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Chapter 9Principles of
Corporate FinanceTenth Edition
Risk and the Cost of Capital
Slides by
Matthew Will
McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
9-2
Topics Covered
Company and Project Costs of CapitalMeasuring the Cost of EquityAnalyzing Project RiskCertainty Equivalents
9-3
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
9-4
Company Cost of Capital
A company’s cost of capital can be compared to the CAPM required return
Required
return
Project Beta0.5
Company Cost of Capital
3.8
0.2
0
SML
9-5
IMPORTANT
E, D, and V are all market values of Equity, Debt and Total Firm Value
Equity of ValueMarket
Debt of ValueMarket
E
D
EDV
VE
equityVD
debtassets rrCOCr
)(
bondson YTM
fmfequity
debt
rrBrr
r
Company Cost of Capital
9-6
Weighted Average Cost of Capital
WACC is the traditional view of capital structure, risk and return.
VE
EVD
Dc rrTWACC )1(
9-7
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 and Equity Cost
9-8
Measuring Betas
The SML shows the relationship between return and risk
CAPM uses Beta as a proxy for riskOther methods can be employed to
determine the slope of the SML and thus Beta
Regression analysis can be used to find Beta
9-9
Measuring Betas
9-10
Measuring Betas
9-11
Measuring Betas
9-12
Estimated Betas
Beta equity
Standard Error
Burlington Northern Santa Fe 1.01 0.19
Canadian Pacific 1.34 0.23CSX 1.14 0.22
Kansas City Southern 1.75 0.29Norfolk Southern 1.05 0.24
Union Pacific 1.16 0.21Industry portfolio 1.24 0.18
9-13
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)
9-14
Company Cost of Capital
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
Assets = Debt + Equity
V
EB
V
DBB equityDebtassets
9-15
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
9-16
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
Company Cost of Capitalsimple approach
9-17
Company Cost of Capital
2.0%nologyknown tech t,improvemenCost
COC)(Company 3.8%business existing ofExpansion
8.0%products New
15.0% ventureseSpeculativ
RateDiscount Category
9-18
Allowing for Possible Bad Outcomes
Example
Project Z will produce just one cash flow, forecasted at $1 million at year 1. It is regarded as average risk, suitable for discounting at a 10% company cost of capital:
100,909$1.1
000,000,1
11
r
CPV
9-19
Allowing for Possible Bad Outcomes
Example- continued
But now you discover that the company’s engineers are behind schedule in developing the technology required for the project. They are confident it will work, but they admit to a small chance that it will not. You still see the most likely outcome as $1 million, but you also see some chance that project Z will generate zero cash flow next year.
9-20
Allowing for Possible Bad Outcomes
Example- continued
This might describe the initial prospects of project Z. But if technological uncertainty introduces a 10% chance of a zero cash flow, the unbiased forecast could drop to $900,000.
000,818$1.1
000,900PV
9-21
Table 9.2
9-22
Risk, DCF and CEQ
tf
tt
t
r
CEQ
r
CPV
)1()1(
9-23
Risk, DCF and CEQ
9-24
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?
9-25
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?
%12
)8(75.6
)(
fmf rrBrr
9-26
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?
%12
)8(75.6
)(
fmf rrBrr
240.2 PVTotal
71.21003
79.71002
89.31001
12% @ PV FlowCashYear
AProject
9-27
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?
%12
)8(75.6
)(
fmf rrBrr
240.2 PVTotal
71.21003
79.71002
89.31001
12% @ PV FlowCashYear
AProject
Now assume that the cash flows change, but are RISK FREE. What is the new PV?
9-28
Risk,DCF and CEQExample
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?.. 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
6% @ PV FlowCashYear
Project B
240.2 PVTotal
71.21003
79.71002
89.31001
12% @ PV FlowCashYear
AProject
9-29
Risk,DCF and CEQExample
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?.. 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
6% @ PV FlowCashYear
Project B
240.2 PVTotal
71.21003
79.71002
89.31001
12% @ PV FlowCashYear
AProject
Since the 94.6 is risk free, we call it a Certainty Equivalent of the 100.
9-30
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
9-31
Risk,DCF and CEQExample
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?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV?
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 12.1
1.06x flow cashRisky
9-32
Risk,DCF and CEQExample
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?.. Now assume that the cash flows change, but are RISK FREE. What is the new PV?
8.840566.1
100 3Year
6.890566.1
100 2Year
6.940566.1
100 1Year
3
2