978-1305637108 Chapter 4 Solution Manual Part 1

Answers and Solutions: 4 -1

or in part.

Chapter 4

Time Value of Money

4-1 a. PV (present value) is the value today of a future payment, or stream of payments,

discounted at the appropriate rate of interest. PV is also the beginning amount that

will grow to some future value. The parameter i is the periodic interest rate that an

account pays. The parameter INT is the dollars of interest earned each period. FVn

(future value) is the ending amount in an account, where n is the number of periods

the money is left in the account. PVAn is the value today of a future stream of equal

payments (an annuity) and FVAn is the ending value of a stream of equal payments,

where n is the number of payments of the annuity. PMT is equal to the dollar amount

of an equal, or constant cash flow (an annuity). In the EAR equation, m is used to

denote the number of compounding periods per year, while iNom is the nominal, or

quoted, interest rate.

b. The opportunity cost rate (i) of an investment is the rate of return available on the best

alternative investment of similar risk.

c. An annuity is a series of payments of a fixed amount for a specified number of

periods. A single sum, or lump sum payment, as opposed to an annuity, consists of

one payment occurring now or at some future time. A cash flow can be an inflow (a

d. An ordinary annuity has payments occurring at the end of each period. A deferred

annuity is just another name for an ordinary annuity. An annuity due has payments

occurring at the beginning of each period. Most financial calculators will

f. An outflow is a deposit, a cost, or an amount paid, while an inflow is a receipt. A

time line is an important tool used in time value of money analysis; it is a graphical

Answers and Solutions: 4 – 2

or in part.

representation which is used to show the timing of cash flows. The terminal value is

the future value of an uneven cash flow stream.

g. Compounding is the process of finding the future value of a single payment or series

of payments. Discounting is the process of finding the present value of a single

payment or series of payments; it is the reverse of compounding.

h. Annual compounding means that interest is paid once a year. In semiannual,

quarterly, monthly, and daily compounding, interest is paid 2, 4, 12, and 365 times

per year respectively. When compounding occurs more frequently than once a year,

rate and the nominal rate are the same. If compounding occurs more frequently, the

effective annual rate is greater than the nominal rate. The nominal annual interest rate

is also called the annual percentage rate, or APR. The periodic rate, iPER, is the rate

charged by a lender or paid by a borrower each period. It can be a rate per year, per

is one that is repaid in equal periodic amounts (or “killed off” over time).

4-2 The opportunity cost rate is the rate of interest one could earn on an alternative

the riskiness and maturity of an investment, and it also varies from year to year

4-3 True. The second series is an uneven payment stream, but it contains an annuity of $400

or in part.

4-4 True, because of compounding effects—growth on growth. The following example

demonstrates the point. The annual growth rate is I in the following equation:

2. Using a financial calculator, input N = 10, I/YR = 10, PV = -1, PMT = 0, and FV = ?.

Solving for FV you obtain $2.59. This formulation recognizes the “interest on

4-5 For the same stated rate, daily compounding is best. You would earn more “interest on

interest.”

Answers and Solutions: 4 – 4

or in part.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

4-1 0 1 2 3 4 5

= $10,000(1.61051) = $16,105.10.

4-2 0 5 10 15 20

5000. Solve for PV = $1,292.10.

4-3 0 18

= 1000000. Solve for I/YR = 8.01% ≈ 8%.

4-4 0 N = ?

$2 = $1(1.065)N.

4-5 0 1 2 N – 2 N – 1 N

| | |    | | |

7%

6.5%

12%

I/YR = ?

10%

Answers and Solutions: 4 -5

4-6 Ordinary annuity:

0 1 2 3 4 5

Solve for FV = $1,725.22.

FVA5 = ?

4-7 0 1 2 3 4 5 6

| | | | | | |

screen.); CF6 = 500 (Note calculator will show CF4 on screen.); and I/YR = 8. Solve for

NPV = $923.98.

4-8 Using a financial calculator, enter the following: N = 60, I/YR = 1, PV = -20000, and FV

= 0. Solve for PMT = $444.89.

EAR =

M

NOM

M

I

1













– 1.0

= (1.01)12 – 1.0

= 12.68%.

Alternatively, using a financial calculator, enter the following: NOM% = 12 and P/YR =

12. Solve for EFF% = 12.6825%. Remember to change back to P/YR = 1 on

your calculator.

7%

8%

4-9 a. 0 1

| | $500(1.06) = $530.00.

6%

-500 FV = ?

c. 0 1

PV = ? 500

4-10 a. 0 1 2 3 4 5 6 7 8 9 10 $500(1.06)10 = $895.42.

| | | | | | | | | | |

-500 FV = ?

d. 0 1 2 3 4 5 6 7 8 9 10

| | | | | | | | | | | $500(1/1.12)10 = $160.99

6%

12%

Answers and Solutions: 4 -7

4-11 a. ?

| |

b. ?

| |

c. ?

| |

d. 100% ?

4-12

a. 0 1 2 3 4 5 6 7 8 9 10

| | | | | | | | | | |

400 400 400 400 400 400 400 400 400 400

FVA10 = ?

With a financial calculator, enter N = 10, I/YR = 10, PV = 0, and PMT = -400. Then

press the FV key to find FV = $6,374.97.

7%

10%

18%

10%

Answers and Solutions: 4 – 8

or in part.

With a financial calculator, enter N = 5, I/YR = 5, PV = 0, and PMT =

-200. Then press the FV key to find FV = $1,105.13.

c. 0 1 2 3 4 5

d. To solve Part d using a financial calculator, repeat the procedures discussed in Parts a,

b, and c, but first switch the calculator to “BEG” mode. Make sure you switch the

calculator back to “END” mode after working the problem.

(2) 0 1 2 3 4 5

| | | | | |

200 200 200 200 200 FVA5 = ?

With a financial calculator set to “BEG” mode, enter N = 5, I/YR = 0, PV = 0, and

PMT =

-400. Then press the FV key to find FV = $2,000.

0%

10%

5%

4-13

a. 0 1 2 3 4 5 6 7 8 9 10

| | | | | | | | | | |

PV = ? 400 400 400 400 400 400 400 400 400 400

With a financial calculator, enter N = 5, I/YR = 5, PMT = -200, and FV = 0. Then

press the PV key to find PV = $865.90.

d. (1) 0 1 2 3 4 5 6 7 8 9 10

| | | | | | | | | | |

400 400 400 400 400 400 400 400 400 400

| | | | | |

200 200 200 200 200

PV = ?

With a financial calculator set to “BEG” mode, enter N = 5, I/YR = 5, PMT = –

10%

(3) 0 1 2 3 4 5

4-14 a. Cash Stream A Cash Stream B

0 1 2 3 4 5 0 1 2 3 4 5

Override I = 8 with I = 0 to find the next PV for Cash Stream A. Repeat for Cash Stream

B to get NPV = PV = $1,300.32.

4-15 These problems can all be solved using a financial calculator by entering the known

values shown on the time lines and then pressing the I/YR button.

With a financial calculator, enter N = 1, PV = 700, PMT = 0, and FV = –749. Then

press the I/YR key to find I/YR = 7%.

With a financial calculator, enter N = 1, PV = -700, PMT = 0, and FV = 749. Then

0%

8%