offered $140,827 to sell his ticket. What rate of return is the buyer expecting to make if Joe accepts the offer? a.​ less than 1% b.​ 15% c.​18% d.​12% ANSWER: b RATIONALE: Solution: PVIFA = $140,827/$22,500 = 6.259; or 15% from Table IV 61.​A bank has agreed to loan you $10,000 at 11% for 5 years. You are required to make equal, annual, end-of-year payments that include both principal and interest on the outstanding balance. Determine the amount of these annual payments (to the nearest dollar). a.​ $2,000 b.​ $3,100 c.​ $2,706 d.​ $1,100 ANSWER: c RATIONALE: Solution: PVANo = $10,000; n = 5; i = 11% PVANo = PMT(PVIFAi,n ) $10,000 = PMT(PVIFA0.11,5 ) = PMT(3.696) PMT = $2,706 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter 5: The Time Value of Money 62.​Sales for Triad Inc. have grown from $2 million to $8.092 million in 10 years. What is the implied growth rate of sales for Triad? a.​ 24.72% b.​ 4.05% c.​ 15.0% d.​ 12.2% ANSWER: c RATIONALE: Solution: 2 = 8.092(PVIFi,10).2472 = PVIFi,10 From Table II, i = 15% 63.​If you invest the $10,000 you receive at graduation (age 22) in a mutual fund that averages a 12% annual return, how much will you have at retirement in 40 years? a.​ $909,090 b.​ $930,510 c.​ $783,879 d.​ $510,285 ANSWER: b RATIONALE: Solution: FV = 10,000(93.051) = $930,510 64.​Five years after an accident, you received $100,000 to pay the medical expenses incurred at the time of the accident. What is the present value (at the time of the accident) of the payment? Assume interest rates are 9%. a.​ $153,900 b.​ $68,100 c.​ $65,000 d.​ $70,800 ANSWER: c RATIONALE: Solution: PV = 100,000(.65) = $65,000 65.​You purchased a piece of property for $30,000 nine years ago and sold it today for $83,190. What was your rate of return on your investment? a.​12% b.​11% c.​10% d.​9% ANSWER: a RATIONALE: Solution: 30,000 = 83,190(PVIFi,9).3606 = PVIFi, 9 From Table II, i = 12% © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.  Chapter 5: The Time Value of Money 66.​ © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money 66.​What is the most you should pay to receive the following cash flows if your required rate of return is 12 percent? Year 1 $5,000 Year 2 $8,000 Year 3 $12,000 Year 4-10 $15,000 a. $58,580 b. $104,135 c. $68,105 d. $40,000 ANSWER:​ c RATIONALE: Solution: PV = $5,000(0.893) + $8,000(0.797) + $12,000(0.712) + $15,000(5.650 – 2.402) = $68,105 67.​Seebee makes quarterly (end of period) payments of $30,000 into a pension fund earning 12 percent per year compounded quarterly for 10 years. How much interest will they have earned in 10 years? a.​ $2,262,030 b.​ $2,105,880 c.​ $905,880 d.​ $1,062,030 ANSWER:​ d RATIONALE: Solution: FVAN40 = $30,000(75.401) = $2,262,030 Fund balance after 10 years of $2,262,030 less Payments of $1,200,000 results in Interest = $1,062,030 68.​John borrowed $20,000 to finance his college education. If the finance charge on the loan is 6 percent, and he will pay off the loan in 10 equal, annual, end of year payments, how much total interest will he pay? a.​ $7,173.90 b.​ $2,717.39 c.​ $12,000.00 d.​ $25,924.23 ANSWER:​ a RATIONALE: Solution: PMT = $20,000/7.360 = $2,717.39; Total payments = $27,173.90 I = $27,173.90 – $20,000 = $7,173.90 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money 69.​Your brother, who is 6 years old, just received a trust fund that will be worth $25,000 when he is 21 years old. If the fund earns 10 percent interest compounded annually, what is the value of the fund today? a.​ $104,602 b.​ $6,575 c.​ $5,975 d.​ $6,875 ANSWER:​ c RATIONALE: Solution: PV = $25,000(0.239) = $5,975 70.​California Life has just offered you a single premium annuity for $5,000 that will pay $5,144.12 per year for 20 years, the first payment being received exactly 31 years from today. What is the implied rate of return on this annuity? a.​ 7% b.​ 8% c.​ 9% d.​ 6.5% ANSWER:​ b RATIONALE: Solution: Trial and error, Try 8% PVAN = $5,144.12(PVIFAi,20) = $5,144.12(9.818) = $50,505 PVAN(PVIFi,30) = $50,505(0.099) = $5,000 71.​Jackie plans to open her own book store in 10 years. To raise the "seed" money she has committed $10,000 she now has in a mutual fund. In addition, she plans to save $2,000 per year (end of year) for the next 5 years and $3,000 per year (end of year) for the following 5 years. How much “seed” money will Jackie have in 10 years if the investments earn 10 percent per year compounded annually? a.​ $76,129 b.​ $63,925 c.​ $44,255 d.​ $159,370 ANSWER:​ b RATIONALE: Solution: FV = $10,000(2.594) + $2,000(6.105)(1.611) + $3,000(6.105) = $63,925 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money 72.​You just purchased a new $25,000 car and agreed to pay for the car in 50 monthly payments. If the monthly interest rate is 1 percent, what is your total financing cost? a.​ $637.82 b.​ $12,500 c.​ $574.25 d.​ $6,891 ANSWER:​ d RATIONALE: Solution: PMT = $25,000/39.196 = $637.82 I = $637.82(50) – $25,000 = $6,891 73.​A zero coupon bond with a $1,000 par value (future value) is selling for $356 and matures in 12 years. What is the implied discount rate (yield to maturity)? a.​ 9% b.​ 9.36% c.​ 9.12% d.​ 9.4% ANSWER:​ a RATIONALE: Solution: PVIF = $356/$1000 = 0.356; or 9% from Table II 74.​Roy, who has just turned 40, would like to have an annual annuity of $20,000 paid over a 20 year period, the first payment occurring on his 66th birthday. How much must Roy save each year (end of year) for the next 25 years to have this annuity, if the investment will earn 12 percent compounded annually? a.​ $16,000 b.​ $19,046 c.​ $1,120 d.​ $944.10 ANSWER:​ c RATIONALE: Solution: PVAN = $20,000(7.469) = $149,380 PMT = $149,380/133.334 = $1,120 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money 75.​Your local bank offers 4-year certificates of deposit (CD) at a 12 percent annual nominal interest rate compounded quarterly. Determine how much additional interest you will earn over 4 years on a $10,000 CD that is compounded quarterly compared with one that is compounded annually. a.​ $6,050 b.​ $0 c.​ $310 d.​ $220 ANSWER:​ c RATIONALE: Solution: PVo = $10,000; inom = 0.12 Quarterly compounding (m = 4) 4x4 FV4 = $10,000(1 + 0.12/4) = $10,000(FVIF0.03,16) = $10,000(1.605) = $16,050 Annual compounding (m = 1) 1x4 FV4 = $10,000(1 + 0.12) = $10,000(FVIF0.12,4) = $10,000(1.574) = $15,740 Difference = $16,050 - $15,740 = $310 76.​How much will you have at the end of 5 years in a European vacation account if you deposit $200 a month in an account that is paying a nominal 12 percent per year, compounded monthly? a.​ $16,334 b.​ $15,247 c.​ $16,497 d.​ $15,817 ANSWER:​ a RATIONALE: Solution: FVAN = $200(81.670) = $16,334 77.​You wish to save $500,000 in the next 25 years. You notice that a corporate bond fund earns about 11 percent per year and that is where you put your savings. How much must you save each year to obtain your goal? a.​ $20,000.00 b.​ $ 3,749.98 c.​ $ 4,370.13 d.​ $ 2,000.00 ANSWER:​ c RATIONALE: Solution: 500,000 = PMT(114.413) PMT = $4,370.13 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money 78.​You plan to lease a Saab automobile that sells for $22,657 and has no salvage value. If the monthly lease is $499, with the first of 60 payments due immediately. What is the implied annual interest rate on your lease? a.​ 10% b.​ 11.5% c.​ 12% d.​ 13.5% ANSWER:​ c RATIONALE: Solution: PVAND = 499(44.955)(1.01) = $22,656.87 The above solution came by either using a trial and error method (using 1%/month or 12%/yr) or a financial calculator to obtain 12% per year. 79.​What is the present value of the following net cash flows if the discount rate is 12%: Year​ Cash Flow 1-5 $10,000 each year 6-10 $15,000 each year 11-15 $17,000 each year a.​ $151,400 b.​ $ 86,462 c.​ $144,037 d.​ $ 79,252 ANSWER: b RATIONALE: Solution: PV = $10,000(3.605) + $15,000(5.65 – 3.605) + $17,000(6.811 – 5.65) = $86,462 80.​If the discount rate is 12%, what is the present value of the following cash flows: Year​ Cash Flow 1 $10,000 2 $11,000 3 $12,000 4 $13,000 5 $14,000 6-15 $15,000 each year a.​ $144,618 b.​ $127,923 c.​ $127,197 d.​ $ 90, 537 ANSWER: d RATIONALE: Solution: PV = $10,000(0.893) + $11,000(0.797) + $12,000(0.712) + $13,000(0.636) + $14,000(0.567) + $15,000(6.811 – 3.605) = $90,537 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money 81.​You wish to have $10,000 per year as a retirement supplement for 20 years (from age 65-85). You are now 40 years old. How much must you save each year for the next 25 years if you assume your savings will earn 12% annually? a.​ $560.17 b.​ $1,499.99 c.​ $5,403.87 d.​ none of these ANSWER:​ a RATIONALE: Solution: PVAN = 10,000(7.469) = 74,690 FVAN = PMT(133.334) PMT = 74,690/133.334 = $560.17 82.​What is the present value of the following net cash flows if the discount rate is 10%? Year​ Net Cash Flow 1-10 $20,000 each year 11-15 $15,000 each year 16-20 $10,000 each year a.​ $217,675 b.​ $153,895 c.​ $322,130 d.​ $167,515 ANSWER: b RATIONALE: Solution: PV = $20,000(6.145) + $15,000(7.606 – 6.145) + $10,000(8.514 – 7.606) = $122,900 + $21,915 + $9,080 = $153,895 83.​The Summer Breeze Hotel borrowed $100,000 from the Meadowlands Bank to pay for a new air conditioning system. The loan is for a period of 5 years at an interest rate of 10% and requires 5 equal end-of-year payments that include both principal and interest on the outstanding balance. What will be the outstanding balance after the third payment? a.​ $60,000 b.​ $20,865 c.​ $45,788 d.​ $50,866 ANSWER: c RATIONALE: Solution: PMT = $100,000/3.791 = $26,378.26 Balance = $100,000 – $16,378 – $18,016 – $19,818 = $45,788 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money 84.​Keith Stone has a 10-year old daughter, Kate, who will be entering college in 8 years. Keith estimates college costs to be $16,000, $17,000, $18,000 and $19,000 payable at the beginning of each of Kate's four years in college. How much must Keith save each year (assume end of year payments) for each of the next 8 years to have enough savings to pay for Kate's education? Assume Keith can earn 9% on his savings. a.​ $5,569 b.​ $7,720 c.​ $5,108 d.​ $7,677 ANSWER: a RATIONALE: Solution: Year​ Present Value 1​ $16,000(1.000) = $16,000 2​ 17,000(0.917) = 15,589 3​ 18,000(0.842) = 15,156 4​ 19,000(0.772) = 14,668 ​ $61,413 PMT = $61,413/11.028 = $5,569 85.​1st Bank offers you a car loan at an annual interest rate of 10% compounded monthly. What effective annual interest rate is the bank charging you? a.​ 10.38% b.​ 10.42% c.​ 10.45% d.​ 10.47% ANSWER:​ d 12 RATIONALE: Solution: ieff = (1 + 0.10/12) – 1 =.1047 or 10.47% 86.​Your monthly statement from your bank credit card shows that the monthly rate of interest is 1.5%. What is the annual effective rate of interest you are being charged on your credit card? a.​ 18.00% b.​ 18.64% c.​ 19.56% d.​ 29.74% ANSWER:​ c 12 RATIONALE: Solution: ieff = (1 + 0.18/12) – 1 =.1956 or 19.56% © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money 87.​What monthly rate of interest will yield an annual effective rate of interest of 14%? a.​ 1.17% b.​ 1.10% c.​ 1.08% d.​ 1.14% ANSWER:​ b 1/12 RATIONALE: Solution: im = (1.14) – 1 =.01098 or 1.1% 88.​What is the present value of $1,000 received 2 years from today if the nominal interest rate is 9% and compounded monthly? a.​ $842 b.​ $914 c.​ $833 d.​ $836 ANSWER:​ d 12×2 RATIONALE: Solution: PV = $1,000/(1 +.09/12) = $836 89.​Cosmos Touring wishes to replace its luxury bus in 10 years by accumulating funds in a special account. The new bus is expected to cost $180,000. How much must Cosmos put into the fund in equal, end-of-year amounts if earnings are expected to be 8% for the first 4 years and 10% thereafter? a.​ $12,107 b.​ $11,465 c.​ $9,901 d.​ $14,727 ANSWER:​ b RATIONALE: Solution: $180,000 = PMT(4.506)(1.772) + PMT(7.716) $180,000 = PMT(15.7006) PMT = $11,465 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money 90.​Al Corbin is 25 years old today and he wishes to accumulate enough money over the next 35 years to provide for a 20 year retirement annuity of $100,000 at the beginning of each year, starting with his 60th birthday. He can save $2,000 at the end of each of the next 10 years and $3,000 each year for the following 10 years. How much must he save each year at the end of years 21 through 35 to obtain his goal? Assume that the average rate of return over the entire period will be 10%. a.​ $9,642 b.​ $26,969 c.​ $12,321 d.​ $24,289 ANSWER:​ c RATIONALE: Solution: PVAN = $100,000(8.514)(1.10) = $936,540 $936,540 = $2,000(15.937)(10.835) + $3,000(15.937)(4.177) + PMT(31.772) $936,540 = $345,355 + $199,707 + 31.772PMT PMT = $12,321 91.​If a 16 year old high school student put $2,000 at the end of each year for 4 years into an IRA that earned a rate of 9%, how much would she have accumulated by age 65? Assume funds are left to accumulate for 45 years (age 20 - 65) at 9%. a.​ $442,014 b.​ $386,616 c.​ $1,767,995 d.​ $9,146 ANSWER:​ a RATIONALE: Solution using a calculator: PART I N = 4 I=9 PMT = –$2,000 Solve for FV = $9,146.26 PART II N = 45 I=9 PV = –$9,146.26 Solve for FV = $442,014 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money 92.​If your parents put $2,000 a year into an IRA account for you in each of your last 4 teenage years (age 16,17,18, and 19), how much would the IRA account have in it at your retirement 45 years later if the account earned 12% each year? (Assume end-of-year payments.) a.​ $1,569,758 b.​ $68,613 c.​ $3,457,169 d.​ $1,148,958 ANSWER:​ a RATIONALE: Solution: FV = 2000(4.779)(93.051)(1.765) = $1,569,758 93.​What is the value in 10 years of $10,000 deposited in an account earning 8% compounded monthly? a.​ $33,004 b.​ $22,285 c.​ $102,530 d.​ $21,589 ANSWER:​ b 12×10 RATIONALE: Solution: FV = 10,000(1 +.08/12 ) = $22,285 94.​Assume you purchased a home and borrowed $100,000 at a rate of 8% compounded monthly over 30 years. What is your monthly payment? a.​ $917.77 b.​ $733.76 c.​ $666.67 d.​ $878.14 ANSWER:​ b RATIONALE: Solution using a calculator: PV = -$100,000 I = 8 ÷ 12 =.6666... N = 30 × 12 = 360 Solve for PMT $733.76 by calculator © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money 95.​Inco purchased a computer for $200,000 and this machine is expected to generate annual cash flows of $48,271 over the next 5 years. What is the expected rate of return on this investment? a.​ 8.84% b.​ 26.58% c.​ 6.61% d.​ none of these ANSWER: c RATIONALE: Solution using a calculator: N=5 PV = –$200,000 PMT = $48,271 Solve for I = 6.61% 96.​When you purchased a car, you borrowed $20,000 from the bank and agreed to make monthly payments of $423.17 for 5 years. What rate of interest is the bank charging you? a.​ 9.82% b.​ 5.00% c.​ 25.39% d.​ 10.00% ANSWER: a RATIONALE: Solution using a calculator: N = 5 × 12 PV = –$20,000 PMT = $423.17 Solve for I =.818 × [12 (convert to annual)] = 9.82% 9.82% by calculator 97.​When you purchased a car, you borrowed $20,000 from the bank at 9.20% and agreed to make monthly payments for 3 years. What is your monthly payment? a.​ $153.33 b.​ $637.86 c.​ $584.12 d.​ $559.78 ANSWER: b RATIONALE: Solution using a calculator: N = 3 × 12 = 360 I = 9.20 ÷ 12 =.7666... PV = –$20,000 Solve for PMT = $637.86 $637.86 by calculator © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money 98.​What is the present value of the following mixed cash flow stream if interest is 6% (rounded)? YEAR CASH FLOW 1 $5,000 2 $8,000 3 $9,500 a.​ $25, 370 b.​ $19,813 c.​ $21,225 d.​ $18,750 ANSWER: b RATIONALE: Solution using a calculator: CF0 = 0 CF1 = 5,000 CF2 = 8,000 CF3 = 9,500 I=6 Solve for NPV = $19,813 by calculator. 99.​Which of the following statements is/are correct? I.​At 6% interest, the present value of: $400 for the first year, $600 for the second year, and $800 for the third year is $1,603.00. II.​ The future value of the following mixed cash flow stream (if it is from an annuity due at 6% interest):$400 for the first year, $600 for the second year, and $800 for the third year is $1,999 (rounded). a.​Only statement I is correct. b.​Only statement II is correct. c.​Both statements I and II are correct. d.​Neither statement I nor II is correct. ANSWER: b RATIONALE: Solution using a calculator: CF0 = 0 CF1 = 400 CF2 = 600 CF3 = 800 I=6 Solve for NPV = $1,583.05 by calculator Calculator should be in END mode N= 4 (An annuity due earns one extra year of interest) I = 6 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money PV = –1,583.05 Solve for FV = $1,998.57 by calculator 100.​Based on the Rule of 72, what interest rate do you need to earn to double your money in 6 years? a.​ 8% b.​ 12% c.​ 7% d.​ 6% ANSWER: b 101.​Approximately how long would it take to double my money if I invest it now at 18%? a.​ 6 years b.​ 4 years c.​ 12 years d.​ It cannot be determined ANSWER: b 102.​Jenny Genius wants to purchase a new car. She knows that she can afford to pay $250 per month and that her bank will charge her 8% interest on the car loan. She intends to pay off the car in five years. Interest will be compounded monthly. Of the following, which is the most expensive vehicle in her price range that she could consider? a.​ A Taurus selling for $11,900 b.​ A Malibu selling for $12,320 c.​ A Civic selling for $14,670 d.​ A Celica selling for $17,500 ANSWER:​ b RATIONALE: Solution using a calculator: N = 5 × 12 = 60 I = 8 ÷ 12 =.6666... PMT = $250 Solve for PV The most she could pay for a car is $12,329.61, therefore she could consider buying the Malibu. © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money 103.​Bill Swill decides to try his luck at Powerball where the projected winnings are $12,000,000. If he wins, he can choose the annuity option (to be paid over 20 years) or a lump sum settlement that he can invest at 8% interest. How much must the lump sum option be to make the lump sum option equal to the annuity option (rounded)? a.​ $2,574,578 b.​ $1,743,620 c.​ $1,130,668 d.​ $1,200,000 ANSWER: a RATIONALE: Solution using a calculator: N = 20 I=8 FV = $12,000,000 Solve for PV $2,574,578.49 by calculator. 104.​Nukin’ Gnats Pest Control wants to offer a contract to its customers that would protect the property of their existing customers against termite infestation. Should termites invade a customer’s home, Nukin’ Gnats will pay for the repairs to the home provided the customer has maintained service with Nukin’ Gnats. The corporation must develop an account with a value of $500,000. They will accumulate this account over three years, after which they will offer this new contract provision. How much must be deposited annually (rounded amount) to accumulate the needed funds if they can get 5% interest at their local bank? a.​ $275,026 b.​ $158,604 c.​ $80,255 d.​ $97,985 ANSWER: b RATIONALE: Answer using a calculator: N=3 I=5 FV = $500,000 Solve for PMT = $158,604 105.​Sherry Smart is buying a $350,000 home and will pay the mortgage monthly for 30 years. She has a good credit score and has qualified for a 5.125% loan interest. How much will she be paying monthly for the home? a.​ $2,013.67 b.​ $1,572.72 c.​ $1,318.69 d.​ $975.88 ANSWER: c RATIONALE: Solution using a calculator: N = 30 × 12 = 360 I = 5.125 ÷ 12 =.427083... PV = –350,000 Solve for PMT = $1,318.69 © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money 106.​What is/are the difference(s) between simple interest and compound interest? ANSWER: Simple interest is earned or paid on principal only. Compound interest is earned or paid on both principal and interest that has not been previously withdrawn. Compounding provides a greater return and would result in a higher effective interest rate. 107.​What is the difference between the nominal interest rate and the effective interest rate? ANSWER: The effective interest rate is the actual rate of interest earned by the lender and is generally the most economically relevant definition of interest rates. The effective interest rate is affected by the frequency of compounding. The nominal interest rate is the stated annual interest rate at the time of the loan. 108.​Why does an annuity due have a greater future value than a regular annuity – all things being equal? ANSWER: An ordinary annuity assumes that payments are made at the end of each period. An annuity due assumes that payments are made at the beginning of each period. In essence, the annuity due earns one extra period of interest as opposed to the regular annuity when using the same time period. 109.​Explain the concept of interest and compare it to rate of interest. ANSWER: Interest is the return earned by or the amount paid to someone who has forgone current consumption or alternative investment opportunities and “rented” money in a creditor relationship. The rate of interest is the percentage on the principal that the borrower pays the lender per time period as compensation for forgoing other investment or consumption opportunities. 110.​Compare the difference between compound interest and simple interest. ANSWER: Simple interest is the money paid on borrowed money or earned on invested money based solely on the principal. Simple interest is equal to the product of the principal times the rate per time period times the number of time periods. Compound interest is interest that is paid not only on the principal but also on any interest earned but not withdrawn during earlier periods. Compound interest provides a higher return on an investment because of this principal. 111.​Explain a perpetuity and list some investment vehicles that can be perpetuities. ANSWER: A perpetuity is a financial instrument that promises to pay an equal cash flow per period forever. It will provide an infinite series of payments. Some bonds and some preferred stocks take the form of a perpetuity because they never mature - there is no redemption of these investments at their face value anytime in the future. © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 5: The Time Value of Money 112.​Explain the sinking fund problem. ANSWER: The sinking fund problem results from trying to determine how money must be invested into an annuity to produce a specified future value. The purpose is to accumulate an amount of money in the future that can be used to pay off a lump sum future obligation or can retire corporate bonds. 113.​What is the net present value rule? ANSWER: The net present value of an investment is equal to the present value of the expected future cash flows generated by the investment minus the initial outlay. The future cash flows are discounted back to the present at a required rate of return that reflects the perceived risk of the investment. The net present value of an investment made by a firm represents the contribution of that investment to the value of the firm, and, as such, to the wealth of the shareholders. © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.