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Fundamentals of Corporate

Finance

Sixth Edition

Richard A. Brealey

Stewart C. Myers

Alan J. Marcus

Slides by

Matthew Will

Chapter 8

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 Nominal

Cost 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.

ExampleA 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.

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500 -500 +Income Accounting

$1,000-$1,000-onDepreciati

500 $ $1,500 InflowCash

2Year 1Year

32.41$)10.1(

500

1.10

500=NPVApparent

2

Cash Flow vs. Accounting Income

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500 +1,500+2,000-FlowCash Free

2,000-CostProject

500 $ $1,500 InflowCash

2Year 1Year Today

14.223$)10.1(

500

)10.1(

500,12,000=NPVCash

2

Cash Flow vs. Accounting Income

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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 project

cash flow without project= -

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Incremental Cash Flows

IMPORTANTIMPORTANT

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.

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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 you

use 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 rate1+inflation rate

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Inflation

Example - nominal figures

$29,073

6,5688,742=8000x1.033

7,014487,8=8000x1.032

491,78,240=8000x1.031

00.000,880000

10% @ PVFlowCash Year

3

2

10.187423

10.184872

10.18240

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Inflation

Example - real figures

29,073

6,5688,0003

7,0148,0002

7,4918,0001

8,0008,0000

PV@6.7961%FlowCash Year

3

2

068.1

8,000068.1

8,000068.1

8,000

= $

9- 12 Separation of Investment & Financing Decisions

When valuing a project, ignore how the project is financed.

Following the logic from incremental analysis 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 of cash flows as coming from three elements

Total cash flow =

+ cash flows from capital investments

+ cash flows from changes in working capital + operating cash flows

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Calculating Cash Flows

Cash Flow from Capital Investments Almost every project requires some 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: Adjusted 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%).Tax

078,4788,3513,3250,3000,3ProfitPretax

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

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

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

039,3679,1225214204575,2500,1in WC Change

0039,3717,4493,4279,4075,4500,1WC

00010Invest Cap

6543210Year

,

(,000s)

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Blooper Industries

Cash Flow From Operations (,000s)Revenues

- Expenses

Depreciation

= Profit before tax

.-Tax @ 35 %

= Net profit

+ Depreciation

= CF from operations

15 000

10 000

2 000

3 000

1 050

1 950

2 000

3 950

,

,

,

,

,

,

,

,

or $3,950,000

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Blooper Industries

Net Cash Flow (entire project) (,000s)

4,3396,3294,2384,0693,9091,37511,500-FlowCash Net

4,6514,4624,2834,1133,950Op from CF

039,31,679225-214-204-2,575-1,500-in WC Change300,1

10,000-

valueSalvage

Invest Cap6543210Year

NPV @ 12% = $4,222,350

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