Risk And Capital Budgeting
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Course Name / Number
Choosing the Right Discount Rate
The numerator focuses on project cash flows,
covered in chapter 8:
CF3
CFN
CF1
CF2
NPV  CF0 


 ... 
2
3
(1  r )
(1  r )
(1  r )
(1  r ) N
The denominator is the discount rate, the focus of
chapter 9.
The
denominator
should:
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Reflect the opportunity costs of the firm’s investors.
Reflect the project’s risk.
Be derived from market data.
A Simple Case
Project discount rate is easy to determine if we
assume :
Firm is financed with 100% equity.
Project is similar to the firm’s
existing assets.
In this case, the appropriate discount rate equals
the cost of equity.
Cost of equity estimated using the CAPM
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E ( Ri )  RF  βi ( E ( Rm )  RF )
All Leather’s Cost of Equity
All Leather Inc., an all-equity firm, is evaluating a proposal
to build a new manufacturing facility.
– Firm produces leather sofas.
– As a luxury good producer, firm very sensitive to
economy.
– All Leather’s stock has a beta of 1.3.
• Managers note Rf = 4%, expect the market risk
premium will be 5%.
E(Re ) = Rf + (E(Rm) - Rf) = 10.5% cost of equity
4
Cost of Equity
Beta plays a central role in determining whether a firm’s cost
of equity is high or low.
What factors influence a firm’s beta?
Operating
leverage
The mix of fixed and variable costs
EBIT Sales
Operating Leverage 

EBIT
Sales
The extent to which a firm finances operations
by borrowing
Financial
Leverage
5
The fixed costs of repaying debt increase a
firm’s beta in the same way that operating
leverage does.
All Leather Inc. and Microfiber
Corp.
The two firms are in the same industry
All Leather Inc
Microfiber Corp
44,000
40,000 sofas
44,000
40,000 sofas
$950
$950
Total Revenue
$41,800,000
$38,000,000
$41,800,000
$38,000,000
Fixed costs per year
$10,000,000
$2,000,000
$600
$800
$36,400,000
$34,000,000
$37,200,000
$34,000,000
$5,400,000
$4,000,000
$4,600,000
$4,000,000
Sales volume
Price
Variable costs per sofa
Total cost
EBIT
What if sales volume increases by 10% ?
6
All Leather’s EBIT increases faster because it has high operating
leverage.
Operating Leverage for All
Leather and Microfiber:
EBIT
All Leather
Microfiber
Sales
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Other things equal, higher operating leverage means that All Leather’s
beta will be higher than Microfiber’s beta.
The Effect of Leverage on Beta:
Firm 1
$250 million
$0
$250 million
Assets
Debt
Equity
Firm 2
$250 million
$100 million
$150 million
Case #1: Gross Return on Assets Equals 25 Percent.
EBIT
Interest
Cash to equity
ROE
$62.5 million
$0
$62.5 million
62.5 ÷ 250 = 25%
$62.5 million
$8.5 million
$54 million
54 ÷ 150 = 36%
Case #2: Gross Return on Assets Equals 5 Percent.
EBIT
Interest
Cash to equity
ROE
8
$12.5 million
$0
$12.5 million
12.5 ÷ 250 = 5%
$12.5 million
$8.5 million
$4 million
4 ÷ 150 = 2.7%
Financial leverage makes Firm 2’s ROE more volatile, so its beta will be
higher.
The Weighted Average Cost of
Capital (WACC)
Cost of equity applies to projects of an all-equity firm.
– But what if firm has both debt and equity?
– Problem akin to finding expected return of portfolio
Use weighted average cost of capital (WACC) as
discount rate:
• An
–
–
–
–
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example…
Comfy Inc builds houses.
Firm has $150 million equity (E), with cost of equity re = 12.5%.
Also has bonds (D) worth $50 million, with rd = 6.5%
Assume initially that there are no corporate taxes.
 D 
 E 
 50 
 150 
WACC  
r

r

6
.
5
%

d 
e 


12.5%  11%
DE
DE
 50  150 
 50  150 
Finding WACC for Firms with
Complex Capital Structures
How do we calculate WACC if firm has long-term (D) debt as well as
preferred (P) and common stock (E)?
E
D
P






WACC  
re  
rd  
rp
 EDP
 EDP
 EDP
An example....
Sherwin Co.
Total value =
211.5 million
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Has 10,000,000 common shares; price = $15/share;
re = 15%.
Has 500,000 preferred shares, 8% coupon, price =
$25/share, $12.5 million value.
Has $40 million long term debt, fixed rate notes
with 8% coupon rate, but 7% YTM. Notes sell at
premium and worth $49 million.
 150 
 49 
 12.5 
WACC  
15%  
7%  
8%  12.73%
 211.5 
 211.5 
 211.5 
Connecting the WACC to the CAPM
WACC consistent with CAPM
Can use CAPM to compute WACC for levered firm.
Calculate beta for bonds of a large corporation:
– First find covariance between bonds and stock market.
– Plug computed debt beta (d), Rf and Rm into CAPM to find rd.
• Debt beta typically quite low for healthy, low-debt firms
– Debt beta rises with leverage.
rd  Rf  d ( RM  Rf )
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Any asset that generates a cash flow has a beta, and that beta
determines its required return as per CAPM.
Calculating Asset Betas and
Equity Betas
The CAPM establishes direct link between required return
on debt and equity and betas of these securities.
D
E
βA  (
) βd  (
) βe
DE
DE
•
•
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An asset beta is the covariance of the cash flows generated by a firm’s
assets with RM, return on market portfolio, divided by variance of
market’s return.
– For all-equity firm, asset beta = equity beta.
– For levered firm, asset beta will be less than equity beta (still
assuming no taxes).
If asset beta known, and debt beta is assumed to be 0, can compute
equity beta directly from A:
D
βE  β A (1  )
E
Discount Rate for Unique Projects
What if a company has diversified investments in many industries?
In this case, using firm’s WACC to evaluate an
individual project would be inappropriate.
Use project’s asset beta adjusted for desired
leverage.
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• An example…
– Assume GE is evaluating an investment in oil and gas
industry.
– GE would examine existing firms that are pure plays
(public firms operating only in oil and industry).
Data for Berry Petroleum and
Forest Oil
Say GE selects Berry Petroleum & Forest Oil as pure plays:
Berry Petroleum
Forest Oil
Stock beta
0.65
0.90
Fraction Debt
0.14
0.39
Fraction Equity
0.86
0.61
D/E ratio
0.16
0.64
Asset beta *
0.56
0.55
* Assumes debt beta = 0 and no taxes
Operationally similar firms, but Berry Petroleum’s E = 0.65
and Forest Oil’s E = 0.90
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Why so different? Reason: Forest Oil uses debt for 39% of financing;
Berry Petroleum: 14%.
Converting Equity Betas to Asset
Betas for Two Pure Play Firms
To determine correct A to use as discount rate for the
project, GE must convert pure play E to A, then average.
– Previous table lists data needed to compute unlevered equity
beta.
– Unlevered equity beta (same as A when taxes are zero) strips
out effect of financial leverage, so always less than or equal to
equity beta.
– Berry’s A = 0.56, Forest’s A = 0.55, so average A = 0.55
• GE capital structure consists of 20% debt and 80% equity (D/E
ratio = 0.25). Compute relevered equity beta:
 GE
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D

  A 1    0.551  0.25  0.69
E

Converting Equity Betas to Asset
Betas for Two Pure Play Firms
Using CAPM, compute rate of return GE shareholders
require for the oil and gas investment.
• Assume risk-free rate of interest is 6% and expected risk
premium on the market is 7%:
E(R) = 6% + 0.69(7%) = 10.83%.
One more step to find the right discount rate for GE’s
investment in this industry: calculate project WACC.
– GE’s financing is 80% equity and 20% debt. Assume investors
expect 6.5% on GE’s bonds:
 E 
 D 
WACC  
re  
rd  10.83%(80%)  6.5%( 20%)  9.96%
DE
DE
16
Accounting for Taxes
• Have thus far assumed away taxes
– Tax deductibility of interest payments favors use of debt.
– Accounting for interest tax shields yields after-tax WACC.
 D 
 E 
WACC  
(1  T )rd  
re
DE
DE
• After-tax formula for equity beta changes to:
– We are still assuming debt beta = 0.
D

 E  U 1  (1  T ) 
E

βU is the beta of an unlevered firm.
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Analogous to asset beta, but not strictly equal to βA due to taxes
Summary: Finding Discount Rate
for Unique Projects
1) Identify pure play firms.
2) Calculate after-tax, unlevered betas for these
firms and average them.
3) Relever beta to reflect the investing firm’s
capital structure.
4) Plug relevered beta into CAPM to obtain re..
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5) Use re, rd, and capital structure weights to
obtain after-tax project WACC.
A Closer Look at Risk
Break-Even Analysis
Managers often want to assess business’ value
drivers:
Useful to assessing operating risk is finding
break-even point.
Break-even point is level of output where all
operating costs (fixed and variable) are covered.
19
Sensitivity Analysis
• Sensitivity analysis allows mangers to test importance of each
assumption underlying a forecast.
– Test deviations from “base case” and associated NPV.
• Best Electronics Inc has new DVD players project. Base case
assumptions (below) yields Exp NPV = $1,139,715.
1.
2.
3.
4.
5.
6.
7.
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8.
9.
10.
11.
The project’s life is five years.
The project requires an up-front investment of $41 million.
BEI will depreciate initial investment on S-L basis for five years.
One year from now, DVD industry will sell 3,000,000 units.
Total industry unit volume will increase by 5% per year.
BEI expects to capture 10% of the market in the first year.
BEI expects to increase its market share one percentage point
each year after year one.
The selling price will be $100 in year one.
Selling price will decline by 5% per year after year one.
Variable production costs will equal 60% of the selling price.
The appropriate discount rate is 14 percent.
Sensitivity Analysis of DVD
Project
NPV
-$448,315
Pessimistic
Assumption
Optimistic
$43,000,000
Initial investment
$39,000,000
+2,727,745
-$1,106,574 2,800,000 un
Market size in year 1
3,200,000 un +3,386,004
-$640,727
2% per year
Growth in market size
8% per year
+3,021,884
-$4,602,832
8%
Initial market share
12%
+6,882,262
-$3,841,884
Zero
Growth in market share
2% per year
+6,121,315
-$2,229,718
$90
Initial selling price
$110
+4,509,149
62% of sales
Variable costs
-$545,002
-$2,064,260 -10% per yr
-$899,413
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NPV
16%
58% of sales +2,824,432
Annual price change
0% per year
+4,688,951
Discount rate
12%
+3,348,720
If all optimistic scenarios play out, project’s NPV rises to $37,635,010.
If all pessimistic scenarios play out, project’s NPV falls to -$19,271,270!
Real Options in Capital Budgeting
Option pricing analysis helpful in examining multistage projects
Embedded options arise naturally from investment;
Called real options to distinguish from financial
options.
Value of a project equals value captured by NPV,
plus option.
Can transform negative NPV projects into positive NPV!
22
Real Options in Capital Budgeting
Expansion
options
Abandonment
options
Follow-on
investment
options
23
Flexibility
options
• If a product is a hit, expand production.
• Can abandon a project if not successful.
• Shareholders have valuable option to
default on debt.
• Similar to expansion options, but more
complex (Ex: movie rights to sequel)
• Ability to use multiple production inputs
(Ex: dual-fuel industrial boiler) or produce
multiple outputs
Risk And Capital Budgeting
All-equity firms can discount their standard investment
projects at cost of equity.
Firms with debt and equity can discount their standard
investment projects using WACC.
WACC and CAPM are connected. Cost of debt and equity are
driven by debt and equity betas.
Use pure play equity betas when invest in unique projects.