Risk And Capital Budgeting
Professor XXXXX
Course Name / Number
Choosing the Right Discount Rate
The numerator focuses on project cash flows covered
in chapter 9.
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 10.
The
denominator
should:
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Reflect opportunity costs to 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
3
E ( Ri )  RF  βi ( E ( Rm )  RF )
Carbonlite Inc. Cost of Equity
Carbonlite Inc., an all-equity firm, is evaluating a
proposal to build a new manufacturing facility.
• Firm manufactures bicycle frames.
• As a luxury good producer, firm is very
sensitive to economy (product demand is
elastic).
• Carbonlite’s stock has a beta of 1.5
• Managers note Rf = 5%, expect the market
return will be 11%.
E(Re ) = Rf + (E(Rm) - Rf) = 5% + 1.5(11%-5%)
= 14% 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
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The fixed costs of repaying debt increase
a firm’s beta in the same way that
operating leverage does.
Carbonlite Inc. vs. Fiberspeed Corp.
The two firms are in the same industry.
Carbonlite Inc
Fiberspeed Corp
11,000
10,000frames
sofas
11,000
10,000frames
sofas
$1,000
$1,000
$11,000,000
$10,000,000
$11,000,000
$10,000,000
$5,000,000
$2,000,000
$400
$700
Total cost
$9,400,000
$9,000,000
$9,700,000
$9,000,000
EBIT
$1,600,000
$1,000,000
$1,300,000
$1,000,000
Sales volume
Price
Total Revenue
Fixed costs per year
Variable costs per frame
What if sales volume increases by 10% ?
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Carbonlite’s EBIT increases faster because it has
high operating leverage.
Operating Leverage for Carbonlite
and Fiberspeed
EBIT
Carbonlite
Fiberspeed
Sales
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Other things equal, higher operating leverage
means that Carbonlite’s beta will be higher than
Fiberspeed’s beta.
The Effect of Financial Leverage on
Beta
Firm 1
$100 million
$0
$100 million
Assets
Debt
Equity
Firm 2
$100 million
$50 million
$50 million
Case #1: Gross Return on Assets Equals 20 Percent
EBIT
Interest
Cash to equity
ROE
$20 million
$0
$20 million
20 ÷ 100 = 20%
$20 million
$4 million
$16 million
16 ÷ 50 = 32%
Case #2: Gross Return on Assets Equals 5 Percent
EBIT
Interest
Cash to equity
ROE
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$5 million
$0
$5 million
5 ÷ 100 = 5%
$5 million
$4 million
$1 million
1 ÷ 50 = 2%
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 is akin to finding expected return of
portfolio.
Use weighted average cost of capital (WACC) as
discount rate.
• Lox-in-a-Box is a chain of fast food stores.
• Firm has $100 million equity (E), with cost of equity re = 15%;
• Also has bonds (D) worth $50 million, with rd = 9%.
• Assume that the investment considered will not change the cost
structure or financial structure.
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 D 
 E 
 50 
 100 
WACC  
r

r

9
%

d 
e 


15%  13%
DE
DE
 50  100 
 50  100 
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
LT
P






WACC  
re  
rd  
rp
EDP
E  D P
EDP
An example....
S.D. Williams
Total value =
$50 million
10
Has 1,000,000 common shares; price =
$50/share; re = 15%.
Has 200,000 preferred shares, 8% coupon,
price = $80/share, 10% rate of return, $16
million value.
Has $47.1 million long term debt, fixed rate
notes with 8% coupon rate, but 7% YTM.
Notes sell at premium and worth $49 million.
 50 
 49 
 16 
WACC  
15%  
7%  
10%  10.9%
 115 
 115 
 115 
Rules for Selecting an Appropriate
Project Discount Rate
Cost of equity is the appropriate discount rate for
an all-equity firm.
When a levered firm invests in a project similar to
its existing projects, the WACC is the right
discount rate.
When a firm invests in a project different than its
existing projects, using the WACC may lead to
mistakes.
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Accounting for Taxes in Finding
WACC
We have thus far assumed away taxes, which are
often important in financing decisions.
• Tax deductibility of interest payments favors use
of debt.
• Accounting for interest tax shields yields after-
tax WACC.
 D 
WACC  
(1  tc )rd
DE
 E 

re
DE
Accounting for taxes doesn’t change the rules for
selecting the discount rate.
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A Closer Look at Risk
Break-Even Analysis
Managers often want to assess business’ value
drivers.
Finding the break-even point is often useful for
assessing operating risk.
Break-even point (BEP) is level of output where all
operating costs (fixed and variable) are covered.

 
Fixed Costs
Fixed Costs

  
BEP  

 Contribution margin   Price/unit  Variable Cost/unit 
13
Break-Even Point for Carbonlite
Costs &
Revenues
Total revenue
Total costs
$5,000,000
Fixed costs
8,333 units
14
Units
Carbonlite has high fixed costs ($5,000,000), but also high
contribution margin ($600/bike). High BEP, but once FC
covered, profits grow rapidly.
Break-Even Point for Fiberspeed
Costs &
Revenues
Total revenue
Total costs
Fixed costs
$2,000,000
6,667 units
15
Units
Fiberspeed has low fixed costs ($2,000,000), but also low
contribution margin ($300/bike). Low BEP, but profits grow
slowly after FC covered.
Sensitivity Analysis
Sensitivity analysis allows mangers to test
importance of each assumption underlying a
forecast.
• Test deviations from “base case” and associated NPV
GTI has developed a new skateboard. Base case
assumptions yield NPV = $236,000.
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1. The project’s life is five years.
2. The project requires an up-front investment of $7
million.
3. GTI will depreciate initial investment on straight
line basis for five years.
Sensitivity Analysis
4. One year from now, the skateboard industry will
sell 500,000 units.
5. Total industry unit volume will increase by 5%
per year.
6. BEI expects to capture 5% of the market in the
first year.
7. BEI expects to increase its market share one
percentage point each year after year one.
8. The selling price will be $200 in year one
9. Selling price will decline by 10% per year after
year one.
10. Variable production costs will equal 60% of the
selling price.
11. The appropriate discount rate is 14 percent.
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Sensitivity Analysis of Skateboard Project
Dollar values in thousands except price
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NPV
Pessimistic
Assumption
Optimistic
NPV
-$558
$8,000
Initial investment
$6,000,000
$1,030
-343
450,000 units
Market size in year 1
550,000 units
815
-73
2% per year
Growth in market size
8% per year
563
-1,512
3%
Initial market share
7%
1,984
-1,189
0%
Growth in market share
2% per year
1,661
-488
$175
Initial selling price
$225
960
-54
62% of sales
Variable costs
58% of sales
526
-873
-20% per year
Annual price change
0% per year
1,612
-115
16%
Discount rate
12%
617
Real Options in Capital Budgeting
Option pricing analysis is 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!
19
Real Options in Capital Budgeting
Expansion
options
Abandonment
options
Follow-on
investment
20
• If a product is a hit, expand
production.
• Firm can abandon a project if not
successful.
• Shareholders have valuable option to
default on debt.
options
• Similar to expansion options, but
more complex (Ex: movie rights to
sequel)
Flexibility
options
• 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.
A variety of tools exist to assist managers in
understanding the sources of uncertainty of a
project’s cash flows.