chapter 9

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McGraw Hill/Irwin Copyright © 2003 by The McGraw-Hill Companies, Inc. All rights reserved

Chapter 9

Capital Budgeting and Risk

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Topics Covered

Company and Project Costs of Capital Measuring the Cost of Equity Capital Structure and COC Discount Rates for Intl. Projects Estimating Discount Rates Risk and DCF

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Company Cost of Capital

A firm’s value can be stated as the sum of the value of its various assets

PV(B)PV(A)PV(AB) valueFirm

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10%nologyknown tech t,improvemenCost

COC)(Company 15%business existing ofExpansion

20%products New

30% ventureseSpeculativ

RateDiscount Category

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A company’s cost of capital can be compared to the CAPM required return

Required

return

Project Beta1.26


13

5.5

0

SML

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Measuring Betas

The SML shows the relationship between return and risk

CAPM uses Beta as a proxy for risk Other methods can be employed to determine

the slope of the SML and thus Beta Regression analysis can be used to find Beta

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Measuring Betas

Dell Computer

Slope determined from plotting the line of best fit.

Price data – Aug 88- Jan 95

Market return (%)

Dell return (%

)R2 = .11

B = 1.62

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Measuring Betas

Dell Computer


Price data – Feb 95 – Jul 01

Market return (%)

Dell return (%

)R2 = .27

B = 2.02

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Measuring Betas

General Motors



Market return (%)

GM

return (%)R2 = .13

B = 0.80

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Measuring Betas

General Motors



Market return (%)

GM

return (%)R2 = .25

B = 1.00

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Measuring Betas

Exxon Mobil



Market return (%)

Exxon M

obil return (%)

R2 = .28

B = 0.52

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Measuring Betas

Exxon Mobil



Market return (%)

Exxon M

obil return (%)

R2 = .16

B = 0.42

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Beta Stability % IN SAME % WITHIN ONE RISK CLASS 5 CLASS 5 CLASS YEARS LATER YEARS LATER

10 (High betas) 35 69

9 18 54

8 16 45

7 13 41

6 14 39

5 14 42

4 13 40

3 16 45

2 21 61

1 (Low betas) 40 62

Source: Sharpe and Cooper (1972)

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Company Cost of Capitalsimple approach

Company Cost of Capital (COC) is based on the average beta of the assets

The average Beta of the assets is based on the % of funds in each asset

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Company Cost of Capitalsimple approach

Company Cost of Capital (COC) is based on the average beta of the assets

The average Beta of the assets is based on the % of funds in each asset

Example1/3 New Ventures B=2.01/3 Expand existing business B=1.31/3 Plant efficiency B=0.6

AVG B of assets = 1.3

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Capital Structure - the mix of debt & equity within a company

Expand CAPM to include CS

R = rf + B ( rm - rf )becomes

Requity = rf + B ( rm - rf )

Capital Structure

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Capital Structure & COC

COC = rportfolio = rassets

rassets = WACC = rdebt (D) + requity (E)

(V) (V)

Bassets = Bdebt (D) + Bequity (E)

(V) (V)

requity = rf + Bequity ( rm - rf )

IMPORTANT

E, D, and V are all market values

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0

20

0 0.2 0.8 1.2

Capital Structure & COC

Expected return (%)

Bdebt Bassets Bequity

Rrdebt=8

Rassets=12.2

Requity=15

Expected Returns and Betas prior to refinancing

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Union Pacific Corp.

Requity = Return on Stock

= 15%

Rdebt = YTM on bonds

= 7.5 %

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Union Pacific Corp.

.17.50PortfolioIndustry

.21.40PacificUnion

.26.52SouthernNorfolk

.24.46tionTransporta CSX

.20.64Northern Burlington

Error Standard.Beta

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Union Pacific Corp.

Example

100 valueFirmAssets Total

70ueEquity val

30Debt value100Assets

%75.12%157030

70%5.7

7030

30

assets

equitydebtassets

R

requitydebt

equityr

equitydebt

debtR

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International Risk

0.77.302.58Venezuela

1.39.482.91Thailand

0.81.421.93Poland

0.55.183.11Egypt

Betatcoefficien

nCorrelatioRatio

Source: The Brattle Group, Inc.

Ratio - Ratio of standard deviations, country index vs. S&P composite index

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Asset Betas

)PV(revenue

PV(asset)B

)PV(revenue

cost) ePV(variablB

)PV(revenue

cost) PV(fixedBB

assetcost variable

cost fixedrevenue

)PV(revenue

PV(asset)B

)PV(revenue

cost) ePV(variablB

)PV(revenue

cost) PV(fixedBB

assetcost variable

cost fixedrevenue

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Asset Betas

PV(asset)

cost) PV(fixed1B

PV(asset)

cost) ePV(variabl-)PV(revenueBB

revenue

revenueasset

PV(asset)

cost) PV(fixed1B

PV(asset)

cost) ePV(variabl-)PV(revenueBB

revenue

revenueasset

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Risk,DCF and CEQ

tf

tt

t

r

CEQ

r

CPV

)1()1(

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Risk,DCF and CEQ

Example

Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project?

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Risk,DCF and CEQ

Example


%12

)8(75.6

)(

fmf rrBrr

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Risk,DCF and CEQ

Example


%12

)8(75.6

)(

fmf rrBrr

240.2 PVTotal

71.21003

79.71002

89.31001

12% @ PV FlowCashYear

AProject

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Risk,DCF and CEQ

Example


%12

)8(75.6

)(

fmf rrBrr

240.2 PVTotal

71.21003

79.71002

89.31001


AProject

Now assume that the cash flows change, but are RISK FREE. What is the new PV?

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Risk,DCF and CEQ

ExampleProject A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV?

240.2 PVTotal

71.284.83

79.789.62

89.394.61


Project B

240.2 PVTotal

71.21003

79.71002

89.31001


AProject

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Risk,DCF and CEQ


240.2 PVTotal

71.284.83

79.789.62

89.394.61


Project B

240.2 PVTotal

71.21003

79.71002

89.31001


AProject

Since the 94.6 is risk free, we call it a Certainty Equivalent of the 100.

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Risk,DCF and CEQ

Example

Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market premium of 8%, and beta of .75, what is the PV of the project? DEDUCTION FOR RISK

15.284.81003

10.489.61002

5.494.61001riskfor

DeductionCEQFlowCash Year

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Risk,DCF and CEQ


The difference between the 100 and the certainty equivalent (94.6) is 5.4%…this % can be considered the annual premium on a risky cash flow

flow cash equivalentcertainty 054.1

flow cashRisky

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Risk,DCF and CEQ


8.84054.1

100 3Year

6.89054.1

100 2Year

6.94054.1

100 1Year

3

2

chapter 9

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