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Chapter 12 - Strategy and the Analysis of Capital Investments
12-76
12-54 (Continued-4)
1See part (1), Problem 12-53, reproduced as follows:
Years 1 and 2:
Depreciation expense per year (SL basis):
($120,000 – $20,000) 10 years = $10,000
Income Tax Rate (t) × 0.40
Tax savings on depreciation, Years 1 and 2 $ 4,000
Years 3, 4, and 5:
Book value before overhaul (end of original useful life) $ 20,000
2Savings from the improved productivity = $10/hr. × 8,000 hours × 20% = $16,000
Less: Income Taxes on the savings (@40.0%) = – 6,400
After-tax savings $9,600
3Years 1 and 2:
Book value at the time of overhaul: $10,000 × 2 + $20,000 = $ 40,000
Overhaul cost + 80,000
Total amount to be depreciated $120,000
Number of years 2
Depreciation expense per year $60,000
4. As a follow-up to (3) above: although the cost difference between
the two alternatives is only $2,852.4, which is less than 0.3% of the
Chapter 12 - Strategy and the Analysis of Capital Investments
12-77
to undertake the overhaul two years early.
12-55 Comparison of Capital-Budgeting Techniques, Sensitivity Analysis
(75minutes)
1. Effects of the new equipment on operating income after tax:
Sales $195 × 10,000 = $1,950,000
Cost of goods sold:
Variable manufacturing costs per unit $ 90
Fixed manufacturing costs per unit:
Additional fixed manufacturing overhead:
$250,000 ÷ 10,000 units = $25
Depreciation on new equipment, per unit:
($995,000 – $195,000) ÷ 4 = $200,000/year
$200,000 ÷ 10,000 units per year = + 20 + 45
Total manufacturing cost per unit (@ 10,000 units) $135
Times: Number of units × 10,000
Total cost of goods sold (CGS) 1,350,000
Gross margin $ 600,000
Operating Expenses:
Variable marketing: Cost per unit $ 10
$210,000 each year.
2. Years
1 to 3 Year 4
After-tax operating income (see #1 above) $210,000 $210,000
Add: increased depreciation expense (SL basis) 200,000 200,000
*The NBV at the end of year four = estimated salvage (terminal) value.
Therefore, there is no taxable gain or loss on this transaction.
Chapter 12 - Strategy and the Analysis of Capital Investments
12-78
12-55 (Continued-1)
3. Under the assumption that cash inflows occur evenly throughout the
year, the payback period is as follows:
4. Average investment = ($995,000 + $195,000) ÷ 2 = $595,000
Average after-tax operating income = $210,000
5. Using PV and Annuity Tables:
PV of after-tax cash inflows (@14%):
Years 1 through 3: $410,000 × 2.322 = $ 952,020
Year 4 ($410,000 + $195,000): $605,000 × 0.592 = 358,160
Using the NPV Function in Excel:
Chapter 12 - Strategy and the Analysis of Capital Investments
12-55 (Continued-2)
6. Trial-and-Error Approach (initial investment outlay = $995,000):
PV of cash flows @ 25%:
($410,000 × 1.952) + ($605,000 × 0.410) $1,048,370
PV of cash flows @ 30%:
Based on the built-in function in Excel, the estimated IRR of this
project = 27.80%, as follows:
7. The modified internal rate of return (MIRR) = 22.12%, as follows:
Chapter 12 - Strategy and the Analysis of Capital Investments
12-80
12-55 (Continued-3)
8. a. Based on an estimated NPV of $315,078 (part 5, above), the PV of
any after-tax increase in variable costs associated with units produced
by the new machine = $315,078. Thus, the annual after-tax increase
Therefore, the variable cost per unit can increase by a maximum of
$154,466 ÷ 10,000 units = $15.45 per unit. At this increase, the new
equipment would generate a rate of return of exactly 14%—its cost of
capital.
b. The maximum pre-tax decrease in selling price = $154,466 (see (a)
above). On a per-unit basis, for all units sold, the maximum decrease
in unit selling price is therefore equal to $7.72 (rounded), that
9. Strategic considerations--among the additional factors to be considered:
• What is the associated risk of not expanding capacity? (e.g., loss of
• In the absence of increased volume, would Nil Hill be able to match
the anticipated lower prices by competitors?
Chapter 12 - Strategy and the Analysis of Capital Investments
12-81
12-55 (Continued-4)
• Are there any strategic factors associated with this investment?
a) Impact of the new equipment on customer response time?
b) Impact of the new equipment on plant safety?
c) Impact of the new equipment on environmental performance/
f) Are there any more profitable uses of the existing space?
That is, would this space best be used to increase capacity
of the particular product in question?
Chapter 12 - Strategy and the Analysis of Capital Investments
12-82
12-56 Sensitivity Analysis; Equipment-Replacement Decision (45-60
minutes)
1. The maximum amount of annual variable operating expenses, pre-tax,
that would make this an attractive investment from a present-value
PV (@ 12%) of salvage differential, from year 6 = $45,597
Net investment outlay − PV of salvage differential = $414,403
Year PV factor s (@ 12%)
1 0.892857143 (1 ÷ (1+0.12)1)
2 0.797193878 (1 ÷ (1+0.12)2)
3 0.711780248 etc.
4 0.635518078
5 0.567426856
6 0.506631121
Annuity factor = 4.111407324
PV of annuity = annuity amount × annuity factor
Annuity amount = PV of annuity ÷ annuity factor
Chapter 12 - Strategy and the Analysis of Capital Investments
12-83
12-56 (Continued-1)
2. Recalculation, based on an after-tax basis:
Combined (federal and state) income tax rate = 40.00%
After-tax WACC (discount rate) =
10.00%
Net pre-tax investment outlay, time 0 =
$460,000
Tax effect of loss on sale of existing asset =
$4,000
12-56 (Continued-1)
Net-of-tax initial investment outlay, time 0 =
$456,000
Differential salvage value, e-o-y 6 =
$90,000
Tax effect on differential salvage values =
$36,000
Net-of-tax differential salvage value, e-o-y 6 = $54,000
Differential tax shield, depreciation deductions:
Annual tax shield, existing asset =
$3,333
Annual tax shield, replacement asset =
$33,333
$30,000
PV of differential depreciation tax shield (@10%) =
$30,000 × 4.344261 (see below) = $130,658
Annual pre-tax operating expenses, existing asset = $200,000
Annual post-tax operating expenses, existing asset =
$200,000 × (1 − 0.4) = $120,000
Chapter 12 - Strategy and the Analysis of Capital Investments
12-84
12-56 (Continued-2)
Year PV factor (@ 10%)
1
0.90909
2
0.82645
3
0.75131
4
0.68301
5
0.62092
6
0.56447
4.35526
PV of after-tax variable operating costs, replacement asset
=
after-tax net investment outlay − PV of after-tax differential
salvage values − PV of differential tax savings due to
depreciation deductions
= $456,000 − $30,481 − $130,658 = $294,861
PV of annuity = annuity amount × annuity factor
annuity amount = PV of annuity ÷ annuity factor
= $294,861 ÷ 4.355261 = $67,702
Therefore, maximum annual after-tax variable operating expenses new
asset
=
$120,000
−
$67,702
=
$52,298
or, maximum pre-tax variable operating expenses =
$87,163
Chapter 12 - Strategy and the Analysis of Capital Investments
12-85
3. Additional (i.e., strategic) factors that might bear upon this decision:
a) Are any competitors of the Mendoza Company contemplating a similar
investment? Would such investments by competitors pose a strategic
d) Is Mendoza competing on the basis of price? Would the proposed
investment allow the company to establish/maintain its position as a
low-cost competitor?
Chapter 12 - Strategy and the Analysis of Capital Investments
12-86
12-57 Present Value Analysis; Sensitivity Analysis; Spreadsheet Applications (60
Minutes)
1. The minimum volume of car sales, per year, in the six-year life of the plant that is
needed to make this proposed investment acceptable using NPV as decision criterion
Formula, cell D52:
=(D50*D51*E43)+(D50*D51*E44)+(D50*D51*E45)+(D50*D51*E46)+(D50*D51*E47)
+(D50*D51*E48)
Note: The discount factors in Column D were calculated using the following equation:
PV factori = 1 ÷ (1 + r)i, where r = discount rate (WACC) and i = year (i = 1, 8).
Goal Seek Window:
Chapter 12 - Strategy and the Analysis of Capital Investments
12-87
12-57 (Continued-1)
And the GOAL SEEK window will have changed to:
Check:
Discount
Year
Volume
(000s)
Cash Flows
(000s)
Factor
(@15%)
Present
Value (000s)
1
($750,000)
0.869565217
($652,174)
2
($1,750,000)
0.756143667
($1,323,251)
3
197.234
$690,319
0.657516232
$453,896
4
197.234
$690,319
0.571753246
$394,692
5
197.234
$690,319
0.497176735
$343,211
6
197.234
$690,319
0.432327596
$298,444
7
197.234
$690,319
0.375937040
$259,516
8
197.234
$690,319
0.326901774
$225,666
($0)
Chapter 12 - Strategy and the Analysis of Capital Investments
12-88
12-57 (Conitnued-2)
2. Sensitivity analysis:
a. if the company’s pre-tax WACC is 16% (rather than 15%), then the
required annual volume changes to 203,155 units (% change =
3.00%), as follows:
Cash
Discount
Present
Year
Flows (000s)
Factor (@16%)
Value (000s)
1
($750,000)
0.862068966
($646,552)
2
($1,750,000)
0.743162901
($1,300,535)
($1,947,087)
3
0.640657674
4
0.552291098
5
0.476113015
6
0.410442255
7
0.353829530
8
0.305025457
cm/unit sold =
$3,500
Annual volume = 203,155
PV of inflows =
$1,947,087,000
% increase in volume = 3.00%
% increase in discount rate = 6.67%
b. if the company’s pre-tax WACC is 14% (rather than 15%), then the
12-89
12-57 (Continued-3)
The above results were generated using the following GOAL SEEK entries:
2c. Sensitivity issue: based on the limited analysis above, it does not
appear that the results are very sensitive to the assumption
units produced).
3. Selected strategic considerations, including those related to risk
management, that would likely bear on this decision:
Chapter 12 - Strategy and the Analysis of Capital Investments
12-90
12-57 (Continued-4)
a) Given volatility in the demand for fossil fuels, and wide price swings in
the cost of gasoline, are there any embedded options ("real options") in
this investment project?
b) A rather substantial investment outlay is required. How sensitive is the
product line(s)?
e) Would the company be at competitive risk were it not to invest in the
new technology? That is, is this new-car option available to the
company's competitors? If these competitors invest in this area, would
the company be at strategic risk?
f) Does the company compete on the basis of product differentiation?
That is, is the new product consistent with the strategy the company is
pursuing? Will, for example, the new facilities allow for reduced
