Chapter 12 – Strategy and the Analysis of Capital Investments
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Chapter 12 – Strategy and the Analysis of Capital Investments
12-52 Real Options (60 Minutes)
1. Annual after-tax cash flows, both scenarios (possible outcomes):
Product Demand
Optimistic Pessimistic
Selling price/unit $80.00 $70.00
Variable cost/unit $40.00 $40.00
CM/unit $40.00 $30.00
Volume (units) 100,000 40,000
Pre-tax Cash Flow $4,000,000 $1,200,000
Less: Depreciation $1,200,000 $1,200,000
2. Expected NPV of Proposed Investment:
PV of Cash Inflows $17,327,3511$6,780,2682
Initial Investment Outlay $12,000,000 $12,000,000
Expected NPV = (0.50 × $5,327,351) + (0.50 × ($5,219,732))
Strictly speaking, the project would be accepted because its expected NPV is
positive. However, the expected NPV is close to zero; in fact, it’s basically a
“toss up” as to whether or not this project is profitable in a present-value
sense.
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Chapter 12 – Strategy and the Analysis of Capital Investments
12-52 (Continued-1)
3. Sensitivity Analysis Results:
WACC Expected NPV
10% $1,108,410
11% $563,695
14% ($872,287)
Sample Calculation:
Note: the figures reported above were generated in Excel, using the built-in NPV
function. Because the annuity factors in Table 2 are rounded (to three decimal places),
your answers will be slightly different from the above if you use the annuity factors
rather than the built-in Excel function.
As can be seen from the above results, the Expected NPV (given the indicated
probabilities for each outcome/state-of-nature) is sensitive to the assumption regarding
the discount rate.
4. Inclusion of abandonment option:
Abandonment value, end of year 1 $10,400,000
Cash flow, end of year 1:
After-tax operating cash flow $1,200,000
Gross proceeds, equipment $10,400,000
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Chapter 12 – Strategy and the Analysis of Capital Investments
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Chapter 12 – Strategy and the Analysis of Capital Investments
12-52 (Continued-2)
NPV of project, with abandonment option:
PV of Total Cash Flow, Year 1 $10,476,190
Less: Investment Outlay, t = 0 $12,000,000
Expected NPV of investment, with abandonment option:
Scenario Prob. NPV Weighted NPV
Note that the abandonment option adds considerable value to the proposed
investment: if demand turns out to be “pessimistic,” then the company can minimize
its losses by abandoning the project at the end of year 1. As you can see, the NPV in
the abandonment scenario is negative $1,523,810. Compare this amount to the
original value, negative $5,219,732. In short, the situation of pessimistic demand is
not as disastrous when an abandonment option exists. Note, too, that the expected
NPV of the proposed project is now clearly positive.
Chapter 12 – Strategy and the Analysis of Capital Investments
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Chapter 12 – Strategy and the Analysis of Capital Investments
12-53 Equipment-Replacement Decision; Strategy (60 minutes)
1. & 3.
PV Present After-tax Cash Flows (000s)
Factor Value 0 1 2 3 4 5
Overhaul AccuDril
Operating Cost1(48.0) (48.0) (38.4) (38.4) (38.4)
Overhaul cost (capitalized) (100.0)
Tax savings on deprec.24.0 4.0 16.0 16.0 16.0
Other cash expenses, after tax3(57.0 ) (57.0 ) (57.0 ) (57.0 ) (57.0 )
After-tax cash flows:
Year 1 0.893 ($90,193) (101.0)
Year 2 0.797 (160,197) (201.0)
Buy RoboDril 1010K
Net Equip. Purchase4($240,000)(240.0)
After-tax cash operating costs5(86,520) (24.0) (24.0) (24.0) (24.0) (24.0)
Tax savings on depr.6 69,216 19.2 19.2 19.2 19.2 19.2
Other cash expenses, after tax7(118,965) (33.0) (33.0) (33.0) (33.0) (33.0)
After-tax salvage value8 17 ,010 30.0
After-tax cash flows (240.0) (37.8) (37.8) (37.8) (37.8) (7.8)
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NOTES
1Years 1 and 2: $10 per hour × 8,000 hours × (1 − t) = $48,000
Years 3, 4, and 5: $48,000 × (1 − 20%) = $38,400
2Years 1 and 2:
Depreciation expense per year (SL basis):
Overhaul cost, Year 3 100,000
Total amount to be depreciated $120,000
Number of years 3
Depreciation expense per year $ 40,000
Income Tax Rate (t) × 40%
Trade-in allowance for AccuDril – 40,000
Net purchase cost $240,000
5 ($10/hour × 4,000 hours) × (1 – t) = $40,000 x 0.60 = $24,000
6 Depreciation expense per year: $240,000 5 Years = $48,000
Income Tax Rate (t) × 0.40
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Chapter 12 – Strategy and the Analysis of Capital Investments
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2. Net After-tax Cash Flows Difference in Cumulative
Year AccuDril RoboDril Cash Flows Difference
0 $0 ($240,000) ($240,000)
($240,000)
1 ($101,000) ($37,800) $63,200 ($176,800)
4. Among other factors that the firm should consider before the final decision are:
Changes in technology for equipment
Changes in market, especially demand for the product and competitors
Chapter 12 – Strategy and the Analysis of Capital Investments
12-54 Sensitivity Analysis; Spreadsheets (75 minutes)
1. Difference in PV between the two alternatives = $402,441 – $359,259 =
$43,182. We focus on the reduction in variable operating cost needed
each year (3 through 5) after the old machine is overhauled.
The equivalent annuity factor needed to convert this stream of after-tax
cash flows (cost savings) to a present value is found in either of two
ways:
(1) Annuity factor (@12%) for three years = 2.402; this annuity factor
Thus, the additional annual after-tax operating cost savings needed from
improvement to make the overhaul of AccuDril a financially attractive
choice = $22,549, as follows:
$43,182 ÷ 1.915 = $22,549
On a before-tax basis (given an income tax rate of 40%), the required
operating cost savings in each of years 3, 4, and 5 would be:
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