Chapter 9
Risk And Capital Budgeting
Professor John Zietlow
MBA 621
Chapter 9: Overview
• 9.1 Choosing the Right Discount Rate
– The cost of equity
– The weighted average cost of capital (WACC)
– Connecting WACC to the CAPM
– Asset betas and project discount rates
• 9.2 A Closer Look at Risk
– Breakeven analysis
– Sensitivity analysis
– Scenario analysis and Monte Carlo simulation
– Decision trees
Chapter 9: Overview (Continued)
• 9.3 Real Options
– Why NPV doesn’t always give the right answer
– Types of real options
• Expansion options
• Abandonment options
• Follow-on investment options
– The surprising link between risk and real option values
• 9.4 Strategy and Capital Budgeting
– Competition and NPV
– Strategic thinking and real options
• 9.5 Summary
Choosing the Right Discount Rate
• To calculate an NPV, an analyst must evaluate project’s risk
– Often, the best place to look for clues is a firm’s securities
• What discount rate should managers use in cap budgeting?
– Rate should reflect opportunity cost of all firm’s investors
– Rate should also reflect the risk of the specific project
• To find discount rate, start with simplifying assumptions:
– Assume all equity financing, so only have to satisfy S/Hs
– Assume firm makes all investments in a single industry
• These allow firm to use cost of equity as discount rate
– Know from chapter 6 that cost of equity found with CAPM
E ( Ri )  RF  βi ( E ( Rm )  RF )
(Eq 9.1)
Determining 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%, believe market’s return will be 9%
– Can use CAPM to find All Leather’s cost of equity
E(Re ) = Rf + (E(Rm) - Rf) = 4% + 1.3 (9% - 4%) = 10.5% cost of equity
• All Leather beta is 1.3 due partly to high economic
sensitivity
– Higher risk must be reflected in discount rate used to
evaluate new manufacturing facility
– Low beta company (food processor) would use lower rate
Finding All Leather’s Cost of Equity (Cont)
• Other factors, besides economic sensitivity, impact beta
– A firm’s cost structure & production process very important
– Mix of variable & fixed costs determines operating leverage
• OL implies CF volatility will rise with fixed cost
– Substituting fixed for variable cost increases profits more
than proportionally when sales increase, but hurt if sales fall
• Define degree of operating leverage (DOL) as % in EBIT
divided by % in sales
– High DOL: small change in sales  large change in EBIT
DOL 
ΔEBIT ΔSales

EBIT
Sales
(Eq 9.2)
• Table on next slide details All Leather’s & competitor’s costs
& prices
– Microfiber also produces sofas, but less fixed costs
Financial Data for All Leather Inc. and
Microfiber Corp.
All Leather Inc
Microfiber Corp
$10,000,000
$2,000,000
Variable costs per sofa
$600
$800
Price
$950
$950
Contribution margin
$350
$150
40,000 sofas
40,000 sofas
$4,000,000
$4,000,000
Fixed costs per year
Last year’s sales volume
EBIT
• Suppose both firms achieve 10% rise in sales volume to 44,000 sofas
next year, holding all other figures constant. Fixed cost don’t change.
• Both firms’ revenues go from $38,000,000 to $41,800,000; a 10% rise
• All Leather’s total costs increase by $600/sofa, or $2,400,000 total
• Microfiber’s total costs increase by $800/sofa, or $3,200,000 total
• All Leather’s EBIT increases by $350/sofa, $1,400,000 total
• Microfiber’s EBIT increases by $150/sofa, $600,000 total
Calculating Operating Leverage for All
Leather and Microfiber
•
Using data from previous table, can compute OL for both firms
– Note key terms: EBIT= contribution margin - fixed costs
– Contribution margin = gross profit per unit of sales
– Gross profit = price per unit - variable cost per unit
DOLAll Leather =
DOLMicrofiber =
EBIT Sales $1,400,000 $3,800,000



 0.35  0.10  3.5
EBIT
Sales
$4,000,000 $38,000,000
EBIT Sales
$600,000
$3,800,000



 0.15  0.10  1.5
EBIT
Sales
$4,000,000 $38,000,000
• All Leather has a degree of operating leverage (DOL) of 3.5
– EBIT increases by 35% if sales increase by 10%
• Microfiber has lower DOL of 1.5 due to lower fixed costs
– EBIT increases by only 15% if sales increase by 10%
– But firm would weather sales decline better than All Leather
Operating Leverage for All Leather and
Microfiber
EBIT
All Leather
Microfiber
Sales
Measuring Financial Leverage and its Impact
on Firm’s Stock Beta
• Operating leverage: using fixed cost assets to magnify
(leverage) impact of change in sales on change in EBIT
– Increasing OL yields increasing stock beta
• Firms also use fixed cost financing (debt & PS) to magnify
effect of given change in EBIT on net income
– Measured as degree of financial leverage (DFL)
ΔNI ΔEBIT
DFL 

NI
EBIT
• If sales and EBIT increase, FL will yield magnified rise in NI
– But also works on downside; if sales & EBIT fall, so will NI
• FL increases expected net profits, but also increases risk
– Thus use of FL also increases a firm’s stock beta
Measuring Financial Leverage (Cont.)
• Demonstrate FL with firms on next table; same except
financing
– Firm 1: 100% equity, Firm 2: 60% equity, 40% debt
– Cost of Firm 2’s debt = 8.5%; assume neither firm pays tax
– Both firms have $250mn assets, identical production process
• Case #1: Assume both firms generate 25% gross return on
assets, or $62.5mn EBIT, and both pay out net income to S/H
– Firm 1 pays no interest, so $62.5 mn paid to S/Hs; 25% ROE
– Firm 2 pays $8.5mn int, so $54mn paid to S/Hs; 36% ROE
• Case #2: Assume both firms generate 5% gross return on
assets, $12.5mn EBIT; again both pay out net income to S/H
– Firm 1 pays no interest, so $12.5 mn paid to S/Hs; 5% ROE
– Firm 2 pays $8.5mn int, so only $4mn paid to S/Hs; 2.7% ROE
• If EBIT high, FL increases ROE; decreases ROE if EBIT low
The Effect Of Financial Leverage on
Shareholder Returns
Assets
Debt
Equity
Firm 1
Firm 2
$250 million
$250 million
$0
$100 million
$250 million
$150 million
Case #1: Gross Return on Assets Equals 25 Percent
EBIT
Interest
Cash to equity
ROE
$62.5 million
$62.5 million
$0
$8.5 million
$62.5 million
$54 million
62.5 ÷ 250 = 25%
54 ÷ 150 = 36%
Case #2: Gross Return on Assets Equals 5 Percent
EBIT
Interest
Cash to equity
ROE
$12.5 million
$12.5 million
$0
$8.5 million
$12.5 million
$4 million
12.5 ÷ 250 = 5%
4 ÷ 150 = 2.7%
The Weighted Average Cost of Capital
(WACC)
• Cost of equity the right discount rate for all-equity firm
– But what if firm has both debt and equity?
– Problem akin to finding expected return of portfolio
• Use weighted avg cost of capital (WACC) as discount rate
– Let D and E represent market values of debt & equity
• Demonstrate using Comfy Inc’s capital structure
– Comfy Inc builds residential houses
– Firm has $150mn equity (E), with cost of equity re = 12.5%
– Also has bonds (D) worth $50mn O/S, with rd = 6.5%
– Calculate WACC = 11%
 D 
 E 
 50 
 150 
WACC  
rd  
re  
6.5%  
12.5%
DE
DE
 50  150 
 50  150 
 50 
 150 

6
.
5
%



12.5%  0.256.5%  0.7512.5%  11%
 200 
 200 
Finding the WACC (Cont)
• How can Comfy’s managers be sure WACC = 11%?
– First way: assume wealthy investor purchases all firm’s debt
and equity. This is return he/she would earn
• Second way: Suppose firm invests in a project earning 11%
and distributes return to investors. Will they be satisfied?
– Following table shows CF generated & distributed satisfies
claims
Cash distributions to Comfy investors
Total CF available to distribute ($200m x 11%)
$22 million
Interest owed on bonds ($50m x 6.5%)
$3.25 million
Cash available to shareholders ($22m - $3.25m)
$18.75 million
Rate of return earned by S/Hs ($18.75m ÷ $150m)
12.5%
Finding WACC for Firms with Complex
Capital Structures
• How to calculate WACC if firm has long-term (LT) debt as
well as preferred (P) & common stock (E)?
– Find weighted average of individual capital costs
E
LT
P






WACC  
re  
rd  
rp
EDP
E  D P
EDP
• Assume S.N. Sherwin Co. wants to determine its WACC
– Has 10,000,000 common shares O/S; price = $15/sh; rc = 15%
– Has $40mn L-T, fixed rate notes with 8% coupon rate, but 7%
YTM; notes sell at premium and worth $49mn
– Has 500,000 pref shrs, 8% coupon, $75price, $12.5mn value
• Total value = $150m E+ $49m LT+$12.5m P =$211.5m
 150 
 49 
 12.5 
WACC  
15
%

7
%





8%  12.73%
 211.5 
 211.5 
 211.5 
Connecting the WACC to the CAPM
• Developed separately, but WACC consistent with CAPM
– Have so far looked only at all-equity firm
– But can use CAPM to compute WACC for levered firm
• Calculate beta for bonds of a large corporation
– First find covariance between bonds & stock market, then
– Plug computed debt beta (d), Rf & Rm into CAPM to find rd
• Debt beta typically quite low for healthy, low-debt firms
– Debt beta rises with leverage, approaches equity beta in B/R
rd  Rf  d ( RM  Rf )  4%  0.1  (12.5%  4%)  4.85%
• Example shows CAPM can be used for any security
– Any asset that generates a CF 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 D & E and betas of these securities
• Beta of firm’s assets equals weighted avg of D & E betas
βA  (
D
E
) βd  (
) βe
DE
DE
(Eq 9.4)
• A firm’s asset beta thus equals the cov of firm’s CFs with
RM, return on market p/f, divided by var of market’s return
– For all-equity firm, asset beta = equity beta
– For levered firm, asset beta will be less than equity beta
• If asset beta known, and debt beta is assumed to be 0, can
compute equity beta directly from A
βE  β A (1 
D
)
E
(Eq 9.5)
Finding Equity Betas from Asset Betas, and
Vice Versa
• If market values of D & E known, and any two of the three
betas are known, can compute the other beta
– Usually assume debt beta known (say d = 0.15)
• Assume firm has manufacturing assets with asset beta = 1.2
– If firm unlevered, equity beta equals asset beta, E = A =1.2
– Now suppose firm decides to raise 20% of funding needs by
issuing relatively safe bonds (d = 0.15) & retiring equity
– Use Eq 9.4 to find E, given A = 1.2 and d = 0.15
 A  1.2  (0.2)(0.15)  (0.8)  E
1.2  (0.2)(0.15)
  E  1.46
0.8
Finding Equity Betas from Asset Betas, and
Vice Versa (Cont)
• Can only use Eq 9.5 if debt beta assumed = 0
– Since debt = 20% of capital and equity = 80%, the debt-toequity ratio D/E = 0.2 ÷ 0.8 = 0.25
– Not surprisingly, equity beta is higher if debt beta assumed 0


 E   A 1 
D
 0.2 
  1.21 
  1.21.25  1.5
E
 0.8 
• Can now state decision rule for determining discount rate
to use for projects with asset betas similar to firm’s own
– For all equity firm, use cost of equity given by CAPM
– For levered firm, use WACC computed using CAPM and
betas of individual capital components
• If a project’s asset beta differs from firm’s asset beta, must
compute and use project betas
Finding the Discount Rate to Use for
Projects Unrelated to Firm’s Industry
• 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
– Instead use project’s asset beta adjusted for desired leverage
• Assume GE evaluating an investment in oil & gas industry
– Much different from any of GE’s existing businesses
– Instead GE would examine existing firms that are pure plays
– These are public firms operating only in O&G industry
• Say GE selects Berry Petroleum & Forest Oil as pure plays
– Operationally similar firms, but Berry Petroleum’s E = 0.65
and Forest Oil’s E = 0.90; why so different?
– Reason: Forest uses debt for 39% of financing; Berry: 14%
– Even if core business the same risk (A equal), E will differ
Data for Berry Petroleum and Forest Oil
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
• Computed using Eq 9.4 and assuming debt beta = 0
Berry Petrol: A = (%D)d + (%E)E = (0.14)(0) + (0.86)(0.65) = 0.56
Forest Oil:
A = (%D)d + (%E)E = (0.39)(0) + (0.61)(0.90) = 0.55
Converting Equity Betas to Asset Betas for
Two Pure Play Firms
• To determine correct A to use as discount rate for O&G
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) 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   A 1 
D
  0.551  0.25  0.69
E
Converting Equity Betas to Asset Betas for
Two Pure Play Firms (Continued)
• Assume risk-free rate of interest is 6% and expected risk
premium on the market is 7%
– Using CAPM equation, compute rate of return GE shareholders
require for the oil and gas investment
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
Summarizing Rules for Selecting an
Appropriate Project Discount Rate
• When an all equity firm invests in an asset similar to its
existing assets, the cost of equity is the appropriate
discount rate to use in NPV calculations.
• When a levered firm invests in an asset similar to its
existing assets, the WACC is the right discount rate.
• When a firm invests in an asset that is different than its
existing assets, it should look for pure play firms to find the
right discount rate.
– Firms can calculate an industry asset beta by unlevering the
betas of pure play firms
– Given the industry asset beta, firms can determine an
appropriate discount rate using the CAPM
Accounting for Taxes in Finding WACC
• Have thus far assumed away taxes, but often important
– 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




(Eq 9.6)
• Can likewise present method of computing after-tax equity
beta from asset beta
– Again assuming debt beta = 0, equity beta given by eq below
– Accounting for taxes doesn’t change key lessons above


 E   A 1  (1  T )
D

E
(Eq 9.7)
A Closer Look at Risk
Break-Even Analysis
• Managers often want to assess business’ key value drivers
– Key to assessing operating risk is finding break-even point
• Break-even point (BEP) is level of output where all
operating costs (fixed and variable) are covered
– BEP found by dividing FC by contribution margin (CM)

 
Fixed Costs
FC

  
BEP  

Contributi
on
m
arg
in
Pr
ice
/
unit

VC
/
unit


 
• Use this to find BEP for All Leather & Microfiber
– All Leather: FC = $10,000,000; Pr = $950/un; VC = $600/un
– Microfiber: FC = $2,000,000; Pr = $950/un; VC = $800/un
 $10,000,000   $10,000,000 
BEPAllLeather  

  28,572 sofas
$350
 $950  $600  

 $2,000,000   $2,000,000 
BEPMicrofiber  

  13,334 sofas
 $950  $800   $150 
Break-Even Point for All Leather
Costs &
Revenues
Total revenue
Total costs
$10,000,000
Fixed costs
28,572 units
Units
All Leather has high fixed costs ($10,000,000), but also high contribution
margin ($350/sofa). High BEP, but once FC covered, profits grow rapidly.
Break-Even Point for Microfiber
Costs &
Revenues
Total revenue
Total costs
Fixed costs
$2,000,000
13,334 units
Units
Microfiber has low fixed costs ($2,000,000), but also low contribution
margin ($150/sofa). 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
• Best Electronics Inc (BEI) has new DVD players project. Base
case assumptions (below) yields Exp NPV = $1,139,715
–
–
–
–
–
–
–
–
–
–
–
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.
8. The selling price will be $100 in year one.
9. Selling price will decline by 5% per year after year one.
10. Variable production costs will equal 60% of the selling price.
11. The appropriate discount rate is 14 percent.
1.
2.
3.
4.
5.
6.
7.
Sensitivity Analysis of DVD Project
NPV
-$448,315
Pessimistic
Assumption
$43,000,000 Initial investment
Optimistic
$39,000,000
NPV
+2,727,745
-$1,106,574 2,800,000 un Market size in year 1
3,200,000 un +3,386,004
-$640,727
8% per year
+3,021,884
12%
+6,882,262
2% per year
+6,121,315
$110
+4,509,149
2% per year Growth in market size
-$4,602,832
8%
-$3,841,884
Zero
Growth in market share
-$2,229,718
$90
Initial selling price
-$545,002
Initial market share
62% of sales Variable costs
-$2,064,260 -10% per yr Annual price change
-$899,413
16%
Discount rate
58% of sales +2,824,432
0% per year
+4,688,951
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!
Using Decision Trees to Make Multi-Step
Investment Decisions
• Many real investment projects are conditional & multistage: will only proceed to stage 2 if stage 1 successful
– Occurs frequently with new product introductions
– Begin selling in test market; if successful, build factory for
full-scale production & nationwide roll-out
– Very hard to evaluate in standard cap budgeting framework
• Decision trees allow managers to break investment
analysis into distinct phases
– Forces managers to perform extended “if--then” analysis
• Assume Trinkle Foods (Canada) has invented new salt
substitute, Odessa; assessing market testing in Vancouver
– Market test will cost C$5 million, but no new facilities needed
– If test successful, Trinkle will spend additional C$50mn to
build factory and launch nationwide one year later
Using Decision Trees (Cont)
• If market test successful, Trinkle predicts full product
launch will generate +C$12mn NCF per year for 10 years
– If test unsuccessful, expect full product launch to generate
only +C$2 mn NCF per year for 10 years.
– If Trinkle’s WACC=15% should Trinkle invest? If so, in what?
• Next figure shows decision tree for investment problem
– Initially, firm can choose to spend C$5 mn on market test
– If market test executed, expect probability of success = 0.5
• Proper way to use tree: begin at end & work backwards
– Suppose in one year, Trinkle learns test is successful.
– At that point, the NPV of launching the product is:
NPV  50 
12
12
12
12



...

 10.23
1.15 1.15 2 1.15 3
1.1510
• Clearly, Trinkle would invest if it winds up on this branch
Decision Tree From Odessa Investment
Using Decision Trees (Cont)
• But what if the initial tests are unfavorable?
– In that case, project’s NPV equals -C$39.96 mn & firm
should walk away--not fund nationwide roll-out.
– Note that C$5 mn test market cost is a sunk cost at t=1, so
the NPV of doing nothing at time one is zero
2
2
2
2
NPV  50 


 ... 
 39.96
2
3
10
1.15 1.15 1.15
1.15
• Now have set of simple “if--then” decision rules from tree
– If test successful, launch nationwide and NPV = C$10.23 mn
– If test unsuccessful, don’t invest C$50 mn for national launch
Using Decision Trees (Cont)
• Now must decide (at t=0) whether to spend C$5 mn for test
– Must realize NPVs computed at t=1 and use prob (success)
 10.23 
 0 
NPV  5  0.5

0
.
5


  0.55
 1.15 
 1.15 
• Seems unwise to invest in market test
– But very sensitive to discounting future CF at 15% rate
– Since test results known t=1, may use lower rate afterwards
Real Options in Capital Budgeting
• Though decision trees helpful in examining multi-stage
projects, most promising method is option pricing analysis
– Imbedded options arise naturally from investment
– Called real options to distinguish from financial options
– Options are valuable rights, not obligations
• Can transform negative NPV projects into positive NPV
– Value of a project equals value captured by NPV, plus option
• Several types of real options frequently encountered:
1. Expansion options: If a product is a hit, expand production
2. Abandonment options: Can abandon a project if not
successful; S/Hs have valuable option to default on debt
3. Follow-on investment options: Similar to expansion
options, but more complex (Ex: movie rights to sequel)
4. Flexibility options: Ability to use multiple production inputs
(Ex: dual-fuel industrial boiler) or produce multiple ouputs