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9- 1

Fundamentals

of Corporate

Finance

Sixth Edition

Richard A. BrealeyStewart C. Myers

Alan J. Marcus

Chapter 9

McGraw Hill/Irwin Copyright 2009 by The McGraw-Hill Companies, Inc. All rights reserved

Using Discounted Cash Flow

Analysis to Make Investment

Decisions

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Topics Covered

Identifying Cash Flows

Discount Cash Flows, Not Profits

Discount Incremental Cash Flows

Discount Nominal Cash Flows by the NominalCost of Capitol

Separate Investment & Financing Decisions

Calculating Cash Flows

Example: Blooper Industries

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Cash Flow vs. Accounting Income

Discount actual cash flows

Using accounting income, rather than cash flow,

could lead to erroneous decisions.

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 bedepreciated at $1,000 per year. Given a 10% required

return, compare the NPV using cash flow to the NPV

using accounting income.

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9- 4

500-500+IncomeAccounting

$1,000-$1,000-onDepreciati

500$$1,500InflowCash

2Year1Year

32.41$)10.1(

500

1.10

500

=NPVApparent 2 !

Cash Flow vs. Accounting Income

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9- 5

5001,

500+2,

000-loashree

2,000-ostProject

500$$1,500In loash

2ear1earToday

14.223$)10.1(

500

)10.1(

500,12,000=NPVCash2

!

Cash Flow vs. Accounting Income

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9- 6

Relevant Cash Flows

The cash flows that should be included in acapital budgeting analysis are those that will

only occur if the pro ect is accepted

These cash flows are called incrementalcash flows

Thestand-alone principle allows us to

analyze each pro ect in isolation from the

firm simply by focusing on incremental cash

flows

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9- 8

Incremental Cash Flows

Discount incremental cash flows

Include All Indirect Effects

Forget Sunk Costs

Include Opportunity Costs

Recognize the Investment in Working Capital

Beware of Allocated Overhead Costs

Remember Shutdown Cash Flows

Incremental

Cash Flow

cash flow

with pro ect

cash flow

without pro ect= -

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9- 9

Incremental Cash Flows

IMPORTANTIMPORTANT

Ask yourself this question

Would the cash flow still exist if the pro ect

does not exist?

If yes, do not include it in your analysis.

If no, include it.

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Inflation

INFLATION RULEINFLATION RULE

Be consistent in how you handle inflation!!

Use nominal interest rates to discount

nominal cash flows.

Use real interest rates to discount real cash

flows.

You will get the same results, whether youuse nominal or real figures

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Inflation

Example

You own a lease that will cost you $8,000 next year,

increasing at 3% a year (the forecasted inflation

rate) for 3 additional years (4 years total). If

discount rates are 10% what is the present value

cost of the lease?

1 real interest rate =1+nominal interest rate

1+inflation rate

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Inflation

Example - nominal figures

$29,0736,

5688,

742

=8

000x1.

033

7,014487,8=8000x1.032

491,78,240=8000x1.031

00.000,880000

10%@PVFloCashear

3

2

10.1

8742310.1

8487210.1

8240

!

!

!

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Inflation

Example - real figures

29,073

6,5688,0003

7,0148,0002

7,4918,00018,

0008,

0000

PV 6.7961%FlowCashYear

3

2

068.1

8,000068.1

8,000068.1

8,000

= $

!

!

!

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9- 14 Separation of Investment &Financing Decisions

When valuing a pro ect, ignore how the

pro ect is financed.

Following the logic

from incrementalanalysis ask yourself the following

question:Is the project existence dependent

on the financing? If no, you must separate

financing and investment decisions.

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Calculating Cash Flows

Think ofcash flows ascoming from threeelements

Total cash flow =

+ cash flows from capital investments

+ cash flows from changes in working capital

+ operating cash flows

Operating cash flows = 1) Net income + depreciation if theres

no interest expense or

2) EBIT + depreciation taxes or

3) (Sales costs) (1-tax rate)+ Depreciation *Tax rate = > Tax

Shield approach: this last form is particularly useful when

purchasing equipment

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More on NWC

Why do we have to considerchanges in NWCseparately? GAAP requires that sales be recorded on the income

statement when made, not when cash is received

GAAP also requires that we record cost of goodssoldwhen the corresponding sales are made, regardless ofwhen we actually pay oursuppliers

So,cash flow timing differences exist between thepurchase of inventory, revenue and costs from itssale on

the income statement, and the actual cash collection fromitssale

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Depreciation

The depreciation expense used forcapitalbudgeting should be the depreciationschedule required by the IRS for tax

purposes

Depreciation itself is a non-cash expense;consequently, it is only relevant because itaffects taxes

Depreciation tax shield = DxT D = depreciation expense

T = marginal tax rate

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Computing Depreciation

Straight-line depreciation D = (Initial cost salvage) / number of years

Very few assets are depreciated straight-line for taxpurposes

MACRS Need to know which asset class is appropriate for tax

purposes

Multiply percentage given in table by the initial cost

Depreciate to zero Mid-yearconvention

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After Tax Salvage

If the salvage value is different from the bookvalue of the asset, then there is a tax effect

Book value = initial cost accumulated

depreciation After tax salvage = salvage T(salvage

book value)

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9- 20 Example: Depreciation and After-Tax

Salvage

You purchase equipment for $100,000 and itcosts $10,000 to have it delivered and installed.

Based on past information, you believe that you

can sell the equipment for $17,000 when you are

done with it in 6 years. The companys marginal

tax rate is40%. What is the depreciation expense

each year, and the after tax salvage in year 6, for

each of the following situations?

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Example: Straight-line Depreciation

Suppose the appropriate depreciationschedule isstraight-line

D = ($110,000 17,000) / 6 = $15,500 every year

for 6 years BV in year 6 = $110,000 6(15,500) = $17,000

After-tax salvage = $17,000 - .4(17,000 17,000)

= $17,000

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Example: Three-year MACRS

Year MACRSpercent

D

1 .3333 .3333(110,000) =

36,663

2 .4444 .4444(110,000) =48,884

3 .1482 .1482(110,000) =

16,302

4 .0741 .0741(110,000) =8,151

BV in year 6 =110,000 36,663 48,884 16,302 8,151 = 0

After-tax salvage= 17,000 -.4(17,000 0) =$10,200

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Calculating Cash Flows

Cash Flow from Capital Investments Almost every pro ect requiressome sort of initial

investment. This is often capitalized from an

accounting perspective. In finance, the investment

represents a negative cash flow.

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Calculating Cash Flows

Operating Cash Flow Operating cash flow =

+ Revenue

- Costs

- Taxes

Methods of Handling Depreciation

Method l: Dollars in Minus Dollars Out

Method 2: Ad usted Accounting Profits Method 3: Add Back Depreciation Tax Shield

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Blooper Industries

650,2462,2283,2113,2950,1Profit

427,1326,1230,1137,1050,1(35%).Tax078,4788,3513,3250,3000,3ProfitPretax

000,2000,2000,2000,2000,2onDepreciati

155,12576,11025,11500,10000,10Expenses

233,18364,17538,16750,15000,15Revenues

039,3679,1225214204575,2500,1in WCChange0039,3717,4493,4279,4075,4500,1WC

00010InvestCap

6543210Year

,

(,000s)

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Blooper Industries

Cash Flow From Operations (,000s)Revenues

- xpenses

Depreciation= Pro it be ore tax

.-Tax @ 35%

= Net pro it+ Depreciation

= CF rom operations

15 000

10 000

2 000

3 000

1 050

1 9502 000

3 950

,

,

,

,

,

,

,

,

or $3,950,000

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Blooper Industries

Net Cash Flow (entire pro ect) (,000s)

4,3396,3294,2384,0693,9091,37511,500-FlowCashNet

4,6514,4624,2834,1133,950OpromCF

039,31,679225-214-204-2,575-1,500-in WCChange

300,1

10,000-

valuealvage

InvestCap

6543210Year

NPV 12% = $4,222,350

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QuickQuiz

How do we determine ifcash flows arerelevant to the capital budgeting decision?

What are the common types ofcash flows?

How do we determine operatingca

sh flow

s?

What are the other 2 components of total

cash flows from a pro ect?

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