Chapter 10 - Project Analysis
CHAPTER 10
Project Analysis
Answers to Problem Sets
1.
a.
False. The capital budget is not the final sign-off for specific projects. Most
companies require for each project appropriation requests, which include more
detailed analysis.
b.
True. Strategic planning requires consideration of alternatives.
c.
True. Cash flow forecasts are regularly overstated.
Est. Time: 01 - 05
2.
a.
Cash flow forecasts are overstated.
b.
One project proposal may be ranked below another simply because cash
flows are based on different forecasts.
c.
Project proposals may not consider strategic alternatives.
Est. Time: 01 - 05
3.
a.
Analysis of how project profitability and NPV change if different
assumptions are made about sales, cost, and other key variables
b.
Project NPV is recalculated by changing several inputs to new, but
consistent, values.
c.
Determines the level of future sales at which project profitability or NPV
equals zero.
d.
An extension of sensitivity analysis that explores all possible outcomes
and weights each by its probability
e.
A graphical technique for displaying possible future events and decisions
taken in response to those events
f.
Option to modify a project at a future date
g.
The additional present value created by the option to bail out of a project
and recover part of the initial investment if the project performs poorly.
h.
The additional present value created by the option to invest more and
10-1
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Chapter 10 - Project Analysis
expand output if a project performs well
Est. Time: 06 - 10
4.
a.
False. Sensitivity analysis may show where additional information would
be most useful.
b.
True
c.
True
d.
True
e.
False. A business with high fixed costs has high operating leverage.
f.
True
Est. Time: 01 - 05
5.
a.
Describe how project cash flow depends on the underlying variables.
b.
Specify probability distributions for forecast errors for these cash flows.
c.
Draw from the probability distributions to simulate the cash flows.
Est. Time: 01 - 05
6.
a.
True
b.
True
c.
False. Just as the option to expand has value, the option to terminate also
raises the present value of the project.
d.
False. The optimal date to undertake an investment is the one that
maximizes its contribution to the firm today.
Est. Time: 01 - 05
7.
Adding a fudge factor to the discount rate pushes project analysts to submit more
optimistic forecasts.
Est. Time: 01 - 05
9.
a.
10-2
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Chapter 10 - Project Analysis
NPVF  $9,000 
$6,000  (1 - 0.08) $5,000  (1 - 0.08) $4,000  (1 - 0.08)


1.10
(1.10) 2
(1.10) 3
= $2,584.67.
NPVG  $9,000 
b.
c.
12.
$1,800  (1 - 0.08)
 $7,560.
0.10
$6,000 $5,000 $4,000


 $2,110.19.
1.18
(1.18) 2 (1.18) 3
$1,800
NPVG  $9,000 
 $1,000.
0.18
NPVF  $9,000 
The 18% discount rate would give an approximation to the correct NPVs
for projects with all (or most) of the inflows in the first year.
The present value of $1 to be received one year from now, discounted at
18% is: $0.8475.
The present value of $1 × (1 – 0.08) (that is, $0.92) to be received one
year from now, discounted at 10% is: $0.8364.
The former calculation overstates the correct answer by approximately
1.3%. However, for cash flows five or ten years into the future,
discounting by 18% understates the correct present value by
approximately 23% and 46%, respectively. The error increases
substantially because the incorrect factor (i.e., 1.18) is compounded,
causing the denominator of the present value calculation to be greatly
overstated so that the present value is greatly understated.
a.
Year 0
Investment
1. Revenue
2. Variable Cost
3. Fixed Cost
4. Depreciation
5. Pretax Profit (1 − 2 − 3 − 4)
6. Tax
7. Net Operating Profit (5 − 6)
8. Operating Cash Flow (4 + 7)
Years 1–10
¥30 B
NPV =
¥37.500 B
26.000
3.000
3.000
¥5.500
2.750
¥2.750
5.750
+ ¥5.33 B
b.
10-3
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Chapter 10 - Project Analysis
Unit Sales
(000’s)
0
100
200
Inflows
Revenues Investment
Yrs 1–10
Yr 0
0.00
30.00
37.50
30.00
75.00
30.00
Outflows
V. Costs
F. Cost
Yr 1–10
Yr 1–10
0.00
3.00
26.00
3.00
52.00
3.00
Taxes
Yr 1–10
-3.00
2.75
8.50
PV
Inflows
0.00
230.42
460.84
PV
Outflows
-30.00
-225.09
-420.18
NPV
-30.00
5.33
40.66
Note that the break-even point can be found algebraically as follows:
NPV = -investment + [(PVA10/10%)  (t  depreciation)] +
[quantity  (price – V. cost) – F. cost](1 – t)(PVA10/10%)
Set NPV equal to zero and solve for Q:
Q
I  (PVA 10/10%  D  t)
F

(PVA 10/10% )  (P  V)  (1  t) P  V

30,000,000 ,000  9,216,850, 659
3,000,000, 000

6.144567  (375,000  260,000)  0.50 375,000  260,000

20,783,149 ,341 3,000,000, 000

 58,824  26,087  84,911
353,313
115,000
Proof:
1. Revenue
2. Variable Cost
3. Fixed Cost
4. Depreciation
5. Pretax Profit
6. Tax
7. Net Profit
8. Operating Cash Flow
NPV 
10

t 1
¥31.84 B
22.08
3.00
3.00
¥3.76 B
1.88
¥1.88
¥4.88
4.88
 30  29.99  30   0.01
(1.10) t
(difference due to rounding)
10-4
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Chapter 10 - Project Analysis
Break-Even
PV (Billions of Yen)
500
450
400
350
300
250
200
150
100
50
0
PV Inflows
PV Outflows
Break-Even
NPV = 0

0
100
200
Units
(000's)
c.
The break-even point is the point where the present value of the cash
flows, including the opportunity cost of capital, yields a zero NPV.
d.
To find the level of costs at which the project would earn zero profit, write
the equation for net profit, set net profit equal to zero, and solve for
variable costs:
Net profit = (R – VC – FC - D)  (1 – t)
0 = (37.5 – VC – 3.0 – 1.5)  0.50
VC = 33.0
This will yield zero profit.
Next, find the level of costs at which the project would have zero NPV.
Using the data in Table 11.1, the equivalent annual cash flow yielding a
zero NPV would be:
¥15 B/PVA10/10% = ¥2.4412 B
If we rewrite the cash flow equation and solve for the variable cost:
NCF = [(R – VC – FC – D)  (1 – t)] + D
2.4412 = [(37.5 – VC – 3.0 – 1.5)  0.50] + 1.5
VC = 31.12
This will yield NPV = 0, assuming the tax credits can be used elsewhere
in the company.
10-5
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manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 10 - Project Analysis
e.
DOL = 1 + (fixed costs / profit).
Fixed costs rise 1.5 due to additional depreciation of the 15 billion yen
investment. Profits increase by 0.4 reflecting the lower variable costs.
This gives us a DOL = 1 + ((3 + 1.5 + 1.5) / 3.4) = 2.76.
16.
a.
Operating leverage 
% change in operating income
.
% change in sales
For a 1% increase in sales, from 100,000 units to 101,000 units:
Operating leverage 
b.
0.075 / 3
 2.50
0.375 / 37.5
Operating leverage  1 
1 
c.
Operating leverage 
fixed cost  depreciation
operating profit
(3.0  1.5)
 2.5
3.0
% change in operating income
.
% change in sales
For a 1% increase in sales, from 200,000 units to 202,000 units:
Operating leverage 
(10.65 - 10.5)/10.5
 1.43
(75.75 - 75) /75
10-6
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manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.