CHAPTER 20: CAPITAL BUDGETING
QUESTIONS
20-1 Capital budgeting decisions (a) are long-term in nature (i.e., they affect profitability
and cash flows for many years into the future), and (b) involve substantial amounts
of investment funds (capital). Because of these, formal models that focus on
discounted after-tax flows are needed for investment-analysis purposes.
20-2 As members of managerial decision-making teams, accountants can add value to
the capital budgeting process in at least four ways: (1) ensuring linkage between the
capital budgeting process and the organization’s master budget; (2) ensuring
linkage to the strategic plans of the organization (e.g., integrating capital budgeting
into an organization’s Balanced Scorecard); (3) generating relevant cash-flow
estimates for capital budgeting decision models; and (4) participating in the conduct
of post-audits for capital investments. The first area relates to the planning, the
second and fourth areas relate to the control function of management, while the
third area relates to the decision-making function of management.
20-3 The analytic hierarchy process (AHP) is one of several multi-criteria decisionmaking techniques, that is, decision models that include more than a single decision
criterion. As such, the model can incorporate both financial and nonfinancial
(strategic) decision criteria, weighted according to managerial preferences.
Dedicated software (e.g., Expert Choice) is available to guide the process of
determining the weights associated with various decision criteria and the selection
of investment projects based on these criteria. The AHP has been applied
successfully to numerous decision contexts.
20-4 Project Initiation:
 Purchase price of equipment
 Transportation/insurance costs for new equipment
 Installation costs
 Training costs
 Investment tax credits (if applicable)
 Gross proceeds from sale of old asset (if applicable)
 Tax-savings associated with deductibility of loss on sale of old asset (if
applicable)
Project Operation:
 Inflows: After-tax fees from patients/third-party payers (insurance companies,
the government)
 Inflows: Income-tax savings due to depreciation deductions
 Outflows: After-tax salary, wages, and benefits for additional professional
medical staff including: Physicians, Technicians, Nurses, and Clerks
 Outflows: After-tax operating expenses for the scanner, such as Utilities,
Supplies, and Maintenance expenses
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Project Disposal:
 After-tax proceeds from sale/disposal of asset
 After-tax disposal costs
20-5 After 20 years of operation, the company needs to ensure that there is no residual
effect on the environment before abandoning the chemical factory. Restoration of
the site to remove any environmental effect to the neighborhood the factory might
have caused over the years is the most critical step the firm needs to take. Very
likely it is also among the most expensive processes and as such should be
included in any capital budgeting decision model used to evaluate the proposed
investment.
20-6
Income-tax effects represent changes (i.e., increases or decreases) to the incometax liability of the firm. Tax effects of a decision to acquire new factory equipment
may include:
 Decreases in income taxes because of the deductibility of depreciation
expenses of the factory equipment.
 Increases in tax payments for taxable gains (or decreases in tax payments for
tax-deductible losses) on disposal of the old equipment.
 Increases in tax payments for taxable gains (or decreases in tax payments for
tax-deductible losses) on disposal of the new assets at the end of their useful
lives.
 Investment tax credit (if applicable).
 Income-tax shield associated with any equipment-related operating expenses
(e.g., maintenance).
20-7 Book value of an existing asset is, by itself, irrelevant in terms of the decision to
replace the asset. However, any taxable gain or loss recognized on the disposal of
an asset is partly a function of the tax basis of the asset. Such gains or losses
affect the tax payments, and therefore cash flows, of the firm. These cash-flow
effects are relevant in capital budgeting decisions.
20-8 Among the limitations of the payback period decision model are its failure to
consider a project’s total profitability over its useful life and failure to incorporate the
time value of money. The present value payback period model considers the time
value of money. However, it too fails to consider the profitability of a project over the
project’s entire lifetime. Critics maintain, therefore, that the use of this method for
investment analysis may bias decisions away from long-term, strategic investments
in favor of short-lived projects—that is, toward those that have a quick payback
period.
20-9 The book (accounting) rate of return of an investment is not likely to yield a true
measure of the rate of return on the investment because it does not consider the
time value of money and because it includes in its computation accrual-based
accounting numbers (rather than after-tax cash flows). In contrast, the internal rate
of return (IRR) of a project, because it focuses on discounted cash flows, represents
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20-2
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an estimate of the true (i.e., economic) rate of return on a proposed investment. For
example, a project with an estimated IRR of 14% means that the cash flows from
the project are adequate both to recover the initial investment outlay of the project
and earn a financial return of 14% on the project over the project’s useful life.
Because of this, we can say that the decision rule using the IRR is well defined; by
contrast, the decision rule associated with the ARR is defined heuristically. Further,
students should understand that in practice uniformity does not exist regarding how
the ARR is calculated. Such differences can complicate inter-divisional profitability
comparisons.
20-10 The decision criterion for the NPV method is the amount and direction of the net
present value. A proposed investment with a positive NPV should be accepted.
Furthermore, a higher NPV signals a better capital investment.
The IRR method uses a different decision criterion for evaluating capital
investments. The decision criterion is the desired rate of return for the investment
project. A project is a good investment if the estimated rate of return on the project
(i.e., the IRR) exceeds the desired rate of return. The desired rate of return can be
the weighted-average cost of capital of the firm (for “average-risk” projects) or a rate
that the firm sets for the investment based on the unique risk characteristics of the
proposed project.
20-11 Discounted cash flow (DCF) techniques such as NPV or IRR focus on the after-tax
cash flows of a proposed investment. Some maintain that such a focus might leave
out other important factors relevant to a proper analysis of a proposed investment,
such as effects of the investment on the firm’s strategic position, competitive
advantage, community in which the firm locates or serves, or relationships with
unions. Multi-criteria decision models, such as the AHP, incorporate both financial
and nonfinancial/qualitative criteria. The counter to this argument is that the
financial effect of such factors should be embodied in cash-flow estimates used for
investment analysis.
20-12 Sensitivity analysis is a tool managers can use to address uncertainty/risk
associated with the evaluation of proposed capital expenditures. Essentially, the
goal is to determine the sensitivity of the decision (e.g., whether to accept or reject a
proposed investment) to estimates of the input variables in a decision model (e.g.,
project life, or discount rate in DCF decision models). Three approaches to
sensitivity analysis, in increasing complexity, are discussed in the text: “what-if”
analysis; scenario analysis; and, Monte Carlo simulation.
20-13 Among important behavioral factors that might affect capital investment decisions
are:
 Desires of managers to grow through acquisitions and new investments
 Tendency to escalate commitments
 Effects of prospects on capital investment decisions
 Propensity of not wanting to spend additional time and effort needed to secure
capital investments
 Intolerance of uncertainty/risk
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20-14 The NPV method weighs early cash flows heavier than cash flows in the distant
future in at least two ways. First, amounts of discount applied to early cash flows are
less than those of later cash flows. Thus, one dollar to be received in the first year
increases the NPV of the investment project more than that of one dollar to be
received in, say, the fifth year of the investment. Second, each dollar earns
additional returns in each of the subsequent periods. Thus, an early dollar earns
returns over a longer period of time than that of a late dollar.
20-15 No—depreciation expenses affect capital investment decisions in two ways:
1. They decrease periodic net incomes from investment and, thereby, provide a
reduction in income-tax payments.
2. They decrease the book value of the investment and, as a result, increase the
gain or decrease the loss from the disposal of the investment at the end of its
economic life, which in turn affects the tax liability of the firm in the year of asset
disposal.
20-16 The minimum rate of return that a firm requires may change from one year to the
next because of changes in factors associated with the estimation of the firm’s
weighted-average cost of capital; for example, the weights associated with its
targeted capital structure may change, the estimated risk-free rate of interest may
change, or the average interest rate on debt issued by the firm may change.
Also, as explained in the chapter, financial theory suggests that a firm’s
estimated weighted-average cost of capital becomes the minimum acceptable rate
of return for proposed investments of “average risk.” Thus, the discount rate used to
evaluate a particular investment may differ from the WACC due to the perceived
risk characteristics of that investment. The procedures for handling such
adjustments are covered in finance texts and advanced treatments of capital
budgeting.
20-17 a. The firm can expect to earn a higher return than the cost of funds needed for the
investment; thus, using the IRR decision model, this project should be accepted.
It promises to fully recover the initial investment in the project plus provide an
economic return of 11% over the life of the project.
b. A capital project that has an NPV of $148,000 based on 10 percent discount rate
(weighted-average cost of capital) indicates that the investment will earn the firm
a present-value return of $148,000 above the required 10 percent rate of return.
20-18 A firm that chooses to build often faces many uncertainties, uses evolving
technologies, and operates in environments that are not familiar to management
and that can change rapidly. Capital budgeting processes in these firms are often
less formal, rely less on formal analyses, use more nonfinancial and nonquantifiable data (such as market share potential and competitors’ actions), and
apply subjective evaluation/decision criteria. These firms are likely to allow relatively
long payback periods or low discount rates in DCF models.
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In contrast, a firm that chooses to harvest is more likely to be in a mature
market. As a result, its capital budgeting processes are more likely to be formalized.
Most data needed for capital investment decisions are quantifiable and financial in
nature. For such firms, required payback periods tend to be relatively short and
discount rates (because of underlying risk) relatively high.
20-19 1. Capital budgeting is a process of assessing projects that require commitments of
large sums of funds and that generate benefits stretching well into the future.
Examples of capital budgeting projects include: purchase of new manufacturing
equipment, acquisition of new facilities, development and introduction of new
products, and expansion into new sales territories. (Additional examples are
offered at the beginning of the chapter.)
2. Differences between payback and NPV methods of capital budgeting include
recognition of time value of money, decision criterion for selecting the best
investment, number of periods considered, and the nature of the decision rule.
The payback method ignores the time value of money and, as such, treats a
dollar today the same as a dollar in the future. These two methods also differ in
terms the decision rule employed. Using the payback period method, a superior
investment is the one with a short or quick payback. The decision criterion of the
NPV method is the NPV of a proposed investment. Under normal circumstances
(see the Appendix to the chapter for the exception to this general statement), a
superior investment is the one with the highest NPV. In addition, the payback
period method considers only cash flows needed to recover the initial
investment. Cash flows after the payback period are not included when using the
payback period method. In contrast, the NPV method includes all cash flows.
Finally, the decision rule for the NPV method is well defined conceptually: accept
a project if it has a positive NPV. In contrast, the decision rule for the payback
period model is determined subjectively/heuristically.
3. The “cost of capital” of a firm is the weighted average of the cost of the funds
that comprise the firm’s targeted capital structure. Conceptually, market rates of
return for the firm’s securities are used to estimate the WACC. Further, the
weights used in determining the WACC are based on market, not accounting/
book, values.
4. Financial accounting data often are not suitable for use in capital budgeting
because financial accounting uses accrual accounting in all of its
measurements. Thus, the net income of a period may include revenues not yet
paid by customers and exclude payments made to suppliers for future deliveries.
Receivables included in the revenues of the period are not available to the firm
for payments. The amount of cash paid is no longer available for other
payments, even though the payment is not an expense of the period. In short,
accrual-based accounting data, though required for external reporting and tax
purposes, do not provide relevant cash-flow data used in DCF decision models.
One way accountants can add value to the organization is through the
estimation of all relevant cash flows associated with a proposed investment
project.
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
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5. As part of the overall control of capital expenditures, firms may conduct what are
referred to as post-audits (post-implementation audits). The goal is to compare
realized benefits and costs (including nonfinancial benefits and costs) to those
that were used to secure funds for the investment. In practice, it may be difficult
to untangle such items for individual projects. That is, information gathering
costs associated with individual projects can be significant. For this reason,
some companies conduct post-audits for only a sample of investment projects.
20-20 (Appendix): With unlimited funds available at 10 percent cost, the firm needs to
ensure that all investments will earn an economic return of at least 10 percent. As
explained in the appendix, if the firm operates under a capital constraint, it needs to
compare relative returns of competing investment opportunities (e.g., through the
use of Profitability Index information) in constructing its optimal capital budget. The
PI of a proposed investment is the ratio of the NPV of the project to its initial outlay
cost. As such, it provides a measure of the profitability of the investment per dollar
of invested capital.
20-21 (Appendix): The NPV model and the IRR model may yield conflicting results when
two investment projects are being compared and these projects differ in:
 Size of initial investment
 Timing of net cash inflows
 Pattern of net cash inflow
 Length of useful life
20-22 (Appendix): Because of the scaling process, the size of initial investment has no
effect on the rate of return as determined using the IRR model. However, a project
with a larger initial investment will likely have a higher NPV than a project with a
smaller initial investment (simply because it is bigger) and often becomes the
preferred investment when using a NPV method to analyzing capital investments.
An analogy can be drawn here to evaluating the financial performance of
organizational subunits: bigger units are advantaged when evaluated using absolute
performance measures, a situation that can be addressed by using relative
performance indicators such as ROI or IRR. Perhaps this explains the popularity in
practice of using ROI for divisional financial performance evaluation.
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-6
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BRIEF EXERCISES
20-23 Calculating After-tax Cash Flows
Given a marginal income-tax rate of 34%:
a) The after-tax cash effect of a $1,000 increase in cash contribution margin =
increase in pre-tax cash operating income x (1 – t)
= $1,000 x (1 – 0.34) = $660.00 increase
b) The after-tax cash effect of a $500 increase in cash operating expenses =
increase in pre-tax cash expense x (1 – t)
= $500 x (1 – 0.34) = $330.00 decrease
20-24 Present Value of a Single Amount
Present value of $1,000 to be received two years from now (note that the
difference in answers below is attributable to the rounding):
a) Using PV table (Table 1, page 870):
1) @ 10%: $1,000 x 0.826 = $826.00
2) @ 14%: $1,000 x 0.769 = $769.00
3) @ 20%: $1,000 x 0.694 = $694.00
b) Using Excel:
20-25 Present Value of an Annuity
Given a 5-year stream of cash flows, $500 per year, at 14%:
a) Using the annuity table (see text, page 871):
PV of annuity = PV annuity factor x $500
= 3.433 x $500 = $1,716.50
b) Using the built-in PV function in Excel:
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-7
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20-26 SL Depreciation Calculation Using Excel
20-27 Calculating After-tax Cash Flows
Indirect Method:
Pre-tax Income ($260 – $140 – $50)
Less: Income-tax Expense
After-tax Income
Plus: Non-cash charges (depreciation)
After-tax cash flow
Direct Method:
After-tax cash operating income
($260 – $140) x (1 – 0.35)
Plus: Depreciation tax shield
($50 x 0.35)
After-tax cash flow
=
=
=
=
=
$70.00
24.50
$45.50
50.00
$95.50
=
$78.00
=
=
$17.50
$95.50
20-28 MACRS Depreciation Calculations
3-year property, cost = $10,000:
Year 1 =
Year 2 =
Year 3 =
Year 4 =
$10,000 x 33.33% = $3,333
$10,000 x 44.45% = $4,445
$10,000 x 14.81% = $1,481
$10,000 x 7.41% = $ 741
Sum
= $10,000
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20-29 Present Value of MACRS Depreciation Deductions
Net present value of depreciation tax deductions, given an after-tax discount
rate of 12.00%, MACRS 3-year property, and an asset-acquisition cost of
$10,000 = $3,218, as follows:
Asset Cost =
After-tax Discount Rate =
Marginal Income-Tax Rate =
MACRS
Depreciation
Year
%
Deduction
1
33.33%
$3,333
2
44.45%
$4,445
3
14.81%
$1,481
4
7.41%
$741
100.00%
$10,000
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$10,000
12.00%
40.00%
Tax
Savings
$1,333
$1,778
$592
$296
$4,000
20-9
PV
Factor
0.893
0.797
0.712
0.636
Present
Values
$1,191
$1,417
$422
$189
$3,218
©The McGraw-Hill Companies 2008
20-30 Sensitivity Analysis: Use of “Goal Seek” Function in Excel
Starting point = solution to 20-29, as follows:
Then, use the following Goal Seek commands in Excel:
Final solution: the income-tax rate must be 49.72%
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-10
©The McGraw-Hill Companies 2008
20-31 After-tax Proceeds, Asset Disposals
Given a NBV of $25,000 and a marginal income-tax rate of 34%:
a) If net sales price = $35,000 (i.e., gain situation):
After-tax proceeds = (net sales price – NBV) x (1 – t)
= ($35,000 – $25,000) x (1 – 0.34)
= $10,000 x 0.66 = $6,600
b) If net sales price = $15,000 (i.e., loss situation):
After-tax proceeds = net sales price + tax savings due to loss
deduction
= $15,000 + [($25,000 – $15,000) x t ]
= $15,000 + $3,400 = $18,400
20-32 Unadjusted Payback Period and NPV Using Excel
The project’s NPV = $459, as follows:
Unadjusted payback period = 4.0 years
20-33 Estimating Weighted-Average Cost of Capital (WACC)
The weighted-average cost of capital (WACC) = 9.83%, as follows:
Source of Funds
Long-term Debt
Preferred Stock
Common Stock
Market Value
$40
$20
$60
$120
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(1)
Required Rate of
Return
7.00%
9.00%
12.00%
20-11
(2)
Weights
0.3333
0.1667
0.5000
1.0000
(1) x (2)
2.33%
1.50%
6.00%
9.83%
©The McGraw-Hill Companies 2008
EXERCISES
20-34 Basic Capital Budgeting Techniques (45 min)
a. Project A:
Payback Period 
$5,000
$1,800
 2.78 years
Or, 2 years and 10 months
b. Project B:
Year
1
2
3
4
After-tax
Cash Inflows
$ 500
1,200
2,000
2,500
Payback Period  3 
Cumulative
After-tax Cash Inflows
$ 500
1,700
3,700
($5,000  $3,700)
$2,500
 3.52 years
Or, 3 years and 7 months
c. Project C:
Depreciation expense per year: $5,000 ÷ 5 = $1,000
Taxable income each year: $2,500 – $1,000 = $1,500
Income taxes each year: $1,500 x 25% = $375
Annual after-tax net cash inflow: $2,500 – $375 = $2,125
Payback Period 
$5,000
$2,125
 2.35 years
Or, 2 years and 5 months
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20-12
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20-34 (Continued-1)
d. Project D:
(1) Depreciation expense per year: ($5,000 – $500) ÷ 5 = $900
Taxable income:
Sales
Expenses:
Cash expenditures
$1,500
Depreciation
900
Operating income before taxes
Income taxes (25%)
Operating income after taxes
$4,000
2,400
$1,600
400
$1,200
Book rate of return = $1,200  $5,000 = 24.00%
(2) Average book value = ($5,000 + $500)  2 = $2,750
Book rate of return = $1,200  $2,750 = 43.64%
e. Net Present Values (@8%), rounded:
($1,800 x 3.993) – $5,000 =
$7,187 – $5,000 = $2,187
Project A:
Project B:
Year
0
1
2
3
4
5
After-tax
Cash Flows
8% Discount
Factor
$ 500
0.926
1,200
0.857
2,000
0.794
2,500
0.735
2,000
0.681
Net Present Value (NPV) =
Present
Values
<$5,000>
463
1,028
1,588
1,838
1,362
$1,279
($2,125 x 3.993) – $5,000 =
$8,485 – $5,000 = $3,485
Project C:
Project D:
Present value of cash inflows:
Years 1 through 4
Year 5
Initial investment
Net present value (NPV)
($1,200 + $900) x 3.312 =
($2,100 + $500) x 0.681 =
Present value of cash inflows =
=
=
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-13
$6,955
1,771
$8,726
5,000
$3,726
©The McGraw-Hill Companies 2008
20-35 Weighted-Average Cost of Capital (WACC) (15 min)
a. Bond interest expense before taxes
$5,000,000 x 9% =
$450,000
$450,000 x 30% =
135,000
=
$315,000
$5,000,000 x 110% =
$5,500,000
$315,000 ÷ $5,500,000 =
5.73%
Income taxes on bond interest
After-tax bond interest expense
Market value of bond:
Current after-tax cost of this debt:
b. After-tax cost of preferred stock = dividend per share/market price per
share = $3 ÷ $30 = 10.00%
c. Using weights based on the current market values of debt and equity, the estimated
WACC for this firm is 13.08%, as follows:
Bond
Preferred
Stock
Common
Stock
Total
Interest
or
Dividend
Book Value
Rate
$5,000,000
9%
After-tax
Rate or
Expected
Return
5.73%
Current
Market
Values
$ 5,500,000
Cost of
Capital
Weights Components
0.275
1.58%
5,000,000
10%
10.00%
6,000,000
0.300
3.00%
500,000
$10,500,000
N/A
20.00%
8,500,000
$20,000,000
0.425
1.000
8.50%
13.08%
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20-14
©The McGraw-Hill Companies 2008
20-36 Future and Present Values Using Excel (20 min)
A. To calculate future values, use the following Excel function:
FV(rate,nper,pmt,pv,type)
1. Between January 1, 1701 and December 31, 2007 there are 614 six-month
periods (nper). Thus, at the end of year 2007, at an annual interest rate of 6%
compounded semiannually, the $24.00 will have grown to $1,829,225,347, as
follows:
FV(0.06/2,614,0,-24,0)
2. FV(0.08/2,614,0,-24,0) = $$689,733,898,953
3. a. FV(0.06/4,1228,0,-24,0) = $2,091,756,483
b. FV(0.08/4,1228,0,-24,0) = $873,418,055,163
4. FV(0.08/2,12,0,-9500000000,0) = $15,209,806,076
B. To calculate present values, use the following Excel function:
PV(rate,nper,pmt,fv,type)
1. For a stream of ten (10) end-of-year payments of $25,200,000 (ordinary
annuity) and a discount rate of 12%, we have:
PV(0.12,10,-25200000,0,0) = $142,385,620
2. If the first payment is received the day the contract is assigned (annuity due),
we have:
PV(0.12,10,-25200000,0,1) = $159,471,895
3. Given an income-tax rate of 45%, the after-tax cost of (1) above is:
PV(0.12,10,-25200000*0.55,0,0) = $78,312,091.17
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20-37 After-Tax Net Present Value (NPV) and IRR (40 min)
A. 1. Net cash inflow each year: $62,000 – $30,000 = $32,000
Present value of net cash inflows (@10%) = $32,000 x 3.170 = $101,440
Therefore, NPV = $101,440 - $60,000 = $41,440
2. Net cash inflow before depreciation
Depreciation expense ($60,000/4 years)
Increase in net income before taxes
Income taxes rate
Income taxes
$32,000
15,000
$17,000
x
30%
$5,100
Net after-tax cash inflow = $32,000 – $5,100 = $26,900 per year
Present value of net cash inflows = $26,900 x 3.170 = $85,273
Therefore, NPV = $85,273 – $60,000 = $25,273
3. Double-declining balance depreciation (non-MACRS):
Year
0
1
2
3
4
Beginning
Book Value
Depreciation
Expense
$60,000
30,000
15,000
7,500
$30,000
15,000
7,500
7,500
Pre-Tax
DDB
Cash
Depreciation
Year Inflows
Expense
0
1 $32,000 $30,000
2
32,000
15,000
3
32,000
7,500
4
32,000
7,500
Taxable
Income
$ 2,000
17,000
24,500
24,500
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
30%
Income
Taxes
Accumulated
Depreciation
$30,000
45,000
52,500
60,000
After-tax
Net Cash
Inflow
Ending
Book Value
$60,000
30,000
15,000
7,500
0
10%
Discount
Factor
Present
Values
<$60,000>
$ 600
$31,400
0.909
28,543
5,100
26,900
0.826
22,219
7,350
24,650
0.751
18,512
7,350
24,650
0.683
16,836
Net Present Value (NPV) = $26,110
20-16
©The McGraw-Hill Companies 2008
20-37 (Continued)
b. 1.
$60,000 = $32,000 x A?, 4
A?, 4 = 1.875, which corresponds to a rate of return > 30%.
Using the IRR function of Excel, IRR = 39.08%
2.
$60,000 = $26,900 x A?, 4
A?, 4 = 2.230, which corresponds to 25% < IRR < 30%
By interpolation:
Discount Rate
25%
25%
?
30%
Difference
5%
?
Discount Factor
2.362
2.362
2.230
2.166
0.196
0.132
Therefore, Internal rate of return (IRR) =
25% 
0.132
 5%  28.37%
0.196
Or, using the IRR function in Excel, IRR = 28.27%:
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-17
©The McGraw-Hill Companies 2008
20-38 Basic Capital Budgeting Techniques: Uniform Net cash inflows, No
Income Taxes, Non-MACRS-Based Depreciation (45 min)
a.
Unadjusted Payback Period: As shown above, the payback period occurs between
years 4 and 5. Alternatively, the payback period = $500,000  $120,000/year =
4.17 years (about 4 years and 2 months)
b.
Book (accounting) rate of return:
As indicated above, the average increase in net income over the ten-year period =
$700,000/10 years = $70,000/year. Thus, the ARR
(1)
On initial investment:
(2)
On average investment:
Average investment:
Book rate of return:
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
$70,000/$500,000 =
14.00%
($500,000 + 0)/2 =$250,000
$70,000  $250,000 =
28.00%
20-18
©The McGraw-Hill Companies 2008
20-38 (Continued)
c.
NPV: using the PV factors from Table 2 (p. 871), NPV = $178,120
Based on the NPV function of Excel, the NPV = $178,027 (the difference in NPV
estimates is due to rounding that takes place when using the PV factors provided
in the Table 2 rather than the built-in NPV function)
d.
Present value payback period: as indicated in the above schedule, the present
value payback period is “6-plus” years; this is the time it takes for the present
value of future cash inflows to cover the original investment outlay of $500,000
$6,560
6 years +
= 6.12 years (6 years, 2 months)
$54,240
e.
Internal rate of return: as indicated in the above schedule, we can use the built-in
function in Excel to estimate the IRR for this proposed investment; IRR = 20.18%
Alternatively, we can estimate the IRR as follows. We are looking for an
interest/discount rate that provides for a NPV = $0 (i.e., a rate that provides a
present value of future cash inflows equal in amount to the original investment
outlay, $500,000). Thus,
PV of net cash inflows:
At 20% (i.e., a rate too low): $120,000 x 4.192
At 25% (i.e., a rate too high): $120,000 x 3.571
Difference in PV with 5% difference in discount rate
IRR = 20% +
$503,040 - $500,000
=
=
=
$503,040
428,520
$ 74,520
 5% = 20.20%
$74,520
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-19
©The McGraw-Hill Companies 2008
20-39 Basic Capital Budgeting Techniques: Uneven Net Cash Inflows, Income Taxes, Non-MACRS Depreciation
Calculations (50 min)
a.
Unadjusted Payback Period: as shown by the above schedule, the payback period is between 4 and 5 years.
Using a linear interpolation, we estimate the payback period as
Payback Period = 4 years +
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-21
$125,000
= 4.68 year s
$183,000
©The McGraw-Hill Companies 2008
20-39 (Continued)
b.
Book (accounting) rate of return:
As indicated above, the average increase in after-tax operating income over the ten-year period = $812,000/10
years = $81,200/year. Thus, the ARR
c.
(1)
On initial investment:
$81,200/$500,000 = 16.24%
(2)
Average investment = ($500,000 + 0)/2 =
$250,000
Book rate of return on Average Investment = $81,200  $250,000 = 32.48%
NPV: using the PV factors from Table 2 (p. 871), NPV = $203,866
Based on the NPV function of Excel, the NPV = $203,781 (the difference in NPV estimates is due to rounding
that takes place when using the PV factors provided in the Table 2 rather than the built-in NPV function).
d.
Present value payback period: as indicated in the above schedule, the present value payback period is “4-plus”
years; this is the time it takes for the present value of future cash inflows to cover the original investment outlay
of $500,000.
e.
Internal rate of return (IRR): as indicated in the above schedule, we can use the built-in function in Excel to estimate
the IRR for this proposed investment; thus, IRR = 19.88%
Alternatively, we can estimate the IRR as follows. We are looking for a interest/discount rate that produces a NPV =
$0 (i.e., a present value of cash inflows equal in amount to the original investment outlay, $500,000). Thus,
PV of net cash inflows at 18% (i.e., an interest rate too low):
PV of net cash inflows at 20% (i.e., an interest rate too high):
Difference in PV with 2% difference in discount rate
$540,042
$497,623
$ 42,419
Therefore,
Internal rate of return (IRR)
=
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
18% +
20-22
$540,042 - $500,000
 2% = 19.89%
$42,419
©The McGraw-Hill Companies 2008
20-40 Basic Capital Budgeting Techniques: Uneven Net Cash Inflows, Income Taxes, and MACRS Depreciation (60
min)
1. Payback period: as shown by the above schedule, the payback period is between 4 and 5 years. Using a linear
interpolation, we estimate the payback period as
Payback Period = 4 years +
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
$60,920
$185,280
20-26
= 4.33 years
©The McGraw-Hill Companies 2008
20-40 (Continued)
2. Book rate of return (ARR):
Average after-tax operating income/year:
$812,000/10 =
$81,200
Book (accounting) rate of return (ARR):
a. On initial investment:
$81,200/$500,000 = 16.24%
b. On average investment:
Computation of Simple Average Annual Investment:
Book Value,
Beginning-ofYear
Year
Average
investment:
1
$500,000
2
400,000
3
240,000
4
144,000
5
86,400
6
28,800
7
8
9
10
Totals
Depreciation
Average BV
Expense for
Book Value,
During the
the Year
End-of-Year
Year
$1,149,200/10
=
$114,920
$100,000
$400,000
$450,000
160,000
240,000
320,000
96,000
144,000
192,000
57,600
86,400
115,200
57,600
28,800
57,600
28,800
0
14,400
0
0
0
0
0
0
0
0
0
0
0
0
$500,000
$1,149,200
Book rate of return (ARR): $81,200/$114,920 = 70.66%
3. Net Present Value (NPV): as indicated in the above schedule, the NPV of the proposed
investment is $229,821 (based on PV factors from Table 1, p. 870). Based on the builtin NPV function in Excel, the estimated NPV is $229,743. The difference in estimates is
due to the rounding that is embodied in the PV factors taken from Table 1.
4. Internal Rate of Return (IRR): as indicated in the above schedule, we can use the
built-in function in Excel to estimate the IRR for this proposed investment; IRR =
21.46%. Alternatively, we can use a linear interpolation procedure to estimate the
project’s IRR, as follows: we are looking for an interest/discount rate that produces a
PV of cash inflows equal to the net original investment outlay ($500,000). Thus,
PV of net cash inflows at 20% (a rate that is too low):
PV of net cash inflows at 22% (a rate that is too high):
Difference in PV with 2% difference in discount rate:
Thus,
IRR = 20% +
$27,875
$527,875
$490,273
$ 37,602
 2% = 21.48%
$37,602
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-27
©The McGraw-Hill Companies 2008
20-41 Straightforward Capital Budgeting with Income Taxes (Non-MACRS-based
Depreciation) and Sensitivity Analysis (20 min)
1.
Depreciation per year, SL basis: ($30,600 – $600)/6 years = $5,000
Taxable income
$8,000 – $5,000 =
Tax rate
3,000
x
Income taxes
40%
$1,200
Pre-tax annual cash flow (cash savings) = $8,000
Net after-tax annual cash inflow: $8,000 – $1,200 = $6,800
2.
Payback period: $30,600/$5,000 = 6.12 years (if cash flows are assumed to occur
at end of year, then the appropriate answer would be 7 years)
3.
PV of annual after-tax cash savings
$5,000 x 4.623 =
PV of salvage value
$ 600 x 0.63 =
Total Present Value of Cash Inflows
378
$23,493
Initial Investment Cash Outlay
30,600
NPV
4.
$23,115
($7,107)
The minimum net after-tax annual cost savings needed to justify this investment =
$6,537
Let X = minimum after-tax annual cost savings, and let NPV =0. The Initial
Investment Outlay ($30,600) is reduced by the PV of the salvage value of the asset
@ an 8% discount rate (i.e., $378). Thus, when NPV = $0, we have (by definition):
PV of After-tax Cash Inflows = PV of Cash Outflows
4.623 X = $30,600 – $378
X = $30,222/4.623 = $6,537
(or, an increase of approximately 31% over the $5,000 amount given assumed
above in 2 and 3)
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-28
©The McGraw-Hill Companies 2008
20-42
Capital Budgeting with Tax, Non-MACRS Depreciation, and Sensitivity
Analysis (35 min)
Annual after-tax net cash inflow:
$1,200 x (1 – 0.35) =
($6,000/10) x 0.35 =
Cash revenue
Tax saving on depreciation expense
Total
1. Payback period:
$6,000
$990
$780
210
$990
= 6.06 years
2. Estimated Operating Income per year:
Sales
Depreciation
Operating income before taxes
Taxes
Operating income
$1,200
600
$ 600
210
$ 390
Therefore,
Book rate of return =
3.
$390
$6,000
= 6.5%
The maximum initial investment is such that the project at this level of investment
would yield a NPV = $0 (i.e., a situation where PV of cash inflows = PV of cash
outflows). The appropriate annuity factor for 10 years, 15% is 5.019. Let X =
maximum initial investment, then:
X = $990 x 5.019 = $4,969
4.
Required annual (pre-tax) cash revenue:
Given an initial investment outlay of $6,000, the after-tax
annual cash flow needed per year to generate a return
of 15% = $6,000/5.019 =
$1,195
Less: Annual Tax savings on depreciation expense =
210
Required after-tax annual cash revenue
$985
 (1 – t)
 0.65
Annual (pre-tax) cash revenue needed
$1,515
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-29
©The McGraw-Hill Companies 2008
20-42 (Continued)
5.
NPV Calculations under different assumptions regarding the discount rate (required
rate of return) and annual after-tax net cash inflows. Assume a ten-year life and an
initial investment outlay of $6,000.
Discount
Rate
10%
15%
20%
PV Annuity
Factor
6.145
5.019
4.192
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
Annual Net After-Tax Cash Flow
$500
$1,000
$2,000
($2,928)
$145
$6,290
($3,491)
($981)
$4,038
($3,904)
($1,808)
$2,384
20-30
©The McGraw-Hill Companies 2008
20-43 Basic Capital Budgeting (10-15 mins)
1. The after-tax cash flow from disposal of the old machinery =
after-tax gain on sale = ($1,800 – $0) x (1 – t) = $1,800 x 0.60 =
$1,080
2. The PV of after-tax operating cash savings = pre-tax operating cash savings x (1
– t) x PV annuity factor = $12,500 x 0.60 x 3.17 = $23,775
3. The PV of the depreciation tax-shield, year 1 = depreciation deduction x incometax rate x PV factor = $10,000 x 0.40 x 0.909 = $3,636
4. C
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-31
©The McGraw-Hill Companies 2008
20-44
PROBLEMS
Equipment Replacement Decision; Strategy (60 min)
1. & 3.
Overhaul AccuDril
Operating Cost1
Overhaul cost
Tax savings on deprec.2
Other Expenses3
Net after-tax cash flows:
Year 1
Year 2
Year 3
Year 4
Year 5
Total PV
Buy RoboDril 1010K
Net Equip. Purchase4
Operating Cost5
Tax savings on depr.6
Other expenses7
Salvage value8
Total PV
PV/
Annuity
Factor
Present
Value
0
After-tax Cash Flows (000s)
1
2
3
(48.0)
4.0
(57.0)
0.893
0.797
0.712
0.636
0.567
($90,193)
(160,197)
( 56,533)
( 50,498)
( 45,020)
($402,441)
1.000
3.605
3.605
3.605
0.567
($240,000)
(86,520)
69,216
(118,965)
17,010
($359,259)
(48.0)
(100.0)
4.0
(57.0)
4
(38.4)
(38.4)
(38.4)
16.0
(57.0)
16.0
(57.0)
16.0
(57.0)
(101.0)
(201.0)
(79.4)
(79.4)
(79.4)
(240.0)
(24.0)
19.2
(33.0)
(24.0)
19.2
(33.0)
(24.0)
19.2
(33.0)
(24.0)
19.2
(33.0)
PV difference in cash flow between alternatives= $402,441 – $359,259 = $43,182 in favor of RoboDril
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-33
5
©The McGraw-Hill Companies 2008
(24.0)
19.2
(33.0)
30.0
20-44 (Continued-1)
NOTES
1 and 2: $10 per hour x 8,000 hours x (1 – t) =
Years 3, 4, and 5: $48,000 x (1 – 20%) =
1Years
2
$48,000
$38,400
Years 1 and 2:
Depreciation expense per year (SL basis):
($120,000 – $20,000)  10 =
Income Tax Rate (t)
Tax savings on depreciation, Years 1 and 2
x
Years 3, 4, and 5:
Book value before overhaul (end of original useful life)
Overhaul cost, Year 3
Total amount to be depreciated
Number of years
Depreciation expense per year
Income Tax Rate (t)
Tax savings on depreciation, Years 3, 4, and 5
3
$95,000 x (1 – t) = $95,000 x 0.60 = $57,000
4
Purchase price
Installation, testing, rearrangement, and training
Subtotal
Trade-in allowance for AccuDril
Net purchase cost
$10,000
0.40
$ 4,000
$ 20,000
100,000
$120,000

3
$ 40,000
x
40%
$ 16,000
$250,000
30,000
$280,000
–
40,000
$240,000
+
5
($10/hour x 4,000 hours) x (1 – t) = $40,000 x 0.60 =
6
Depreciation expense per year: $240,000  5 Years =
Income Tax Rate (t)
Annual Tax savings on depreciation deduction
7
$55,000 x (1 – t) = $55,000 x 0.60 =
$33,000
8
($50,000 - $0) x (1 – t) = $50,000 x 0.60 =
$30,000
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-34
$24,000
$48,000
x
0.40
$19,200
©The McGraw-Hill Companies 2008
20-44 (Continued-2)
2.
Year
0
Net After-tax Cash Flows
AccuDril
RoboDril
$0
($240,000)
Difference in
Cash Flows
($240,000)
Cumulative
Difference
($240,000)
1
($101,000)
($37,800)
$63,200
($176,800)
2
($201,000)
($37,800)
$163,200
($13,600)
3
($79,400)
($37,800)
$41,600
Thus, the payback period for investing in the new machine is 2-plus years. Using a
linear interpolation method, we estimate the payback period as:
Payback period = 2 years +
$13,600
= 2.33 years
$41,600
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
 Reliability of the new machine and the expected effects of overhaul
 Reliability of AccuDril and accuracy of the estimates given
 Competitive strategy of the firm
 Differences in product qualities manufactured by the two machines
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-35
©The McGraw-Hill Companies 2008
20-45 Sensitivity Analysis (75 min)
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 needs to be
brought back two years, to get a present value of the cash flows in years 3
through 5: 2.402 x 0.797 = 1.914
(2) Alternatively, we could sum the PV factors from years 3, 4, and 5:
0.712 + 0.636 + 0.567 = 1.914
Thus, the additional annual after-tax operating cost savings needed from improvement
to make the overhaul of AccuDril a financially attractive choice = $22,561, as follows:
$43,182
= $22,561
1.914
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:
$22,561
= $37,602
0.6
$37,602
$80,000
= 47%
In sum, for the replacement decision to be in error financially, the after-tax variable
operating costs would have to be reduced, in years 3-5, by 47%.
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-36
©The McGraw-Hill Companies 2008
20-45 (Continued-1)
2. The beginning spreadsheet contains the PV of each alternative:
Then, use the following Goal Seek commands in Excel:
This produces the following result (cell E11): the maximum amount that the annual
after-tax operating costs for the new machine can be = $36,000 (a 50% increase
from the current $24,000):
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-37
©The McGraw-Hill Companies 2008
20-45 (Continued-2)
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-38
©The McGraw-Hill Companies 2008
20-45 (Continued-3)
3.
Discount
Factor
Present
Value
0
Cash Flows (in 000s of dollars)
1
2
3
4
Overhaul in 2 years:
Tax savings from depreciation1
Overhaul cost
4.0
0.893
0.797
0.712
0.636
0.567
$3,572
$(76,512)
$11,392
$10,176
$ 9,072
$(42,300)
PV of overhaul in 2 years
16.0
16.0
1
3
4
5
4.0
4.0
4.0
33.6
Thus, by a small amount, it is better (financially) to overhaul now and again in 2 years.
20-39
2
(30.0)
9.6
24.0
(80.0)
Difference in cost between the two alternatives: $42,300 - $39,466 = $2,834
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
16.0
16.0
9.6
24.0
$(80,000)
$30,005
$2,869
$2,848
$2,544
$2,268
$(39,466)
16.0
(96.0)
(80.0)
1.000
0.893
0.797
0.712
0.636
0.567
PV of Overhaul now and again in 2 years
16.0
4.0
0
Overhaul now and again in 2 years:
Overhaul cost
Savings from Improved efficiency2
Tax savings on depreciation3
4.0
(100.0)
5
©The McGraw-Hill Companies 2008
3.6
4.0
4.0
4.0
20-45 (Continued-4)
1See
part (1), Problem 20-44, reproduced as follows:
Years 1 and 2:
Depreciation expense per year (SL basis):
($120,000 – $20,000)  10 years =
Income Tax Rate (t)
Tax savings on depreciation, Years 1 and 2
$10,000
x
0.40
$ 4,000
Years 3, 4, and 5:
Book value before overhaul (end of original useful life)
Overhaul cost, Year 3
Total amount to be depreciated
Number of years
Depreciation expense per year
Income Tax Rate (t)
Tax savings on depreciation, Years 3, 4, and 5
2
$ 20,000
100,000
$120,000

3
$ 40,000
x
40%
$ 16,000
Savings from the improved productivity = $10/hr. x 8,000 hours x 20% = $16,000
Less: Income Taxes on the savings (@40.0%) =
– 6,400
After-tax savings
$9,600
3 Years
1 and 2:
Book value at the time of overhaul: $10,000 x 2 + $20,000 =
Overhaul cost
Total amount to be depreciated
Number of years
Depreciation expense per year
Tax Rate
Tax savings on depreciation
$ 40,000
80,000
$120,000

2
$60,000
x
0.40
$24,000
+
Years 3, 4, and 5:
Overhaul cost
Number of years
Depreciation expense per year
Income tax Rate
Tax savings on depreciation
$30,000

3
$10,000
x
0.40
$ 4,000
4. As a follow-up to (3) above: although the cost difference between the two
alternatives is only $2,834, which is less than 0.3% of the annual sales dollars
($1,000,000), the benefit from offering higher quality products two years earlier
will most likely persuade the firm to undertake the overhaul two years early.
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-40
©The McGraw-Hill Companies 2008
20-46
Comparison of Capital Budgeting Techniques; Sensitivity Analysis (50 min)
1. Effects of the new equipment on operating income after tax:
Sales
$195 x 10,000 = $1,950,000
Cost of goods sold:
Variable manufacturing costs
$ 90
Fixed manufacturing costs:
Additional fixed manufacturing overhead:
$250,000/10,000 units =
$25
Depreciation on new equipment:
($995,000 – $195,000)/4 = $200,000/year
$200,000/10,000 units per year = + 20 + 45
Manufacturing cost per unit
$135
Times: Number of units
x 10,000
Total cost of goods sold
1,350,000
Gross margin
$ 600,000
Operating Expenses:
Variable marketing: Cost per unit
$ 10
Number of units
x 10,000 $100,000
Additional fixed marketing cost
+ 200,000
300,000
Operating income before taxes
$300,000
Income taxes (@30%)
–
90,000
Operating income after tax
$210,000
Thus, the company will increase its after-tax operating income by $210,000 each
year.
2.
After-tax operating income
Add: increased depreciation expense
After-tax cash inflow from disposal of equipment
Total cash inflow
Years
1 to 3
$210,000
200,000
$410,000
Year 4
$210,000
200,000
195,000
$605,000
The new machine will increase cash inflows by $410,000 in each of the first three years
and $605,000 in Year 4.
3.
Payback Period =
$995,000
= 2.43 years
$410,000
4.
Average investment = ($995,000 + $195,000)/2 = $595,000
Average after-tax operating income = $210,000
Book rate of return (ARR) based on average investment =
$210,000/$595,000 = 35.29%
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-41
©The McGraw-Hill Companies 2008
20-46 (Continued-1)
5.
Using PV and Annuity Tables:
PV of after-tax cash inflows (@14%):
Years 1 through 3:
$410,000 x 2.322 =
Year 4 ($410,000 + $195,000):
$605,000 x 0.592 =
Total present value future after-tax cash inflows
=
Less: Initial investment outlay
NPV of the proposed investment
$ 952,020
358,160
$1,310,180
995,000
$ 315,180
Using the NPV Function in Excel:
Thus, the estimated NPV of the investment = $315,078 (note the rounding error
that occurs when using the PV and annuity factors)
6.
Trial-and-Error Approach (initial investment outlay = $995,000):
PV of cash flows @ 25%:
($410,000 x 1.952) + ($605,000 x 0.410)
PV of cash flows @ 30%:
($410,000 x 1.816) + ($605,000 x 0.350)
Difference in PV of after-tax cash inflows
$1,048,370
$ 956,310
$ 92,060
Thus, the estimated IRR for this investment is:
IRR = 25% +
$1,048,370 - $995,000
 5% = 27.90%
$92,060
Based on the built-in function in Excel, the estimated IRR of this project =
27.80%, as follows:
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-42
©The McGraw-Hill Companies 2008
20-46 (Continued-2)
7. 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 that would be permissible =
$315,078/2.914 = $108,126.
To convert this annual cost to a pre-tax basis, we would have to divide by the
quantity (1 – t), where t = the income-tax rate (30.0%). Thus, the maximum increase
in pre-tax variable cost = $108,126/0.70 = $154,466.
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 is, $154,466/20,000 units. This would
represent a decrease of approximately 4% ($7.72/$195.00).
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-43
©The McGraw-Hill Companies 2008
20-47
1.
Replacing a Small Machine: Capital Budgeting Techniques and
Sensitivity Analysis (50 min)
Although the new machine has the capacity of turning out 18,000 units per year, the
analysis should be based on 10,000 units per year because there is currently no
demand for the last 8,000 units. This is a mistake that students often make.
Year 0
Purchase price of the new machine
Proceeds from disposal of old machine
Income taxes on gain on disposal (@20%)
Net cash flow, year of purchase
($100,000)
$3,000
(600)
Years 1-4
After-tax cash operating costs, current machine:
($40,000 + 10,000 + 10,000) x (1 – 0.20)
=
After-tax cash operating costs, new machine:
($30,000 + 2,000 + 1,000) x (1 – 0.20)
=
After-tax savings in cash operating costs with the new machine
Incremental tax savings—depreciation expense:
Deprec. expense, new machine: $100,000  5 =
$20,000
Income tax rate = x
20%
Annual income-tax savings, new machine
=
$4,000
Less: Tax savings due to depreciation on
old machine
=
$0
Incremental after-tax cash inflows per year
Year 5
Incremental after-tax cash inflows, operating cost savings
Incremental after-tax disposal value of new machine:
After-tax cash inflow, disposal of new machine:
$5,000 x (1 – 0.20) =
$4,000
After-tax cash inflow, disposal of old machine:
$1,000 x (1 – 0.20) =
$800
Total cash inflow in year 5
2,400
($97,600)
$48,000
26,400
$21,600
$4,000
$25,600
$25,600
$3,200
$28,800
2.
PV of incremental after-tax cash inflows, years 1–4: $25,600 x 3.170 = $ 81,152
PV of incremental after-tax cash inflow, year 5: $28,800 x 0.621
=
17,885
Total PV of incremental after-tax cash inflows
$99,037
Less: Net initial after-tax cash outlay
– 97,600
NPV of proposed investment (@ 10%)
$ 1,437
3.
Payback period = $97,600  $25,600 = 3.81 years
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-44
©The McGraw-Hill Companies 2008
20-47 (Continued-1)
4.
The annuity factor needed is approximately 3.904 ($97,600  $25,000)
Interest Rate
8%
8%
?
9%
1%
?
Discount Factor
3.993
3.993
3.904
3.890
0.103
0.089
Thus, the estimated IRR of the proposed investment is 8.86%, as follows:
IRR = 8% +
0.089
 1% = 8.86%
0.103
5. Trial-and-Error Approach (Using Table 1, p. 870)--we are looking for a discount rate
that, when applied to the given cash flows, produces a $0 NPV (given the initial
investment outlay of $97,600):
Year
1
2
3
4
5
Cash
Inflows
$20,000
22,000
25,000
30,000
40,000
Interest Rate
10%
10%
?
12%
2%
?
Discount
factor at 10%
0.909
0.826
0.751
0.683
0.621
PV at
10%
$ 18,180
18,172
18,775
20,490
24,840
$100,457
Discount
factor at 12%
0.893
0.797
0.712
0.636
0.567
PV at
12%
$17,860
17,534
17,800
19,080
22,680
$94,954
PV of net cash inflows
$100,457
$100,457
97,600
94,954
$5,503
$2,857
Thus, the estimated IRR of the project equals approximately 11%, as follows:
IRR = 10% +
$2,857
$5,503
 2% = 11.04%
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-45
©The McGraw-Hill Companies 2008
20-47 (Continued-2)
Using Built-in Function in Excel: the projected IRR for this investment is 11.02%, as
follows:
6. PV of allowable after-tax increase in variable cost = NPV of the investment  annuity
factor (10%, 5 years) = $1,437  3.791 =
$379
1 – income-tax rate

0.8
Allowable pre-tax increase in variable costs per year
$474
Number of units
 10,000
Allowable cost increase per unit
$0.0474
Thus, the indifference point = $3.3474 ($3.30 + 0.0474) per unit. As such, the purchase
of SP1000 will be the correct decision as long as management is confident that the
estimated new variable cost will be within 1.4 percent of the estimated amount
($0.0474/$3.30). This is not likely a large margin of error. Thus, the decision may
ultimately rest on qualitative/ strategic factors.
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-46
©The McGraw-Hill Companies 2008
20-48
Capital Budgeting with Sum-of-the-Years’-Digits Depreciation; Spreadsheet
Application (25 min)
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-47
©The McGraw-Hill Companies 2008
20-49
Working Backward: Determine Initial Investment Based on Book Rate of
Return (15 min)
Let Y = Cost of the new machine (i.e., required initial investment)
Then,
($6,750 
Y
)  (1  0.20)
10
 0.10
Y
($6,750 – 0.10Y) x 0.8 = 0.10Y
 Initial investment = $30,000
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-48
©The McGraw-Hill Companies 2008
20-50 Determine Initial Investment Based on Internal Rate of Return (10 min)
Let C be the cost of the machine. Then,
after-tax cash flow per year x annuity factor for 6 years, 10% = C
[$20,000 – (($20,000 – C/6) x 0.20)] x 4.355 = C
[$20,000 – $4,000 + 0.03333C] x 4.355 = C
$69,680 + 0.14517C = C
C = $69,680/0.8548 = $81,516
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-49
©The McGraw-Hill Companies 2008
20-51 Determine Periodic Cash Flow Based on Book (Accounting) Rate of Return
(ARR) (15 min)
Let Y be the firm's after-tax operating income. Then,
Y
= 0.15
$60,000
 Y = $9,000 per year
Pre-tax operating income = After-tax operating income/(1 - t)
= $9,000/(1 - 0.25) = $12,000 per year
Now, let X = pre-tax cash flow from operations. Then,
Operating income before taxes = X
$12,000 = X
– Non-cash charges
– ($60,000/5)
So that,
X = $12,000 + $12,000 = $24,000
Check:
Pre-tax Operating Income
Less: Income Taxes ($12,000 x 0.25)
After-tax Operating Income
Plus: Depreciation Expense
After-tax cash flow
Plus: Income taxes
Pre-tax operating cash flow
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-50
$12,000
($3,000)
$9,000
+ $12,000
$21,000
+ $3,000
$24,000
©The McGraw-Hill Companies 2008
20-52
Machine Replacement and Sensitivity Analysis without Taxes
(40 - 50 min)
Net additional cash outlay for the new machine (@ March 5, 2008):
$8,000 – $3,000 = $5,000
1. a.
Payback period: $5,000/$750 = 6.67 years
b.
Depreciation:
Old
($5,000 – $600)/11
New
($8,000 – $400)/10
= $400
Difference
= $760
$360
Operating expense (cash)
($750)
Difference in annual pre-tax income (reduction in expenses)
$390
Loss on trade-in of existing asset (at March 5, 2008) =
book value of asset – trade-in value = ($5,000 – $400) – $3,000
= $1,600 (this loss complicates the determination of ARR, but not
NPV or IRR for the proposed investment)
Book values:
3/5/2008
($5,000 – $400 deprec.)
3/5/2018
Average Investment (Book Value)
Old
$4,600
New
$8,000
600
400
$2,600
$4,200
Therefore, the incremental average investment on the new machine
= $4,200 - $2,600 = $1,600
The average incremental income, including recognition of the loss on disposal of the
existing machine, is $130, as follows:
Ten-Year Difference in Pre-tax Income = 10 x $390 =
Less: Loss on disposal of existing asset = $4,600 - $3,000 =
Total income difference in favor of new machine =
Average annual income difference =
$3,900
($1,600)
$2,300
$230
Thus, under the specified treatment of the loss on disposal of the existing machine, the
ARR of the proposed replacement decision is slightly over 14%, as follows:
ARR =
$230
= 14.38%
$1,600
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-51
©The McGraw-Hill Companies 2008
20-52 (Continued)
Students should be alerted to other possible treatments for the loss and to the
fact that this is a good example of one of the ambiguities associated with the use
of the ARR for capital investment decision-making.
c. NPV = ($750 x 5.650) – ($8,000 – $3,000) – [($600 - $400) x 0.322]
= $4,237.50 – $5,000.00 – $64.40 = ($826.90)
d. Given a negative NPV, we know that the IRR must be less than the discount
rate (12%). We are looking for a discount rate that produces a PV of future
cash inflows = $5,000 (net investment outlay for the new machine). We try,
somewhat arbitrarily, 7% and 8%, as follows:
PV of net cash inflows at 7% = ($750 x 7.024) – ($200 x 0.508)
=
$5,166
PV of net cash inflows at 8% = ($750 x 6.710) – ($200 x 0.463)
=
4,940
Difference
=
$ 226
 the estimated IRR = 7.73%, as follows:
7% + 
166
226
 1%  = 7.73%
2.
No, because NPV < $0 (NPV is – $826.90). Note that the decision based on the
ARR is ambiguous.
3.
Because the expected NPV of the project is negative, the firm would have to
realize operating cost savings greater than those originally assumed. Let the
required pre-tax annual savings = Y. Then, to make NPV = $0, we must have:
PV of Cash Savings
=
Original Investment Outlay
5.650Y - ($200 x 0.322)
=
$5,000
5.650Y =
$5,064.40
Y=
$896.35
(That is, the maximum savings per year before the decision not to invest is changed.
This revised amount represents a change of approximately 19.5% above the current
estimate of $750. Note that at annual cash savings of $896.35, the IRR on the
proposed investment would exactly equal 12%, the company’s cost of capital.)
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-52
©The McGraw-Hill Companies 2008
20-53 Value of Accelerated Depreciation (25 min)
1.
The incremental PV of using SYD depreciation rather than SL depreciation, at a
discount rate of 8%, is $1,272, as follows:
Year
1
2.
Depreciation Method
SYD
S-L
$40,000
$25,000
Difference
Amount
Tax Effect
$15,000
$6,000
PV
Factor
at 8%
0.926
PV of
Tax Effect
$ 5,556
2
30,000
25,000
5,000
2,000
0.857
1,714
3
20,000
25,000
(5,000)
(2,000)
0.794
(1,588)
4
10,000
25,000
(15,000)
(6,000)
0.735
(4,410)
$100,000
$100,000
$1,272
The incremental PV of using DDB depreciation rather than SL depreciation, at a
discount rate of 8%, is $1,615, as follows:
Year
1
Depreciation Method
DDB
S-L
$50,000
$25,000
Difference
Amount Tax Effect
$25,000
$10,000
PV
Factor
at 8%
0.926
PV of
Tax Effect
$9,260
2
25,000
25,000
-0-
-0-
0.857
3
12,500
25,000
(12,500)
(5,000)
0.794
(3,970)
4
12,500
25,000
(12,500)
(5,000)
0.735
(3,675)
$100,000
$100,000
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
-0-
$1,615
20-53
©The McGraw-Hill Companies 2008
20-53
3.
(Continued)
The incremental PV of using MACRS depreciation, rather than SL depreciation, at a
discount rate of 8%, is $1,345, as follows:
Year
1
Depreciation Method
MACRS
S-L
$33,3301
$25,000
Difference
Amount Tax Effect
$8,330
$3,332
PV
Factor
PV of
at 8% Tax Effect
0.926
$3,085
2
44,4502
25,000
19,450
7,780
0.857
6,667
3
14,8103
25,000
(10,190)
(4,076)
0.794
(3,236)
4
7,4104
25,000
(17,590)
(7,036)
0.735
(5,171)
$100,000
$100,000
$1,345
Notes:
1 $100,000 x 33.33%
2 $100,000 x 44.45%
3 $100,000 x 14.81%
4 $100,000 x 7.41%
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-54
©The McGraw-Hill Companies 2008
20-54 Capital Budgeting with Sensitivity Analysis (45 min)
1.
Expected annual net cash inflows ($600,000 + $100,000)
Income taxes at 30%
After-tax net cash inflows
=
=
=
$700,000
210,000
$490,000
The buyer is essentially purchasing an eight-year stream of after-tax rental incomes
and income-tax savings associated with the depreciation deduction. Thus, a rational
purchase price would be the PV of these future cash flows, using 12% as the discount
rate. Note, however, that the depreciation deduction is a function of the purchase
price, which we are trying to estimate. Therefore, let P denote the maximum price the
buyer would be willing to pay. The amount is approximately $3 million, as follows:
P = [$490,000 x A.12, 8] + [(P/8 x 0.3) x A.12, 8]
P = [$490,000 x 4.968] + [P/8 x 0.3 x 4.968]
P = $2,434,320 + 0.1863P
0.8137P = $2,434,320
P = $2,991,668
2.
From Meidi’s perspective, the selling price should be set such that it would cover three
things: (1) the PV of the after-tax rental incomes she is foregoing, (2) capital gains
taxes she would have to pay on the sale of the real estate, and (3) the sales
commission (5%) she has to pay the real estate broker. Thus, if this is the case,
Let S denote the minimum price Meidi would be willing to accept
S
S
S
0.57S
S
3.
=
=
=
=
=
[$460,000 x A.10, 8] + [(S – $800,000 – 0.05S) x 0.40] + 0.05S
[$460,000 x 5.335] + [0.38S – $320,000] + 0.05S
$2,454,100 + 0.43S – $320,000
$2,134,100
$3,744,035
MACRS depreciation increases to the buyer the PV of the depreciation write-offs
(compared to the use of the SL method, as in (1) above). Thus, to the extent the
buyer could realize these tax savings, the buyer would be willing to pay a higher price
for the property.
As in (1) above, we represent the maximum price the buyer would be willing to pay as
the sum of two components: the PV of after-tax rental incomes ($2,434,320) plus the
PV of the tax savings due to the depreciation deductions over the life of the property.
This second component is represented as 0.2214397P (where P represents the
purchase price, and therefore depreciable cost, of the property), as follows:
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-55
©The McGraw-Hill Companies 2008
20-54 (Continued)
Year
1
2
3
43
5
6
(1)
MACRS
Depreciation1
0.2000P
0.3200P
0.1920P
0.1152P
0.1152P
0.0576P
(2)
Tax Effect2
0.06000P
0.09600P
0.05760P
0.03456P
0.03456P
0.01728P
(3)
PV Factor
0.893
0.797
0.712
0.636
0.567
0.507
(2) x (3)
Present Value
0.0535800P
0.0765120P
0.0410112P
0.0219801P
0.0195955P
0.0087609P
0.2214397P
Notes:
1
See text, Exhibit 20.6 for MACRS depreciation rates, 5-year property
2
Assuming a 30% marginal income-tax rate.
3
First year of switching to SL depreciation method.
Thus, the maximum amount that a rational buyer would be willing to pay has
increased to $3,126,694, as follows:
P = $2,434,320 + 0.2214397P
0.7785603P = $2,434,320
P = $3,126,694 (an increase of $135,026 over the amount
calculated above in (1))
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-56
©The McGraw-Hill Companies 2008
20-55
1.
Cash Flow Analysis and NPV (40 min)
Item & Description
a. After-tax rent foregone
($5,000 x 0.6)
b. All are irrelevant
c. Remodeling cost
Deprec. tax savings2
d. Investment in net
working capital
Recovery
e. Irrelevant
f. Sales ($900 x 0.6)
Operating expenses
($500 x 0.6)
g. Sales Promotion ($100 x 0.6)
h. Termination ($50 x 0.6)
NPV
PV
Factor
PV
0
N/A
($128,931)1
($100,000)
$14,032
$7,382
$ 3,888
$2,557
$2,242
(100)
0.877
0.769
0.675
0.592
0.519
($600,000)
$311,400
(600)
0.519
3.433
(36)
(36)
(36)
5
(36)
(36)
16
9.6
5.76
4.32
4.32
600
$1,853,820
3.433 ($1,029,900)
($60,000)
0.519
($15,570)
$260,920
CASH FLOWS IN YEAR (in '000)
1
2
3
4
540
540
540
540
540
(300)
(300)
(300)
(300)
(300)
(60)
(30)
Notes:
1Use the PV function in Excel to determine the PV of a stream of 60 monthly cash receipts ($3000 per month,
after-tax). The appropriate formula is: =PV(0.14/12,60,3000)
2
Depreciation deductions found using the VDB function in Excel, as follows:
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-57
©The McGraw-Hill Companies 2008
20-55 (Continued)
The advantage of using the VDB function in Excel, rather than the DDB function, is that
there is a (default) option in the former that provides an automatic switch to the SL
method when it is advantageous to do so.
2. The positive NPV, $260,920, suggests that, compared to the leasing alternative, it is
financially advantageous to convert the facility into a factory outlet. The NPV from
converting the facility into a factory outlet is also better then the alternative of selling the
warehouse for $200,000 (see item b).
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-58
©The McGraw-Hill Companies 2008
20-56
Machine Replacement with Tax Considerations (30 - 45 min)
Present Value of Costs with the Original Equipment:
Present value of tax savings from depreciation deductions:
($2,500,000  4) x 0.45 x 2.577 =
Present value of cash operating costs:
[$1,800,000 x (1 – 0.45)] x 2.577 =
Present value of salvage value:
[$50,000 x (1 – 0.45)] x 0.794 =
Present value of costs with the original equipment =
($724,781)
$2,551,230
($21,835)
$1,804,614
Present value of Costs with the New Machine:
Initial outlay cost
$2,000,000
Present value of tax savings from depreciation deductions:
Beginning
Depreciation Tax
Tax
Discount
1
Year Book Value
Expense
Rate Savings
Factor
1
$2,000,000 $1,333,333 x 0.45 = $600,000 x 0.926 =
($555,600)
2
666,667
444,445 x 0.45 = 200,000 x 0.857 =
(171,400)
3
222,223
222,223 x 0.45 = 100,000 x 0.794 =
(79,400)
Cash proceeds from sale of the old machine
($300,000)
Tax savings related to loss on disposal of the old machine:
($1,875,0002 – $300,000) x 0.45
=
($708,750)
Present value of cash operating costs: $1,000,000 x (1 – 0.45) x 2.577 = $1,417,350
Present value of costs with the new machine
$1,602,200
Notes:
1DDB
depreciation charges were calculated using the VDB function in Excel, as
follows:
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-59
©The McGraw-Hill Companies 2008
20-56 (Continued)
2
Book value of old asset at time of sale =
Original cost – accumulated depreciation =
$2,500,000 – [($2,500,000/4) x 1 year] =
$2,500,000 – $625,000 = $1,875,000
PV of savings from using the new machine:
$1,804,614 – $1,602,200 = $202,414
The total cost of the new machine, including the purchase cost and the cash operating
cost in each of the three years, is in present value terms $202,414 below the total cost
of continuing with the original equipment. Therefore, from a purely financial standpoint,
the purchase of the new machine is a good investment.
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-60
©The McGraw-Hill Companies 2008
20-57
1. a.
b.
Equipment Replacement (35 – 50 min)
Selling price per unit
Variable cost per unit:
Direct materials
Direct manufacturing labor
Indirect manufacturing costs
Contribution margin per unit
$30.00
$0.25 x 8 =
$8.00 x 2 =
$2.00
16.00
0.30
18.30
$11.70
The standard overhead application rate per unit, based on a “normal capacity” of
100,000 units per year, consists of a variable and a fixed cost component, as
follows:
$0.3 +
$25,000
= $0.55
100,000
c.
Current level of fixed overhead costs per year
Increase in equipment depreciation:
New equipment
($100,000 – $10,000)  10 =
Current (SL) depreciation charges
Total budgeted fixed overhead costs per year
$25,000
$9,000
2,000
7,000
$32,000
New variable overhead cost per unit = old cost + $0.10 = $0.40.
Therefore, the total budgeted overhead cost per year
= $32,000 + [$0.40 per unit x units manufactured]
d. Based on a normal capacity level of 100,000 units, the new overhead rate per unit
would be $0.72, as follows:
$32,000
+ $0.40 = $0.72
100,000
e.
Selling price per unit
Variable cost per unit:
Direct materials (unchanged)
Direct labor ($8 per hour x 1 hour)
Indirect manufacturing costs
Contribution margin per unit
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
$30.00
$2.00
8.00
0.40
20-61
10.40
$19.60
©The McGraw-Hill Companies 2008
20-57
f.
g.
2.
(Continued)
Net purchase price of new saw
Gross proceeds from selling the old saw
Tax savings from loss on disposal:
Book value of old saw (given)
$20,000
Selling price
4,000
Loss on sale
$16,000
Income-tax rate
0.40
Net additional investment required for the new saw
Expected net additional cash flow per year:
Increase in cm/unit = $19.60 – 11.70 =
$ 7.90
Number of units per year
x 100,000
Increase in total contribution margin before taxes
Less: Increase in income taxes = $790,000 x 40%
Increase in total contribution margin after taxes
Plus: Additional tax savings from depreciation = $7,000 x 0.4
Expected additional net cash inflow per year
$100,000
$4,000
6,400
=
=
=
=
=
10,400
$89,600
$790,000
316,000
$474,000
2,800
$476,800
With over forty percent of the households in the community having at least one
member working for the firm, the firm is a major employer of the community. Unless
alternative employment opportunities can be created, a fifty percent reduction in its
workforce will have a major impact on the economy of the community.
To remain competitive, the firm needs to upgrade its equipment. However, the
shareholders and management should not be the only beneficiaries from the additional
net cash inflows. Although the firm may be able to ease the pain of layoffs by not filling
positions vacated through retirement or resignation, a reduction of one-half of its
employment will definitely be a major blow to the community. Thus, the firm needs to
consider using the additional net cash inflows to create new job opportunities for the
labor force that will be reduced.
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-62
©The McGraw-Hill Companies 2008
20-58
Equipment Replacement with MACRS Depreciation (35 - 45 min)
1. Per-unit profit margin of the additional units:
Sales price per unit
Current manufacturing cost
Current gross margin per unit
Cost savings per unit with the new machine
Gross margin (cash flow) per unit for the additional units
Net cash inflows:
Present
Item Description
Value
Purchase cost
($608,000)
Installation cost
($12,000)
After-tax proceeds from disposing old
$30,000
Gross margin/unit (above)
Additional units
Pre-tax cash flow from additional units (‘000)
Efficiency savings (‘000)
Total increase in pre-tax incomes/cash flow (‘000)
Income taxes (‘000)
Increase in after-tax cash flow before depreciation (‘000)
After-tax proceeds from disposal ($80,000 x 0.6)
Tax savings from depreciation (‘000)
After-tax cash inflows
$155,243
$168,286
$97,516
$109,115
Net Present Value (NPV)
($59,840)
$3,500
2,450
$1,050
+
150
$1,200
-
Discount
Factor
0.870
0.756
0.658
0.572
2010
2011
2012
2013
$1,200
30
$ 36
125
$161
64.4
$96.60
$1,200
50
$ 60
125
$185
74
$111
$1,200
50
$ 60
125
$185
74
$111
81.84
$178.44
111.60
37.20
$1,200
70
$ 84
125
$209
83.6
$125.4
48
17.36
VacuTech can expect to have a negative NPV of $59,840 if it purchases the new pump.
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-63
©The McGraw-Hill Companies 2008
222.60
148.20
190.76
20-58 (Continued)
2. Other factors the firm needs to consider include:







Maintenance costs of the machines
Reliability of the machines
Changes and timing of newer machine
Effects on production workers
Learning effect on using the new machine
Changes in market
Competitor reaction
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-64
©The McGraw-Hill Companies 2008
20-59
Joint Venture (10 – 20 min)
Present value of net cash inflows (at risk-adjusted
discount rate of 20%, 10 years)
=
($900,000 x 0.8) x 4.192
=
$3,018,240
Less: Initial investment outlay
=
3,000,000
NPV
=
$18,240
Yes. The group can expect a positive NPV of $18,240.
Note that the projected IRR of this project (20.18%) exceeds the minimum
required rate of return (20.00%), as follows:
This problem provides a good opportunity for the instructor to discuss why the
discount rate for certain types of investments (such as a joint venture in an emerging
economy) would likely exceed the organization’s weighted-average cost of capital
(WACC). The appropriate risk adjustment, as noted in the text, is the subject of
advanced discussions in corporate finance textbooks.
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-65
©The McGraw-Hill Companies 2008
20-60
1.
Risk and NPV (45 min)
PV of future cash inflows @ 12% = $275,000 x 6.194 =
Less: Initial investment outlay, year 0
=
Net present value (NPV)
=
$1,703,350
$1,500,000
$ 203,350
Since the NPV > $0, the project should be accepted.
2.
PV of future cash inflows @ 15% = $275,000 x 5.421 =
Less: Investment outlay, year 0
=
Net present value (NPV)
=
$1,490,775
$1,500,000
$(9,225)
Since the NPV < $0, the project should not be accepted.
3.
The “break-even” initial investment outlay is the amount that would produce a NPV
= $0, given the annual after-tax flows of $275,000 and a discount rate of 15.00%.
We can use Excel to solve, in two steps, for this “break-even” amount =
$1,490,670:
Step 1: Estimate the Project’s NPV (compare with 2 above)
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-66
©The McGraw-Hill Companies 2008
20-60 (Continued)
Step 2: Complete the following “goal seek” dialog box:
4.
Many firms raise the discount rate in evaluating a particular capital investment in
view of uncertainties underlying the investment. This approach allows managers to
factor in risks and uncertainties. The higher the risk or uncertainty a project has,
the higher the discount rate.
An alternative is to use a direct approach in dealing with risk or uncertainty. For
example, if a firm considers that revenues from an investment are likely to differ
from the projected figures, the firm should adjust the projected revenues. If the
expenses are likely to be higher, adjusting the projected expenses would allow the
firm to be aware of the need for a higher amount of cash outflows. Some believe
that using a direct approach (if possible) is better than simply using a higher
discount rate. In any case, the topic of risk adjustments is handled more
completely in financial management textbooks.
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-67
©The McGraw-Hill Companies 2008
20-61
1.
Sensitivity Analysis (40 min)
NPV of proposed investment,15-year project life:
PV of after-tax cash inflows = $600,000 x 6.142 = $3,685,200
Since NPV = $185,200, the investment should be undertaken.
NPV of proposed investment, 12-year project life:
PV of after-tax cash inflows = $600,000 x 5.660 = $3,396,000
Since NPV = ($104,000), the investment should not be undertaken.
2.
We are given annual after-tax cash inflows of $600,000 and an initial
investment outlay of $3,500,000. To generate an IRR of exactly 14.00%, the
following must hold:
PV of Future Cash Inflows = Initial Investment Outlay
$600,000 x An,14% = $3,500,000
Thus, we need to solve for the particular n that balances the preceding equation.
An, 14% = $3,500,000/$600,000 = 5.833. This annuity factor, at 14%, approximates
a 13-year life (see Table 2, page 871). Therefore, the number of years needed for
the Seattle facility to earn at least a 14% return is approximately 13 years.
Though not discussed in the text, we can solve exactly for the number of years, n,
once we know the formula to calculate the PV of an ordinary annuity (i.e., the
formula for the factors included in Table 2, page 871). This formula is:
Annuity Factor = [1/r * [1 – [1/rn]], where n = the number of periods and r =
the discount rate (defined in terms of n, e.g., in years)
In the present case, the annuity factor = 5.83333 and r = 0.14. Thus, we have
5.83333 = [1/0.14] * [1 – [1/(1.14)n]]
(1) First, divide both sides by (1/0.14), which yields:
0.8166662 = 1 – (1/(1.14)n)
(2) Next, subtract 1 from both sides, to yield:
-0.1833338 = – 1/(1.14)n
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-68
©The McGraw-Hill Companies 2008
20-61 (Continued)
(3) Multiply both sides by –1:
0.1833338 = 1/(1.14)n
(4) By rule of exponents (i.e., 1/xn = x-n), the right-hand side of the above
can be expressed as:
1/(1.14)n = 1.14-n
(5) This gives us:
0.1833338 = 1.14-n
(6) Take the log of each side of (5), which gives us:
log 0.1833338 = log 1.14-n
(7) Now, by a rule of logs the right-hand side of (6) can be re-expressed
as follows:
log 0.1833338 = –n log 1.14
(8) Finally,
–n = log 0.1833338/log 1.14
– n = –12.94718
n = 12.9 years
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-69
©The McGraw-Hill Companies 2008
20-62 Uneven Cash Flows (40 min)
1.
Present value of net cash inflows:
Year 1
-0-
Year 2
$1,000,000 x 0.797 =
Year 3
$1,000,000 x 0.712 =
712,000
Year 4
$2,500,000 x 0.636 =
1,590,000
($3,000,000 x 4.111) x 0.636 =
7,843,788
Years 5-10
$
797,000
Present value of net cash inflows
$10,942,788
Less: Initial investment outlay, year 0
15,000,000
NPV (@12%)
$(4,057,212)
Alternatively, the built-in functions in Excel can be used to estimate the NPV and
the IRR of this project, as follows:
2. The maximum purchase price the seller would be willing to offer, given a discount rate
of 12% and the indicated cash flows, would be slightly less than $11,000,000, as
follows:
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-70
©The McGraw-Hill Companies 2008
20-62 (Continued)
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-71
©The McGraw-Hill Companies 2008
20-63
1.
Environmental Cost Management (60 - 75 min)
Solvent System
Initial investment
Present
Value
$400,000
After-tax paint cost
Year 1
Year 2
$228,000
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Year 9
Year 10
$228,000 $228,000 $228,000
$228,000 $228,000 $228,000
$228,000
$228,000
$228,000
After-tax environ. costs
$383,845
$383,845 $383,845 $383,845
$383,845 $383,845 $383,845
$383,845
$383,845
$383,845
Total after-tax cash costs
$611,845
$611,845 $611,845 $611,845
$611,845 $611,845 $611,845
Year 11
0
$611,845
$611,845
$611,845
Depreciation (MACRS)
40,000
72,000
57,600
46,080
36,880
29,480
26,200
26,200
26,240
26,200
13,120
Tax saving on deprec.
16,000
28,800
23,040
18,432
14,752
11,792
10,480
10,480
10,496
10,480
5,248
$597,093 $600,053 $601,365
Net after-tax cash costs
$595,845
Discount factor (12%)
Present value
3,360,365
Total cost
$3,760,365
Powder System
Initial investment
$1,200,000
After-tax paint cost
$601,349
$601,365
(5,248)
0.797
0.712
0.636
0.567
0.507
0.452
0.404
0.361
0.322
0.287
532,090
464,867
419,229
377,411
338,552
304,227
271,817
242,951
217,087
193,640
(1,506)
$240,000 $240,000 $240,000
$240,000
$240,000
$240,000
0
78,600
78,720
78,600
39,360
$240,000
Depreciation (MACRS)
120,000
Tax saving on deprec.
Net after-tax cash costs
Discount factor (12%)
PV
$601,365
0.893
1,064,182
Total cost
$2,264,182
Difference in total cost
$1,496,183
$583,045 $588,805 $593,413
$240,000 $240,000 $240,000
216,000
172,800
138,240
110,640
88,440
78,600
48,000
86,400
69,120
55,296
44,256
35,376
31,440
31,440
31,488
31,440
15,744
192,000
153,600
170,880
184,704
195,744
204,624
208,560
208,560
208,512
208,560
(15,744)
0.893
0.797
0.712
0.636
0.567
0.507
0.452
0.404
0.361
0.322
0.287
171,456
122,419
121,667
117,472
110,987
103,744
94,269
84,258
75,273
67,156
(4,519)
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-72
©The McGraw-Hill Companies 2008
20-63 (Continued)
Notes:
(1) Annual after-tax paint cost, solvent system = $0.19/unit x 2,000,000 units/year
x (1 – 0.40) = $228,000.
(2) MACRS depreciation rates, 10-year property:
Year
1
2
3
4
5
Rate
10.00%
18.00%
14.40%
11.52%
9.22%
Year
6
7
8
9
10
11
Rate
7.37%
6.55%*
6.55%
6.56%
6.55%
3.28%
* first year switching to SL method
(3) Additional environmental costs, Solvent Paint System:
Item
Pit cleaning
Waste disposal
Superfund Fee
Worker training
Insurance
Amortization of air-emission permit
Air-emission fee
Recordkeeping
Wastewater treatment
Pre-tax Total
Times (1 - 0.40)
After-tax environmental costs
Annual Cost
$12,000
$549,000
$3,177
$3,000
$10,000
$200
$1,115
$11,250
$50,000
$639,742
x 0.60
$383,845
(4) Annual after-tax paint cost, Powder Paint System = $0.20/unit x 2,000,000
units/year x (1 – 0.40) = $240,000.
2. Based solely on financial considerations, the maximum the company should spend
on the Powder-Based System = original estimate + difference in PVs of costs (from
Part 1) = $1,200,000 + $1,496,183 = $2,696,183 (i.e., an increase of up to 125%
over the original price).
Blocher, Stout, Cokins, Chen, Cost Management, 4/e
20-73
©The McGraw-Hill Companies 2008