978-1305661653 Chapter 4 Solutions Manual

Chapter 4 CFIN5

Chapter 4 Solutions

(Most solutions are rounded in the final answers, not in the intermediate computations.)

0 1 2 3 4

4-1

-700 FV = ?

0 1 2 14 15

4-2

-2,500 FV = ?

0 1 2 14 20

4-3 a.

-500 FV = ?

0 1 2 79 80

b.

-500 FV = ?

0 1 2 239 240

c.

-500 FV = ?

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r = 4%

r = 6% …

r = 12% …

r = 3%

r = 1%

Interest payments

…

Chapter 4 CFIN5

4-4 Staci’s investment:

0 1 2 59 60

-950 FV = ?

Shelli’s investment:

0 1 2 19 20

-900 FV = ?

0 1 2 13 14

4-5 a.

PV = ? FV14 = 1,500

0 1 2 13 14

b.

PV = ? FV14 = 1,500

PV = $1,500/(1.10)14 = $1,500(0.263331) = $395.00

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r = 0.6% Interest payments

r = 2% Interest payments

r = 5% Interest payments

…

r = 10% Interest payments

…

Chapter 4 CFIN5

0 1 2 11 12

4-6

PV = ? FV12 = 12,500

0 1 2 3 4 5

4-7 a.

PV = ? FV5 = 2,500

0 1 2 19 20

b.

PV = ? FV5 = 2,500

0 1 2 59 60

c.

PV = ? FV5 = 2,500

PV = $2,500/(1.0075)60 = $2,500(0.638700) = $1,596.75

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r = 7% Interest payments

…

r = 9%

r = 2.25% Interest payments

…

Interest payments

r = 0.75% Interest payments

…

Chapter 4 CFIN5

0 1 2 35 36

4-8

PV = ? FV3 = 22,000

0 1 2 3 4 5 6 7 8

4-9 a.

-385 -385 -385 -385 -385 -385 -385 -385

FVA8 = ?

8

(1.07) – 1

FVA = 385 = 385(10.259803) = 3,950.02

0.07

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Using a financial calculator, enter N = 8, I/Y= 7, PV = 0, and PMT = -385, compute FV = 3,950.02

0 1 2 3 4 5 6 7 8

b.

-385 -385 -385 -385 -385 -385 -385 -385

FVA(DUE)8 = ?

8

(1.07) – 1

FVA(DUE) = 385 ×(1.07) = 385(10.977989) = 4,226.53

0.07

ì ü

é ù

ï ï

ê ú

í ý

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ï ï

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Using a financial calculator, “flip the switch” to BGN, enter N = 8, I/Y= 7, PV = 0, and PMT = -385,

compute FV = 4,226.53

0 1 2 3 4 5 13 14

4-10 a.

-450 -450 -450 -450 -450 -450 -450

FVA14 = ?

14

(1.08) – 1

FVA = 450 = 450(24.214920) = 10,896.71

0.08

é ù

ê ú

ë û

Using a financial calculator, enter N = 14, I/Y= 8, PV = 0, and PMT = -450, compute FV = 10,896.71

0 1 2 3 4 5 13 14

b.

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r = 1% …

r = 7%

r = 8% …

Chapter 4 CFIN5

-450 -450 -450 -450 -450 -450 -450

FVA(DUE)14 = ?

14

(1.08)

(1.08) – 1

FVA(DUE) = 450 = 450(26.152114) = 11,768.45

0.08 ´

ì ü

é ù

í ý

ê ú

ë û

î þ

Using a financial calculator, “flip the switch” to BGN, enter N = 14, I/Y= 8, PV = 0, and PMT = -450,

compute FV = 11,768.45

0 1 2 3 4 5 14 15

4-11 a.

PVA = ? 230 230 230 230 230 230 230

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ê ú

ë û

15

1

(1.11)

1-

PVA = 230 = 230(7.190870) = 1,653.90

0.11

Using a financial calculator, enter N = 15, I/Y= 11, PMT = 230, and FV = 0; compute PV = 1,653.90

0 1 2 3 4 5 14 15

b.

230 230 230 230 230 230 230

PVA(DUE) = ?

15

1

(1.11) (1.11)

1-

PVA(DUE) = 230 = 230(7.981865) = 1,835.83

0.11

´

ì ü

é ù

ï ï

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í ý

ê ú

ï ï

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î þ

Using a financial calculator, “flip the switch” to BGN, enter N = 15, I/Y= 11, PMT = 230, and FV = 0;

compute PV = 1,835.83

0 1 2 3 4 5 107 108

4-12 a.

PVA = ? 450 450 450 450 450 450 450

108

1

(1.007)

1–

PVA = 450 = 450(75.602985) = 34,021.34

0.007

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Using a financial calculator, enter N = 9 x 12 = 108, I/Y= 8.4/12 = 0.7, PMT = 450, and FV = 0; compute

PV = -34,021.34

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r = 11% …

r = 0.7% …

Chapter 4 CFIN5

0 1 2 3 4 5 107 108

b.

450 450 450 450 450 450 450

PVA(DUE) = ?

108

1

(1.007)

1-

PVA(DUE) = 450 (1.007) = 450(76.132206) = 34,259.49

0.007 ´

ì ü

é ù

ï ï

ê ú

í ý

ê ú

ï ï

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î þ

Using a financial calculator, “flip the switch” to BGN, enter N = 108, I/Y= 0.7, PMT = 450, and FV = 0;

compute PV = -34,259.49

0 1 2 3 4 5 59 60

4-13 a.

-100 -100 -100 -100 -100 –100 -100

FVA = ?

60

(1.005) – 1

FVA = 100 = 100(69.770031) = 6,977.00

0.005

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ê ú

ë û

0 1 2 3 4 5 59 60

b.

-100 -100 -100 -100 -100 -100 –100

FVA(DUE) = ?

60

(1.005) – 1

FVA(DUE) = 100 (1.005) = 100(70.118881) = 7,011.89

0.005 ´

ì ü

é ù

í ý

ê ú

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î þ

Using a financial calculator, “flip the switch” to BGN, enter N = 60, I/Y= 0.5, PV = 0, and PMT = -100;

compute FV = 7,011.89

0 1 2 3 4 5 179 180

4-14 a.

PVA = ? 150 150 150 150 150 150 150

180

1

(1.006)

1-

PVA = 150 = 150(109.884466) = 16, 482.67

0.006

é ù

ê ú

ë û

Using a financial calculator, enter N = 15 x 12 = 180, I/Y=7.2/12 = 0.6, PMT = 150, and FV = 0; compute

PV = -16,482.67

0 1 2 3 4 5 179 180

b.

150 150 150 150 150 150 150

PVA(DUE) = ?

´

ì ü

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ï ï

ê ú

í ý

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180

1

(1.006)

1–

PVA(DUE) = 150 (1.006) = 150(110.543773) = 16,581.57

0.006

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r = 0.7% …

r = 0.5% …

r = 0.6% …

Chapter 4 CFIN5

0 1 2 3

4-15 a.

PVCF3 = ? 500 400 30

+

1 2 3

500 400 300

PVCF = + = 500(0.930233) + 400(0.865333) + 300(0.804961)

(1.075) (1.075) (1.075)

= 465.12 + 346.13 + 241.49 = 1,052.74

Using the cash flow register on a financial calculator, enter CF0 = 0, CF1 = 500, CF2 = 400, CF3 = 300,

and I = 7.5; compute NPV = 1,052.74

0 1 2 3

b.

500 400 300

+

0 1 2

500 400 300

PVCF = + = 500(1.000000) + 400(0.930233) + 300(0.865333)

(1.075) (1.075) (1.075)

= 500.00 + 372.09 + 259.60 = 1,131.69

Using the cash flow register on a financial calculator, enter CF0 = 500, CF1 = 400, CF2 = 300, and I = 7.5;

compute NPV = 1,131.69

0 1 2 3

4-16 a.

500 400 300

FVCF3 = ?

2 1 0

+FVCF = 500(1.075) + 400(1.075) 300(1.075)

= 500(1.155625) + 400(1.075000) + 300(1.000000)

= 577.81 + 430.00 + 300.00 = 1,307.81

Using the cash flow register on a financial calculator, enter CF0 = 0, CF1 = 500, CF2 = 400, CF3 = 300,

and I = 7.5; compute NPV = 1,052.74, and then compute the future value of the NPV—that is, FV =

1,052.74(1.075)3 = 1,307.82 (rounding)

0 1 2 3

b.

500 400 300

3 2 1

+FVCF = 500(1.075) + 400(1.075) 300(1.075)

= 500(1.242297) + 400(1.155625) + 300(1.075000)

= 621.15 + 462.25 + 322.50 = 1,405.90

Using the cash flow register on a financial calculator, enter CF0 = 500, CF1 = 400, CF2 = 300, and I = 7.5;

compute NPV = 1,131.69, and then compute the future value of the NPV—that is, FV = 1,131.69(1.075)3

= 1,405.89 (rounding)

0 1 2 3 4 5 -1 

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r = 7.5%

r = 4% …

Chapter 4 CFIN5

4-17 a.

PVP = ? 320 320 320 320 320 320 320

320

PVP = = 8,000.00

0.04

0 1 2 3 4 5 -1 

b.

PVP = ? 320 320 320 320 320 320 320

320

PVP = = 4,000.00

0.08

0 1 2 3 4 5 -1 

c.

PVP = ? 320 320 320 320 320 320 320

320

PVP = = 3,200.00

0.10

When more interest is earned during an investment period, less money must be invested today to

receive particular amounts in the future.

0 1 2 8 9 10

4-18

-1,250 3,550

n

10

110 0.10

1

FV PV (1 r)

1

3,550 1,250 (1 r)

3,550

r 1 (2.8400) 1 0.11 11.0%

1,250

é ù

=ê ú

+

ë û

é ù

=ê ú

+

ë û

é ù

= – = – = =

ê ú

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Using a calculator, enter N = 10, PV = -1,250, PMT = 0, and FV = 3,550; compute I/Y= 11%.

4-19 0 1 2 n-1 n Months

12,000 -526 -526 -526 -526

1

n

(1 r)

n

(1.004)

1

PVA PMT r

12,000 526 0.004

+

é ù

–

ê ú

=ê ú

ê ú

=ê ú

ê ú

ë û

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r = 8% …

r = 10% …

r = ? …

r = 0.4%

…

Chapter 4 CFIN5

Using a calculator, enter I/Y= 0.4, PV = 12,000, FV = 0, and PMT = -526; compute N = 23.97 ≈ 24

months, which equals two (2) years.

4-20 0 1 2 n-1 n Years

-2,260 4,750

n

Using a calculator, enter I/Y= 7, PV = -2,260, PMT = 0, and FV = 4,750; compute N = 10.98 ≈ 11 years.

Alternative solution (using logarithms):

n

4,750 2,260(1.07)

4,750

(1.07) 2.10177

2,260

ln[(1.07) ] ln(2.10177)

=

= =

=

Because ln[(1.07)n] = n[ln(1.07)], the solution is as follows:

n[ln(1.07)] ln(2.10177)

ln(2.10177) 0.74278

n 10.98

ln(1.0700) 0.06766

=

= = =

4-21 rEAR = (1 + r/m)m – 1.0

4-22 a. APR = 6.0%

b. rEAR = [1 + (0.06/12)]12 – 1.0 = (1.005)12 – 1.0 = 0.0617 = 6.17%

4-23 a. 0 1 2 119 120 Months

b. After three years of payments, William is faced with the following cash flow timeline:

0 1 2 83 84 Months

PVA = ? 511 511 511 511

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r = 7%%

…

r = 0.35%

…

r = 0.35%

Chapter 4 CFIN5

1

84

(1.0035)

1

PVA 510.99 0.0035

510.99(72.668817) 37,133.04

é ù

–

ê ú

=ê ú

ê ú

ë û

= =

4-24 a. 0 1 2 359 360 Months

PVA = 220,000 PMT PMT PMT PMT

1

360

(1.005)

1

PVA 220,000 PMT 0.005

220,000

PMT 1,319.01

166.791614

é ù

–

ê ú

= = ê ú

ê ú

ë û

= =

Calculator solution: N = 360, I/Y= 6/12 = 0.5, PV = 220,000, and FV = 0; PMT = ? = -1,319.01.

b. Because it is 12 years after she bought the house, Sarah Jean has 216 = (30 – 12) x 12 payments

remaining and she is now faced with the following cash flow timeline:

0 1 2 215 216 Months

4-25 a. 0 1 2 59 60 Months

PVA = 32,000 PMT PMT PMT PMT

1

60

(1.0025)

1

PVA 32,000 PMT 0.0025

32,000

PMT 575.00

55.652358

é ù

–

ê ú

= = ê ú

ê ú

ë û

= =

Calculator solution: N = 60, I/Y= 3/12 = 0.25, PV = 32,000, and FV = 0; PMT = ? = -575.00

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…

r = 0.5%

…

r = 0.25%

…

Chapter 4 CFIN5

b. After making 24 payments, Nona would have 36 payments remaining and she would be faced with

the following cash flow timeline:

0 1 2 35 36 Months

PVA = ? 575 575 575 575

1

36

(1.0025)

1

PVA 575 0.0025

575(34.386465) 19,772.22

é ù

–

ê ú

=ê ú

ê ú

ë û

= =

Calculator solution: N = 36, I/Y= 3/12 = 0.25, PMT = 575, FV = 0; PV = ? = -19,772.22

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…

r = 0.25%