Chapter 10
Making Capital Investment Decisions
Chapter 9
REVIEW
I. Discounted cash flow criteria
A. Net present value (NPV). The NPV of an investment is the
difference between its market value and its cost. The NPV
rule is to take a project if its NPV is positive. NPV has no
serious flaws; it is the preferred decision criterion.
B. Internal rate of return (IRR). The IRR is the discount rate that
makes the estimated NPV of an investment equal to zero. The
IRR rule is to take a project when its IRR exceeds the required return.
When project cash flows are not conventional, there may be no IRR or
there may be more than one.
C. Profitability index (PI). The PI, also called the benefit-cost ratio, is the
ratio of present value to cost. The profitability index rule is to take an
investment if the index exceeds 1.0. The PI measures the present value per
dollar invested.
II. Payback criteria
A. Payback period. The payback period is the length of time until the sum of an
investment’s cash flows equals its cost. The payback period rule is to take a
project if its payback period is less than some pre-specified cutoff.
B. Discounted payback period. The discounted payback period is the length of
time until the sum of an investment’s discounted cash flows equals its cost. The
discounted payback period rule is to take an investment if the discounted
payback is less than some pre-specified cutoff.
III. Accounting criterion
A. Average accounting return (AAR). The AAR is a measure of
accounting profit relative to book value. The AAR rule is to take an
investment if its AAR exceeds a benchmark.
Chapter 10
Making Capital Investment Decisions
Chapter Organization
•Incremental Cash Flows
•Terminology
•Cash Flows vs. Accounting Income
•Pro Forma Financial Statements and Project
Cash Flows
•More on Project Cash Flows
•Alternative Definitions of Operating Cash Flow
•Some Special Cases of Discounted Cash
Flow Analysis
•Summary and Conclusions
Fundamental Principles of Project Evaluation:
Project evaluation - the application of one or more capital
budgeting decision rules to estimated relevant project cash flows in
order to make the investment decision.
Relevant cash flows - the incremental cash flows associated with
the decision to invest in a project.
The incremental cash flows for project evaluation consist of any and all changes
in the firm’s future cash flows that are a direct consequence of taking the project.
Stand-alone principle- evaluation of a project based on the project’s
incremental cash flows.
Incremental Cash Flows
Incremental
Cash Flow
=
cash flow
with project
-
cash flow
without project
IMPORTANT
Ask yourself this question
Would the cash flow still exist if the project does not exist?
•If yes, do not include it in your analysis.
•If no, include it.
Terminology
A.
Sunk costs
B.
Opportunity costs
C.
Side effects
D.
Net working capital
E.
Financing costs
F.
Other issues
A. Sunk costs
Suppose $100,000 had been spent last
year to improve the production line
site. Should this cost be included in
the analysis?
• NO. This is a sunk cost, already spent and
irretrievable, so “forget it”, “water under
the bridge”, SUNK. Focus on incremental
investment and operating cash flows.
B. Opportunity costs
Suppose the plant space could be
leased out for $25,000 a year. Would
this affect the analysis?
• Yes. Accepting the project means we will
not receive the $25,000. This is an
opportunity cost and it should be charged
to the project.
C. Side effects
If the new product line would decrease
sales of the firm’s other products by
$50,000 per year, would this affect the
analysis?
• Yes. The effects on the other projects’ CFs
are “externalities” or “spillover effects”.
• Net CF loss per year on other lines would be
a cost to this project.
• Externalities will be positive if new projects
are complements to existing assets, negative
if substitutes.
D. Net working capital
NWC = CA - CL
In estimating cash flows we must account for the fact that some of the
incremental sales associated with a project will be on credit, and that some costs
won’t be paid at the time of investment. How?
Answer: Estimate changes in NWC. Assume:
1.
2.
Fixed asset spending is zero.
The change in net working capital spending is $200:
0
A/R
1
Change
$100 $100
0
INV
100
350
+250
- A/P
50
100
-50
NWC $150 $350
Change in NWC = $200
E. Financing costs
Should CFs include interest
expense? Dividends?
• NO. The costs of capital are already
incorporated in the analysis since we use
them in discounting.
• If we included them as cash flows, we
would be double counting them.
F. Other issues
Depreciation Basics
Depreciable Basis = Cost
+ Shipping
+ Installation
T10.7 Modified ACRS Property
Classes (Table 10.6)
Class
Examples
3-year
Equipment used in research
5-year
Autos, computers
7-year
Most industrial equipment
T10.8 Modified ACRS
Depreciation Allowances (Table 10.7)
Property Class
5-Year 7-Year
Year
3-Year
1
33.33%
20.00%
14.29%
2
44.44
32.00
24.49
3
14.82
19.20
17.49
4
7.41
11.52
12.49
5
11.52
8.93
6
5.76
8.93
7
8.93
8
4.45
Cash flow estimation bias
• CFs are estimated for many future periods.
• If company has many projects and errors are
random and unbiased, errors will cancel out
(aggregate NPV estimate will be OK).
• Studies show that forecasts often are biased
upward (overly optimistic revenues,
underestimated costs). Agency Problems?
What steps can management take to
eliminate the incentives for cash flow
estimation bias?
• Routinely compare CF estimates with those
actually realized and reward managers who are
forecasting well, penalize those who are not.
• When evidence of bias exists, the project’s CF
estimates should be lowered or the cost of
capital raised to offset the bias.
Option value
• Investment in a project may lead to other
valuable opportunities.
• Investment now may extinguish
opportunity to undertake same project in
the future.
• True project NPV = NPV + Value of
options.
Cash Flow -VS- Accounting Income
•Discount actual cash flows
•Using accounting income, rather than cash flow, could lead to
erroneous decisions.
Cash Flow -VS- Accounting Income
Example
A project costs $2,000 and is expected to last 2 years,
producing cash income of $1,500 and $500 respectively. The cost
of the project can be depreciated at $1,000 per year. Given a 10%
required return, compare the NPV using cash flow to the NPV
using accounting income.
Cash Flow -VS- Accounting Income
Year 1 Year 2
Cash Income
$1500 $ 500
Depreciation
- $1000 - $1000
Accounting Income + 500 - 500
Cash Flow -VS- Accounting Income
Year 1 Year 2
Cash Income
$1500 $ 500
Depreciation
- $1000 - $1000
Accounting Income + 500 - 500
500  500
Accounting NPV =

 $41.32
2
1.10 (110
. )
Cash Flow -VS- Accounting Income
Today
Cash Income
Project Cost
Free Cash Flow
- 2000
- 2000
Year 1 Year 2
$1500 $ 500
+1500
+ 500
Cash Flow -VS- Accounting Income
Today
Cash Income
Project Cost
Free Cash Flow
- 2000
- 2000
Year 1 Year 2
$1500 $ 500
+1500
+ 500
1500
500
Cash NPV = - 2000 

 $223.14
1
2
(1.10) (1.10)
Pro Forma Financial Statements and Project Cash Flows
Suppose we want to prepare a set of pro forma financial statements
for a project for Norma Desmond Enterprises. In order to do so, we
must have some background information. In this case, assume:
1.
Sales of 10,000 units/year @ $5/unit.
2.
Variable cost per unit is $3. Fixed costs are $5,000 per year.
The project has no salvage value. Project life is 3 years.
3.
Project cost is $21,000. Depreciation is $7,000/year.
4.
Additional net working capital is $10,000.
5.
The firm’s required return is 20%. The tax rate is 34%.
Pro Forma Financial Statements
Projected Income Statements
Sales
$______
Var. costs
______
$20,000
Fixed costs
5,000
Depreciation
7,000
EBIT
Taxes (34%)
Net income
$______
2,720
$______
Pro Forma Financial Statements
Projected Income Statements
Sales
Var. costs
$50,000
30,000
$20,000
Fixed costs
5,000
Depreciation
7,000
EBIT
Taxes (34%)
Net income
$ 8,000
2,720
$ 5,280
Projected Balance Sheets
0
1
2
3
NWC
$______
$10,000
$10,000
$10,000
NFA
21,000
______
______
0
Total Invest
$31,000
$24,000
$17,000
$10,000
Projected Balance Sheets
0
1
2
3
NWC
$10,000
$10,000
$10,000
$10,000
NFA
21,000
14,000
7,000
0
Total
$31,000
$24,000
$17,000
$10,000
Now let’s use the information from the previous
example to do a capital budgeting analysis.
Project operating cash flow (OCF):
EBIT
Depreciation
Taxes
OCF
$8,000
+7,000
-2,720
$12,280
Project Cash Flows
0
OCF
1
$12,280
Chg. NWC
______
Cap. Sp.
-21,000
Total
______
2
3
$12,280
$12,280
______
$12,280
$12,280
$______
Project Cash Flows
0
OCF
Chg. NWC
-10,000
Cap. Sp.
-21,000
Total
-31,000
1
2
$12,280
$12,280
3
$12,280
10,000
$12,280
$12,280
$22,280
Capital Budgeting Evaluation:
NPV
=
-$31,000 + $12,280/1.201 + $12,280/1.20 2 + $22,280/1.20 3
=
$655
IRR
=
21%
PBP
=
2.3 years
AAR =
$5280/{(31,000 + 24,000 + 17,000 + 10,000)/4} = 25.76%
Should the firm invest in this project? Why or why not?
Yes -- the NPV > 0, and the IRR > required return
Proposed Project
• Cost: $200,000 + $10,000 shipping
+$30,000 installation.
• Depreciable cost $240,000.
• Inventories will rise by $25,000 and
payables will rise by $5,000.
• Economic life = 4 years.
• Salvage value = $25,000.
• MACRS 3-year class.
Incremental gross sales = $250,000.
Incremental cash operating costs = $125,000.
Tax rate = 40%.
Cost of capital = WACC = 10%
Set up without numbers a
time line for the project CFs.
0
1
Initial
Outlay
OCF1
NCF0
NCF1
2
3
OCF2
OCF3
NCF2
NCF3
4
OCF4
+ Terminal
CF
NCF4
What is the annual
depreciation?
Year
1
2
3
4
Rate x
0.33
0.45
0.15
0.07
1.00
Basis
$240
240
240
240
Depreciation
$ 79
108
36
17
$240
Due to half-year convention, a 3-year
asset is depreciated over 4 years.
Operating cash flows ($000):
1
2
Sales
$250 $250
Cash costs
125 125
Depreciation
79 108
EBIT
$ 46 $ 17
Taxes (40%)
18
7
Net Income
28
10
Add: Depreciation
79 108
Operating Cash flow $107 $118
3
$250
125
36
$ 89
36
53
36
$ 89
4
$250
125
17
$108
43
65
17
$ 82
Net Investment Outlay
At t=0
Equipment
($200,000)
Ship + Install
(40,000)
Change in NWC (20,000)
Net CF0
($260,000)
 NWC = $25,000 - $5,000
Net Terminal Cash Flow
At t = 4
Salvage value
$25,000
Tax on SV
(10,000)
Recovery on NWC
20,000
Net Termination CF $35,000
Project net CFs on a time line:
0
(260)
1
2
3
107
118
89
4
117
Enter CFs in CFLO register and I = 10.
NPV = $81,573
IRR = 23.8%
What is the project’s MIRR?
0
(260)
1
2
3
107
118
89
4
117
97.9
(260)
MIRR = ?
142.8
142.4
500.1
What is the project’s payback?
0
(260)
1
2
3
107
118
89
Cumulative:
(260)
(153)
(35)
54
Payback = 2 + 35/89 = 2.4 years
4
117
171
If this were a replacement
rather than a new project,
would the analysis change?
Yes. The old equipment would be
sold and the incremental CFs would
be the changes from the old to the
new situation.
• The relevant depreciation would be the
change with the new equipment.
• Also, if the firm sold the old machine now,
it would not receive the salvage value at the
end of the machine’s life.
T10.15 Alternative Definitions
• The Tax-Shield Approach
of OCF (concluded)
OCF = (S - C - D) + D - (S - C - D)  T
= (S - C)  (1 - T) + (D  T)
= (S - C)  (1 - T) + Depreciation x T
• The Bottom-Up Approach
OCF = (S - C - D) + D - (S - C - D)  T
= (S - C - D)  (1 - T) + D
= Net income + Depreciation
• The Top-Down Approach
OCF = (S - C - D) + D - (S - C - D)  T
T10.16 Chapter 10 Quick Quiz • Now let’s put our
new-found
knowledge
to work.
Part
1
of
3
Assume we have the following background
information for a project being considered by
Gillis, Inc.
• See if we can calculate the project’s NPV and
payback period. Assume:
Required NWC investment = $40; project cost =
$60; 3 year life
Annual sales = $100; annual costs = $50; straight
line
depreciation to $0
T10.16 Chapter 10 Quick Quiz - Part
of 3are(concluded)
• Project
cash 1
flows
thus:
0
1
2
3
OCF
$39.8 $39.8 $39.8
Chg. in NWC-40
40
Cap. Sp.
-60
-$100 $39.8 $39.8 $79.8
Payback period = ___________
T10.17 Example: A Cost-Cutting
Proposal
Consider a $10,000 machine that will reduce pretax operating costs
by $3,000 per year over a 5-year period. Assume no changes
in net working capital and a scrap (i.e., market) value of $1,000 after five years.
For simplicity, assume straight-line depreciation. The marginal tax
rate is 34% and the appropriate discount rate is 10%.
Using the tax-shield approach to find OCF:
OCF = (S - C)(1 - T) + (Dep  T)
The after-tax salvage value is:
= [$0 - (-3,000)](.66) + (2,000 
.34)
market
value - (increased tax liability) = market value - (market value - book) 
T
= $1,980 + $680 = $2,660
= $1,000 - ($1,000 - 0)(.34) = $660
T10.17 Example: A Cost-Cutting
Proposal (concluded)
The cash flows are
Year OCF
0 $
0
1 2,660
2 2,660
3 2,660
Capital spendingTotal
-$10,000 -$10,000
0
2,660
0
2,660
0
2,660
T10.18 Chapter 10 Quick Quiz Evaluating Cost Cutting Proposals
2
of
3
Cost
= Part
$900,000
Depreciation= $180,000 per year
Life
=
Salvage
=
Cost savings =
Tax rate
=
Add.
to
NWC
sign)
5 years
$330,000
$500,000 per year, before taxes
34 percent
=
–$220,000 (note the minus
 1.
After-tax cost saving: $500K  (______) = $______ per year.
 2.
Depreciation tax shield: $180K  ______ = $______ per year.
 3.
After-tax salvage value: $330K - ($330K - 0)(.34) = $______
T10.18 Chapter 10 Quick Quiz - Part
0 2 of
1 3 (concluded)
2
3
4
5
AT saving
$330.0K$330.0K$330.0K$330.0K
$330.0K
Tax shield
61.2K 61.2K 61.2K 61.2K 61.2K
OCF
_____ _____$391.2K$391.2K
$391.2K
Chg. in NWC____
_____
Cap. Sp.-900K
217.8K
T10.19 Example: Setting the Bid
Price
The Army is seeking bids on Multiple Use Digitizing Devices (MUDDs). The contract calls for
4 units per year for 3 years. Labor and material costs are estimated at $10,000 per MUDD.
Production space can be leased for $12,000 per year. The project will require $50,000 in new
equipment which is expected to have a salvage value of $10,000 after 3 years. Making MUDDs
will require a $10,000 increase in net working capital. Assume a 34% tax rate and a required
return of 15%. Use straight-line depreciation to zero.
Operating
Year cash flow
0
1
2
3
$
0
OCF
OCF
OCF
Increases
in NWC
– $10,000
0
0
10,000
Capital
spending
Total
= cash flow
– $50,000
– $60,000
0
OCF
0
OCF
+ 6,600 OCF + 16,600
T10.19 Example: Setting the Bid
Price
(continued)
• Taking the
present
value of $16,600 in
year 3 ( = $10,915 at 15%) and netting
against the initial outlay of – $60,000
gives
Total
Year cash flow
0
1
–
$49,085
OCF
T10.19
Example:
Setting
the
Bid
• The PV annuity factor for 3 years at 15% is 2.283.
Setting NPV
= $0, (continued)
Price
NPV = $0 = – $49,085 + (OCF  2.283), thus
OCF =OCF
$49,085/2.283
= $21,500
= Net income + Depreciation
 Using the bottom-up approach to calculate OCF,
$21,500 = Net income + $50,000/3 = Net income + $16,667
Net income = $4,833
 Next, since annual costs are $40,000 + $12,000 = $52,000
Net income = (S - C - D)  (1 - T)
$4,833 = (S  .66) - (52,000  .66) - (16,667  .66)
S = $50,153/.66 = $75,989.73
Hence, sales need to be at least $76,000 per year (or $19,000 per MUDD)!
T10.19 Example: Setting the Bid
Background: Suppose we also have the following
Price
(continued)
information.
• 1. The bid calls for 20 MUDDs per year for 3 years.
• 2. Our costs are $35,000 per unit.
• 3. Capital spending required is $250,000; and
depreciation = $250,000/5 = $50,000 per year
• 4. We can sell the equipment in 3 years for half its
original cost: $125,000.
• 5. The after-tax salvage value equals the cash in from
the sale of the
equipment, less the cash out
due to the increase in our tax liability
associated with the sale of the equipment for more
T10.19 Example: Setting the Bid
• The cash flows ($000) are:
Price0 (continued)
1
2
3
OCF
$OCF $OCF
$OCF
Chg. in NWC - $ 60
+ 60
Capital Spending - 250
______
+115.25
Find the______
OCF such that the
NPV is zero at 16%:
+$310,000 - 175,250/1.163
$197,724.74
OCF
=
OCF  (1 - 1/1.163)/.16
- $310 $OCF $OCF $OCF +
=
OCF  2.2459
=
$88,038.50/year
175.25
T10.19 Example: Setting the Bid
Price (concluded)
If the required OCF is $88,038.50, what price must we bid?
Sales
$_________
Costs
Depreciation
EBIT
Tax
Net income
700,000.00
50,000.00
$_________
24,319.70
$ 38,038.50
Sales = $62,358.20 + 50,000 + 700,000 = $812,358.20 per
year, and
T10.20 Example: Equivalent
Annual Cost Analysis
• Two types of batteries are being
considered for use in electric golf
carts at City Country Club. Burnout
brand batteries cost $36, have a
useful life of 3 years, will cost $100
per year to keep charged, and have
a salvage value of $5.
Longlasting brand batteries cost $60
T10.20 Example: Equivalent
Annual Cost Analysis (continued)
• Using the tax shield approach, cash flows
for Burnout are:
OCF = (Sales - Costs)(1 - T) +
Depreciation(T)
= (0 - 100)(.66) + 12(.34)
= -$66 + 4 = -$62
Operating Capital
Total
Yearcash flow- spending= cash flow
T10.20 Example: Equivalent
• Again using the tax shield approach, OCFs
Annual
Cost
Analysis
(continued)
for Longlasting are:
OCF = (Sales - Costs)(1 - T) +
Depreciation(T)
= (0 - 88)(.66) + 12(.34) = -$58 + 4 = $54
Operating
Total
Year
flow
OCF
Capital
- spending
= cash
T10.20 Example: Equivalent
Annual Cost Analysis (continued)
• Using a 15% required return, calculate the
cost per year for the two batteries.
Calculate the PV of the cash flows:
The present value of total cash flows for
Burnout
is -$175.40
T10.20 Example: Equivalent
Annual Cost Analysis
(concluded)
What 3 year annuity has the same PV as
Burnout?
The PV annuity factor for 3 years at
15% is 2.283:
-$175.40 = EAC  2.283
EAC = -$175.40/2.283 = -$76.83
T10.21 Chapter 10 Quick Quiz Part
3
of
3
• Here’s one more problem to test your
skills. Von Stroheim Manufacturing is
considering investing in a lathe that is
expected to reduce costs by $70,000
annually. The equipment costs $200,000,
has a four-year life (but will be
depreciated as a 3-year MACRS asset),
requires no additional investment in net
working capital, and has a salvage value
of $50,000. The firm’s tax rate is 39%
T10.21 Chapter 10 Quick Quiz - Part 3 of 3 (continued)
Depreciation:
YearDep (%) Dep ($)
1
2
3
4
33.33%$_______
44.44% 88,880
14.82% 29,640
7.41% 14,820
100% $200,000
T10.21 Chapter 10 Quick Quiz Partare3thus:
of 3 (concluded)
The cash -flows
0
1
2
3
4
AT saving
$42,700.0$42,700.0$42,700.0
$42,700.0
Tax shield
25,997.434,663.2 11,559.6 5,779.8
OCF
$68,697.4$77,363.2$54,259.6
$48,479.8
Cap. Sp.-200,000
_______