# Capital Budgeting Cash Flows Inflation

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```					         Capital
Budgeting                 7
Cash Flows

Corporate Financial Management 3e
Emery Finnerty Stowe
10-1
Chapter Outline

7.1 An Overview of Estimating
Cash Flows
7.2 Calculating Incremental Cash
Flows
7.3 An Example of Incremental
Cash Flow Analysis
7.4 Inflation

10-2
7.1 An Overview of Estimating
Cash Flows
• Costs and benefits are measured in
terms of cash flow—not income.
• Cash flows are incremental
(marginal).
– The cash flows with the project minus
the cash flows without the project.
• Cash flows are after tax.
• Cash flow timing affects the project’s
value.
• Financing costs are included in the
cost of capital.
10-3
Tax Considerations
• Taxes and the timing of tax
payments significantly affect the
incremental cash flows. The
relevant tax rate is the firm’s
marginal tax rate, T.
• Revenues, represented by R,
increase tax liability by TR. When
the revenue and the tax treatment
occur simultaneously, the after-tax
cash flow is the revenue minus the
tax liability:
after-tax revenue cash flow = R – TR
= (1 – T) R

10-4
Tax Considerations
• Less obvious is that expenses, represented
by E, reduce tax liability.
• When the revenue and the tax treatment
occur When the expense and the tax
treatment occur simultaneously, the
algebraic signs carry through and the
after-tax cash flow is minus the expense
plus the reduced tax liability:

after-tax expense cash flow   =–E+T E
= – (1 – T) E

10-5
• In some cases the cash flow and tax
treatment are separated. This
complicates the analysis.
• The most common situation where
they are separated is when an asset
is capitalized (depreciated).
• Let I0 be a net expenditure to be
capitalized, and Dt be its
depreciation expense to be claimed
in year t.
• The ―separated‖ incremental after-
tax cash flow for each depreciation
expense is +T Dt. (This is just like
the +T E for an expense.)

10-6
Tax Considerations
With depreciation, the stream of after-
tax incremental cash flows for the
expenditure, I0, are then:
t     0      1    2    3
. . .
CF -I0      TD1 TD2 TD3
. . .
The sum of the Dts equals I0. So the
total amount of tax reduction is T(I0 )
whether you depreciate or expense
the item.

10-7
Suppose you pay \$1,000 for an asset. If
capitalized, depreciation would be
straight-line to zero over 4 years, 250
per yr. With a tax rate of 40%, that’s
100 per yr. after-tax.
Time     0        1   2       3     4
Depr.    0       250 250     250   250
ATCF -1,000     100 100     100   100
If expensed: -600 0 0         0     0
Which set of cash flows is preferred?

10-8
Tax Considerations
• The difference between expensing
and depreciating—and between
alternative tax treatments in most
cases, then, is because of the time
value of money.
• If you have a choice, expense rather
than capitalize—because of the time
value of money.
• Unfortunately, you rarely have a
choice!

10-9
7.2 Calculating Incremental
Cash Flows
• Net initial investment outlay.
• Future net operating cash flows.
• Non-operating cash flows required to
support the initial investment outlay.
– E.g., cash flows associated with a major
overhaul.

• Net salvage value received upon
termination of the project.

10-10
Net Initial Investment Outlay

• Cash expenditure.

• Changes in net working capital.
• Net cash flow from sale of old
asset (if any).
• Investment tax credits.

10-11
Cash Expenditure
• Let I0 be the net expenditure to be
capitalized, E0 be the net
expenditure to be expensed
immediately, and T be the firm’s
marginal tax rate.

• Cash expenditure = – I0 – E0 + T E0
= – I0 – (1 – T) E0

10-12
Changes in Net Working Capital
• At the start of a project, an
investment of net working capital
may be required.
–   Operating cash
–   Inventory
–   Accounts receivable
–   But, an increase in accounts payable
offsets some of the net working capital
needs.
• A project could also reduce the net
working capital requirements.
– Asset replacement

10-13
Net Cash Flow from Sale of
Old Asset
• If an existing asset is being replaced
by a new one, the sale of the old
asset may generate a cash flow.
• If the selling price is greater than
the net book value of the old asset,
taxes will have to be paid on this
sale.
• If the selling price is less than the
net book value of the old asset, a
tax credit is generated.

10-14
Net Cash Flow from Sale of Old
Asset
• Let S0 be the selling price of the old asset, and
B0 be its net book value.
• Taxes on the sale will be T (S0 – B0). So the net
cash flow from sale of old asset is:

S0 - T (S0 – B0)

10-15
Net Initial Outlay

• Let C0 be the net initial outlay. Let DW be the
change in the net working capital. Let Ic be the
investment tax credit. Then,

C0 = – I0 – DW – (1 – T) E0 + S0 – T(S0 – B0) + Ic

10-16
Net Operating Cash Flow
• Let DR be the change in periodic revenue and
DE be the change in periodic expenses
associated with the project. Let DD be the
change in the periodic depreciation expense.

• The Net Operating Cash Flow After Tax (CFAT)
is given by

10-17
Net Operating Cash Flow

CFAT = DR - DE - Tax liability
= DR - DE - T(DR - DE - DD)

CFAT = (1 - T)(DR - DE) + TDD

CFAT = after-tax operating income
+ tax credit on depreciation

10-18
Net Operating Cash Flow

• Alternatively, by rearranging the terms, we can
rewrite CFAT as:

CFAT = (1 - T)(DR - DE - DD) + DD
= after-tax net income + depreciation

Note that there is no interest expense, and this
―after-tax net income‖ is not from an accounting
income statement.

10-19
Non-Operating Cash Flows
• These are treated in the same way as the initial
cash expenditure.
• The expensed non-operating cash flows are
multiplied by (1 - T) to adjust for taxes,
because the cash flow and tax treatment occur
simultaneously.
• Capitalized non-operating cash flows create a
cash outflow when they occur, but only in
subsequent years does the tax treatment create
the depreciation tax shields.

10-20
Net Salvage Value
• Let S be the selling price of the asset and B its
book value. Let REX be the cleanup and
removal expenses (to be expensed) and DW the
net working capital recovered upon termination
of the project.

• Net salvage value =
= S - T(S - B) - (1 - T)REX + DW

10-21
10.3 An Example of Incremental Cash
Flow Analysis
• See handout on Perma-Filter Co.,
attached as speaker notes.

10-22
Perma-Filter: By-Item Cash Flows

• Net expenditure to be capitalized is
I0 = 5,100,000 + 400,000 = \$5,500,000
after-tax CF = -\$5,500,000
• Installation cost to be expensed immediately
is E0 = \$200,000, after-tax CF = -\$120,000
• The replacement requires an investment in
net working capital:
– Inventory increase - Accounts Payable increase
– = 40,000 - 25,000 = \$15,000
after-tax CF = -\$15,000
10-23
Perma-Filter: By-Item Cash Flows

• Annual depreciation on the old machine is
(3,000,000 - 0)/10 = \$300,000/yr
• Therefore, the current net book value is
3,000,000 - 5(300,000) = \$1,500,000 = B0
• Selling price of old machine is \$1,750,000 = S0
• Taxes on the difference are \$100,000, so the
after-tax CF for the old machine is \$1,650,000
• There is no investment tax credit, Ic = 0

10-24
Perma-Filter: By-Item Cash Flows

• Annual depreciation expense on the new
machine is
(5,500,000 - 350,000)/10 = \$515,000/yr
after-tax CF is \$206,000/yr, years 1-10
• In the first five years after the replacement,
the firm ―loses‖ the depreciation expense on
the old machine, after that, depreciation on
the old machine (if kept) would be \$0.

10-25
Perma-Filter: By-Item Cash Flows

• Recall that annual depreciation on the old
machine is \$300,000/yr. Therefore, there will be
lost after-tax CF = -\$120,000/yr, years 1-5
• Sales do not increase, and DR = 0.
• Cash expenses decline, so DE = -\$1,200,000/yr,
giving after-tax CF savings = \$720,000/yr, years
1-10.

10-26
Perma-Filter: By-Item Cash Flows

• The new machine is expected to be sold for
S = \$300,000
• But will have a net book value at that time
of        B = \$350,000
• The difference creates a tax credit, so the
after-tax CF = \$320,000
• Removal expenses will be REX = -\$150,000,
and after-tax CF = -\$90,000
• Net working capital (recovered) will be an
after-tax CF = \$15,000
10-27
Net Present Value

See handout on NPV calculation, attached as
speaker notes.

10-28

• The replacement project will create value because the NPV is
positive. How much value would the project add to each share?

• With 500,000 shares outstanding, making the replacement will

893,417 / 500,000 = \$1.79 per share

• NOTE: It is very important to understand that this does not
mean the stock price will increase by this amount when the
project is undertaken. Stock prices are based on expectations.
The stock price could increase by less because the project was
partially anticipated. It could also not change because the
project was fully anticipated, or even fall because the project
produces less value than had been expected.

10-29
The Internal Rate of Return (IRR)

• The IRR is the discount rate that makes
the NPV equal to zero.
• For Perma-Filter’s replacement project,
IRR = 16.95%

10-30
NPV Profile - Perma-Filter Co.
\$6,000

\$5,000
NPV (\$ thousands)

\$4,000

\$3,000

\$2,000

\$1,000

\$-
0%   5%       10%         15%   20%   25%

\$(1,000)

Discount Rate
\$(2,000)
New Project Side Effects

• Innovation can result in the erosion of one or
more existing products.
– Sales reduction
– Decline in market value of existing facilities.
• Innovation can also lead to enhancement of
existing and future products and services.
– Expanding one product line can stimulate sales of
another. (service contracts).
• Both erosion and enhancement must be
incorporated into a capital budgeting analysis.
10-32
10.4 Inflation
• Inflation affects the project’s expected cash
flows.
– Effect on revenues
– Effect on expenses
• Inflation also affects the cost of capital.
– The higher the expected inflation, the higher the
return required by investors.
• So the effects of inflation must be properly
incorporated in the NPV analysis.

10-33
Effect of Inflation on the Cost of
Capital
• Notation:
rr = cost of capital in real terms
rn = cost of capital in nominal terms
i = expected annual inflation rate
(1 + rn) = (1 + rr) (1 + i)

rn = rr + i + irr

10-34
Effect of Inflation on the Cost of
Capital
• Inflation increases the nominal amounts
of both revenues and expenses, even
though their real values may stay the
same.
• However, depreciation expense is fixed.
It is based on historical cost.
– Therefore, inflation decreases the real value
of depreciation tax credits.

10-35
Effect of Inflation on the Cost of
Capital
• If expected future cash flows are given in
nominal terms, then we must use the
nominal cost of capital to calculate their
present value.
• If expected future cash flows are given in
real terms, we must use the real cost of
capital to calculate their present value.

10-36
Inflation and NPV

Wildcat Washer Works (WWW) is evaluating a
new project that costs \$120,000. It has a life of
3 years and no salvage value. Annual revenues,
less operating expenses (excluding depreciation)
are \$65,000 per year in real dollars. WWW will
use straight line depreciation to a zero book
value over 3 years. Its marginal tax rate is 40%.
The real cost of capital is 10% and inflation is
expected to be 8% per year.
Compute the NPV of the project in real and in
nominal dollars.
10-37
NPV in Real Dollars
• Annual after-tax revenues (less expenses),
in real dollars are 65,000(1- 0.40) =
\$39,000 per year.
• Annual depreciation expense (in nominal
dollars) is (120,000 - 0)/3 = \$40,000 per
year.
• Annual depreciation tax credit (in
nominal dollars) is 40,000(0.40) = \$16,000
per year.
10-38
NPV in Real Dollars

• In real dollars, the first year’s depreciation tax
credit is worth 16,000/(1.08) = \$14,815.
• In real dollars, the second year’s depreciation
tax credit is worth 16,000/(1.08)2 = \$13,717.
• In real dollars, the third year’s depreciation
tax credit is worth 16,000/(1.08)3 = \$12,701.
• The annual after-tax cash flow is the after tax
revenues (less expenses) plus the depreciation
tax credit.
10-39
NPV in Real Dollars

Time Item            BTCF    ATCF       PV@10%

0     Initial inv.   -120    -120       -120
1-3   Net rev.       65/yr   39/yr      96.987
1     Depr.          0       14.815     13.468
2     Depr.          0       13.717     11.336
3     Depr.          0       12.701      9.543
NPV=   11.334

10-40
NPV in Nominal Dollars
• Annual depreciation expense (in nominal
dollars) is (120,000 - 0)/3 = \$40,000 per
year.
• Annual depreciation tax credit (in
nominal dollars) is 40,000(0.40) = \$16,000
per year.

10-41
NPV in Nominal Dollars

• In nominal dollars, revenues net of expenses in
year 1 are 65,000(1.08) = \$70,200.
• After-tax net revenues = 70,200(1-0.4) =
\$42,120.
• In nominal dollars, revenues net of expenses in
year 2 are 65,000(1.08)2 = \$75,816
• After-tax net revenues = 75,816(1-0.4) =
\$45,490.
• After-tax net revenues in year 3 are \$49,129.
10-42
NPV in Nominal Dollars
• The nominal cost of capital is:
rn = rr + i + (i)rr
= 0.10 + 0.08 + (0.08)(0.10)
= 0.188
rn = 18.80%

10-43
NPV in Nominal Dollars

Time Item                   BTCF     ATCF        PV@18.8%

0         Initial inv.      -120     -120        -120
1-3       Depr.             0/yr     16/yr       34.347
1         Net rev.          70.200   42.120      35.454
2         Net rev.          75.816   45.490      32.232
3         Net rev.          81.881   49.129      29.301
NPV=    11.334

NOTE:           34.347 = 13.468 + 11.336 + 9.543
And             35.454 + 32.232 + 29.301 = 96.987
10-44
NPV

Time Item            BTCF ATCF         PV

0     Initial inv.   -120     -120     -120
1-3   Net rev.       65/yr    39/yr    96.987 @ 10%
1-3   Depr.          0        16/yr    34.347 @ 18.8%

NPV= 11.334

10-45
Inflation and NPV Analysis
• The NPV of the project is unchanged as
long as the cash flows and the cost of
capital are expressed in consistent terms.

• If inflation is expected to affect revenues
and expenses differently, these
differences must be incorporated in the
analysis.

10-46
Summary

• This chapter describes the critical
problem of estimating a capital budgeting
project’s incremental cash flows.
• We want to leave you with one final
observation:
The accuracy of the estimates used in
capital budgeting is critically
important.

10-47

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