Module 4 Solutions
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University of Texas *
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3320
Subject
Finance
Date
Jan 9, 2024
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25
Uploaded by Anatre
Chapter 9, 10, and 11 Solutions
Chapter 9 Solutions
9-1
Calculator solution: N = 6, I/Y = 10, PMT = 36,950, FV = 0; PV = ? = -160,926.88
9-2
a.
Calculator solution: N = 4, I/Y = 16, PMT = 104,400, FV = 0; PV = ? = -292,130.06
b.
Calculator solution: N = 4, I/Y = 12, PMT = 104,400, FV = 0; PV = ? = -317,099.27
9-3
Calculator solution:
CF
0
= -3,600,000, CF
1
–
CF
10
=600,000, I = 11;
compute NPV = -66,460.79; IRR = 10.56%
Alternative calculator solution using TVM keys:
N = 10, PV = -3,600,000, PMT = 600,000, FV = 0; compute I/Y = 10.56% = IRR
The investment is not acceptable, because NPV < 0 and IRR < r = 11%.
9-4
Calculator solution:
CF0 = -42,000, CF1
–
CF10 =11,000, I = 9; compute NPV = 786.16; IRR = 9.72%
Alternative calculator solution using TVM keys:
N = 5, PV = -42,000, PMT = 11,000, FV = 0; compute I/Y = 9.72% = IRR
The investment is acceptable, because NPV > 0 and IRR > r = 9%.
9-5
Calculator solution: CF
0
= -20,070, CF
1
–
CF
3
= 8,500; compute IRR = 13.0%
Alternative calculator solution using TVM keys: N = 3, PV = -20,070, PMT = 8,500, FV = 0; compute
I/Y = 13.0% = IRR
9-6
Calculator solution: CF
0
= -74,000, CF
1
–
CF
6
= 16,500; compute IRR = 9.0%
Alternative calculator solution using TVM keys:
N = 6, PV = -74,000, PMT = 16,500, FV = 0; compute I/Y = 9.0% = IRR
9-7
a.
Calculator solution: CF
0
= -75,000, CF
1
–
CF
4
= 26,000, I = 14; compute NPV = 756.52
b.
Calculator solution: CF
0
= -75,000, CF
1
–
CF
4
= 26,000; compute IRR = 14.49%
Alternative calculator solution:
N = 4, PV = -75,000, PMT = 26,000, FV = 0; compute I/Y = 14.49%
c.
Because IRR > r = 14% and NPV > 0, the project is acceptable.
9-8
a.
Calculator solution: CF
0
= -34,000, CF
1
–
CF
3
= 14,150, I = 12; compute NPV = -14.09
9-8
b.
Calculator solution: CF
0
= -34,000, CF
1
–
CF
3
= 14,150; compute IRR = 11.98%
Alternative calculator solution:
N = 3, PV = -34,000, PMT = 14,150, FV = 0; compute I/Y = 11.98%
c.
Because IRR < r = 12% and NPV < 0, the project is not acceptable; but, just barely.
9-9
Data for NPV profile: Cost = 64,000, CF = 18,200 for five years
r
NPV
r
NPV
0.00
$27,000.00
0.10
4,992.32
0.01
24,332.45
0.11
3,265.33
0.02
21,784.96
0.12
1,606.93
0.03
19,350.67
0.13
13.61
0.04
17,023.17
0.14
(1,517.93)
0.05
14,796.48
0.15
(2,990.78)
0.06
12,665.02
0.16
(4,407.86)
0.07
10,623.59
0.17
(5,771.90)
0.08
8,667.32
0.18
(7,085.49)
0.09
6,791.65
0.10
4,992.32
9-10.
MIRR:
PV of Cash
FV in Year 3 of
Year
CF
Outflows @ 12%
Cash Inflows @ 12%
0
(82,000)
(82,000.00)
1
35,000
43,904.00
2
70,000
78,400.00
3
(10,450)
(7,438.10)
(89,438.10)
122,304.00
Calculator solution
N =3, PV = -89,438.10, PMT = 0, FV = 122,304; compute I/Y = 11.0% = MIRR
The investment is not acceptable, because MIRR < r = 12%.
9-11
Calculator solution: CF
0
= -5,500, CF
1
–
CF
4
= 1,800; compute IRR = 11.72%
Alternative calculator solution:
N = 4, PV = -5,500, PMT = 1,800, FV = 0; compute I/Y = 11.72%
Calculator solution:
N =4, PV = -5,500, PMT = 0, FV = 8,111; compute I/Y = 10.20% = MIRR
Required Rate of
Return, r (%)
NPV ($)
IRR
13%
The investment is acceptable, because MIRR = 10.2% > r = 8%.
9-12
Calculator solution: CF
0
= -90,000, CF
1
–
CF
2
= 54,000; compute IRR = 13.07%
Alternative calculator solution:
N = 2, PV = -90,000, PMT = 54,000, FV = 0; compute I/Y = 13.07%
Calculator solution:
N =2, PV = -90,000, PMT = 0, FV = 112,860; compute I/Y = 11.98% = MIRR
The investment is acceptable, because MIRR > r = 9% and IRR > r = 9%
9-13
Traditional payback:
Year
CF
CF
0
-270,000
-270,000
1
75,000
-195,000
2
75,000
-120,000
3
75,000
-45,000
4
75,000
30,000
5
75,000
105,000
45,000
PB
3
3.6 years
75,000
=
+
=
Alternative solution:
Because the future cash flows represent an annuity, PB can be computed as follows:
270,000
PB
3.6 years
75,000
=
=
Discounted payback:
Year
CF
PV of CF @ 11%
PV of CF
0
(270,000)
(270,000.00)
(270,000.00)
1
75,000
67,567.57
(202,432.43)
2
75,000
60,871.68
(141,560.75)
3
75,000
54,839.35
(86,721.40)
4
75,000
49,404.82
(37,316.57)
5
75,000
44,508.85
7,192.28 = NPV
37,316.57
DPB
4
4.84 years
44,508.58
=
+
=
Because DPB < 5, the project should be purchased.
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9-14
Traditional payback:
Year
CF
CF
0
-64,000
-64,000
1
16,000
-48,000
2
16,000
-32,000
3
16,000
-16,000
4
16,000
0
5
16,000
16,000
6
16,000
32,000
0
PB
4
4.0 years
16,000
=
+
=
Alternative solution:
Because the future cash flows represent an annuity, PB can be computed as follows:
64,000
PB
4.0 years
16,000
=
=
Discounted payback:
Year
CF
PV of CF @ 12%
PV of C
0
(64,000)
(64,000.00)
(64,000.00)
1
16,000
14,285.71
(49,714.29)
2
16,000
12,755.10
(36,959.18)
3
16,000
11,388.48
(25,570.70)
4
16,000
10,168.29
(15,402.41)
5
16,000
9,078.83
(6,323.58)
6
16,000
8,106.10
1,782.52 = NPV
6,323.58
DPB
5
5.78 years
8,106.10
=
+
=
Because DPB < 6, the project should be purchased.
9-15
a.
CF
0
= -365,000, CF
1
= 260,000, CF
2
= 175,000, I = 13
→
CPT NPV = 2,139.17
b.
Calculator:
CF
0
= -365,000, CF
1
= 260,000, CF
2
= 175,000, I = 13; IRR
→
CPT = 13.48%
c.
Calculator solution: N =2, PV = -365,000, PMT = 0, FV = 468,800;
CPT I/Y = 13.33% = MIRR
The investment is acceptable, because MIRR > r = 13%.
9-16
Project Alpha:
a.
NPV: CF
0
= -270,000, CF
1-3
= 120,000, I = 14;
CPT NPV = 8,595.84
b.
Calculator:
CF
0
= -270,000, CF
1-3
= 120,000; compute IRR = 15.89%
Alternative calculator solution:
N = 3, PV = -270,000, PMT = 120,000, FV = 0;
→
compute I/Y = 15.89%
c.
Discounted payback:
Year
CF
PV of CF @ 12%
PV of C
0
(270,000)
(270,000.00)
(270,000.00)
1
120,000
105,263.16
(164,736.84)
2
120,000
92,336.10
(72,400.74)
3
120,000
80,996.58
8,595.84 = NPV
72,400.74
DPB
2
2.89 years
80,996.58
=
+
=
Project Beta:
a.
Calculator solution: CF
0
= -300,000, CF
1
= 0, CF
2
= -80,000, CF
3
= 555,000, I = 14;
compute NPV = 13,051.79
b.
Calculator solution:
CF
0
= -300,000, CF
1
= 0, CF
2
= -80,000, CF
3
= 555,000, I = 14; compute IRR = 15.53
c.
Discounted payback:
Year
CF
PV of CF @ 12%
PV of C
0
(300,000)
(300,000.00)
(300,000.00)
1
0
0.00
(300,000.00)
2
(80,000)
(61,557.40)
(361,557.40)
3
555,000
374,609.19
13,051.79 = NPV
361,557.40
DPB
2
2.97 years
374,609.19
=
+
=
Summary of computations
Project
NPV
IRR
DPB
Alpha
$8,595.84
15.89%
2.89 years
Beta
$13,051.79
15.53%
2.97 years
If the projects are independent, both should be purchased, because NPV > 0 for both projects. If the projects
are mutually exclusive, Project Beta should be purchased, because NPV
Beta
> NPV
Alpha
.
9-17
Project AB:
a.
Calculator solution: CF
0
= -90,000, CF
1-3
= 39,000, I = 13; compute NPV = 2,084.95
b.
Calculator solution: CF
0
= -90,000, CF
1-3
= 39,000; compute IRR = 14.36%
Alternative calculator solution:
N = 3, PV = -90,000, PMT = 39,000, FV = 0; compute I/Y = 14.36%
c.
Calculator solution
N = 3, PV = -90,000, PMT = 0, FV = 39,000; compute I/Y = 13.87% = MIRR
d.
Discounted payback:
Year
CF
PV of CF @ 13%
PV of C
0
(90,000)
(90,000.00)
(90,000.00)
1
39,000
34,513.27
(55,486.73)
2
39,000
30,542.72
(24,944.01)
3
39,000
27,028.96
2,084.95 = NPV
=
+
=
24,944.01
DPB
2
2.92 years
27,028.96
Project LM:
a.
Calculator solution
CF
0
= -100,000, CF
1-2
= 0, CF
3
= 147,500, I = 13; compute NPV = 2,224.90
b.
Calculator
CF
0
= -100,000, CF
1-2
= 0, CF
3
= 147,500, I = 13; compute IRR = 13.83%
Alternative calculator solution:
N = 3, PV = -100,000, PMT = 0, FV = 147,500; compute I/Y = 13.83%
c.
Calculator solution:
N = 3, PV = -100,000, PMT = 0, FV = 147,500; compute I/Y = 13.83% = MIRR
d.
Discounted payback:
Year
CF
PV of CF @ 13%
PV of CF
0 (100,000)
(100,000.00)
(100,000.00)
1
0
0.00
(100,000.00)
2
0
0.00
(100,000.00)
3
147,500
102,224.90
2,224.90 = NPV
=
+
=
100,000.00
DPB
2
2.98 years
102,224.90
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Project UV:
a.
Calculator solution
CF
0
= -96,500, CF
1
= -55,000, CF
2-3
= 100,000, I = 13; compute NPV = 2,447.12
b.
Calculator solution
CF
0
= -96,500, CF
1
= -55,000, CF
2-3
= 100,000; compute IRR = 13.89%
c.
Calculator solution
N = 3, PV = -145,172.57, PMT = 0, FV = 213,000; compute I/Y = 13.63% = MIRR
d.
Discounted payback:
Year
CF
PV of CF @ 13%
PV of C
0
(96,500)
(96,500.00)
(96,500.00)
1
(55,000)
(48,672.57)
(145,172.57)
2
100,000
78,314.67
(66,857.90)
3
100,000
69,305.02
2,447.12 = NPV
=
+
=
66,857.90
DPB
2
2.96 years
69,305.02
Summary of computations
Project
NPV
IRR
MIRR
DPB
AB
$2,084.95
14.36%
13.87%
2.92 years
LM
2,224.90
13.83
13.83%
2.98 years
UV
2,447.12
13.89
13.63%
2.96 years
If the projects are independent, all should be purchased, because NPV > 0 for all of the projects.
If the projects are mutually exclusive, Project UV should be purchased, because
NPV
UV
> NPV
LM
> NPV
AB
.
9-18
Calculator solution
CF
0
= -16,000, CF
1
= 14,000, CF
2
= 6,000, I = 16; compute NPV = 527.94
Calculator solution
CF
0
= -15,000, CF
1
= 2,000, CF
2
= 18,600, I = 16; compute NPV = 546.97
NPV
T
= 546.97 > NPV
S
= 527.94, thus Project T is the project that should be purchased.
Calculator solution
CF
0
= -15,000, CF
1
= 2,000, CF
2
= 18,600, compute IRR = 18.22%
Note:
Students who use the projects’ IRRs to determine which project should be purchased would
choose Project S, because its IRR is 19.01 percent (Calculator solution: CF
0
= -16,000, CF
1
=
14,000, CF
2
= 6,000, compute IRR = 19.01%); thus, IRR
S
> IRR
T
. But, Project S should not be
purchased because its NPV is lower than Project T’s NPV; that is NPV
S
< NPV
T
.
9-19
a.
Because they are independent and both projects have positive NPVs, both projects are
acceptable.
b.
When a project has a positive NPV, we know that it is acceptable using both the NPV technique
and the IRR technique. Thus, IRR > r for both projects, which means that we can conclude the
firm’s required rate of return, r, is less than 15.5 percent (the
lower IRR).
9-20
a.
Because all of the capital budgeting techniques listed in the table are based on time value of
money (TVM) concepts, they all must agree with respect to the accept/reject decision. The
projects Albert and Kenny evaluated are acceptable, and therefore should be purchased. As a
result, for both projects, the following must exist:
NPV > 0
IRR > r
DPB < Project’s life
Although the firm’s required rate of return is not given, the other two relationships do indeed
exist. Because Albert and Kenny seem to have reported correct results, Josie’s report must have
the error.
If a project is not acceptable, then NPV < 0 and DPB >
Project’s life. For her project, Josie
reports that NPV < 0, which is correct; but the number that she reports for the project’s
discounted payback period indicate DPB = 5.8 years, which is less than the project’s life of 6
years. This is the error, becaus
e when NPV < 0, DPB > Project’s life, which means that the DPB
Josie reports should be greater than six years.
b.
Because IRR > r when a project is acceptable, and IRR < r when a project is not acceptable, the
firm’s required rate of return must be greater than 8 percent (Josie’s project is not acceptable) but
less than 10 percent (Kenny’s project is acceptable).
That is, 8% < r < 10%.
Chapter 10 Solutions
10-1
a.
1
3
Operating income before depreciation
$25,000
$25,000
Depreciation*
(19,800)
(
9,000)
NOI
5,200
16,000
Taxes (0.40)
(
2,080)
(
6,400)
After-tax NOI
$
3,120
$
9,600
*Depreciation, based on MACRS 3-year class:
Depreciation in Year 1 = $60,000(0.33) = $19,800
Depreciation in Year 3 = $60,000(0.15) = $
9,000
b.
1
3
After-tax NOI
$
3,120
$
9,600
ADD: depreciation (non-cash expense)
19,800
9,000
Operating cash flow
$22,920
$18,600
Alternative computation:
Operating income before depreciation
$25,000
$25,000
Taxes
(
2,080)
(6,400)
Operating cash flow
$22,920
$18,600
10-2
a & b
1
2
3
4
Sales
$92,000
$92,000
$92,000
$92,000
Operating costs (0,75 x Sales)
(69,000)
(69,000)
(69,000)
(69,000)
Depreciation
(49,500)
(67,500)
(22,500)
(10,500)
NOI
(26,500)
(44,500)
500
12,500
Interest
0
0
0
0
Taxable income
(26,500)
(44,500)
500
12,500
Taxes (0.35)
9,275
15,575
(
175)
( 4,375)
NI
$(17,225)
$(28,925)
$
325
$
8,125
ADD: Depreciation
49,500
67,500
22,500
10,500
Operating CF
$32,275
$38,575
$22,825
$18,625
Annual Depreciation:
Depreciable basis
$150,000
Depreciation rates
0.33
0.45
0.15
0.07
Depreciation amount
$49,500
$67,500
$22,500
$10,500
Alternative solution for operating cash flows:
Sales
$92,000
$92,000
$92,000
$92,000
Cash operating costs
(69,000)
(69,000)
(69,000)
(69,000)
Taxes
9,275
15,575
(
175)
(
4,375)
Operating CF
$32,275
$38,575
$22,825
$18,625
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10-3
Purchase price
$(350,000)
Shipping cost
(
20,000)
Installation cost
(
50,000)
Depreciable basis $420,000
Year
Depreciation: MACRS 3-year class
1
$138,600 = $420,000 x 0.33
2
$189,000 = $420,000 x 0.45
3
$
63,000 = $420,000 x 0.15
4
$
29,400 = $420,000 x 0.07
5
$
0 = $420,000 x 0.00 (asset was fully depreciated after Year 4)
10-4
Purchase price
$(500,000)
Shipping & installation costs
(
75,000)
Depreciable basis
$575,000
Year
Depreciation: MACRS 5-year class
1
$115,000 = $575,000 x 0.20
2
$184,000 = $575,000 x 0.32
3
$109,250 = $575,000 x 0.19
4
$
69,000 = $575,000 x 0.12
5
$
63,250 = $575,000 x 0.11
10-5
a. Purchase price
$(214,000)
Installation
(
26,000)
Depreciable basis
$(240,000)
Year
Depreciation: MACRS 5-year class
1
$48,000 = $240,000 x 0.20
2
$76,800 = $240,000 x 0.32
3
$45,600 = $240,000 x 0.19
4
$28,800 = $240,000 x 0.12
b.
Selling price at the end of four years = $80,000
Book value at the end of four years
= $240,000 - $48,000 - $76,800 - $45,600 - $28,800 = $40,800
Alternative computation of Book Value:
83 percent of the depreciable basis has been depreciated, so 17 percent remains, i.e.,
0.17 = 1.00
–
0.20
–
0.32
–
0.19
–
0.12.
Thus, the depreciable basis is $40,800 = $240,000(0.17).
Gain on sale = $80,000 - $40,800 = $39,200
Tax on gain = $39,200(0.40) = $15,680
Net cash flow from sale = $80,000 - $15,680 = $64,320
10-6
Because the depreciation expense is the same each year, the supplemental operating cash flow will be the same
for every year.
Operating savings
$110,000
Depreciation
(
84,000) = ($840,000 - $0)/10
NOI
26,000
Taxes (0.34)
(
8,840)
After-tax NOI
17,160
ADD: Depreciation
84,000
Supplemental operating cash flows
$101,160
Alternative computation:
Operating savings
$110,000
Taxes
(
8,840)
Supplemental operating cash flows
$101,160 = $110,000(1
–
0.34) + 0.34($84,000)
10-7
Depreciable basis =$120,000
1
2
3
4
Percent depreciated*
0.33
0.45
0.15
0.07
Depreciation
$39,600
$54,000
$18,000
$8,400
*(3-year MACRS)
1
2
3
4
Savings
$30,000
$30,000
$30,000
$30,000
Depreciation
(39,600)
(54,000)
(18,000)
(
8,400)
NOI
(9,600)
(24,000)
12,000
21,600
Taxes (0.35)
3,360
8,400
(
4,200)
(7,560)
After-tax NOI
(6,240)
(15,600)
7,800
14,040
ADD: Depreciation
39,600
54,000
18,000
8,400
Supplemental operating CF $33,360
$38,400
$25,800
$22,440
Alternative computation:
Savings
$30,000
$30,000
$30,000
$30,000
Taxes
3,360
8,400
(
4,200)
(
7,560)
Supplemental operating CF $33,360
$38,400
$25,800
$22,440
10-8
a.
Old Lathe
New Lathe
Difference
NOI, excluding depreciation
$90,000
$90,000
$
0
Depreciation
(40,000)
(35,000)
5,000
NOI
50,000
55,000
5,000
Interest
(
0)
(
0)
0
Earnings before taxes (EBT)
50,000
55,000
5,000
Taxes (0.40)
(20,000)
(22,000)
(2,000)
Net income
$30,000
$33,000
$3,000
b.
Old Lathe
New Lathe
Difference
Net income
$30,000
$33,000
$3,000
Depreciation
40,000
35,000
(5,000)
Supplemental operating CF
$70,000
$68,000
$(2,000)
Alternative solution:
NOI, excluding depreciation
$90,000
$90,000
$
0
Taxes (0.40)
(20,000)
(22,000)
(2,000)
Supplemental operating CF
$70,000
$68,000
$(2,000)
∆NI = ∆NOI(1 –
T) = $5,000(1 - 0.4) = $3,000
∆Supplemental operating CF = ∆Deprec
iation(T) = -$5,000(1 - 0.4) = -$2,000
10-9
Selling price = $102,000 ///
Book value = $90,000
a.
Gain on sale of machine = $102,000 - $90,000 = $12,000
b.
Tax on sale of machine = $12,000(0.40) = $4,800
After-tax cash flow from sale = $102,000 - $4,800 = $97,200
10-10 Selling price = $4,000
///
Book value = $6,000
a.
Gain on sale of machine = $4,000 - $6,000 =
–
$2,000
Tax on sale of machine = -$2,000(0.35) =
–
$700, which represents a tax refund
b.
After-tax cash flow from sale = $4,000
–
(
–
$700) = $4,700
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10-11 Purchase price $(432,000)
Installation
(
52,000)
Increase in net working capital
(
22,000)
Initial investment outlay
$(506,000)
Depreciable basis = $432,000 + $52,000 = $484,000
Supplemental operating cash flows:
1
2
3
Savings
$185,000
$185,000
$185,000
Depreciation
(159,720)
(217,800)
(
72,600)
NOI
25,280
(
32,800)
112,400
Taxes (0.40)
(
10,112)
13,120
(
44,960)
After-tax NOI
15,168
(
19,680)
67,440
ADD: Depreciation
159,720
217,800
72,600
Supplemental operating CF
$174,888
$198,120
140,040
Depreciation %
0.33
0.45
0.15
Depreciation = $484,000 x Deprec %
$159,720
$217,800
$72,600
Alternative solution:
1
2
3
Savings
$185,000
$185,000
$185,000
Taxes (0.40)
(
10,112)
13,120
(
44,960)
Supplemental operating CF
$174,888
$198,120
140,040
Terminal cash flow:
•
Selling price = $220,000
•
Book value = $484,000(1.0
–
0.33
–
0.45
–
0.15) = $484,000(0.07) = $33,880
•
Gain on sale of machine = $220,000 - 33,800 = $186,120
•
Tax on sale of machine = $186,120(0.40) = $74,448
•
After-tax cash flow from sale = $220,000
–
$74,448 = $145,552
•
Terminal CF = $145,552 + $22,000 = $167,552
Cash flow timeline:
Financial calculator solution:
CF
0
=-506,000
//
CF
1
= 174,888
//
CF
2
= 198,120
//
CF
3
= 307,592
I = 14
//
NPV =7,473.27
//
IRR = 14.8%
NPV > 0,
→
setter should be purchased.
0
1
2
3
(506,000.00)
174,888
198,120
140,040
167,552
307,592
r = 14%
153,410.53
152,446.91
207,615.84
7,473.28 = NPV //
IRR = 14.8%
10-12 Initial investment outlay = Purchase price = $90,000
Supplemental operating cash flows:
1
2
3
4
5
Increase in operating income
$29,800 $29,800
$29,800
$29,800
$29,800
Depreciation
(29,700) (40,500)
(13,500)
(
6,300)
0
NOI
100
(10,700)
16,300
23,500
29,800
Taxes (0.34)
(
34)
3,638
(
5,542)
(
7,990)
(10,132)
After-tax operating income
66
(
7,062)
10,758
15,510
19,668
ADD: Depreciation
29,700
40,500
13,500
6,300
0
Supplemental operating CF
$29,766 $33,438
$24,258
$21,810
$19,668
Alternative solution:
Increase in operating income
$29,800 $29,800
$29,800
$29,800
$29,800
Taxes
(
34)
3,638
(
5,542)
(
7,990)
(10,132)
Supplemental operating CF
$29,766 $33,438
$24,258
$21,810
$19,668
Depreciable basis
$90,000
Depreciation rates
0.33
0.45
0.15
0.07
0.00
Depreciation
$29,700
$40,500
$13,500
$6,300
$0
Terminal cash flow:
Salvage value
$8,000
Tax on sale
(2,720) =0.34($8,000 - $0); asset is fully depreciated after Year 4
Terminal CF
$5,280
Financial calculator solution:
CF
0
=-90,000; CF
1
= 29,766; CF
2
= 33,438; CF
3
= 24,258; CF
4
= 21,810; CF
5
= 24,948
I =15; NPV =1,990.94; IRR = 15.99%
NPV > 0, which means the machine should be purchased.
Cash Flow Timeline:
IRR = 15.99%
0
1
2
3
4
5
(90,000.00)
29,766
33,438
24,258
21,810
19,668
5,280
24,948
r = 15%
25,883.48
25,283.93
15,950.03
12,469.94
12,403.57
1,990.95 = NPV
10-13
Initial investment outlay:
Purchase price of new machine$(37,500)
Salvage of old machine
5,000
Tax on sale of old machine*
1,320
Initial investment outlay
$(31,180)
*tax on sale of old machine = 0.4($5,000 - $8,300) = -$1.320, which represents a tax refund
Supplemental operating cash flows:
1
2
3
operating income
$14,300
$14,300
$14,300
depreciation*
(10,075)
(14,575)
( 3,325)
NOI
4,225
(275)
10,975
Taxes (0.4)
(
1,690)
110
( 4,390)
after-tax operating income
2,535
(165)
6,585
ADD:
depreciation
10,075
14,575
3,325
Supplemental operating CF
$12,610
$14,410
$ 9,910
Alternative solution:
Increase in operating income $14,300
$14,300
$14,300
Taxes
(
1,690)
110
( 4,390)
Supplemental operating CF
$12,610
$14,410
$ 9,910
New machine depreciable basis = $37,500
MACRS rates for new machine:
0.33
0.45
0.15
Depreciation on new machine = $37,500 x (MACRS rate)
*Depreciation
—
new machine
$12,375
$16,875
$5,625
Depreciation
—
old machine
2,300
2,300
2,300
Depreciation
$10,075
$14,575
$3,325
Terminal cash flow:
Salvage value of new machine
$6,000
Tax on sale of new machine
(1,350)
= 0.4($6,000 - $2,625)
Loss of sale of old machine
(2,000)
Taxes on sale of old machine that are not paid
240
= 0.4($2,000 - $1,400)
Terminal cash flow
$2,890
Book value of new machine after three years:
= $37,500
–
($12,375 + $16,875 + $5,625) = $37,500(1.0
–
0.33
–
0.45 -0.15)
= $37,500
–
$34,875 = $37,500(0.07) = $2,625
Book value of old machine after three years:
= $8,300
–
3($2,300) = $8,300 - $6,900 = $1,400
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Financial calculator solution:
CF
0
=-31,180; CF
1
= 12,610; CF
2
= 14,410; CF
3
= 12.800
I = 11; NPV = 1,235.09; IRR = 13.25%
NPV > 0, which means the old machine should be replaced with the new machine.
10-14 Initial investment outlay:
Purchase price
$(153,800)
Salvage value of old machine
10,860
Tax on sale of old machine
(
1,144) = 0.4($10,860 - $8,000)
net working capital
18,000
Initial investment outlay
(126,084)
Supplemental Operating Cash Flows:
1
2
3
4
5
6
operating income
$40,000.0 $40,000.0 $40,000.0 $40,000.0 $40,000.0 $40,000.0
depreciation
(22,760.0) (49,216.0) (29,222.0) (18,456.0) (16,918.0) (
9,228.0)
NOI
17,240.0
(9,216.0) 10,778.0
21,544.0
23,082.0
30,772.0
Taxes (0.40)
( 6,896.0)
3,686.4
( 4,311.2) ( 8,617.6) ( 9,232.8) (12,308.8)
after-tax OI
10,344.0
(5,529.6)
6,466.8
12,926.4
13,849.2
18,463.2
ADD:
depreciation
22,760.0
49,216.0
29,222.0
18,456.0
16,918.0
9,228.0
Supplemental OCF
$33,104.0 $43,686.4 $35,688.8 $31,382.4 $30,767.2 $27,691.2
Alternative solution:
Increase in OI
40,000.0
40,000.0
40,000.0
40,000.0
40,000.0
40,000.0
Taxes
( 6,896.0)
3,686.4
( 4,311.2) ( 8,617.6) ( 9,232.8) (12,308.8)
Supplemental OCF
33,104.0
43,686.4
35,688.8
31,382.4
30,767.2
27,691.2
Depreciable basis
—
new machine: $153,800
MACRS rates
0.20
0.32
0.19
0.12
0.11
0.06
Depreciation--new
$30,760
$49,216
$29,222
$18,456
$16,918
$9,228
Depreciation--old
8,000
0
0
0
0
0
depreciation
$22,760
$49,216
$29,222
$18,456
$16,918
$9,228
Cash Flow Timeline:
IRR = 13.25%
0
1
2
3
(31,180.00)
12,610
14,410
9,910
2,890
12,800
r = 11%
11,360.36
11,695.48
9,359.25
1,235.09 = NPV
Terminal Cash Flow:
Salvage value of new machine
$25,000
Tax on sale of new machine
(10,000) = 0.4($25,000 - $0)
Salvage value of old machine
0
Return net working capital to original level
(18,000)
Terminal cash flow
(
3,000)
Financial calculator solution:
CF
0
= -126,084.0
CF
1
=
33,104.0
CF
2
=
43,686.4
CF
3
=
35,688.8
CF
4
=
31,382.4
CF
5
=
30,767.2
CF
6
=
24,691.2
10-15
r = 4% + (11% - 4%)(0.8) = 9.6%
Calculator solution:
CF
0
= -29,500, CF
1
–
CF
7
= 6,250, I = 9.6; compute NPV = 1,332.53; IRR = 10.95%
Alternative calculator solution using TVM keys:
N = 7, PV = -29,500, PMT = 6,250, FV = 0; compute I/Y = 10.95% = IRR
The new division should be added, because NPV > 0.
10-16 r = 3% + 6%(1.3) = 10.8%
Calculator solution:
CF
0
= -405,000, CF
1
–
CF
3
= 165,000, I = 10.8;
→
NPV = -380.36; IRR = 10.75%
Alternative calculator solution using TVM keys:
N = 3, PV = -405,000, PMT = 165,000, FV = 0; compute I/Y = 10.75% = IRR
The project should not be purchased, because NPV < 0.
Cash Flow Timeline:
IRR = 15.97%
0
1
2
3
4
5
6
(126,084.00)
33,104.0
43,686.4
35,688.8
31,382.4
30,767.2
27,691.2
( 3,000.0)
24,691.2
r = 12%
29,557.14
34,826.53
25,402.58
19,944.08
17,458.14
12,509.33
13,613.80 = NPV
I = 12
NPV = 13,613.80
IRR = 15.97%
NPV > 0, which means the old machine should be replaced
with the new machine
10-17
NPV
Probability
NPV x Probability
$31,500
0.20
$6,300
19,800
0.70
13,860
-20,100
0.10
-2,010
E(NPV) = $18,150
2
= 0.2($31,500 - $18,150)
2
+ 0.7($19,800 - $18,150)
2
+0.1(-$20,100 - $18,150)
2
= 35,644,500 + 1,905,750 + 146,306,250 = 183,856,500
= (183,856,500)
1/2
= $13,559.37
CV = $13,559.37/$18,150 = 0.75
CV = 0.75 < 0.80, so the project should be purchased.
10-18
NPV
Probability
NPV x Probability
$185,400
0.25
$46,350
128,300
0.60
76,980
-77,600
0.15
-11,640
E(NPV) = $111,690
2
= 0.25($185,400 - $111,690)
2
+ 0.60($128,300 - $111,690)
2
+0.15(-$77,600 - $111,690)
2
= 1,358,291,025 + 165,535,260 + 5,374,605,615 = 6,898,431,900
= (6,898,431,900)
1/2
= $83,056.80
CV = $83,056.80/$111,690 = 0.74
The project should not be purchased, because CV > 0.70.
10-19 Project
IRR
Risk
Risk-Adjusted r
Acceptable?
P
10.0%
Low
9% = 11% - 2%
Yes, IRR > r (risk-adjusted)
Q
12.0
Average
11% = 11% + 0%
Yes, IRR > r
R
14.5
High
15% = 11% + 4%
No,
IRR < r (risk-adjusted)
10-20 Project
IRR
Risk
Risk-Adjusted r
Acceptable?
X
14.0%
Average
15% = 15% + 0%
No, IRR < r
Y
19.0
High
20% = 15% + 5%
No, IRR < r (risk-adjusted)
Neither project is acceptable.
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Chapter 11 Solutions
11-1
a.
Calculator solution for YTM
N = 10; PV = -1,077; PMT = 60; FV = 1,000; I/Y = ? = 5.0% = YTM = r
d
The coupon rate of interest on the new bond should be equal to the yield to maturity on the
company’s existing bonds, which is 5 percent.
b.
r
dT
= 5%(1
–
0.4) = 3%
11-2
Interest payment = [0.056($1,000)]/2 = $28
→
N = 12 x 2 = 24
a.
Calculator solution for YTM:
N = 24; PV = -918; PMT = 28; FV = 1,000;
I/Y = ? = 3.3% = YTM/2 = r
d
/2 = six-month rate
→
YTM = 3.3% x 2 = 6.6% = r
d
The coupon rate of interest on the new bond should be equal to the yield to maturity on the
company’s existing bonds, which is 6.6 percent.
b.
Calculator solution for YTM
N = 24; PV = -730; PMT = 28; FV = 1,000
I/Y = ? = 4.7% = YTM/2 = r
d
/2 = six-month rate
YTM = 4.7% x 2 = 9.4% = r
d
11-3
Dividend = 0.05($120) = $6
ps
0
D
$6
r
=
0.08 8.0%
NP
$75
=
=
=
There is no adjustment for taxes, because dividends payment are not a tax-deductible expense.
11-4
a.
Net proceeds to the firm = $50(10,000)(1
–
0.05) = $500,000(0.95) = $475,000
b.
ps
0
D
$4.75
$4.75
r
=
0.10 10.0%
NP
$50(1 0.05)
$47.50
=
=
=
=
−
There is no adjustment for taxes, because dividends payment are not a tax-deductible expense.
11-5
r
s
= r
RF
+ (r
M
- r
RF
)β
s
= 3.5% + (9.0% - 3.5%)1.4 = 11.2%
11-6
r
s
= r
RF
+ (r
M
- r
RF
)β
s
= = r
RF
+ (RP
M
)β
s
= 5% + (7%)2.0 = 19.0%
11-7
Calculator solution for YTM
N = 12; PV = -900; PMT = 20; FV = 1,000;
I/Y = ? = 3.0% = YTM/2 = r
d
/2
→
r
d
= 3% x 2 = 6%
r
s
= 6% + Risk premium = 6% + 4% = 10% (using the mid-point risk premium)
11-8
g = 4%
//
P
0
= $34
//
D
0
= $4.25
// F = 8.5%
a.
Cost of retained earnings, r
s
=
+
=
+
=
+
=
=
1
s
0
ˆ
D
$4.25(1.04)
$4.42
r
g
0.04
0.04
0.17
17.0%
P
$34
$34
b.
Cost of new equity, r
e
=
+
=
+
=
+
=
=
−
1
e
0
ˆ
D
$4.25(1.04)
$4.42
r
g
0.04
0.04
0.182
18.2%
NP
$34(1
0.085)
$31.11
11-9
g = 0% // P
0
= $50
//
D
0
= $6
//
F = 7%
//
β = 0.75 (irrelevant for this problem)
a.
Cost of retained earnings, r
s
=
+
=
+
=
=
=
1
s
0
ˆ
D
$6(1.0)
$6
r
g
0.0
0.12
12.0%
P
$50
$50
b.
Cost of new equity, r
e
=
+
=
+
=
=
=
−
1
e
0
ˆ
D
$6(1.0)
$6
r
g
0.0
0.129
12.9%
NP
$50(1
0.07)
$46.50
11-10 g = 5%
//
P
0
= $28
//
D
0
= $2.40
//
r
e
= 15%
//
F = ?
=
+
=
+
=
+
=
−
−
1
1
e
0
0
ˆ
ˆ
D
D
$2.40(1.05)
r
g
g
0.05
0.15
NP
P (1 F)
$28(1 F)
+
=
→
=
−
−
−
=
−
=
−
→
=
=
$2.52
1
0.05
0.15
0.09
0.10
$28(1
F)
1
F
0.10
0.09
0.09
0.10(1
F)
0.10
0.10F
F
0.10
0.10
Check: If flotation costs equal 10 percent, the cost of new equity, r
e
, is:
=
+
=
+
=
+
=
=
−
−
1
e
0
ˆ
D
$2.40(1.05)
$2.52
r
g
0.05
0.05
0.15
15.0%
P (1 F)
$28(1
0.1)
$25.20
11-11 g = ?
//
P
0
= $32
//
1
ˆ
D
= $3.36
//
r
e
= 15.5%
//
F = 6.5%
Solve for the firm’s growth rate, g:
1
s
0
ˆ
D
$3.36
r
g
g
0.155
P
$32
g
0.155
0.105
0.05
=
+
=
+
=
=
−
=
Cost of new equity, r
e
:
1
1
e
0
0
ˆ
ˆ
D
D
r
g
g
NP
P (1
F)
$3.36
$3.36
0.05
0.05
0.162
16.2%
$32(1
0.065)
$29.92
=
+
=
+
−
=
+
=
+
=
=
−
11-12
Break points associated with the debt:
1
$450,000
BP
$750,000
0.6
=
=
2
$750,000
BP
$1,250,000
0.6
=
=
11-13
There are two break points associated with the new funds
—
(1) when more than $240,000 in debt is
issued and (2) when new common equity must be issued.
Debt
$240,000
BP
$800,000
0.3
=
=
RE
$560,000
BP
$800,000
0.7
=
=
According to this information, Western’s WACC will increase when it raises more than $800,000 in
total funds because both the cost of debt and the cost of equity will increase beyond this point. In other
words, the break point for debt and the break point for equity occur at the same level of funds.
11-14 a.
WACC
1
= w
d
(r
dT
) + w
s
(r
s
) = 0.4[5%(1
–
0.35)] + 0.6(8%) = 6.1%
b.
WACC
2
= w
d
(r
dT
) + w
s
(r
e
) = 0.4[5%(1
–
0.35)] + 0.6(11%) = 7.9%
11-15 w
d
= 20%
r
Dt
= 3.5%
r
e
= 12.4%
w
ps
= 30%
r
ps
= 6.0%
Retained earnings = $100,000
w
s
= 50%
r
s
= 10.2%
Funding needs = $220,000
The retained earnings break point must be computed to determine whether a new common stock issue is
required to raise the $220,000 in total funds that Killer Burgers needs.
RE
$100,000
BP
$200,000
0.5
=
=
Killer Burgers needs to raise $220,000, but it can only raise a total of $200,000 before new common
stock must be issued. As a result, the firm must issue new stock.
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11-15
Alternative solution: If Killer Burgers raises $220,000, following is the breakdown of how the funds will
be raised:
Debt = $220,000(0.2)
= $44,000
Preferred stock = $220,000(0.3)
= $66,000
Common equity = $220,000(0.5)
= $110,00
Total amount
= $220,000
Because the amount of funds that will be raised using common equity is greater than the $100,000
expected increase in retained earnings, new common stock must be issued.
When new common stock must be issued, Killer’s WACC is:
WACC = 3.5%(0.2) + 6.0%(0.3) + 12.4%(0.5) = 8.7%
11-16 w
d
= 60%
r
d
= 5.0% r
e
= 13.0%
w
ps
= 10%
r
ps
= 7.0% Retained earnings = $27,000
w
s
= 30%
r
s
= 11.0%
Funding needs = $85,000
Marginal tax rate = T = 30%
The retained earnings break point must be computed to determine whether a new common stock issue is
required to raise the $85,000 in total funds that FC needs.
RE
$27,000
BP
$90,000
0.3
=
=
FC needs to raise $85,000, and it can raise up to a total of $90,000 before new common stock must be
issued. As a result, the firm does not need to issue new stock.
Alternative solution
If FC raises $85,000, following is the breakdown of how the funds will be raised:
Debt
= $85,000(0.6) = $51,000
Preferred stock
= $85,000(0.1) = $8,500
Common equity
= $85,000(0.3) = $25,500
Total amount
= $85,000
Because the amount of funds that will be raised using common equity is less than the $27,000 expected
increase in retained earnings, new common stock does not need to be issued.
When new common stock must be issued,
FC’s WACC
= [5%(1
–
0.3)](0.6) + 7.0%(0.1) + 11%(0.3) = 6.1%
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11-17
The retained earnings break point must be computed to determine at what point new common stock must
be issued:
RE
$24,000
BP
$40,000
(1
0.4)
=
=
−
Based on this information, we know that WACC = 14 percent as long as the total capital budget is less
than $40,000. If the capital budget is greater than $40,000, WACC = 17 percent. The following table
applies this information to the three projects Lazy Loungers is evaluating:
Project
Cost
Costs
IRR
WACC
Acceptable?*
A
$10,000
$10,000
21.0%
14.0%
Yes, IRR > WACC
B
15,000
$25,000
20.0
14.0
Yes, IRR > WACC
C
25,000
$50,000
16.0
17.0
No,
IRR < WACC
* Indicates whether the project in the row is acceptable.
Projects A and B should be purchased.
11-18
The retained earnings break point must be computed to determine at what point new common stock must
be issued:
RE
$230,000
BP
$287,500
0.8
=
=
As a result, following are the WACCs when no new stock must be issued and when new common stock
must be issued:
Capital budget < $287,500; no new stock is needed:
WACC = 0.2(4.0%) + 0.8(10.0%) =
8.8%
Capital budget > $287,500; new stock must be issued:
WACC = 0.2(4.0%) + 0.8(12.5%) = 10.8%
The following table applies this information to the projects OTC is evaluating:
Project
Cost
Costs
IRR
WACC
Acceptable?*
S
$150,000
$150,000
12.0%
8.8%
Yes, IRR > WACC
L
140,000
$290,000
10.0
10.8
No,
IRR < WACC
* Indicates whether the project in the row is acceptable.
Only Project S should be purchased.
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11-19
The WACCs are:
Total Amount Raised
WACC
$1 - $520,000
11.0%
520,001
–
745,000
12.5
Over 745,000
15.2
Using these WACCs, the following table summarizes the capital budgeting decision:
Project
Cost
Costs
IRR
WACC
Acceptable?*
1
$214,000
$214,000
19.0%
11.0%
Yes, IRR > WACC
3
$214,000
$428,000
18.0
11.0
Yes, IRR > WACC
2
$214,000
$642,000
15.0
12.5
Yes, IRR > WACC
4
$214,000
$856,000
14.0
15.2
No,
IRR < WACC
*Indicates whether the project in the row is acceptable.
Projects 1, 2, and 3 should be purchased.
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11-20
(1)
Compute the break points:
RE
$1,300,000
BP
$2,000,000
0.65
=
=
Debt
$420,000
BP
$1,200,000
0.35
=
=
(2)
Compute the WACC for each interval of funds:
Total Funds: $1 to $1,200,000 (first break point); at the maximum amount of this interval,
Debt
= 0.35($1,200,000) = $420,000
Equity = 0.65($1,200,000) = $780,000
WACC
1
= [5%(1
–
0.4)](0.35) + 12%(0.65) = 8.85%
Total Funds: $1,200,001 to $2,000,000 (second break point); at the maximum amount of this
interval,
Debt
= 0.35($2,000,000) =
$700,000
Equity
= 0.65($2,000,000) = $1,300,000
WACC
2
= [7%(1
–
0.4)](0.35) + 12%(0.65) = 9.27%
Total Funds: Greater than 2,000,000; if the entire project is funded at $2.6 million,
Debt
= 0.35($2,600,000) =
$910,000
Equity
= 0.65($2,600,000) = $1,690,000
WACC
3
= [7%(1 - 0.4)](0.35) + 14%(0.65) = 10.57%
(3)
Determine how much of the project should be purchased.
Because the project’s IRR = 9.5%, Tri
-Q should purchase the project until the WACC = 9.5%,
which means that $2,000,000 of the project should be purchased. The entire project cannot be
purchased because the total cost is $2,600,000, and raising this amount of funds has a WACC =
10.57%, which means IRR < WACC at this point.
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a
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(1)
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Question 20
An analyst estimates that project C's expected rate of return is 10%, your required rate of return of the project C is 7%, what should you do?
O None of the listed choices is correct
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O Accept project C
O All of the listed choices are correct
A Click Submit to complete this assessment.
MacBook Air
20
F3
O00 E4
F1
F2
F5
F6
F7
F8
#
$
*
2
5
7
8.
Q
W
R
T
Y
F
C
V
* 00
B
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i.
ii.
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(-4) x (-4)
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29 o
Consider the following two projects:
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Alpha
C/F
C/F
C/F
C/F
C/F
C/F
C/F
Rate
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20
25
30
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N/A
N/A
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Beta
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25
25
25
25
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25
13%
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A. $31
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OC. $21
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B
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ine = ½, cose =
=
12
√3
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C
√3
sine =
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cose=
==
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√√3
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