Chapter 5 Test Bank

 

Chapter 4 

 Introduction to Valuation: The Time Value of Money 

I.

DEFINITIONS 

Topic: FUTURE VALUE 1. The amount an investment is worth after one or more periods of time is the  ___________. A)

future value

B)

present value

C)

principal value

D)

compound interest rate

E)

simple interest rate

Answer: A

Topic: COMPOUNDING 2. The process of accumulating interest on an investment over time to earn more interest is called: A) B)

Growth. Compounding.

C)

Aggregation.

D)

Accumulation.

Answer: B

Topic: INTEREST ON INTEREST 3. Interest earned on the reinvestment of previous interest payments is called  _____________ .

 

 

A)

free interest

B)

annual interest

C)

simple interest

D)

interest on interest

E)

compound interest

Answer: D

Topic: COMPOUND INTEREST 4. Interest earned on both the initial principal and the interest reinvested from prior  periods is called _______________ _______________ . A)

free interest

B)

annual interest

C)

simple interest

D)

interest on interest

E)

compound interest

Answer: E

 

Topic: SIMPLE INTEREST 5. Interest earned only on the original principal amount invested is called  _____________..  _____________ A)

free interest

B)

annual interest

C)

simple interest

D)

interest on interest

E)

compound interest

Answer: C

Topic: FUTURE VALUE INTEREST FACTOR 6.

The future value interest factor is calculated as:

A)

(1 + r)t

B)

(1 + rt)

C)

(1 + r)(t)

D)

1 + r  –   tt

E)

None of the above are correct

Answer: A

Topic: PRESENT VALUE 7. is called the:

The current value of future cash flows discounted at the appropriate discount rate

A)

Principal value.

B)

Future value.

C)

Present value.

D)

Simple interest rate.

E)

Compound interest rate.

Answer: C

 

 

Topic: DISCOUNTING 8. The process of finding the present value of some future amount is often called  ______________.  _____________ _. A)

growth

B)

discounting

C)

accumulation

D)

compounding

E)

reduction

Answer: B

Topic: PRESENT VALUE INTEREST FACTOR 9.

The present value interest factor is calculated as:

A)

1/(1 + r  –   t) t)

B)

1/(1 + rt)

C)

1/(1 + r)(t)

D)

1/(1 + r)t

E)

1+r+t

Answer: D

 

Topic: DISCOUNT RATE 10. The interest rate used to calculate the present value of future cash flows is called the _________ rate. A)

free interest

B)

annual interest

C)

compound interest

D)

simple interest

E)

discount

Answer: E

II

CONCEPTS 

Topic: PRESENT VALUE FACTORS 11. Suppose you are trying to find the present value of two different cash flows using the same interest rate for each. One cash flow is $1,000 ten years from now, the other $800 seven years from now. Which of the following is true about the discount factors used in these valuations? A) The discount factor for the cash flow ten years away is always less than or equal to the discount factor for the cash flow that is received seven years from now. B)

Both discount factors are greater than one.

C) Regardless of the interest rate, the discount factors are such that the present value of the $1,000 will always be greater than the present value of the $800. D) Since the payments are different, no statement can be made regarding the discount factors. E) soonest.

You should factor in the time differential and choose the payment that arrives the

Answer: A

Topic: SIMPLE VS. COMPOUND INTEREST

 

  12. You are choosing between investments offered by two different banks. One  promises a return of 10% for for three years using simple interes interestt while the other offers a return of 10% for three years using compound interest. You should: A)

Choose the simple interest option because both have the same basic interest rate.

B)

Choose the compound interest option because it provides a higher return.

C)  periods.

Choose the compound interest option only if the compounding is for monthly

D) year.

Choose the simple interest option only if compounding occurs more than once a

E)

Choose the compound interest option only if you are investing less than $5,000.

Answer: B

 

Topic: TIME VALUE FACTORS 13.

Given r and t greater than zero and assuming a lump sum payment:

I. Present value interest interest factors are less than one. II. Future value interest factors are greater than than one. III. Present value interest facto factors rs are greater than future value inte interest rest factors. IV. Present value interest factors grow grow as t grows, provid provided ed r is held constant.

A)

I only

B)

I and II only

C)

I and IV only

D)

II and III only

E)

II and IV only

Answer: B

Topic: PRESENT VALUE 14.

Which of the following statements is/are FALSE, all else the same?

I. Present values increase as the discoun discountt rate increases. II. Present values increase the further away in time the future value. value. III. Present values are smaller than fu future ture values when both r and t are positive.

A)

I only

B)

I and II only

C)

II only

D)

III only

E)

II and III only

Answer: B

 

  III.

PROBLEMS 

Topic: PRESENT VALUE LUMP SUM 15. Fresh out of college, you are negotiating with your prospective new employer. They offer you a signing bonus of $1,000,000 today or a lump sum payment of $1,250,000 three years from now. If you can earn 7% on your invested funds, which of the following is true? A)

Take the signing bonus because it has the lower present value.

B)

Take the signing bonus because it has the higher future value.

C)

Take the lump sum because it has the higher present value.

D)

Take the lump sum because it has the lower future value.

E)

Based on these numbers, you are indifferent between the two.

Answer: C Response: FV of bonus = $1,000,000(1.07)3 = $1,225,043; PV of lump sum = $1,250,00 / (1.07)3 = $1,020,372

 

Topic: FUTURE VALUE LUMP SUM 16. You received a $1 savings account earning 6% on your 1st birthday. How much will you have in the account on your 30th birthday if you don't withdraw any money before then? A)

$3.56

B)

$4.90

C)

$5.42

D)

$5.90

E)

$6.13

Answer: C Response: FV = $1(1.06)29 = $5.42

Topic: FUTURE VALUE LUMP SUM 17. What is the future value of $15,000 received today if it is invested at 7.5% compounded annually for five years? A)

$15,133.35

B)

$17,476.42

C)

$21,534.44

D)

$24,521.75

E)

$28,374.89

Answer: C Response: FV = $15,000(1.075)5 $15,000(1.075)5 = $21,534.44

Topic: PRESENT VALUE LUMP SUM 18. How much would you have to invest today at 9% compounded annually to have $35,000 available for the purchase of a car five years from now? A)

$20,267.26

B)

$22,747.60

C)

$24,147.25

D)

$26,370.10

 

 

E)

$28,149.57

Answer: B Response: PV = $35,000 / (1.09)5 = $22,747.60

Topic: PRESENT VALUE LUMP SUM 19. You will receive a $250,000 inheritance in 25 years. You can invest that money today at 8% compounded annually. What is the present value of your inheritance? A)

$ 17,491.53

B)

$ 29,767.15

C)

$ 36,504.48

D)

$ 65,492.34

E)

$100,000.00

Answer: C Response: PV = $250,000 / (1.08) 25 = $36,504.48

 

Topic: PRESENT VALUE LUMP SUM 20. You just won the lottery and want to put some money away for your child's college education. College will cost $75,000 in 15 years. You can earn 7% compounded annually. How much do you need to invest today? A)

$19,828.18

B) C)

$21,763.07 $23,690.82

D)

$25,258.17

E)

$27,183.45

Answer: E Response: PV = $75,000 / (1.07) 15 = $27,183.45

Topic: PRESENT VALUE LUMP SUM 21. You are supposed to receive $3,000 four years from now. At an interest rate of 8%, what is that $3,000 worth today? A)

$1,591.97

B)

$1,892.43

C)

$2,205.09

D)

$2,497.91

E)

$2,699.01

Answer: C Response: PV = $3,000 / (1.08) 4 = $2,205.09

Topic: INTEREST RATE 22. Your grandfather placed $5,000 in a trust fund for you. In 12 years the fund will  be worth $10,000. What is the rate of return on the trust fund? A)

3.70%

B)

4.16%

C)

5.95%

 

 

D)

6.90%

E)

8.42%

Answer: C Response: r = ($10,000 / 5,000) 1/12 1 = 5.95%

Topic: NUMBER OF PERIODS 23. You need $3,000 to buy a new stereo for your car. If you have $1,200 to invest at 6% compounded annually, how long will you have to wait to buy the stereo? A)

6.58 years

B)

8.42 years

C)

11.60 years

D)

14.58 years

E)

15.73 years

Answer: E Response: t = ln($3,000 / 1,200) / ln (1.06) = 15.73 years

 

Topic: FUTURE VALUE 24. Your parents agree to pay half of the purchase price of a new car when you graduate from college. You will graduate and buy the car two years from now. You have $9,000 to invest today and can earn 12% on invested funds. If your parents match the amount of money you have in two years, what is the maximum you can spend on the new car? A)

$ 7,260

B)

$11,290

C)

$15,000

D)

$19,250

E)

$22,579

Answer: E Response: FV = $9,000(1.12)2 = $11,289.60; $11,289.60 x 2 = $22,579

Topic: RULE OF 72 25. Granny puts $25,000 into a bank account earning 6%. You can't withdraw the money until the balance has doubled. How long will you have to leave the money in the account? A)

6 years

B)

9 years

C)

12 years

D)

14 years

E)

20 years

Answer: C Response: t = 72 / 6 = 12 years

Topic: COMPOUNDING 26. Many economists view a 3% annual inflation rate as "acceptable". Assuming a 3% annual increase in the price of automobiles, how much will a new BMW cost you 8 years from now, if today's price is $40,000? A)

$38,779

B)

$42,110

 

 

C)

$45,575

D)

$47,813

E)

$50,671

Answer: E 8 Response: FV = $40,000(1.03)  = $50,671

Topic: COMPOUNDING 27. In 1889, Vincent Van Gogh's painting "Sunflowers" sold for $125. One hundred years later it sold for $36 million. Had the painting been purchased by your great-grandfather and  passed on to you, what annual annual return on investment investment would your family have have earned on the  painting? A)

9.11%

B)

10.09%

C)

11.88%

D)

11.99%

E)

13.40%

Answer: E Response: r = ($36,000,000 / 125) 1/100 -1 = 13.40%

 

Topic: INTEREST RATE 28. An insurance company promises to pay Jane $1 million on her 65th birthday in return for a one-time payment of $125,000 today. (Jane just turned 30.) At what rate of interest would Jane be indifferent between accepting the company's offer and investing the premium on her own? A)

3.4%

B)

4.5%

C)

5.1%

D)

6.1%

E)

7.2%

Answer: D Response: r = ($1,000,000 / 125,000) 1/35  -1 = 6.12% 6.12%

Topic: PRESENT VALUE LUMP SUM 29. Homer promises Bart that he will give him $8,000 upon his graduation from college at Springfield U. How much must Homer invest today to make good on his promise, if Bart is expected to graduate in 13 years and Homer can earn 6% on his money? A)

$3,235.32

B)

$3,750.71

C)

$4,881.11

D)

$5,012.88

E) Answer: B

$5,979.28 Response: PV = $8,000 / (1.06) 13 = $3,750.71

Topic: ANNUAL INTEREST 30. You have $200 in an account which pays 5% compound interest. How much additional dollars of interest would you earn over 6 years if you moved the money to an account earning 6%? A)

$11.89

 

 

B)

$15.68

C)

$18.93

D)

$22.88

E)

$24.94

Answer: B Response: current: FV = $200(1.05)6 = $268.02; proposed: FV = $200(1.06)6 = $283.70 difference = $283.70 - 268.02 = $15.68

 

Topic: INVESTMENT RETURNS 31. An account was opened with an investment of $2,000 10 years ago. The ending  balance in the account is $3,500. $3,500. If interest was compounded annually, annually, what rate was earned on the account? A)

2.66%

B)

3.22%

C)

3.95%

D)

4.81%

E)

5.76%

Answer: E Response: r = ($3,500 / 2,000)1/10 -1 = 5.76%

Topic: INTEREST ON INTEREST 32. An account was opened with $2,000 10 years ago. Today, the account balance is $3,500. If the account paid interest compounded annually, how much interest on interest was earned? A)

$ 348

B)

$ 521

C)

$ 706

D)

$1,152

E)

$1,500

Answer: A Response: r = ($3,500 / 2,000)1/10 1 = 5.76%; annual simple interest = $2,000 x .0576 . 0576 = $115.20 total simple interest = $115.20 x 10 = $1,152; difference = $1,500 - 1,152 = $348

Topic: SIMPLE INTEREST

 

  33. An account paying annual compound interest was opened with $2,000 10 years ago. Today, the account balance is $3,500. If the same interest rate is offered on an account  paying simple interest, interest, how much income would be earned over the same time period? A)

$ 576

B)

$ 862

C)

$1,152

D)

$1,500

E)

$1,719

Answer: C Response: r = ($3,500 / 2,000)1/10 -1 = 5.76%; annual simple interest = $2,000 x .0576 . 0576 = $115.20 total simple interest = $115.20 x 10 = $1,152

 

Topic: SIMPLE INTEREST 34. An account paying annual compound interest was opened with $2,000 10 years ago. Today, the account balance is $3,500. If the same interest rate is offered on an account  paying simple interest, interest, how much income would be earned each year over the same time period? A)

$ 56.90

B)

$ 80.40

C)

$ 92.60

D)

$115.20

E)

$150.00

Answer: D Response: r = ($3,500 / 2,000)1/10 -1 = 5.76%; annual simple interest = $2,000 x .0576 . 0576 = $115.20

Topic: SIMPLE INTEREST 35. An account was opened with $1,000 three years ago. Today, the account balance is $1,157.63. If the account earns a fixed annual interest rate, how long will it take until the account has earned a total of $225 in simple interest? A)

Less than one more year.

B)

Between one and two more years.

C)

Between two and three more years.

D)

Between three and four more years.

E)

Between four and five more years.

Answer: B Response: r = (1,157.63/1,000)1/3 - 1= 5%; 1,000 x .05 = 50/yr total of 4.5 yr 3yr to date = 1.5 remaining

Use the following to answer questions 36-40:

 

In a growing midwestern town, the number of eating establishments at the end of each of the last five years are as follows:

Topic: GROWTH RATES 36. From the end of year 1 to the end of year 5, the number of eating establishments grew at a rate of _______ compounded annually. A)

3.45%

B)

4.15%

C)

5.95%

D)

6.75%

E) Answer: C

8.25% Response: r = (344 / 273)1/4 -1 = 5.95%

 

Topic: FUTURE VALUE 37. If, over the next five years, eating establishments are expected to grow at the same rate as they did during year 5, forecast the number of eating establishments at the end of year 10. A)

494

B)

510

C)

534

D)

555

E)

629

Answer: A Response: r = (344 / 320)1/1 -1 = 7.5%; FV = 344(1.075)5 = 494

Topic: FUTURE VALUE 38. If the number of eating establishments are expected to grow in year 6 at the same rate as the percentage increase in year 5, how many new eating establishments will be added in year 6? A)

15

B)

22

C)

26

D)

28

E)

31

Answer: C Response: r = (344 / 320)1/1 -1 = 7.5%; new restaurants = 344 x .075 = 26

Topic: PRESENT VALUE 39. If the town's population was 90,000 at the end of year 5, and the population grew at the same annual rate as the number of eating establishments between the end of year 1 and the end of year 5, what was the town's population at the end of year 1? A)

71,423

B)

61,433

 

 

C)

51,223

D)

41,333

E)

31,723

Answer: A Response: r = (344 / 273)

1/4 4  -1 = 5.95%; PV = 90,000 / (1.0595)  = 71,423

Topic: GROWTH RATES 40. Between the end of year 2 and the end of year 3, the number of eating establishments grew at a rate of _________ compounded compounded annually. A)

5.2%

B)

6.7%

C)

7.6%

D)

8.2%

E)

9.3%

Answer: D Response: r = (302 / 279)1/1 -1 = 8.24%

 

 

IV.

ESSAYS 

Topic: PRESENT VALUE AND DISCOUNTING 41. increases.

Explain intuitively why it is that present values decrease as the discount rate

Answer: Intuitively, a dollar today is worth more than a dollar tomorrow. As a practical matter, the discount rate is an opportunity cost, and the higher the rate, the higher the cost.

Topic: COMPOUNDING 42. Explain what compounding is and the relationship between compound interest earned and the number of years over which an investment is compounded.

Answer: Compounding is earning interest on interest. Compounding is not significant over short time  periods, but increases in importance the longer the ttime ime period considered.

Topic: FUTURE VALUES 43. Draw a picture illustrating the future value of $1, using five different interest rates (including 0%) and maturities ranging from today to 10 years from now. Plot time to maturity on the horizontal axis and dollars on the vertical axis. (Note: you need not make any calculations, draw the figure using your intuition.)

Answer: The student should basically replicate Figure 4.2.

Topic: COMPARING LUMP SUMS

 

  44. You are considering two lottery payment streams, choice A pays $1,000 today and choice B pays $1,750 at the end of five years from now. Using a discount rate of 5%, based on present values, which would you choose? Using the same discount rate of 5%, based on future values, which would you choose? What do your results suggest as a general rule for approaching such problems? (Make your choices based purely on the time value of money.)

Answer: PV of A = $1,000; PV of B = $1,371; FV of A = $1,276; FV of B = $1,750. Based on both  present values and future future values, B is the better choice. The sstudent tudent should recog recognize nize that finding  present values and finding finding future values are simply simply reverse processes of one ano another, ther, and that choosing between two lump sums based on PV will always give the same result as choosing  between the same two lump lump sums based on FV.

Topic: RULE OF 72 AND COMPOUNDING 45. At an interest rate of 10% and using the Rule of 72, how long will it take to double the value of a lump sum invested today? How long will it take after that until until the account grows to four times the initial investment? Given the power of compounding, shouldn't it take less time for the money to double the second time?

 

Answer: It will take approximately 7.2 years to double the initial investment, then another 7.2 years to double it again. That is, it takes approximately 14.4 years for the value to reach four times the initial investment. Compounding doesn't doesn't affect the amount of time it takes for an investment to double the second time, but note that during the first 7.2 years, the interest earned is equal to 100% of the initial investment. During the second 7.2 years, the interest earned is equal to 200% of the initial investment. That is the power of compounding.

Topic: THE TIME VALUE OF MONEY 46. Some financial advisors recommend you increase the amount of federal income taxes withheld from your paycheck each month so that you will get a larger refund come April 15th. That is, you take home less today but get a bigger lump sum when you get your refund. Based on your knowledge of the time value of money, what do you think of this idea? Explain.

Answer: Some students may slip in a discussion about the benefits of forced savings, etc., but these issues are based on preferences, not the time value of money. Based on the time value of money, the students should recommend the opposite strategy, that is, withhold as little as possible and pay the tax bill when it comes the following year. This is the usual dollar today versus a dollar tomorrow argument. Of course, the astute student will note the potential tax complications of this strategy, namely the IRS penalty for insufficient withhold withholding, ing, but the basic argument still applies.