Test bank corporate finance 8e ros chap005

The present value of Tammy's and Jeff's money will be equala. Ten years from now, the value of Jeff's money will be equal to the value of Tammy's money.. Tammy's money is worth more than

Multiple Choice Questions

1 The amount an investment will be worth after one or more periods of time is the _ value

4 Interest earned on both the initial principal and the interest reinvested from prior periods is called _ interest

7 The value today of future cash flows discounted at the appropriate discount rate is called the _ value

10 The interest rate used to calculate the present value of future cash flows is called the _ rate

eight years from now Which one of the following statements is correct if both Tammy and Jeff apply a 6 percent discount rate to these amounts?

a The present value of Tammy's and Jeff's money will be equal

b The value of Jeff's money will be less than the value of Tammy's money 15 years from now

C In today's dollars, Jeff's money is worth more than Tammy's.

d Ten years from now, the value of Jeff's money will be equal to the value of Tammy's money

e Tammy's money is worth more than Jeff's money given the 6 percent discount rate

SECTION: 5.2

TOPIC: PRESENT VALUE AND TIME

TYPE: CONCEPTS

13 Tracie deposits $5,000 into an account that pays 3 percent interest compounded annually Chris deposits $5,000 into an account that pays 3 percent simple interest Both deposits were made this morning Which of the following statements are true concerning these two

accounts?

I At the end of one year, both Tracie and Chris will have the same amount in their accounts

II At the end of five years, Tracie will have more money in her account than Chris has in his.III Chris will never earn any interest on interest

IV All else equal, Chris made the better investment

a I and II only

b III and IV only

C I, II, and III only

d I, III, and IV only

e II, III, and IV only

a Kate will have less money when she retires than Kurt

b Kurt will earn more interest on interest than Kate

c Kurt will earn more compound interest than Kate

d If Kurt waits to age 70 to retire, then he will have just as much money as Kate

E Kate will have more money when she retires than Kurt.

SECTION: 5.1

TOPIC: FUTURE VALUE AND TIME

TYPE: CONCEPTS

15 Raoul has $800 today Which one of the following statements is correct if he invests this money at a positive rate of interest for ten years? Assume the interest is compounded

annually

a The higher the interest rate he earns, the less money he will have in the future

b The higher the interest rate, the longer he has to wait for his money to grow to $2,000 in value

c If Raoul can earn 7 percent, he will have to wait about six years to have $1,600 total

d At the end of the ten years, Raoul will have less money if he invests at 9 percent rather than

at 8 percent

E At 7.2 percent interest, Raoul should expect to have about $1,600 in his account at the end

of the ten years

17 Faith invests $4,500 in an account that pays 4 percent simple interest How much money will she have at the end of eight years?

Ending value at 5 percent simple interest = $3,000 + ($3,000 .05 7) = $4,050.00;

Ending value at 5 percent compounded annually = $3,000 (1 + 05)7 = $4,221.30;

19 Jeff invests $3,000 in an account that pays 7 percent simple interest How much more could he have earned over a 20-year period if the interest had compounded annually?

AACSB TOPIC: ANALYTIC

21 Today, you earn a salary of $42,500 What will be your annual salary 10 years from now

if you earn annual raises of 3.2 percent?

22 You own a classic automobile that is currently valued at $67,900 If the value increases by

8 percent annually, how much will the automobile be worth 15 years from now?

23 You hope to buy your dream house 3 years from now Today, your dream house costs

$247,900 You expect housing prices to rise by an average of 7.5 percent per year over the next 3 years How much will your dream house cost by the time you are ready to buy it?

25 What is the present value of $36,800 to be received 6 years from today if the discount rate

27 One year ago, you invested $2,500 Today it is worth $2,789.50 What rate of interest did you earn?

29 Twelve years ago, Jake invested $2,000 Six years ago, Tami invested $4,000 Today, both Jake's and Tami's investments are each worth $9,700 Assume that both Jake and Tami continue to earn their respective rates of return Which one of the following statements is correct concerning these investments?

a Three years from today, Jake's investment will be worth more than Tami's

b One year ago, Tami's investment was worth more than Jake's

c Jake has earned a higher rate of return than Tami

D Tami has earned an average annual interest rate of 15.91 percent.

e Jake has earned an average annual interest rate of 15.47 percent

Jake $9,700 = $2,000 (1 + r)12; r = 14.06 percent; Tami: $9,700 = $4,000 (1 + r)6; r = 15.91 percent; The correct answer states that Tami earned 15.91 percent interest

AACSB TOPIC: ANALYTIC

SECTION: 5.3

TOPIC: INTEREST RATE FOR MULTIPLE PERIODS

TYPE: PROBLEMS

30 Tropical Tans is saving money to build a new salon Three years ago, they set aside

$12,000 for this purpose Today, that account is worth $16,418 What rate of interest is Tropical Tans earning on this money?

32 Six years ago, Home Health Industries (HHI) adopted a plan to expand its services next year At the time the plan was adopted, HHI set aside $125,000 in excess funds to be held for this purpose As of today, that money has increased in value to $186,408 What rate of interest

is the firm earning on these funds?

34 On your thirteenth birthday, you received $1,000 which you invested at 6.5 percent interest, compounded annually Your investment is now worth $5,476 How old are you today?

$5,476 = $1,000 (1 + 065)t; t = 27 years; Age today = 13 + 27 = 40

Note: You received the money when you were 13 years old Thus, you will be 40 (13 + 27) years old when the value reaches $5,476

AACSB TOPIC: ANALYTIC

SECTION: 5.3

TOPIC: NUMBER OF TIME PERIODS

TYPE: PROBLEMS

35 You want to have $260,000 saved 15 years from now How much less do you have to deposit today to reach this goal if you can earn 8 percent rather than 7 percent on your

36 Your big brother deposited $10,000 today at 9 percent interest for 6 years You would like

to have just as much money at the end of the next 6 years as your brother However, you can only earn 7.5 percent interest How much more money must you deposit today than your brother did if you are to have the same amount at the end of the 6 years?

37 Last year, you deposited $25,000 into a retirement savings account at a fixed rate of 7.5 percent Today, you could earn a fixed rate of 8 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 8 percent and still have the same amount as you

currently will when you retire 40 years from today?

38 When you retire 36 years from now, you want to have $2 million You think you can earn

an average of 11.5 percent on your investments To meet your goal, you are trying to decide whether to deposit a lump sum today, or to wait and deposit a lump sum 3 years from today How much more will you have to deposit as a lump sum if you wait for 3 years before makingthe deposit?

39 Marie needs $26,000 as a down payment for a house 4 years from now She earns 5.25 percent on her savings Marie can either deposit one lump sum today for this purpose or she can wait a year and deposit a lump sum How much additional money must Marie deposit if she waits for one year rather than making the deposit today?

40 Wexter and Daughter invested $165,000 to help fund a company expansion project planned for 3 years from now How much additional money will the firm have saved 3 years from now if it can earn 7 percent rather than 5 percent on this money?

41 You just received $278,000 from an insurance settlement You have decided to set this money aside and invest it for your retirement Currently, your goal is to retire 38 years from today How much more will you have in your account on the day you retire if you can earn an average return of 9.5 percent rather than just 9.0 percent?

42 You will be receiving $2,500 from your family as a graduation present You have decided

to save this money for your retirement You plan to retire 40 years after graduation How much additional money will you have at that time if you can earn an average of 12.5 percent

on your investment instead of just 12 percent?

43 You deposit $1,000 in a retirement account today at 8.5 percent interest How much more money will you have if you leave the money invested for 40 years rather than 35 years?

44 You collect old model trains One particular model increases in value at a rate of 6.5 percent per year Today, the model is worth $1,670 How much additional money can you make if you wait 4 years to sell the model rather than selling it 2 years from now?

45 Write a sentence explaining why present values decrease as the discount rate increases

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

AACSB TOPIC: REFLECTIVE THINKING

SECTION: 5.2

TOPIC: PRESENT VALUE AND DISCOUNTING

46 Explain the relationship between compound interest and time

Interest compounds exponentially over time The longer the time period, the greater the annual interest earnings

AACSB TOPIC: REFLECTIVE THINKING

SECTION: 5.1

TOPIC: COMPOUNDING

47 Draw a graph illustrating the future value of $1, using five different interest rates

(including 0 percent) 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 do not need to do any calculations Just draw the graph using your intuition.)

Graphs should illustrate 3 concepts: 1) At zero percent interest, the $1 will not increase in value 2) The higher the interest rate, the higher the future value of $1 3) The future values should illustrate exponential growth

AACSB TOPIC: REFLECTIVE THINKING

SECTION: 5.1

TOPIC: FUTURE VALUES

B pays $1,500 at the end of five years Using a discount rate of 5 percent, based on present values, which would you choose? Using the same discount rate of 5 percent, based on future values five years from now, 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.)

PV of A = $1,000; PV of B = $1,175; FV of A = $1,276; FV of B = $1,500 Based on both present values and future values, B is the better choice The student should recognize that finding present values and finding future values are simply reverse processes of one another, and that choosing between two lump sums based on PV will always give the same result as choosing between the same two lump sums based on FV

AACSB TOPIC: REFLECTIVE THINKING

SECTION: 5.1 AND 5.2

TOPIC: COMPARING LUMP SUMS

49 At an interest rate of 10 percent 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 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?

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 the second time, but note that during the first 7.2 years, the interest earned is equal to 100 percent

of the initial investment During the second 7.2 years, the interest earned is equal to 200 percent of the initial investment That is the power of compounding

AACSB TOPIC: REFLECTIVE THINKING

SECTION: 5.3

TOPIC: RULE OF 72 AND COMPOUNDING

50 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

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 student should recommend just the opposite That is, withhold as little as possible,while still avoiding tax penalties for under withholding, and pay the remaining tax bill when itcomes due the following year as next year's dollars are cheaper than this year's dollars

AACSB TOPIC: REFLECTIVE THINKING

SECTION: 5.3

TOPIC: THE TIME VALUE OF MONEY