Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
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 = ?
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
r = 4%
r = 6% …
r = 12% …
r = 3%
r = 1%
Interest payments
Interest payments
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
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
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
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
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
é ù
ê ú
ê ú
ë û
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
ê ú
ï ï
ë û
î þ
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.
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
r = 1% …
r = 7%
r = 7%
r = 8% …
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
é ù
ê ú
ê ú
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
ê ú
í ý
ê ú
ï ï
ê ú
ë û
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
é ù
ê ú
ê ú
ê ú
ë û
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
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
r = 11% …
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
ê ú
ë û
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
é ù
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
ë û
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
ê ú
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
é ù
ï ï
ê ú
í ý
ê ú
ï ï
ê ú
ë û
î þ
180
1
(1.006)
1-
PVA(DUE) = 150 (1.006) = 150(110.543773) = 16,581.57
0.006
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
r = 0.7% …
r = 0.5% …
r = 0.5% …
r = 0.6% …
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
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
r = 7.5%
r = 7.5%
r = 7.5%
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
ë û
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
ê ú
ë û
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
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
n
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
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
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
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
…
r = 0.5%
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
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible website, in whole or in part.
…
r = 0.25%
