Principles of Finance 6e Chapter 13
Besley/Brigham
13-1
CHAPTER 13
ANSWERS
13-1 Only cash can be spent or reinvested, and because accounting profits do not represent cash, they
13-2 a. The firm has depreciated the asset to a book value less than its salvage value (book value is
b. The change in depreciation simply is the difference between the depreciation associated with
c. A reduction in net working capital would lead to a reduction in net investment. Note that net
d. The cost savings associated with the new machine will result in less cash outflow each year,
13-3 Capital budgeting analysis should only include those cash flows that will be affected by the
decision. Sunk costs are unrecoverable and cannot be changed, so they have no bearing on the
13-4 When a firm takes on a new capital budgeting project, it typically must increase (decrease) its
investment in receivables and inventories, over and above the increase (decrease) in payables and
13-5 Relevant cash flows that should be included in the capital budgeting analysis are:
Irrelevant cash flows that should not be included in the capital budgeting analysis are:
13-2
13-6 a. NPV > 0; if accepted, the project will add value to the firm.
13-7 If a project is determined to be acceptable using one of the techniques that is based on TVM
13-8 The NPV is obtained by discounting future cash flows, and the discounting process actually
13-9 The statement is true. The NPV and IRR methods result in conflicts only if mutually exclusive
projects are being considered because the NPV is positive if and only if the IRR is greater than the
13–10 The NPV and IRR methods both involve compound interest, and the mathematics of discounting
13–11 Yes, if the cash position of the firm is poor and if it has limited access to additional outside
13–12 a. All of the projects are acceptable, because they all have NPV > 0. However, because the
13–14 a. True. If r = 12 %, NPV > 0
Principles of Finance 6e Chapter 13
Besley/Brigham
13-3
13–15 Beta (market) risk refers to the project’s effect on the corporate beta coefficient. Within-firm
13–16 The consolidated company should view its divisions as having separate risk characteristics, thus
use the required rates of return for each division. Because investors respond primarily to beta
13–17 The required rate of return for average-risk projects would be the firm’s required rate of return, 10
_______________________________________________________________
SOLUTIONS
13-1 a. Depreciable basis = $340,000 + $50,000 = $390,000
13-2 Initial investment outlay = $40,000. (Old machine has a zero book value and no salvage.)
Chapter 13 Principles of Finance 6e
Besley/Brigham
13-4
–1
10
(1.10)
1
13-3 1. Initial investment outlay:
2. After-tax
Year Earningsa + ΔDep x Tb = Annual CFt
1 $16,200 $ 6,600 $22,800
2 16,200 10,560 26,760
Dep Dep
Year Rate Basis Depreciation Depreciation x T
1 0.20 $82,500 $16,500 $ 6,600
2 0.32 82,500 26,400 10,560
3. Now find the NPV of the replacement machine:
Year CFt 1/(1.12)t PV of CFt
1 $22,800 0.89286 $ 20,357
)10.1(
1
1
6
−
Chapter 13 Principles of Finance 6e
Besley/Brigham
NPV solution:
)12.1(
1
1
7
−
Principles of Finance 6e Chapter 13
Besley/Brigham
)IRR1(
000,81
000,48
4
P
+
=−
Chapter 13 Principles of Finance 6e
Besley/Brigham
13-8
13–11
n
)MIRR1(
TV
Cost +
=
13–12 Year Project G Project J Project K
0 $(180,000) $(240,000) $(200,000)
G
IRR
Principles of Finance 6e Chapter 13
Besley/Brigham
13-9
Project J:
%04.161604.00.1)5625.1(IRR
5625..1
000,240
000,375
)IRR1(
)IRR1(
000,375
000,240
3
1
J
3
J
3
J
==−=
==+
+
=
Project K:
3
K
2
K
1
K)IRR1(
000,205
)IRR1(
000,205
)IRR1(
000,100
000,200 +
+
+
+
+
−
=
Chapter 13 Principles of Finance 6e
Besley/Brigham
13–10
%10.151510.00.1
30.719,287
700,438
MIRR
)MIRR1(
30.719,287
3
1
3
==−
=
+
=
Summary of computations:
Project IRR MIRR
G 15.96% 15.25%
13–13 a. Using a financial calculator:
NPVP = $448.86 NPVQ = $607.20
Project P Project Q
Year CF PV of CF ∑(PV of CF) CF PV of CF ∑(PV of CF)
0 $(15,000) $(15,000) $(15,000) $(37,500) $(37,500) $(37,500)
1 4,500 3,947 (11,053) 11,100 9,737 (27,763)
Principles of Finance 6e Chapter 13
Besley/Brigham
47.745,29
)MIRR1(
14.0
1)14.1(
500,4
000,15
)MIRR1(
TV
Cost
5
P
5
n
P
P
=
+
−
==
+
=
Chapter 13 Principles of Finance 6e
Besley/Brigham
)14.1(
900$
)14.1(
000,1$
)14.1(
800,1$
)14.1(
0$
500,2$NPV 4321
Q
++++−=
13–16
4321
Y)10.1(
000,6$
)10.1(
000,7$
)10.1(
000,9$
)10.1(
000,10$
000,25$NPV ++++−=
)68301.0(000,6$)75131.0(000,7$)82645.0(000,9$)90909.0(000,10$000,25$
++++−=
13–13
13–17 a. PB = $52,125/$12,000 = 4.34, so the payback is about 4 years.
b. Numerical solution:
12.0
1
000,12$125,52$NPV
8
)12.1(
1
−
+−=
c. Let NPV = 0. Therefore,
−
=
=
−
+−=
+
+
IRR
1
000,12$125,52$
0
IRR
1
000,12$125,52$NPV
8
8
)IRR1(
1
)IRR1(
1
Numerical Solution: Without a financial calculator, you must use a trial-and-error process—
plug in values for IRR until the right side of the computation equals $52,125.
Financial calculator: Input the appropriate cash flows into the cash flow register and then
solve for IRR = 16%.
d. Project L’s discounted payback period is calculated as follows:
Annual Discounted @12%
Period Cash Flows Cash Flows Cumulative
0 ($52,125) ($52,125.00) ($52,125.00)
19.428,5$
Payback
13–18 a. Required return: r = 5% + (4%)1.4 = 5% + 5.6% = 10.6%.
Chapter 13 Principles of Finance 6e
Besley/Brigham
13–14
1
5
)106.1(
1
−
13–19 a. r = 8% + 5%(1.4) = 15%.
13–20 Project IRR Risk Risk-adjusted r Decision
A 8.0% Low 7% = 9% – 2% Accept
13–21 Because NPV = 0 for Project QUE, the firm’s required rate of return is 11 percent. The NPVs
will change if risk-adjusted discount rates are used.
Project NPV IRR Risk Risk-adjusted r Decision
LOM $1,500 12.5% High 13% = 11% + 2% Reject
13–22 Pulley System:
Principles of Finance 6e Chapter 13
Besley/Brigham
)43308.3(100,5$100,17$
14.0
1
100,5$100,17$NPV
5
)14.1(
1
+−=
−
+−=
Chapter 13 Principles of Finance 6e
Besley/Brigham
13–16
%2.17172.00.1
430,22
576,49
MIRR
5
1
Truck
==−
=
PV of
CF
Year Expected
CF
r = 14% Cumulative PV of
CF
0 $(22,430) $(22,430) $(22,430)
1 7,500 6,579 (15,851)
13-23 Electric-powered:
75.860,3$)11141.4(290,6$000,22$
12.0
1
290,6$000,22$NPV
6
)12.1(
1
E=+−=
−
+−=
Principles of Finance 6e Chapter 13
Besley/Brigham
13–17
13–24 a. The initial investment outlay is $178,000:
Cost of investment at t = 0:
Base price ($140,000)
b. The supplemental operating cash flows are:
Year 1 Year 2 Year 3
Notes:
(2) The depreciation expense in each year is the depreciable basis, $170,000, times the
MACRS allowance percentages. The annual depreciation expense and the depreciation
tax savings are:
Recovery Depreciation Tax Savings
Year Allowance Expense = Depr x 0.40
c. The terminal cash flow is $48,760:
Chapter 13 Principles of Finance 6e
Besley/Brigham
13–18
12%
d. The cash flow time line for this project is:
0 1 2 3
(178,000) 52,440 60,600 40,200
13–25 a. The initial investment outlay is $126,000:
Price ($108,000)
b. The supplemental operating cash flows are:
Year 1 Year 2 Year 3
Notes:
(2) The depreciation expense in each year is the depreciable basis, $120,500, times the
MACRS allowance percentages. The annual depreciation expense and the depreciation
tax savings are:
Recovery Depreciation Tax Savings
Year Allowance Expense = Depr x 0.34
c. The terminal cash flow is $51,268:
Principles of Finance 6e Chapter 13
Besley/Brigham
13–19
12%
d. The cash flow time line for this project is:
0 1 2 3
(126,000) 42,560 47,477 35,186
13–26 First determine the initial investment outlay:
Purchase price ($8,000)
Sale of old machine 3,000
Now, examine the operating cash inflows:
Depreciation:
Year 1 2 3 4 5 6
Newa $1,600 $2,560 $1,520 $ 960 $ 880 $ 480
Chapter 13 Principles of Finance 6e
Besley/Brigham
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13–20
times the MACRS percentage allowances of 0.20, 0.32, 0.19, 0.12, 0.11, and 0.06 in Years 1–6,
respectively.
b Depreciation tax savings = T(Depreciation) = 0.4(Depreciation).
Now recognize that at the end of Year 6 Dauten would recover its net working capital
investment of $1,500, and it would also receive $800 from the sale of the replacement machine.
However, because the machine would be fully depreciated, the firm must pay 0.40($800) =
$320 in taxes on the sale. Also, by undertaking the replacement now, the firm forgoes the right
to sell the old machine for $500 in Year 6; thus, this $500 in Year 6 must be considered an
opportunity cost in that year. No tax would be due because the $500 salvage value would equal
the old machine’s Year 6 book value.
Finally, place all the cash flows on a time line:
0 1 2 3 4 5 6
Net investment (6,660)
After-tax revenue increase 1,500 1,500 1,500 1,500 1,500 1,500
13-27 a. Old depreciation = ($70,000 – $10,000)/6 = $10,000 per year.
Current book value = $70,000 – 2($10,000) = $50,000.
15%