Appendix – Capital Investment Decisions: An Overview
App-1
Appendix
Capital Investment Decisions: An Overview
Appendix Outline
I. INTRODUCTION
II. ANALYZING CASH FLOWS FOR PRESENT VALUE ANALYSIS
♦ Distinguishing between revenues, costs, and cash flows
III. NET PRESENT VALUE
♦ Applying present value analysis
IV. CAPITAL INVESTMENT ANALYSIS: AN EXAMPLE
V. CATEGORIES OF PROJECT CASH FLOWS
A. Investment cash flows
B. Periodic operating cash flows
C. Cash flows from the depreciation tax shield
D. Disinvestment cash flows
VI. PREPARING THE NET PRESENT VALUE ANALYSIS
VII. USING MICROSOFT EXCEL TO PREPARE THE NET PRESENT VALUE
ANALYSIS
Key Concepts
♦ Capital investment decisions are the responsibility of managers of investment centers.
• Specific investments over a certain dollar amount require approval by the board of
directors in many companies.
• Cost accountants estimate the amount and timing of the cash flows used in capital
investment decision models to help managers make those decisions.
♦ Capital investment models are based on the future cash flows expected from a particular asset
investment opportunity.
• The amount and timing of the cash flows from a capital investment project determine its
economic value.
• Because of the timing of cash flows, any investment project has an opportunity cost for
cash committed to it.
• The time value of money conveys the concept that cash received earlier is worth more
than cash received later.
• The future cash flows associated with a project are adjusted to their present value using
a predetermined discount rate to recognize the time value of money.
Appendix – Capital Investment Decisions: An Overview
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• The discount rate is the interest rate used to compute net present value.
• Net present value (NPV) represents the economic value of a project at a point in time.
Net present value = Sum of discounted future cash flows – Initial investment.
• If the net present value of a project is positive, the project will earn a rate of interest
higher than its discount rate.
• The decision models used for capital investments attempt to optimize the economic
value to the firm by maximizing the net present value of future cash flows.
♦ It is important to distinguish cash flows from revenues and costs when timing difference exists.
• Capital investment analysis uses cash flows, not revenues and costs as recognized in
accrual concept.
♦ The present value of cash flows is the amount of future cash flows discounted to their
equivalent worth today.
• The net present value of a project can be computed as
NPV =
0
(1 )
Nn
n
n
Cd
, where
Cn = Cash to be received or disbursed at the end of time period n,
d = Appropriate discount rate for the future cash flows,
n = Time period when the cash flow occurs, and
N = Life of the investment (in years).
• The term (1+d)-n is called a present value factor. Tables of present value factors are at
the end of this appendix in Exhibit A.8.
Example 1: On his 16th birthday, John was notified by an attorney that he will inherit
$150,000 from a rich uncle when he reaches 21 years of age. Assuming a discount rate
of 6 percent, what is John’s worth now with respect to the inheritance money?
The money (cash inflow) will be vested in 5 years. That is,
Year
0
1
2
3
4
5
Appendix – Capital Investment Decisions: An Overview
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?
$150,000
The present value factor of (1 + 6%)-5 is 0.747. The present value of John’s future
inheritance is $150,000 × 0.747 = $112,050.
• An annuity is a constant (equal) payment over a period of time. The present value
factors for an annuity, based on the formula [
–
1 – (1 ) n
d
d
], are shown in Exhibit A.9.
• The present value of an annuity can be calculated by summing the present value of the
individual payments over the annuity period, or it can be calculated by multiplying the
annuity payment by the sum of the present value factors.
Example 2: Jenny is 71 years old. She bought an insurance policy years ago that pays
her $15,000 every year to supplement her income. With a life expectancy of 86 years
and an assumed discount rate of 8 percent, what is the remaining value of the annuity
now? (The cost of the policy is considered sunk and not relevant for this question.)
The timeline below shows the pattern of cash inflows for the next 15 years.
Year
0
1
2
3
4
…
15
?
$15,000
$15,000
$15,000
$15,000
…
$15,000
The present value factor of the annuity, [1 – (1 + 8%)–15] ÷ 8%, is 8.559. The present
value of Jenny’s annuity for her expected remaining life is worth $15,000 × 8.559 =
$128,385.
Example 3: A developer is considering three possible investment opportunities. All
three require the same initial investment of $20,000 and will last for 3 years. Project 1
will return $9,000 every year at the end of next three years. Project 2 is expected to
generate $12,000 at year 2 and $15,000 at year 3. Finally, Project 3 will return $27,000
at the end of the third year. The developer uses a discount rate of 12 percent. Which
project should the developer choose?
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Project 1
Cash inflow
$9,000 × 2.402a
$21,618
Cash outflow
(20,000)
Net present value
$1,618
a Present value factor of an annuity at 12% for three years.
Project 2
Cash inflow
$12,000 × 0.797b + $15,000 × 0.712c
$20,244
Cash outflow
(20,000)
Net present value
$244
b Present value factor at 12% for two years.
c Present value factor at 12% for three years.
Project 3
Cash inflow
$27,000 × 0.712c
$19,224
Cash outflow
(20,000)
Net present value
$(776)
c Present value factor at 12% for three years.
Even though the total (undiscounted) cash inflows are the same, $27,000, for the
projects under consideration, the timing of the cash flows does make a difference. By
receiving cash inflows early and often, Project 1 outperforms the other two in terms of
the net present value. Project 2 is less appealing but still acceptable with a positive
NPV. A negative NPV, such as that of Project 3, indicates a return less than the
discount rate used.
♦ Four major categories of cash flows for a project are:
(1) Investment cash flows,
(2) Periodic operating cash flows,
(3) Cash flows from the depreciation tax shield, and
(4) Disinvestment cash flows.
• There are three types of investment cash flows: Asset acquisitions, working capital
commitments, and investment tax credit, if any.
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• Asset acquisition involves the costs of purchasing and installing an asset, including any
resulting gain or loss on disposal.
• All acquisition costs are listed as cash outflows in the years in which they occur.
Installation costs are also considered a cash outflow.
• The tax effect as a result of the difference between depreciation tax basis and proceeds
from the sale of the replaced equipment will be considered a cash inflow (for a loss) or a
cash outflow (for a gain).
• Working capital represents cash, accounts receivable, and other short-term assets
required to maintain an activity.
• The working capital committed to a project normally remains constant over the life of
the project, although it is sometimes increased because of inflation.
• Investment tax credit (ITC) reduces federal income taxes as a result of certain asset
purchases.
• Investment tax credits effectively shrinks the cost of making investments by giving
companies a credit against their corporate income taxes equal to a certain percentage of
the purchase price.
• The primary reason for acquiring long-term assets is usually to generate positive
periodic operating cash flows as the results of revenue-generating activities and cost-
saving programs.
• Periodic operating flows include
(1) Periodic cash inflows (+) and outflows (-) before taxes, and
(2) Income tax effects of inflows (-) and outflows (+).
• Costs that do not involve cash (such as depreciation, depletion, and amortization) are
excluded, so are financing costs (under the assumption that the financing decision is
separate from the asset-acquisition decision).
• The cost of financing is included in the discount rate.
• A tax shield refers to the reduction in tax payments because of depreciation deducted
for tax purposes. It is one of the primary incentives used by tax policy makers to promote
investment in long-term assets.
• The depreciation deduction computed for the tax shield (using accelerated write-offs) is
not necessarily the same amount as the depreciation computed for financial reporting
purposes (using predominantly straight-line method).
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======================
Demonstration Problem 1
Kahn Industry, Inc. decides to add a new machine to its assembly line. The new machine costs
$120,000 with a useful life of 6 years and no salvage value. The new machine is expected to
bring cash inflows of $80,000 while incurring cash outflows of $50,000 every year. The
company uses straight-line method to calculate its depreciation. The tax rate is assumed to be 40
percent.
Required:
Determine the tax shield of the purchase.
Solution:
The annual depreciation charge associated with the new machine is $20,000 (= $120,000 ÷ 6
years).
Change in
net income
Change in
cash flows
Change in
cash flows
without
depreciation
Cash inflows
$80,000
$80,000
$80,000
Cash outflows
(50,000)
(50,000)
(50,000)
Before-tax net flows
$30,000
$30,000
$30,000
Depreciation
(20,000)
Before-tax NI
$10,000
Tax (40%)
(4,000)
(4,000)
(12,000)
After-tax NI
$6,000
After-tax net flows
$26,000
$18,000
The tax shield is worth $8,000 (= $20,000 × 40%, or $12,000 – $4,000) as the result of
depreciation deduction.
======================
• The faster an asset’s cost can be written off for tax purposes, the sooner the tax
deductions are realized and, therefore, the higher the net present value of the tax shield.
• The depreciation tax shield affects the net present value analysis in two ways:
(1) Depreciation tax shield on acquired assets, and
(2) Forgone depreciation tax shield on disposed assets.
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• Disinvestment flows are cash flows that take place at the termination of a capital
project, including
(1) Cash freed from working capital commitment,
(2) Salvage value of the long-term assets,
(3) Tax consequences for differences between salvage proceeds and the remaining
depreciation tax basis of the asset, and
(4) Other cash flows, such as employee severance payments and restoration costs.
• The tax basis is the remaining tax–depreciable “book value” of an asset for tax purposes.
• The difference between the book value (tax basis) and the net salvage value can result
in a taxable gain or loss.
• For an asset replacement decision, the forgone salvage value (and related tax effects)
from the old assets must be considered.
======================
Demonstration Problem 2
A company wants to expand its operations. One capital investment proposal under consideration
is the acquisition of additional equipment. The cost of initial investment is estimated to be
$75,000 with useful life of 6 years and the disposal value of $15,000. Straight-line depreciation
method will be used for both financial and tax purposes.
The expansion will bring in an estimated $38,000 cash every year; the annual operating expenses
are around $17,000. At the end of the third year, a one-time tune-up is required for a cost of
$8,000. Because of the expansion, working capital in the amount of $14,000 must be committed.
The tax rate and the discount rate are 40 percent and 12 percent, respectively.
Required:
1. Evaluate the expansion proposal using the net present value analysis.
2. Assume that at the end of the fourth year, because of unforeseen reasons, the equipment
is salvaged for $50,000. What are the tax consequences of the disposal?
Solution:
1. As soon as the cash flow data have been gathered, they are assembled into the following
schedule that shows the cash flows for each year of the project’s life. These flows are
classified into the four categories discussed earlier.
(1) Investment cash flows.
(2) Periodic operating cash flows.
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(3) Cash flows from the depreciation tax shield.
(4) Disinvestment cash flows.
Year
0
1
2
3
4
5
6
Investment flows:
New equipment
$(75,000)
Working capital
(14,000)
Annual cash flows:
Operating cash flowsa
$12,600
$12,600
$7,800
$12,600
$12,600
$12,600
Depreciation tax shieldb
4,000
4,000
4,000
4,000
4,000
4,000
Disinvestment flows:
Return of working capital
14,000
Proceeds on disposal
15,000
Total cash flows
$(89,000)
$16,600
$16,600
$11,800
$16,600
$16,600
$45,600
Present value factor at 12%
1.0
0.893
0.797
0.712
0.636
0.567
0.507
Present value
$(89,000)
$14,824
$13,230
$8,402
$10,558
$9,412
$23,119
Net present value
$(9,455)
a For years 1 through 6, except year 3, the operating cash flows are calculated as
($38,000 – $17,000) × (1 – 40%) = $12,600.
For year 3, the operating cash flows are calculated as
($38,000 – $17,000 – $8,000) × (1 – 40%) = $7,800.
b The annual depreciation expense is $10,000 (= ($75,000 – $15,000) ÷ 6 years). The tax shield
represents tax savings as a result of depreciation deduction, calculated as
$10,000 × 40% = $4,000.
The negative net present value indicates that the expansion will earn less than the 12 percent
used to discount the cash flows, making this proposal less desirable.
2. At the end of the fourth year, the tax basis will be $35,000 (= $75,000 Cost – $10,000
Annual depreciation × 4), same as the net book value, since the straight-line method is used
for both.
The tax payment due to disposal will be $6,000 (= ($50,000 Proceeds from disposal –
$35,000 Tax basis) × 40%).
The after-tax cash inflow becomes $44,000 (= $50,000 Proceeds from disposal – $6,000 Tax
payment).
======================
• Exhibit A.2 contains the analysis for an investment decision.
• All the calculations are available in spreadsheet programs such as Microsoft Excel with
built-in functions, as shown in Exhibits A.3 – A.7.
Appendix – Capital Investment Decisions: An Overview
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Matching
A.
Asset acquisition
F.
Present value
B.
Discount rate
G.
Tax basis
C.
Disinvestment flows
H.
Tax shield
D.
Investment tax credit
I
Time value of money
E.
Net present value
J.
Working capital
_____ 1. Cash flows that take place at the termination of a capital project.
_____ 2. The reduction in tax payment because of depreciation deducted for tax purposes.
_____ 3. Cash, accounts receivable, and other short-term assets required to maintain an activity.
_____ 4. Reduces federal income taxes as a result of certain asset purchases.
_____ 5. Involves the costs of purchasing and installing an asset, including any resulting gain
or loss on disposal.
_____ 6. The amount of future cash flows discounted to their equivalent worth today.
_____ 7. Conveys the concept that cash received earlier is worth more than cash received later.
_____ 8. The interest rate used to compute net present value.
_____ 9. The economic value of a project at a point in time.
_____ 10. The remaining tax-depreciable “book value” of an asset for tax purposes.
Appendix – Capital Investment Decisions: An Overview
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Answers
1. C
2. H
3. J
4. D
5. A
6. F
7. I
8. B
9. E
10. G