31 questions

8/2/2019 31 Questions

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Chapter 05 - Introduction to Valuation: The Time Value of Money

5-1

31. You just received a $5,000 gift from your grandmother. You have decided to save thismoney so that you can gift it to your grandchildren 50 years from now. How much additionalmoney will you have to gift to your grandchildren if you can earn an average of 8.5 percentinstead of just 8 percent on your savings?

A. $47,318.09B. $52,464.79C. $55,211.16D. $58,811.99E. $60,923.52

Future value = $5,000 v (1 + .085)50 = $295,431.58

Future value = $5,000 v (1 + .08)50 = $234,508.06

Difference = $295,431.58 - $234,508.06 = $60,923.52


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5-2

32. You are depositing $1,500 in a retirement account today and expect to earn an averagereturn of 7.5 percent on this money. How much additional income will you earn if you leavethe money invested for 45 years instead of just 40 years?A. $10,723.08

B. $11,790.90C. $12,441.56D. $12,908.19E. $13,590.93

Future value = $1,500 v (1 + .075)45 = $38,857.26

Future value = $1,500 v (1 + .075)40 = $27,066.36Difference = $38,857.26 - $27,066.36 = $11,790.90

AACSB: AnalyticBloom's: Analysis

Difficulty: Intermediate

Learning Objective: 5-1

Section: 5.1Topic: Future value


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5-3

33. You collect old coins. Today, you have two coins each of which is valued at $250. Onecoin is expected to increase in value by 6 percent annually while the other coin is expected toincrease in value by 4.5 percent annually. What will be the difference in the value of the twocoins 15 years from now?

A. $115.32B. $208.04C. $241.79D. $254.24E. $280.15

Future value = $250 v (1 + .06)15 = $599.14

Future value = $250 v (1 + .045)15 = $483.82

Difference = $599.14 - $483.82 = $115.32

AACSB: AnalyticBloom's: AnalysisDifficulty: Intermediate

Learning Objective: 5-1Section: 5.1

Topic: Future value


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5-4

34. Your father invested a lump sum 26 years ago at 4.25 percent interest. Today, he gave youthe proceeds of that investment which totaled $51,480.79. How much did your fatheroriginally invest?A. $15,929.47

B. $16,500.00C. $17,444.86D. $17,500.00E. $17,999.45

Present value = $51,480.79 v [1/(1 + .0425)26] = $17,444.86

AACSB: AnalyticBloom's: ApplicationDifficulty: Basic


Topic: Present value

35. What is the present value of $150,000 to be received 8 years from today if the discountrate is 11 percent?A. $65,088.97

B. $71,147.07C. $74,141.41D. $79,806.18E. $83,291.06

Present value = $150,000 v [1/1 + .11)8] = $65,088.97

AACSB: Analytic

Bloom's: Application

Difficulty: BasicLearning Objective: 5-2Section: 5.2



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36. You would like to give your daughter $75,000 towards her college education 17 yearsfrom now. How much money must you set aside today for this purpose if you can earn 8percent on your investments?A. $18,388.19

B. $20,270.17C. $28,417.67D. $29,311.13E. $32,488.37

Present value = $75,000 v [1/(1 + .08)17] = $20,270.17

AACSB: AnalyticBloom's: Application

Difficulty: Basic

Learning Objective: 5-2Section: 5.2Topic: Present value


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37. You want to have $35,000 saved 6 years from now to buy a house. How much less do youhave to deposit today to reach this goal if you can earn 5.5 percent rather than 5 percent onyour savings? Today's deposit is the only deposit you will make to this savings account.A. $733.94

B. $791.18C. $824.60D. $845.11E. $919.02

Present value = $35,000 v [1/(1 + .05)6] = $26,117.54

Present value = $35,000 v [1/(1 + .055)6] = $25,383.60Difference = $26,117.54 - $25,383.60 = $733.94


Difficulty: IntermediateLearning Objective: 5-2

Section: 5.2



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5-7

38. Your older sister deposited $5,000 today at 8.5 percent interest for 5 years. You wouldlike to have just as much money at the end of the next 5 years as your sister will have.However, you can only earn 7 percent interest. How much more money must you deposittoday than your sister did if you are to have the same amount at the end of the 5 years?

A. $321.19B. $360.43C. $387.78D. $401.21E. $413.39

Future value = $5,000 v (1 + .085)5 = $7,518.28

Present value = $7,518.28 v [1/(1 + .07)5] = $5,360.43

Difference = $5,360.43 - $5,000 = $360.43

AACSB: Analytic

Bloom's: AnalysisDifficulty: Intermediate

Learning Objective: 5-1 and 5-2Section: 5.1 and 5.2Topic: Present and future values


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5-8

39. A year ago, you deposited $30,000 into a retirement savings account at a fixed rate of 5.5percent. Today, you could earn a fixed rate of 6.5 percent on a similar type account. However,your rate is fixed and cannot be adjusted. How much less could you have deposited last year ifyou could have earned a fixed rate of 6.5 percent and still have the same amount as you

currently will when you retire 38 years from today?A. $2,118.42 lessB. $3,333.33 lessC. $5,417.09 lessD. $7,274.12 lessE. $9,234.97 less

Future value = $30,000 v (1 + .055)38+1 = $242,084.61

Present value = $242,084.61 v [1/(1 + .065)38+1] = $20,765.03

Difference = $30,000 - $20,765.03 = $9,234.97

AACSB: AnalyticBloom's: Analysis




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5-9

40. When you retire 40 years from now, you want to have $1.2 million. You think you canearn an average of 12 percent on your investments. To meet your goal, you are trying todecide whether to deposit a lump sum today, or to wait and deposit a lump sum 2 years fromtoday. How much more will you have to deposit as a lump sum if you wait for 2 years before

making the deposit?A. $1,414.14B. $2,319.47C. $2,891.11D. $3,280.78E. $3,406.78

Present value = $1,200,000 v [1/(1 + .12)40] = $12,896.16

Present value = $1,200,000 v [1/(1 + .12)38] = $16,176.94

Difference = $16,176.94 - $12,896.16 = $3,280.78

AACSB: Analytic

Bloom's: AnalysisDifficulty: Intermediate


Section: 5.2Topic: Present value


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5-10

41. Theo needs $40,000 as a down payment for a house 6 years from now. He earns 3.5percent on his savings. Theo can either deposit one lump sum today for this purpose or he canwait a year and deposit a lump sum. How much additional money must he deposit if he waitsfor one year rather than making the deposit today?

A. $878.98B. $911.13C. $1,138.90D. $1,348.03E. $1,420.18

Present value = $40,000 v [1/(1 + .035)6] = $32,540.03

Present value = $26,000 v [1/(1 + .035)5] = $33,678.93

Difference = $33,678.93 - $32,540.03 = $1,138.90

AACSB: Analytic

Bloom's: Analysis




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5-11

42. One year ago, you invested $1,800. Today it is worth $1,924.62. What rate of interest didyou earn?A. 6.59 percentB. 6.67 percent

C. 6.88 percentD. 6.92 percentE. 7.01 percent

$1,924.62 = $1,800 v (1 + r)1; r = 6.92 percent


Difficulty: BasicLearning Objective: 5-3

Section: 5.3

Topic: Interest rate

43. According to the Rule of 72, you can do which one of the following?A. double your money in five years at 7.2 percent interestB. double your money in 7.2 years at 8 percent interestC. double your money in 8 years at 9 percent interest

D. triple your money in 7.2 years at 5 percent interestE. triple your money at 10 percent interest in 7.2 years

Rule of 72 = 72/8 years = 9 percent interest

AACSB: Analytic

Bloom's: ApplicationDifficulty: BasicLearning Objective: 5-3

Section: 5.3Topic: Interest rate


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44. Forty years ago, your mother invested $5,000. Today, that investment is worth$430,065.11. What is the average annual rate of return she earned on this investment?A. 11.68 percentB. 11.71 percent


$430,065.11 = $5,000 v (1 + r)40; r = 11.78 percent

AACSB: Analytic




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45. Sixteen years ago, Alicia invested $1,000. Eight years ago, Travis invested $2,000. Today,both Alicia's and Travis' investments are each worth $2,400. Assume that both Alicia andTravis continue to earn their respective rates of return. Which one of the following statementsis correct concerning these investments?

A. Three years from today, Travis' investment will be worth more than Alicia's.B. One year ago, Alicia's investment was worth less than Travis' investment.C. Travis earns a higher rate of return than Alicia.D. Travis has earned an average annual interest rate of 3.37 percent.E. Alicia has earned an average annual interest rate of 6.01 percent.

Alicia: $2,400 = $1,000 v (1 + r)16; r = 5.62 percent

Travis: $2,400 = $2,000 v (1 + r)8; r = 2.31 percent

Since both Alicia and Travis have equal account values today and since Alicia earns thehigher rate of return, her account had to be worth less than Travis' account one year ago.

AACSB: AnalyticBloom's: Synthesis

Difficulty: IntermediateLearning Objective: 5-3Section: 5.3



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46. Penn Station is saving money to build a new loading platform. Two years ago, they setaside $24,000 for this purpose. Today, that account is worth $28,399. What rate of interest isPenn Station earning on this investment?A. 6.39 percent

B. 7.47 percentC. 8.78 percentD. 9.23 percentE. 9.67 percent

$28,399 = $24,000 v (1 + r)2; r = 8.78 percent

AACSB: AnalyticBloom's: AnalysisDifficulty: Basic

Learning Objective: 5-3Section: 5.3Topic: Interest rate

47. Fifteen years ago, Jackson Supply set aside $130,000 in case of a financial emergency.Today, that account has increased in value to $330,592. What rate of interest is the firmearning on this money?

A. 5.80 percentB. 6.42 percentC. 6.75 percentD. 7.28 percentE. 7.53 percent

$330,592 = $130,000 v (1 + r)15; r = 6.42 percent


Difficulty: BasicLearning Objective: 5-3Section: 5.3



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48. Fourteen years ago, your parents set aside $7,500 to help fund your college education.Today, that fund is valued at $26,180. What rate of interest is being earned on this account?A. 7.99 percentB. 8.36 percent


$26,180 = $7,500 v (1 + r)14; r = 9.34 percent

AACSB: Analytic



49. Some time ago, Julie purchased eleven acres of land costing $36,900. Today, that land isvalued at $214,800. How long has she owned this land if the price of the land has beenincreasing at 10.5 percent per year?A. 13.33 years

B. 16.98 yearsC. 17.64 yearsD. 19.29 yearsE. 21.08 years

$214,800 = $36,900 v (1 + .105)t; t = 17.64 years


Learning Objective: 5-4Section: 5.3Topic: Time period


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50. On your ninth birthday, you received $300 which you invested at 4.5 percent interest,compounded annually. Your investment is now worth $756. How old are you today?A. age 29B. age 30

C. age 31D. age 32E. age 33

$756 = $300 v (1 + .045)t; t = 21 years; Age today = 9 + 21 = 30

AACSB: Analytic

Bloom's: ApplicationDifficulty: Basic

Learning Objective: 5-4Section: 5.3Topic: Time period

Essay Questions

51. You want to deposit sufficient money today into a savings account so that you will have

$1,000 in the account three years from today. Explain why you could deposit less moneytoday if you could earn 3.5 percent interest rather than 3 percent interest.

Student answers will vary but should present the idea that when you can earn more interest,you need less of your own money to reach the same future dollar amount. They can also basetheir answer on the present value formula.

Feedback: Refer to section 5.2

AACSB: Reflective thinkingBloom's: Analysis


Section: 5.2



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52. You are considering two separate investments. Both investments pay 7 percent interest.Investment A pays simple interest and Investment B pays compound interest. Whichinvestment should you choose, and why, if you plan on investing for a period of 5 years?

Simple interest is interest earned on the initial principal amount only. Compound interest isinterest earned on both the initial principal and all prior interest earnings that have beenreinvested. You should choose Investment B which pays compound interest as you will earnmore interest income over the 5 years by doing so.


AACSB: Reflective thinkingBloom's: Analysis


Section: 5.1Topic: Simple and compound interest

53. What lesson does the future value formula provide for young workers who are lookingahead to retiring some day?

The future value formula is: FV = PV (1 + r)t. Time is the exponent. While the rate of returnis important and has a direct effect on the growth of an investment account, time is critical. Tomaximize retirement income, workers need to commence saving when they are young so thatreinvested earnings have time to compound.


AACSB: Reflective thinkingBloom's: Evaluation


Section: 5.1

Topic: Future value


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54. You are considering two lottery payment options: Option A pays $10,000 today andOption B pays $20,000 at the end of ten years. Assume you can earn 6 percent on yoursavings. Which option will you choose if you base your decision on present values? Whichoption will you choose if you base your decision on future values? Explain why your answers

are either the same or different.

PV of A = $10,000; PV of B = $11,167.90; FV of A = $17,908.48; FV of B = $20,000. Basedon both present values and future values, B is the better choice. Students should explain thatcomputing present values and computing future values are simply inverse processes of oneanother, and that choosing between two lump sums based on present values will always givethe same result as choosing between the same two lump sums based on future values.

Feedback: Refer to sections 5.1 and 5.2

AACSB: Reflective thinkingBloom's: EvaluationDifficulty: Intermediate


55. At an interest rate of 10 percent and using the Rule of 72, how long will it take to doublethe value of a lump sum invested today? How long will it take after that until the accountgrows to four times the initial investment? Given the power of compounding, shouldn't it takeless time for the money to double the second time?

It will take 7.2 years to double the initial investment, then another 7.2 years to double it again.That is, it takes 14.4 years for the value to reach four times the initial investment.Compounding doesn't affect the amount of time it takes for an investment to double in value.However, you should note that during the first 7.2 years, the interest earned is equal to 100percent of the initial investment. During the second 7.2 years, the interest earned is equal to200 percent of the initial investment. That is the power of compounding.


AACSB: Reflective thinkingBloom's: AnalysisDifficulty: IntermediateLearning Objective: 5-4

Section: 5.3

Topic: Rule of 72


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EOC Problem Questions

56. Assume the total cost of a college education will be $300,000 when your child enterscollege in 16 years. You presently have $75,561 to invest. What rate of interest must you earnon your investment to cover the cost of your child's college education?

A. 7.75 percentB. 8.50 percentC. 9.00 percentD. 9.25 percentE. 9.50 percent

$300,000 = $75,561 (1 + r)16; r = 9 percent

AACSB: Analytic


EOC #: 5-6


57. At 11 percent interest, how long would it take to quadruple your money?

A. 6.55 yearsB. 6.64 yearsC. 13.09 yearsD. 13.28 yearsE. 13.56 years

$4 = $1 v (1 + .11)t; t = 13.28 years


Difficulty: Basic


Section: 5.3Topic: Time period


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58. Assume the average vehicle selling price in the United States last year was $41,996. Theaverage price 9 years earlier was $29,000. What was the annual increase in the selling priceover this time period?A. 3.89 percent

B. 4.20 percentC. 4.56 percentD. 5.01 percentE. 5.40 percent

$41,996 = $29,000 v (1 + r)9; r = 4.20 percent

AACSB: Analytic


EOC #: 5-8



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59. You're trying to save to buy a new $160,000 Ferrari. You have $56,000 today that can beinvested at your bank. The bank pays 6 percent annual interest on its accounts. How manyyears will it be before you have enough to buy the car? Assume the price of the car remainsconstant.

A. 16.67 yearsB. 17.04 yearsC. 17.41 yearsD. 17.87 yearsE. 18.02 years

$160,000 = $56,000 v (1 + .06)t; t = 18.02 years


Difficulty: BasicEOC #: 5-9Learning Objective: 5-4

Section: 5.3Topic: Time period


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60. Imprudential, Inc. has an unfunded pension liability of $850 million that must be paid in25 years. To assess the value of the firm's stock, financial analysts want to discount thisliability back to the present. The relevant discount rate is 6.5 percent. What is the presentvalue of this liability?

A. $159,803,162B. $171,438,907C. $176,067,311D. $184,519,484E. $191,511,367

PV = $850,000,000 v [1/(1.065)25] = $176,067,311

AACSB: Analytic

Bloom's: ApplicationDifficulty: BasicEOC #: 5-10




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61. You have just received notification that you have won the $1.4 million first prize in theCentennial Lottery. However, the prize will be awarded on your 100th birthday, 70 years fromnow. The appropriate discount rate is 8 percent. What is the present value of your winnings?A. $4,288.16

B. $6,404.20C. $15,309.91D. $23,333.33E. $25,000.00

PV = $1,400,000 v [1/(1.08)70] = $6,404.20


EOC #: 5-11Learning Objective: 5-2Section: 5.2



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62. Your coin collection contains fifty-four 1941 silver dollars. Your grandparents purchasedthem for their face value when they were new. These coins have appreciated at a 10 percentannual rate. How much will your collection be worth when you retire in 2060?A. $3,611,008

B. $3,987,456C. $4,122,394D. $4,421,008E. $4,551,172

FV = $54 v (1.10)119 = $4,551,172

AACSB: Analytic


EOC #: 5-12

Learning Objective: 5-1Section: 5.1Topic: Future value


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63. In 1895, the winner of a competition was paid $110. In 2006, the winner's prize was$70,000. What will the winner's prize be in 2040 if the prize continues increasing at the samerate?A. $389,400

B. $421,122C. $479,311D. $505,697E. $548,121

$70,000 = $110 v (1 = r)111; r = 5.988466 percent

FV = $70,000 v (1 + .05988466)34 = $505,697

AACSB: Analytic

Bloom's: AnalysisDifficulty: Basic

EOC #: 5-13Learning Objective: 5-1 and 5-3Section: 5.1 and 5.3

Topic: Interest rate and future value


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64. Suppose that the first comic book of a classic series was sold in 1954. In 2000, theestimated price for this comic book in good condition was about $340,000. This represented areturn of 27 percent per year. For this to be true, what was the original price of the comicbook in 1954?

A. $5.00B. $5.28C. $5.50D. $5.71E. $6.00

PV = $340,000 v [1/(1 + .27)46; PV = $5.71






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65. Suppose you are committed to owning a $140,000 Ferrari. You believe your mutual fundcan achieve an annual rate of return of 9 percent and you want to buy the car in 7 years. Howmuch must you invest today to fund this purchase assuming the price of the car remainsconstant?

A. $74,208.16B. $76,584.79C. $77,911.08D. $78,019.82E. $79,446.60

PV = $140,000 v [1/(1 + .09)7; PV = $76,584.79

AACSB: Analytic

Bloom's: ApplicationDifficulty: IntermediateEOC #: 5-17




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66. You have just made a $1,500 contribution to your individual retirement account. Assumeyou earn a 12 percent rate of return and make no additional contributions. How much morewill your account be worth when you retire in 25 years than it would be if you waited another10 years before making this contribution?

A. $8,306.16B. $9,658.77C. $16,311.18D. $16,907.17E. $17,289.75

FV = $1,500 v (1 + .12)25 = $25,500.10

FV = $1,500 v (1 + .12)15 = $8,210.35

Difference = $17,289.75

AACSB: Analytic

Bloom's: ApplicationDifficulty: Intermediate

EOC #: 5-18Learning Objective: 5-1

Section: 5.1Topic: Future value


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67. You are scheduled to receive $30,000 in two years. When you receive it, you will invest itfor 5 more years, at 8 percent per year. How much money will you have 7 years from now?A. $39,909.19B. $41,381.16

C. $44,079.84D. $47,209.19E. $51,414.73

FV = $30,000 v (1 + .08)(7-2) = $44,079.84

AACSB: Analytic

Bloom's: ApplicationDifficulty: IntermediateEOC #: 5-19

Learning Objective: 5-1Section: 5.1Topic: Future value

68. You expect to receive $9,000 at graduation in 2 years. You plan on investing this moneyat 10 percent until you have $60,000. How many years will it be until this occurs?A. 18.78 years

B. 19.96 yearsC. 21.90 yearsD. 23.08 yearsE. 25.00 years

$60,000 = $9,000 v (1 + .10)t; t = 19.90 years

Total time = 2 + 19.90 = 21.90 years

AACSB: Analytic

Bloom's: ApplicationDifficulty: Intermediate


Topic: Time period


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