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Chapter 11
Cash Flows and Capital Budgeting
Learning Objectives
1. Explain why incremental after-tax free cash flows are relevant in evaluating a project, and
be able to calculate them for a project.
2. Discuss the five general rules for incremental after-tax free cash flow calculations, and
explain why cash flows stated in nominal (real) dollars should be discounted using a
nominal (real) discount rate.
3. Describe how distinguishing between variable and fixed costs can be useful in forecasting
operating expenses.
4. Explain the concept of equivalent annual cost, and be able to use it to compare projects
with unequal lives, decide when to replace an existing asset, and calculate the opportunity
cost of using an existing asset.
5. Determine the appropriate time to harvest an asset.
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I.
Chapter Outline
11.1
Calculating Project Cash Flows

In capital budgeting, we estimate the NPV of the cash flows that a project is expected to
produce in the future.

A.
All of the cash flow estimates are forward-looking.
Incremental After-Tax Free Cash Flows

The cash flows we discount in an NPV analysis are the incremental after-tax free
cash flows, which refers to the fact that these cash flows reflect the amount by which
the firm’s total after-tax free cash flows will change if the project is adopted. See
Equation 11.1:
o FCFProject = FCFFirm with project – FCFFirm without project

The term free cash flows (FCF) refers to the fact that the firm is free to distribute
these cash flows to creditors and stockholders because these are the cash flows that
are left over after a firm has made necessary investments in working capital and
long-term assets.
Note: Setting up timelines and performing calculations are typically the least burdensome
portion of the task of capital budgeting. Rather, the difficulties arise principally in two areas: (1)
generating good investment projects, and (2) developing reliable cash flow estimates for these
projects. It should be pointed out that investing in fixed assets differs from investing in financial
assets in at least one important sense. It is easy to find the investment opportunity set for
financial assets and then perform an analysis to decide among the opportunities. Preparation of a
capital budget, on the other hand, requires that people investigate and develop new project
proposals, estimate the cash flows associated with these projects, and only then perform the
analyses. Developing reliable cash flow estimates ranges from being a relatively minor task (say
a simple replacement project) to one that is subject to a great deal of uncertainty. This requires
all the analytical tools available as well as experience.
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B.
The FCF Calculation

Referring to 11.2, which is a more detailed version of 11.1:
FCF = [(Revenue – Op Exp – D&A) x (1 – t)] + D&A – Cap Ex – Add WC

We first compute the incremental cash flow from operations (CF Opns), which is the
cash flow that the project is expected to generate after all operating expenses and
taxes have been paid.

We then subtract the incremental capital expenditures (Cap Ex) and incremental
additions to working capital (Add WC) required for the project to obtain FCF.
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
The FCF is therefore a measure of the after-tax cash flows from operations over and
above what is necessary to make any required investments.

The idea that we can evaluate the cash flows from a project independently of the cash
flows for the firm is known as the stand-alone principle. It is another way of saying
that we can treat the project as if it is a stand-alone firm that has its own revenue,
expenses, and investment requirements.
C.
Cash Flows from Operations

Note that the incremental cash flow from operations, CF Opns, equals the
incremental net operating profits after tax (NOPAT) plus the incremental
depreciation and amortization (D&A) associated with the project.

We exclude interest expenses when calculating NOPAT because the cost of
financing a project is reflected in the discount rate that is used in the NPV
calculation.
Note: In finance, we separate the investment and financing decisions. A project’s cash flows are
estimated regardless of how we plan to finance the project and the required rate of return (also
referred to as the “cost of capital”). The investment and financing decisions are brought together
when we apply a decision rule (NPV, IRR, etc.) and the associated required rate of return to our
cash flow estimates.

We use the firm’s marginal tax rate (t) to calculate NOPAT because the profits from
a project are assumed to be incremental to the firm.

We add incremental depreciation and amortization (D&A) to NOPAT when
calculating CF Opns because, as in the accounting statement of cash flows, D&A
represents a noncash charge that reduces the firm’s tax obligation.

However, since D&A is a noncash charge, we have to add it back to NOPAT
in order to get the cash flow from operations right.
D.
Cash Flows Associated with Investments
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
Once we have estimated CF Opns, we simply subtract cash flows associated with
required investment to obtain FCF for a project in a particular period.

Investments can be required to purchase long-term tangible assets and intangible
assets, or to fund current assets.
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E.
FCF versus Accounting Earnings

The impact of a project on a firm’s overall value or on its stock price does not depend
on how the project affects the company’s accounting earnings. It depends only on
how the project affects the company’s free cash flows.

Accounting earnings can differ from cash flows for a number of reasons, making
accounting earnings an unreliable measure of the costs and benefits of a project.

Accounting earnings also reflect noncash charges, such as depreciation and
amortization, which are intended to account for the costs associated with
deterioration of the assets in a business as those assets are used.
11.2
Estimating Cash Flows in Practice
A.
Five General Rules for Incremental Cash Flow Calculations

Rule 1: Include cash flows and only cash flows in your calculations. Do not include
allocated costs or overhead unless they reflect cash flows.

Rule 2: Include the impact of the project on cash flows from other product lines. If
the product associated with a project is expected to cannibalize or boost sales of
another product, you must include the expected impact of the new project on the cash
flows from the other product in the analysis.
Example: The projected sales for a new soft drink are $4,000,000 per year, although it is
estimated that $750,000 of these sales are from current customers that will switch from one of
the firm’s other soft drink flavors. What is the correct incremental revenue from the new soft
drink that should be used in the capital budgeting decision?

Rule 3: Include all opportunity costs. By opportunity costs, we mean the cost of
giving up another opportunity.
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Example: The soft-drink company mentioned above owns a factory that is not currently being
used which can provide the manufacturing capacity for the new soft drink. The original cost of
the factory was $7,000,000 and its current market value is $12,000,000. Alternatively, the
factory could be leased to another firm for $500,000 per year. What are the relevant cash flows
that should be considered when making the decision?

Rule 4: Forget sunk costs. Sunk costs are costs that have already been incurred, but
all that matters when you evaluate a project at a particular point in time is how much
you have to invest in the future and what you could expect to receive in return for
that investment; this means that past investments are irrelevant.
Example: The soft-drink company has spent $1,000,000 on product testing, surveys, and
development and is deciding whether or not to market a new soft drink. Should the $1,000,000
be included in the project cash flow estimates when making the decision?

Rule 5: Include only after-tax cash flows in the cash flow calculations. The
incremental pretax earnings of a project only matter to the extent that they affect the
after-tax cash flows that the firm’s investors receive.
B.
Nominal versus Real Cash Flows

Nominal dollars are the dollars that we typically think of. They represent the actual
dollar amounts that we expect a project to generate in the future, without any
adjustments.

When prices are going up, a given nominal dollar amount will buy less and less over
time.
o Real dollars represent dollars stated in terms of constant purchasing power.

We can write the cost of capital , k, as
o 1 + k = (1 + ∆Pe) x (1 + r)

r is the real cost of capital
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

(∆Pe) is the expected rate of inflation

(r) is the real rate of return
It is important to make sure that all cash flows are stated in either nominal dollars or
real dollars.
C.
Tax Rates and Depreciation

A progressive tax system, which we have in the United States, is one in which the
marginal tax rate at low levels of income is lower than the marginal tax rate at high
levels of income.

One especially important difference from a capital budgeting perspective is that the
depreciation methods allowed by GAAP differ from those allowed by the IRS.
o The straight-line depreciation method illustrated earlier in this chapter in the
NASCAR racetrack example is allowed by GAAP and is often used for
financial reporting.
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o An “accelerated” method of depreciation, called the Modified Accelerated
Cost Recovery System (MACRS), has been in use for U.S. federal tax
calculations since the Tax Reform Act of 1986 went into effect.

MACRS thus enables a firm to deduct depreciation charges sooner,
thereby realizing the tax savings sooner and increasing the present
value of the tax savings.
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MACRS Depreciation
The Staple Supply Co. has just purchased a new computerized information system with an installed cost
of $160,000. The computer is treated as five-year property. What are the yearly depreciation
allowances? Based on historical experience, we think that the system will be worth only $10,000 when
we get rid of it in four years. What are the tax consequences of the sale? What is the total aftertax cash
flow from the sale?
The yearly depreciation allowances are calculated by just multiplying $160,000 by the five-year
percentages in the table above:
Notice that we have also computed the book value of the system as of the end of each year. The book
value at the end of Year 4 is $27,648. If we sell the system for $10,000 at that time, we will have a loss
of $17,648 (the difference) for tax purposes. This loss, of course, is like depreciation because it isn't a
cash expense.
What really happens? Two things. First: We get $10,000 from the buyer. Second: We save .34 ×
$17,648 = $6,000 in taxes. So, the total aftertax cash flow from the sale is a $16,000 cash inflow.
D.
Computing the Terminal-Year FCF

The FCF in the last, or terminal, year of a project often includes cash flows that are
not typically included in the calculations for other years.
o For instance, in the final year of a project, the assets acquired during the life
of the project may be sold and the working capital that has been invested may
be recovered.
 Add WC = Change in cash and cash equivalents + Change in accounts
receivable + Change in inventories – Change in accounts
payable.
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o When an asset is expected to have a salvage value, we must include the
salvage value realized from the sale (net of any tax consequences) of the asset
and the impact of the sale on the firm’s taxes in the terminal-year FCF
calculations.
E.
Expected Cash Flows

We are estimating when we forecast FCF in an NPV analysis.
o The expected FCF for a particular year equals the sum of the products of the
possible outcomes (FCFs) and the probabilities that those outcomes will be
realized.



Evaluating NPV Estimates
The Basic Problem - Computing an NPV is putting a market value on uncertain future cash
flows. Projecting the future involves the potential for error. Major error sources are biases and
omissions. There are two main reasons for positive NPVs: (1) we have constructed a good
project, or (2) we have done a bad job of estimating NPV. Similarly, a negative computed NPV
might be reflective of a bad project, or of a bad job of estimating NPV. Estimated cash flows are
expectations, or averages, of possible cash flows, not exact figures (although if an exact figure
were available, you would use it).
Forecasting Risk - the danger of making a bad (value destroying) decision because of errors in
projected cash flows. This risk is reduced if we systematically investigate common problem
areas.
Sources of Value - The first and best guard against forecasting risk is to keep in mind that
positive NPVs are economic rarities in competitive markets. In other words, for a project to have
a positive NPV, it must have some competitive edge – be first, be best, be the only. Keep in
mind the economic axiom that in a competitive market excess profits (the source of positive
NPVs) are zero.
In “Corporate Strategy and the Capital Budgeting Decision” (Midland Corporate Finance
Journal, Spring, 1985, pp. 22-36), Alan Shapiro states that a firm’s capital budgeting program
should “establish strategic options in order to gain competitive advantage.” Further, successful
investments, according to Shapiro, are those investments “that involve creating, preserving, and
even enhancing competitive advantages that serve as barriers to entry.” The following are
project characteristics associated with positive NPVs.
1) Economies of scale
2) Product differentiation
3) Cost advantages
4) Access to distribution channels
5) Favorable government policy
Shapiro’s article serves both to take us past the standard number-crunching and to encourage us
to think of capital budgeting from the strategic, or “big-picture” standpoint: how will this project
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(or group of projects) benefit the firm as a whole.
11.3.1 Forecasting Free Cash Flows
A.
Cash Flows from Operations

To forecast incremental cash flows from operations we must forecast the incremental
net revenue, operating expenses, and depreciation and amortization associated with
the project, as well as the firm’s marginal tax rate

When forecasting operating expenses, analysts often distinguish between variable
costs and fixed costs
B.
Investment Cash Flows

We must consider two general classes of investments when calculating FCF:
incremental capital expenditures and incremental additions to working capital
1. Capital Expenditures
o Capital expenditure forecasts in an NPV analysis reflect the expected level of
investment during each year of the project’s life.
o Capital expenditures are typically required at the beginning of a project
2. Working Capital
o Cash flow forecasts in an NPV analysis include four working capital items:
1)cash and cash equivalents, 2) accounts receivable, 3) inventories, and 4)
accounts payable
11.4
Special Cases
A.
Projects with Different Lives

A problem that arises quite often in capital budgeting involves choosing between two
mutually exclusive investments where the investments have different lives.
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o In a situation like this, we can effectively make the lives of the mowers the same
by assuming repeated investments over some identical period and then
comparing the NPVs of their costs.
o A less cumbersome and more powerful method to handle the problem is to
compute the equivalent annual cost (EAC). The EAC can be calculated as
follows:
EACi = kNPVi [(1 + k)t / (1 + k)t – 1]
 1  k t 
EACi  k NPVi 

t
 1  k  1

k is the opportunity cost of capital

NPVi is the normal NPV of the investment i

t is the life of the investment

EAC simply reflects the annuity that has the same present value as the
∆FCFs of an investment over the investment period we are considering.
B.
When to Harvest an Asset

The optimal time to harvest is the point in time at which the rate of increase in cash
flows, from period to period, is no longer greater than the cost of capital.

At this point in time, it becomes optimal to harvest the trees and invest the
proceeds in alternative investments that yield the opportunity cost of capital.
C.
When to Replace an Existing Asset

Two fundamental questions: Do the benefits of replacing the existing asset exceed
the costs, and, if they do not now, when will they?

Solving this problem is simply a matter of computing the EAC for the new asset and
comparing it with the annual cash inflows from the old asset.
D.
The Cost of Using an Existing Asset
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
The third rule of calculating incremental after-tax cash flows is to include all
opportunity costs that are not always directly observable.
o Sometimes they have to be computed by first figuring the EAC for a given set of
cash flows and then adjusting the EAC by the appropriate discount rate and time,
if the EAC is not in present value form.
Additional Considerations in Capital Budgeting



Managerial Options and Capital Budgeting - The opportunity to change plans, dependent upon
future events. These options are valuable. Because they involve real (as opposed to financial)
assets, such options are often called “real” options.
o Contingency planning involves determining what will be done if this or that actually
happens. This can be explored with “what if” analysis.
o Option to expand (call option) - ignoring this option can result in underestimating the
NPV because of the possibility of profitable “follow-on” projects.
o Option to abandon (put option) - ignoring this option can result in underestimating NPV
because the right to quit a loser is valuable.
o Option to wait (call option) - waiting for favorable conditions or simply for some
uncertainty to be resolved is a valuable option.
Strategic options are possible future investments that may result from an investment under
consideration today.
Capital Rationing
Capital budgeting rules are distorted when soft or hard rationing occur. Soft rationing is selfimposed rationing, usually by top-level decision-makers within the firm. It often occurs for
administrative reasons that have little or nothing to do with value maximization. The important
thing about soft rationing is that the corporation as a whole isn't short of capital; more can be
raised on ordinary terms if management so desires. Ongoing soft rationing means we are
constantly bypassing positive NPV investments. This contradicts our goal of the firm. Hard
rationing, the lack of funds at any rate, is often associated with market imperfections or
financial distress.
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Chapter 11 - Sample Problems
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Provo, Inc., had revenues of $10 million, cash operating expenses of $5 million, and depreciation and
amortization of $1 million during 2008. The firm purchased $500,000 of equipment during the year
while increasing its inventory by $300,000 (with no corresponding increase in current liabilities). The
marginal tax rate for Provo is 40 percent.
1. Free cash flow: What is Provo's cash flow from operations for 2008?
a.
$2,400,000
b.
$2,600,000
c.
$3,400,000
d.
$4,000,000
2. Free cash flow: What is Provo's free cash flow for 2008?
a.
$2,400,000
b.
$2,600,000
c.
$3,400,000
d.
$4,000,000
3. Free cash flow: What is Provo's NOPAT for 2008?
a.
$2,400,000
b.
$2,600,000
c.
$3,400,000
d.
$4,000,000
4. Free cash flow: What is Provo's cash flows associated with investments for 2008?
a.
$300,000
b.
$500,000
c.
$800,000
d.
None of the above.
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5. Computing the terminal-year FCF: Miles Cyprus Corp. purchased a truck that currently has a
book value of $1,000. If the firm sells the truck for $5,000 today, then what is the amount of
cash that it will net after taxes if the firm is subject to a 30 percent marginal tax rate?
a.
$1,200
b.
$3,800
c.
$4,000
d.
$5,000
6. Projects with different lives: Your firm is deciding whether to purchase a durable delivery vehicle
or a short-term vehicle. The durable vehicle costs $25,000 and should last five years. The shortterm vehicle costs $10,000 and should last two years. If the cost of capital for the firm is 15
percent, then what is the equivalent annual cost for the best choice for the firm? (Round to the
nearest dollar.)
a.
$5,000, either vehicle
b.
$5,000, short-term vehicle
c.
$6,151, short-term vehicle
d.
$7,458, long-term vehicle
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Chapter 11 - Sample Problems
Answer Section
MULTIPLE CHOICE
1.
ANS: C
Refer To: Ref 11-1
Learning Objective: LO 1
Level of Difficulty: Medium
Feedback:
Provo, Inc.
Revenue
- Operating Ex
EBITDA
$10,000,000
5,000,000
$ 5,000,000
- D&A
1,000,000
EBIT
$ 4,000,000
x (1 – t)
NOPAT
+ D&A
CF Opns
60%
$ 2,400,000
1,000,000
$ 3,400,000
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2.
ANS: B
Refer To: Ref 11-1
Learning Objective: LO 1
Level of Difficulty: Medium
Feedback:
Provo, Inc.
Revenue
$10,000,000
- Operating Ex
5,000,000
EBITDA
$ 5,000,000
- D&A
1,000,000
EBIT
$ 4,000,000
x (1 – t)
60%
NOPAT
$ 2,400,000
+ D&A
1,000,000
CF Opns
$ 3,400,000
- Cap Exp
$500,000
- Add WC
300,000
FCF
$ 2,600,000
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3.
ANS: A
Refer To: Ref 11-1
Learning Objective: LO 1
Level of Difficulty: Medium
Feedback:
Provo, Inc.
Revenue
- Operating Ex
EBITDA
5,000,000
$ 5,000,000
- D&A
1,000,000
EBIT
$ 4,000,000
x (1 – t)
NOPAT
4.
$10,000,000
60%
$ 2,400,000
ANS: C
Refer To: Ref 11-1
Learning Objective: LO 1
Level of Difficulty: Medium
5.
ANS: B
Learning Objective: LO 2
Level of Difficulty: Hard
Feedback: The gain on the sale was $5,000 – $1,000 = $4,000
Taxes on the gain are: $4,000 x .3 = $1,200
Net cash flow from the sale is $5,000 – $1,200 = $3,800
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6.
ANS: C
Learning Objective: LO 4
Level of Difficulty: Hard
Feedback:
, therefore the
, since we are analyzing costs, we
should choose the lowest cost per year, which is the short-term vehicle.
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