978-0134083285 Chapter 5 Part 1

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Foundations of Finance, 9e (Keown/Martin/Petty)

Chapter 5 The Time Value of Money

Learning Objective 5.1

1) The time value of money is the opportunity cost of passing up the earning potential of a dollar today.

Keywords: Time Value of Money, Opportunity Cost

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

2) A rational investor would prefer to receive $1,200 today rather than $100 per month for 12 months.

Keywords: Time Value of Money

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

3) A timeline identifies the timing and amount of a stream of cash flows, along with the interest rate it

earns.

Keywords: Timelines

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

4) Timelines are used for simple time value of money problems, but cannot be used for more complex

problems.

Keywords: Timelines

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

5) If you only earned interest on your initial investment, and not on previously earned interest, it would

be called simple interest.

Keywords: Simple Interest

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

6) An investment earning simple interest is preferred over an investment earning compound interest

because the simplicity adds value.

Keywords: Simple Interest, Compound Interest

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

7) When using a financial calculator, cash outflows generally have to be entered as negative numbers,

because a financial calculator sees money “leaving your hands.”

Keywords: Financial Calculator

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

8) $10,000 invested at 10% per year for 5 years earns interest equal to $6,105.10; therefore, $10,000 invested

at 10% per year for 10 years will earn interest equal to $12,210.20 (2 times $6,105.10).

Keywords: Interest, Time Periods, Compounding

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

9) When solving time value of money problems on a financial calculator, you must select the “end mode”

when you enter the final year’s cash flow.

Keywords: Ordinary Annuity, Financial Calculator

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

10) When solving a problem involving an annuity due, you must select the “beg” or beginning mode on

your financial calculator.

Keywords: Annuity Due, Financial Calculator

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

11) When solving time value of money problems using Excel, the type = 0 variable means payments are

made at the end of each period, and the type = 1 variable means payments are made at the beginning of

each period.

Keywords: Annuity, Excel

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

12) Inputs using an Excel spreadsheet are almost identical to those on a financial calculator, except the

interest rate is entered either as a decimal (.05) or a whole number followed by a % sign (5%) rather than

simply a whole number (5) as you would enter using a financial calculator.

Keywords: Excel, Financial Calculator

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

13) Tim has $100 in a bank account paying 2% interest per year. At the end of 5 years, Tim‘s bank account

balance will be $110 if interest is not compounded, but will be greater than $110 if interest is

compounded.

Keywords: Time Value of Money, Compound Interest

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

14) At an annual interest rate of 9%, an initial sum of money will double approximately every 8 years.

Keywords: Time Value of Money

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

15) A car manufacturer offers either $2,000 cash back or zero percent financing for 5 years. A rational

consumer will always take the cash back because money received today is worth more than money

received in the future.

Keywords: Time Value of Money, Present Value

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

16) The present value of a single future sum of money is inversely related to both the number of years

until payment is received and the discount rate.

Keywords: Present Value, Single Sum, Discount Rate

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

17) The same underlying formula is used for computing both the future value and present value.

Keywords: Present Value, Future Value

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

18) Artificially low interest rates helped create the housing bubble because low interest rates (r value)

create higher values (higher PVs).

Keywords: Interest Rates, Present Value, Time Value of Money

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

19) Tim invested $1,000 in a mutual fund paying 8% per year. John invested $500 in the same fund. If

both Tim and John keep their money invested for the same period of time, Tim will end up with twice as

much money as John.

Keywords: Future Value, Lump Sum

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

20) Suppose a corporation can change its depreciation method so that its tax payments will decrease by

$5,000 this year but increase by $5,000 next year.

A) The change will have no impact on the value of the company because its cash flow over time will be

the same.

B) The change will decrease the value of the company because investors don‘t like changes in accounting

methods.

C) The change will decrease the value of the company because lower tax payments this year result from

lower reported income.

D) The change will increase the value of the company because the value of the cash savings this year

exceeds the cost of the cash payments next year.

Keywords: Time Value of Money, Depreciation

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

21) The present value of a single future sum

A) increases as the number of discount periods increases.

B) is generally larger than the future sum.

C) depends upon the number of discount periods.

D) increases as the discount rate increases.

Keywords: Present Value

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

22) U.S. Savings Bonds are sold at a discount. The face value of the bond represents its value on its future

maturity date. Therefore,

A) the current price of a $50 face value bond that matures in 10 years will be greater than the current price

of a $50 face value bond that matures in 5 years.

B) the current price of a $50 face value bond that matures in 10 years will be less than the current price of

a $50 face value bond that matures in 5 years.

C) the current prices of all $50 face value bonds will be the same, regardless of their maturity dates

because they will all be worth $50 in the future.

D) the current price of a $50 face value bond will be higher if interest rates increase.

Keywords: Time Value of Money, Present Value

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

23) The present value of $1,000 to be received in 5 years is ________ if the discount rate is 12.78%.

A) $368

B) $494

C) $548

D) $687

Keywords: Present Value, Discount Rate

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

24) You decide you want your child to be a millionaire. You have a son today and you deposit $10,000 in

an investment account that earns 7% per year. The money in the account will be distributed to your son

whenever the total reaches $1,500,000. How old will your son be when he gets the money (rounded to the

nearest year)?

A) 82 years

B) 74 years

C) 60 years

D) 49 years

Keywords: Future Value

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

25) At what rate must $287.50 be compounded annually for it to grow to $650.01 in 14 years?

A) 6 percent

B) 5 percent

C) 7 percent

D) 8 percent

Keywords: Future Value

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

26) Assuming two investments have equal lives, a high discount rate tends to favor

A) the investment with large cash flow early.

B) the investment with large cash flow late.

C) the investment with even cash flow.

D) neither investment since they have equal lives.

Keywords: Time Value of Money, Discount Rate

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

27) What is the present value of $11,463 to be received 7 years from today? Assume a discount rate of

3.5% compounded annually and round to the nearest $1.

A) $5,790

B) $6,508

C) $7,210

D) $9,010

Keywords: Present Value

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

28) How much money must be put into a bank account yielding 6.42% (compounded annually) in order

to have $1,671 at the end of 11 years (round to nearest $1)?

A) $921

B) $886

C) $843

D) $798

Keywords: Present Value

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

29) Biff deposited $9,000 in a bank account, and 10 years later he closes out the account, which is worth

$18,000. What annual rate of interest has he earned over the 10 years?

A) 6.45%

B) 7.18%

C) 9.10%

D) 10.0%

Keywords: Interest Rates, Time Value of Money

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

30) How much money do I need to place into a bank account that pays a 1.08% rate in order to have $500

at the end of 7 years?

A) $332.54

B) $751.81

C) $463.78

D) $629.51

Keywords: Present Value

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

31) You plan to go to Asia to visit friends in three years. The trip is expected to cost a total of $10,000 at

that time. Your parents have deposited $5,000 for you in a Certificate of Deposit paying 6% interest

annually, maturing three years from now. Uncle Lee has agreed to pay for all remaining expenses. If you

are going to put Uncle Lee’s gift in an investment earning 10% over the next three years, how much must

he deposit today, so you can visit your friends three years from today?

A) $3,757

B) $3,039

C) $5,801

D) $3,345

Keywords: Future Value, Present Value

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

32) A zero coupon bond pays no annual coupon interest payments. When it matures at the end of 7.5

years it pays out $1,000. If investors wish to earn 2.35% per year on this bond investment, what is the

current price of the bond? (Round to the nearest dollar.)

A) $533

B) $561

C) $875

D) $840

Keywords: Present Value, Zero Coupon Bond

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

33) Which of the following conclusions would be true if you earn a higher rate of return on your

investments?

A) The greater the present value would be for any lump sum you would receive in the future.

B) The lower the present value would be for any lump sum you would receive in the future.

C) Your rate of return would not have any effect on the present value of any sum to be received in the

future.

D) The greater the present value would be for any annuity you would receive in the future.

Keywords: Time Value of Money, Present Value, Discount Rate

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

34) You have a savings bond that will be worth $750 when it matures in 3 years, but you need cash today.

If the current going rate of interest is 5%, what is your bond worth if you sell it today (rounded to the

nearest dollar)?

A) $675

B) $648

C) $625

D) $612

Keywords: Present Value, Bond

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

35) A bond maturing in 10 years pays $80 each year (including year 10) and $1,000 upon maturity.

Assuming 10 percent to be the appropriate discount rate, the present value of the bond is

A) $877.11.

B) $1,000.00.

C) $416.39.

D) $1,785.67.

Keywords: Present Value, Annuity, Single Sum, Bond

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

36) Your parents are complaining about the price of items today compared to what they cost years ago. If

an automobile that cost $12,000 in 1980 costs $40,000 in 2010, calculate the annual growth rate in the

automobile’s price.

Keywords: Annual Growth Rate, Present Value, Future Value

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

37) You borrow $30,000 and agree to pay it off with one lump sum payment of $40,000 in 6 years. What

annual rate of interest will you be charged?

Keywords: Time Value of Money, Annual Rate of Interest

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

38) You just invested $50,000 into an account that earns 7 percent compounded annually. At the end of

each year you can withdraw $4,971. How many years can you continue to make the withdrawals?

Keywords: Time Value of Money, Number of Periods

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

39) Bill wants to buy a new boat in 7 years. He expects the new boat will cost $28,000. Bill has $18,000 in

an investment account today. What rate of return must Bill earn on his investments to be able to buy the

boat on time?

Keywords: Future Value, Present Value, Interest Rate, Time Value of Money

Learning Obj.: L.O. 5.1

AACSB: Analytical Thinking

40) How does compound interest differ from simple interest?

Answer: Compound interest occurs when interest paid on the investment during the first period is

added to the principal; then, during the second period, interest is earned on this new sum. The situation

in which interest is earned on interest that was earned in the past is referred to as compound interest. If

you only earned interest on your initial investment, it would be referred to as simple interest.

Diff: 1 Page Ref: 155, 156

Keywords: Simple Interest, Compound Interest

Learning Obj.: L.O. 5.1

AACSB: Reflective Thinking

Learning Objective 5.2

1) If the future value of annuity A is greater than the future value of annuity B, then the present value of

annuity A must also be greater than the present value of annuity B.

Keywords: Time Value of Money, Annuity Due, Ordinary Annuity

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

2) The future value of an annuity will increase if the interest rate goes up, but the present value of the

same annuity will decrease as the interest rate goes up.

Keywords: Time Value of Money, Annuity

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

3) If the future value of an annuity is known, then the present value of the annuity can be found using the

present value of a lump sum formula, even if the amount of each annuity payment is unknown.

Keywords: Time Value of Money, Annuity

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking

4) If the interest rate is positive, then the future value of an annuity due will be greater than the future

value of an ordinary annuity.

Keywords: Time Value of Money, Annuity, Annuity Due

Learning Obj.: L.O. 5.2

AACSB: Analytical Thinking