CAPITAL INVESTMENT
Capital Investment (Capital Budgeting) involves the allocation of large amounts of
resources in long-term investments.
Examples:
=>
Replacement of Equipment
=>
Expansion of Existing Product Lines
=>
Development of New Product Lines
=>
Intangibles:
=>
Research & Development
=>
Patents
=>
Advertising campaigns
Success:
Texas Instruments - semiconductor in 1950s and 1960s; microchip in 1970s
Microsoft - Bought Quick and Dirty Operating System for $50,000
Failure:
Ford Edsel (Loss of $250 million in 1957-59, or approximately $2 billion today)
Once the Investment is made, it is almost impossible to back out. Unlike a surplus of
inventory which can be quickly corrected, an unutilized refinery just sits vacant.
The firm's existence is a series of capital investment decisions that are necessary for the
company to grow, remain competitive, etc.
Basic Concept: Accept all projects that yield a return that exceeds the cost of financing the
project. Thus, if we are maximizing stockholder wealth, we would accept Projects A – D and
%
A
B
C
Cost of
Capital
D
E
F
G
$
reject the remainder:
Numerous investment alternatives exist. We need a means of ranking the projects from
best to worst in order to select those that are most valuable to the firm; i.e., a means of evaluating
and ranking proposals.
The primary concern in the investment decision regards cash flows:
=>
=>
=>
=>
=>
=>
Incremental Revenues
Incremental Costs
Taxes
Depreciation considerations
Investment in Working Capital
Cost Savings
Any cash inflow or outflow.
EVALUATION TECHNIQUES
A)
Payback Period
Year 0
Year 1
Year 2
Year 3
Proj. A
--------(3,000)
1,000
2,000
3,000
Payback = 2 years
Proj. B
--------(3,000)
2,000
1,000
4,000
Payback = 2 years
Both projects have a payback of two years, so the payback method indicates that the two projects
are equally desirable.
Problems:
1)
Ignores the Time Value of Money
2)
Ignores cash flows beyond the payback period
Project B returns $1,000 a year earlier than Project A and also returns an additional $1,000 in the
last year.
Present Value (or Discounted) Payback, which utilizes the present value of each year's cash flow,
overcomes the first problem, but not the second.
B)
Present Value (Discounted) Payback
Year 0
Year 1
Year 2
Year 3
Proj. A
--------Cash Flow PV of CF
(3,000)
(3,000)
1,100
1,000
2,420
2,000
3,000
2,254
Proj. B
--------Cash Flow
(3,000)
2,200
1,210
4,000
PV Payback = 2 years
C)
PV of CF
(3,000)
2,000
1,000
3,005
PV Payback = 2 years
Net Present Value (NPV)
We need a methodology that takes into account all of the cash flows as well as the time
value of money. Net Present Value is one such technique:
NPV = PV of Cash Inflows - PV of Cash Outflows
Required Rate of Return = 10%
0
(4,000)
1
2
3
1,000
2,000
3,000
PV at 10% for 1 year
909
PV at 10% for 2 years
1,653
PV at 10% for 3 years
2,254
NPV @ 10% =
816
To calculate the NPV on an HP 10B financial calculator,
Clear All
Enter 4000 and change the sign (+/-) and press CFj
Enter 1000 and press CFj again
Enter 2000 and press CFj
Enter 3000 and press CFj
Enter 10 and press I/YR
Press the shift key and press NPV
NPV represents the increase in the value of the firm that occurs by accepting the project. In other
words, it represents the amount by which the value of the project exceeds its cost.
Proof:
Year 0 Investment
Return of Investment
4,000
(600)
-------3,400
(1,660)
-------1,740
(2,826)
-------(1,086)
0.7513
--------816
Year 1 Investment
Return of Investment
Year 2 Investment
Return of Investment
Surplus Return
PVIF10%,3
Present Value
Cash Flow - Year 1
Less: Interest
1,000
(400) (10%*$4,000)
-------Return of Investment
600
Cash Flow - Year 2
Less: Interest
Return of Investment
Cash Flow - Year 3
Less: Interest
Return of Investment
2,000
(340) (10%*$3,400)
-------1,660
3,000
(174) (10%*$1,740)
-------2,826
The problem with NPV is that there is no consideration of cost, or what is referred to as size
disparity.
Proj. A
Proj. B
-------------Present Value of Inflows
1,050
125
Cost
(1,000)
(100)
-------------Net Present Value
50
25
If these are mutually exclusive projects (i.e., choose one or the other, but not both), the NPV
criterion says to choose Project A. While Project A increases the value of the firm by twice the
amount of Project B, it costs ten times as much. The NPV does not indicate how efficiently
money has been invested.
Capital Rationing - the allocation of a scarce resource, in this case money.
D)
Profitability Index (PI) (or Benefit-Cost Ratio) - a measure of efficiency of investment
Profitability Index 
PV of Inflows
PV of Outflows
PIA = 1.05
PIB = 1.25
The interpretation of PI is that of the amount of money in today's dollar terms that you get per
dollar of investment. This indicates how efficiently you have invested money.
E)
Internal Rate of Return (IRR)
Another measure of the efficiency of investment is the Internal Rate of Return. When
someone asks what rate of return an investment is earning, they mean the Internal Rate of
Return. The IRR can be defined as
PV of Inflows @ IRR = PV of Outflows @ IRR
or
NPV @ IRR = 0
This is the actual rate of interest that is being earned on the investment. While the present
value and annuity tables can be used in certain cases, the more general situation of uneven
cash flows requires that the IRR be found by trial and error.
From the previous example, it is clear that more than 10% is being earned, since the NPV is $816.
Calculating the IRR on the HP 10B is almost identical to calculating the NPV:
Clear All
Enter 4000 and change the sign (+/-) and press CFj
Enter 1000 and press CFj again
Enter 2000 and press CFj
Enter 3000 and press CFj
Press the shift key and press IRR/YR
The Internal Rate of Return is 19.44%
Year 0 Investment
Return of Investment
4,000
(222)
Year 1 Investment
Return of Investment
3,778
(1,266)
Return of Investment
Year 2 Investment
Return of Investment
2,512
2,512
Cash Flow -- Year 2
Less: Interest
2,000
(734) (19.44% * $3,778)
Return of Investment
1,266
Cash Flow -- Year 3
Less: Interest
3,000
(488) (19.44% * $2,512)
Return of Investment
2,512
Surplus Return
0
Cash Flow -- Year 1
Less: Interest
1,000
(778) (19.44% * $4,000)
222
Hence, it is the rate of interest earned on the funds that remain invested within the project. This is
the economic interpretation of the mathematical solution.
Project A
Project B
Year 0
Year 1
Year 2
Year 3
NPV @ 10%
PI @ 10%
IRR
(15,000)
(48,000)
10,000
30,000
10,000
30,000
0
0
2,355
4,066
1.16
1.08
21.5%
16.3%
Which project is better? The major difference is the costs of the projects.
Project C
Project D
Year 0
Year 1
Year 2
(10,000)
(10,000)
8,000
0
5,600
0
Year 3
NPV @ 10%
PI @ 10%
IRR
1,901
2,772
1.19
1.28
24.9%
19.3%
0
17,000
Which project is better? The major difference is the timing of the cash flows.
Note that all three measures agree as to whether a project is acceptable or not. The
conflict is in the ranking of the investment proposals.
Note also that the Profitability Index, a measure of efficiency of investment, does not
always agree with IRR in terms of which is the most efficient use of funds.
THE REINVESTMENT ASSUMPTION
Consider the following two projects, their NPVs, PIs, and IRRs.
Project X
Year 0
Year 1
Year 2
Year 3
(886)
100
100
1,100
Cash Flows
NPV @ 10% = 114
PI @ 10% =
1.13
IRR =
15.0%
Project Y
Year 0
Year 1
Year 2
Year 3
(886)
900
150
55
Cash Flows
NPV @ 10% = 97
PI @ 10% = 1.11
IRR =
20.0%
Most academicians claim that the conflict is a consequence of the reinvestment
assumption. Net Present Value and Profitability Index assume reinvestment at the discount rate.
Internal Rate of Return can be thought of as a special case of NPV (when it equals zero). Hence,
it assumes reinvestment at the IRR.
Realistically, investments are made to maximize future wealth. Present value (discounted
cash flow techniques) are used since we know the value of a dollar today. The reinvestment
assumption is invoked in order to make the future value (terminal value) rankings consistent with
the present value rankings. To see this, let's reinvest the cash flows of Projects X and Y at the
discount rate of 10%.
Project X
Cash Flows
Year 0
Year 1
(886)
100
Year 2
Year 3
100
1,100
1.21
121
1.10
110
Terminal Value =
1,331
Project Y
Cash Flows
Year 0
Year 1
Year 2
Year 3
(886)
900
150
55
1.21
1,089
1.10
165
Terminal Value =
1,309
Since the costs are the same, the terminal values are both relative to the same size of
investment. The $1,331 terminal value of Project X represents a 14.53% rate of return on an
investment of $886 over three years while the $1,309 terminal value of Project Y is a 13.89%
return on the initial investment. The difference in the terminal values of $22 has a present value
of $17 which is the same as the difference in NPVs of the two projects (114 - 97 = 17). Thus, the
terminal value rankings are consistent with the NPV and PI rankings that indicate Project X is
superior to Project Y. Similarly, if the cash flows of each project are reinvested at their respective
IRRs, the following is obtained:
Project X
Cash Flows
Year 0
Year 1
Year 2
Year 3
(886)
100
100
1,100
1.3223
132
1.15
115
Terminal Value =
1,347
Project Y
Cash Flows
Year 0
Year 1
(886)
900
Year 2
Year 3
150
55
1.4400
1,296
1.2000
180
Terminal Value =
1,531
Since the costs are identical, it is clear that Project Y is better since it maximizes future
wealth, and agrees with the rankings of the IRRs. Moreover, the terminal value of $1,347 of
Project X represents a 15% return on the cost of the project, while the $1,531 terminal value of
Project Y is a 20% return on the investment in Project Y.
NON-NORMAL (NON-CONVENTIONAL) PROJECTS
Multiple Internal Rates of Return
Another criticism of the IRR method is that non-normal (or non-conventional) projects
can have multiple IRRs. Consider the following project:
Cash Flows
Year 0
Year 1
Year 2
Year 3
Year 4
(3,000)
2,000
4,500
3,500
(7,200)
Two IRRs exist: IRR1 = 3.2% and IRR2 = 47.16%. Which one is correct? Technically, both of
them provide a solution to the discount rate that yields a Net Present Value = 0. The text refers
to the question of "A borrowing rate or an investment rate?" in explaining why both are correct.
Let's look at the 3.2% solution:
0
1
2
3
4
(3,000)
2,000
4,500
3,500
(7,200)
(3,000) * (1.032) =
(3,096)
+ 2,000
(1,096) * (1.032) =
(1,131)
+ 4,500
3,369 * (1.032) =
3,477
+ 3,500
6,977 * (1.032) =
Terminal Value =
7,200
+( 7,200)
-0-
In this case, if you only require a 3.2% rate of return, your 3.2% rate of return and your principal
are returned early in Year 2, and you only need to earn a return of 3.2% on the investment of
surplus funds in order to have enough to payoff the cost of $7,200 at the end of the 4th year.
The same is true with the IRR of 47.16%:
0
1
2
3
4
(3,000)
2,000
4,500
3,500
(7,200)
(3,000) * (1.4716) = (4,415)
+ 2,000
(2,415) * (1.4716) = (3,554)
+ 4,500
946 * (1.4716) =
1,393
+ 3,500
4,893 * (1.4716) =
Terminal Value =
7,200
+( 7,200)
-0-
Because of the higher rate of return (47.16%), it takes longer to receive your rate of return and
principal back (not until almost the end of the 2nd year since more of the cash flow is rate of
return rather than return of principal) and you must now earn a 47.16% rate of return on the
surplus funds to cover the cost of $7,200 at the end of the project life. (Check out the NPV of
this project at 3.2% and 47.16% to verify that you'll get an NPV of zero.)
In short, the economic interpretation (that it is the return on invested funds) is lost because
it also requires that the surplus funds earn the same rate of interest in order to cover the cash
outflow in the last year. In fact, there is an IRR for each time that the cash flows change sign (in
this case only two).
Many believe this is the primary reason to prefer NPV over IRR as an evaluation tool.
Unfortunately, the concept of a rate of return (such as IRR) is preferred by almost all practitioners,
particularly since it can be compared to the cost of funds or other investment opportunities.
Another shortfall to NPV is if the risk of the project (or future cash outflow) is higher than
the risk of the average investment for the company. Consider the above example where the
outflow is associated with a great deal of uncertainty about the cost (such as decommissioning a
nuclear power plant). The greater uncertainty implies a higher discount rate be used in calculating
the present value. Yet a higher discount rate makes the present value of the cost lower, and
hence the project more attractive rather than less. One solution to this is to discount future cash
outflows at a separate discount rate from the cash inflows. In fact, the more risky the future cash
outflow, the lower the discount rate that should be employed. This has its own problems: as
shown previously, if NPV assumes cash flows are reinvested at the discount rate, then an
above-average risk project assumes that the (positive) cash flows will continue to be reinvested in
above-average risk projects (i.e., earn a high rate of return) while the above-average risk costs
(being discounted at a lower discount rate as mentioned) have a below-average cost of capital.
Confusing, isn't it?
RELEVANT CASH FLOWS
Incremental Cash Flows
The relevant cash flows for investment analysis is the change in the cash flows that would
occur by accepting a proposal, or what is referred to by the term incremental cash flows.
An opportunity cost is a cash flow given up as a consequence of a decision, and is
generally defined as the next-best-alternative. Since an opportunity cost is a change in cash flow,
it is relevant to the investment decision.
A sunk cost refers to past expenditures. Sunk costs are not relevant since they occurred
in the past and the decision of whether or not to undertake a project does not change the past.
A general (simplified) format for analyzing a capital expenditure that considers all
incremental cash flows is on the following page. Note that the relevant cash flows include those
found on the income statement as well as those that are not on the income statement (such as
working capital). Also, some cash flows are only reflected on the income statement in part (such
as the gain or loss on the sale of an asset).
CASH FLOW ANALYSIS
PURCHASE/REPLACEMENT DECISION
Today
A. <Cash outlay for new asset>
B. Cash proceeds from sale
of old asset
C. Tax effect of gain or loss
on disposal of old asset1
D. <Additional working capital
needed to support new asset>
Intervening Years
E. Incremental Revenues
from new asset
F. Less: Incremental Costs
from new asset
G. Less: Incremental Depreciation
------------------------------------------Change in Taxable Income
Less: Taxes on Tax. Inc. (t)
------------------------------------------Change in Net Income
Plus: Incremental Depreciation
------------------------------------------Incremental Operating Cash Flow
Last Year
I. Salvage of new asset
J. Tax effect of gain or
loss on disposal of
new asset1
K. <Salvage value lost
on old asset>
L. Tax effect of gain or
loss on disposal of
old asset1
M. Recovery of working
capital
H. <Additional working capital>
In a Purchase Decision, the relevant occurrences are A, D, E, F, H, I, J, and M
In a Replacement Decision, the relevant occurrences are A through M
1
If the asset is sold for less than the book value, the company incurs a loss which is tax-deductible. This loss reduces taxable income
and thereby creates a tax savings equal to the difference between the market value of the asset and its book value multiplied by the tax
rate: Loss * t
If the asset is sold for more than the book value, the company must report the difference as a profit to be taxed as ordinary income to
the extent that the profit is less than the accumulated depreciation for the asset: Gain * t In the event that the asset is sold for more
than the original purchase price, the gain above the original purchase price is subject to the capital gains tax rate while the accumulated
depreciation is taxed as ordinary income.
< > indicates that the cash flow is an outflow.
t = applicable tax rate
The Replacement Decision
The classic capital investment decision is that of whether or not to replace a large piece of
equipment.
Example
Kinky's Copying Service is considering expanding operations to include new holographic
color copying services. The new service is expected to result in additional sales of $600,000 in
the first year, increasing by 12% per year as word of the color copies spreads. Labor and material
costs are predicted to rise by $480,000 in the first year, increasing at a 6% annual rate due
primarily to inflation. To accommodate the service, a new color copier will have to be purchased
at a cost of $280,000. The new machine will be depreciated using the MACRS rates for 5-year
assets (20%, 32%, 19.2%, 11.52%, 11.52%, 5.76%), even though you expect that after three
years of 24-hour per day operation, it will have a resale value of only $50,000 and will have to be
replaced. Since the holographic color copier can also make regular color copies, one of the small
existing color copy machines can be sold to a local university for $45,000 rather than keeping it for
the remaining three years of its useful life and scrapping it for $8,000. The existing color copy
machine was purchased for $90,000 two years ago and is also being depreciated using the same
MACRS rates for 5-year assets. The expanded service would use existing floor space in an
adjacent room which would result in an allocation of depreciation totaling $5,000 per year. Also,
$6,000 in administrative expenses would be allocated to the project each year; however, only
$2,000 of the amount represents an actual increase in expenses not otherwise incurred by the
firm (also increasing by 6% per year). The existing floor space of the adjacent room could be
leased annually for $4,500 on a fixed three-year lease if the project is not accepted. An
investment in working capital of $85,000 will initially be required, with additional increments of 8%
per year due to both inflation and increasing sales, all of which will be recovered in the third year.
Kinky's is in the 40% tax bracket. Calculate the net cash flows for each year of the project's life.
Solution
Year 1
Year 2
Year 3
Incremental Revenues
Increased sales
Lost lease payments
600,000 x 1.12 = 672,000 x 1.12 = 752,640
(4,500)
(4,500)
(4,500)
Total Incremental Revenues
595,500
667,500
748,140
Incremental Costs
Labor & materials
Administrative expense
480,000 x 1.06 = 508,800 x 1.06 = 539,328
2,000 x 1.06 =
2,120 x 1.06 =
2,247
Total Incremental Costs
482,000
510,920
541,575
Year 1
Year 2
280,000
20.00%
280,000
32.00%
280,000
19.20%
New Depreciation
56,000
89,600
53,760
Old Machine
MACRS rate
90,000
19.20%
90,000
11.52%
90,000
11.52%
Old Depreciation
17,280
10,368
10,368
Incremental Depreciation
38,720
79,232
43,392
Incremental Depreciation
New Machine
MACRS rate
Sale of Equipment
Old machine - Yr. 0
Market Value
Book Value
Gain (loss)
Tax rate
45,000
43,200
1,800
40%
Tax due (refund)
720
Old machine - Yr. 3
Market Value
Book Value
8,000
5,184
Gain (loss)
Tax rate
2,816
40%
Tax due (refund)
1,126
New machine - Yr. 3
Market Value
Book Value
50,000
80,640
Gain (loss)
Tax rate
(30,640)
40%
Tax due (refund)
(12,256)
Working Capital
(90,000*48%)
(90,000*5.76%)
(280,000*28.8%)
Year
Required
Change
0
1
2
3
85,000
91,800
99,144
107,076
85,000
6,800
7,344
7,932
Year 3
Putting it all together
Year 0
Year 1
Year 2
Year 3
595,500
(482,000)
(38,720)
667,500
(510,920)
(79,232)
748,140
(541,575)
(43,392)
Change in Taxable Income
Less: Taxes (40%)
74,780
(29,912)
77,348
(30,939)
163,173
(65,269)
Change in Net Income
Add-back depreciation
44,868
38,720
46,409
79,232
97,904
43,392
Change in Operating Cash Flow
83,588
125,641
141,296
( 6,800)
( 7,344)
( 7,932)
107,076
Operating Cash Flows
Revenues
Less: Costs
Less: Depreciation
Working Capital Requirements
Additional Working Capital
Working Capital Recovery
New Machine
Purchase
Sale - Yr. 3
Tax Savings on Sale
Old Machine
Sale - Yr. 0
Tax on Sale
( 85,000)
(280,000)
50,000
12,256
45,000
( 720)
Lost Sale - Yr. 3
Taxes Saved on Lost Sale
Total Incremental Cash Flows
(8,000)
1,126
(320,720)
76,788
118,297
295,822