YU C Solution HW5 26
Chapter 6 problems: 4(ignore part h in the information),13 14,19
4.
Cash Flow Forecasts:
Panel A Capital Investment
Investment in Fixed Assets
Sale of Fixed Assets
Less Tax on Sale
Cash Flow from Capital Investment
Panel B Operating Cash Flow
Revenues
Cost of Goods Sold
Depreciation
Pretax Profit
Tax
Profit after Tax
Operating Cash Flow
Panel C Investment in Working Capital
Working Capital
Change in Working Capital
Cash flow from investments in working capital
Panel D Project Valuation
Total Project Cash Flow
Discount Factor (with six month lag)
Discounted Cash Flow
NPV
13.
0
-$40,000
1
$40,000
-$40,000
-$8,400
-$31,600
$8,400
0
$0
$0
0
-$31,600
1.0000
-$31,600
$6,252
3
4
$0
$0
$0
$12,000
$2,520
$9,480
1
$20,000
$7,000
2
$20,000
$7,000
3
$20,000
$7,000
4
$20,000
$7,000
$13,000
$2,730
$10,270
$10,270
$13,000
$2,730
$10,270
$10,270
$13,000
$2,730
$10,270
$10,270
$13,000
$2,730
$10,270
$10,270
1
$10,000
$10,000
-$10,000
2
$10,500
$500
-$500
3
$5,000
-$5,500
$5,500
4
$0
-$5,000
$5,000
1
2
$9,770
0.8250
$8,060
3
$15,770
0.7639
$12,046
4
$24,750
0.7073
$17,505
-$40,000
0
2
$270
0.8910
$241
If the $50,000 installation cost is expensed at the end of year 1, the value of the tax
shield is:
PV = ($50,000 × .25) / (1 + .05) = $11,905
If the $50,000 cost is capitalized and then depreciated using a five-year straight-line
depreciation, the value of the tax shield is:
PV = (.25 × $50,000) × (.20 / (1 + .05) + .20 / (1 + .05)2 + .20 / (1+.05)3 +
.20 / (1 + .05)4 + .20 / (1 + .05)5
= $10,824
If the installation cost can be expensed, then the tax shield is larger, which means
the after-tax cost is smaller.
14.
The Better Mousetrap cashflow forecast is outlined in the table below and Net
Present Value is calculated from these annual cashflow estimates:
Better Mousetrap's (in $1,000's)
Capital Expenditure
∆ (Inc.) Dec. Net Working Capital
Depreciation Tax Shield
Revenues
Operating Costs (exclude Dep'n)
Tax @ 25.0%
Net Cash Flow
(6,200)
Year 1
(40)
300
2,000
(500)
(375)
1,385
Year 2
(160)
300
2,400
(600)
(450)
1,490
Year 3
300
4,000
(1,000)
(750)
2,550
Year 4
160
300
4,000
(1,000)
(750)
2,710
Year 5
500
240
300
2,400
(600)
(575)
2,265
$ 1,047
NPV at 12.0% =
19.
Year 0
(6,000)
(200)
a.
1
1
NPVA –$100, 000 $26, 000
5
.08 .08 (1 .08 )
NPVA $3,810
NPVB – investment PV aftertax cash flow PV depreciation tax shield
1
1
NPVB –$100, 000 $26, 000 1 – .21
.21 $100, 000
5
.08 .08 (1 .08 )
NPVB $3, 010
b.
To calculate the effective tax rate, first compute the project cash flows for each
year. For years 1 and after, you can use this formula:
After-tax cash flowT = (pretax cash flowT × (1 – tax rate) + (initial investment ×
depreciation rateT × tax rate)
After-tax cash flows:
Year:
0
1
2
3
4
5
Company A
-100,000
26,000
26,000
26,000
26,000
26,000
Company B
-79,000
20,540
20,540
20,540
20,540
20,540
IRRA = 9.4%
IRRB = 9.4%
Although project A is more valuable, the IRR on each project is the same
since the taxable project’s cashflows are lower by (1—Tc). However, NPV
indicates that Company A’s project is more valuable.
Chapter 5 problems: 1, 6, 7,12, 16, 20
1.
6.
a.
A = 3 years; B = 2 years; C = 3 years
b.
B
c.
A, B, and C
d.
B and C (At 10%, NPVA = –$1,011; NPVB = $3,378; NPVC = $2,405)
e.
True. The payback rule ignores all cash flows after the cutoff date, meaning that future years’
cash inflows are not considered. Thus, payback is biased towards short-term Projects.
a.
NPV = –$6,750 + $4,500 / (1 + 0) + $18,000 / (1 + 0)2 = $15,750
NPV = –$6,750 + $4,500 / (1 + .50) + $18,000 / (1 + .50)2 = $4,250
NPV = –$6,750 + $4,500 / (1 + 1) + $18,000 / (1 + 1)2 = $0
b.
IRR = 100% (Note: NPV = 0 when the discount rate is 100 percent)
7.
r=
-17.44%
0.00%
10.00%
15.00%
20.00%
25.00%
45.27%
Year 0 –3,000.00 –3,000.00 –3,000.00 –3,000.00 –3,000.00 –3,000.00 –3,000.00 –3,000.00
Year 1
3,500.00 4,239.34 3,500.00 3,181.82 3,043.48 2,916.67 2,800.00 2,409.31
Year 2
4,000.00 5,868.41 4,000.00 3,305.79 3,024.57 2,777.78 2,560.00 1,895.43
Year 3 –4,000.00 -7,108.06 -4,000.00 -3,005.26 -2,630.06 -2,314.81 -2,048.00 -1,304.76
PV =
12
-.31
500.00
482.35
437.99
379.64
312.00
-.02
The two IRRs for this project are (approximately): –17.44% and 45.27%.
Between these two discount rates, the NPV is positive.
a.
Because Project A requires a larger capital outlay, it is possible that Project A has both a
lower IRR and a higher NPV than Project B. (In fact, NPVA is greater than NPVB for all
discount rates less than 10%.) Because the goal is to maximize shareholder wealth, NPV is
the correct criterion.
b.
To use the IRR criterion for mutually exclusive projects, calculate the IRR for the
incremental cash flows:
A-B
C0
C1
C2
IRR
−200
+110
+121
10%
Because the IRR for the incremental cash flows exceeds the cost of capital, the additional
investment in A is worthwhile.
c.
NPVA = –$400 + $250 / 1.09 + $300 / 1.092
NPVA = $81.86
NPVB = –$200 + $140 / 1.09 + $179 / 1.092
NPVB = $79.10
16.
The following table and plot outline each project’s sensitivity to the discount rate:
C0
Project
A
$
B
C1
(200)
$
(200)
C2
80
$
100
C3
80
100
$
80
C4
$
IRR
80
22%
-
23%
100
Net Present Value: Sensitivity Analysis
Discount Rate
Project A
Project B
54
48
43
38
33
28
24
19
15
11
7
49
44
40
36
32
28
25
21
17
14
11
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
Net Present Value: Sensitivity to Discount Rate
60
Net Present Value
50
40
30
20
Project B
Project A
10
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
Discount Rate
a.
At an 11% discount rate, both projects are acceptable with positive NPV.
b.
If mutually exclusive, project A yields a higher NPV than project B
c.
At a 16% discount rate, Project B is more favorable than Project A.
d.
Project A is fully paid back by year 3.
Project B is fully paid back by year 2.
e.
The project with the highest NPV depends on the discount rate.
f.
Project A has an IRR of 22%.
Project B has an IRR of 23%.
g.
The project with the highest NPV depends on the discount rate.
h.
Profitability Index = NPV/investment
Profitability IndexA = $48/$200 = 0.24
Profitability IndexB = $44/$200 = 0.22
20.
In this case, since the investment amounts are the same, both NPV and profitability index
indicate the same answer: pick project A at an 11% discount rate. If capital is rationed, then
profitability index is preferable and used to accept projects with the highest index descending
until the capital ration is exhausted. Without capital rationing, accept all projects with a positive
NPV.
Using the fact that profitability index = (net present value / investment), we find:
Project
NPV
Investment
Profitability Index (NPV/Investment)
1
$66
$300
0.22
2
-4
200
-0.02
3
43
250
0.17
4
14
100
0.14
5
7
100
0.07
6
63
350
0.18
7
48
400
0.12
Thus, given the budget of $1 million, the best the company can do is to accept Projects 1, 3, 4, and 6.
If the company accepted all positive NPV projects, the market value (compared to the market value
under the budget limitation) would increase by the NPV of Projects 5 and 7 ($7,000 + $48,000 =
$55,000). The budget limit costs the company $55,000 in terms of market value.
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