Transcript FINANCIAL ADMINISTRATION OF THE FIRM FIN 5043--930

Chapter 9
Risk And Capital Budgeting
Dr. Del Hawley
FIN 634
Fall 2003
Choosing the Right Discount Rate
• What discount rate should managers use in capital
budgeting?
– Rate should reflect the opportunity cost of all of the firm’s
investors (the cost of capital)
– 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 the cost of equity as discount rate
– Know from MBA 611 that the cost of equity is found with the
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 that produces leather
sofas, is evaluating a proposal to build a new manufacturing
facility.
• As a producer of luxury goods, the firm’s performance is
very sensitive to economic conditions. This is reflected in
the firm’s 1.3 stock beta.
– Note: The higher risk must be reflected in the discount rate
used to evaluate the new manufacturing facility unless the
project’s risk is not average relative to the firm’s other current
investments.
Determining All Leather’s Cost of Equity
• Based on current market conditions, the financial manager
will use Rf = 4%. Her market analysis provided an expected
market return of 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
How to Choose Rf in the CAPM
E(Re ) = Rf + (E(Rm) - Rf)
Any rate on the yield curve for government securities is a riskfree rate. So which one do you use?
– Today’s yield curve runs from about 1.5% to 5% on risk-free
yields. This is wide spread by historical standards.
– Since you will be using the CAPM to set a discount rate for longterm investments, you need the market’s estimate of the inflation
premium, but you do not need the other parts of the long-term
rate that have to do with liquidity or preferences.
How to Choose Rf in the CAPM
The Adjusted T-Bond Method uses the current rate on a 20-year
T-Bond less the average spread between 20-year and 1-year Tbonds – about 1.2%
Current yield on 20-year T-Bond
Less the average spread
Adjusted T-Bond Rate
5.0%
-1.2%
3.8%
Current Yield on a 1-year T-Bill
1.5%
How to Choose RM in the CAPM
RM needs to be the expected rate of return on the market
portfolio in the future, on average, over a long time. How do we
know that?
How to Choose RM in the CAPM
RM needs to be the expected rate of return on the market
portfolio in the future, on average, over a long time. How do we
know that?
Base it on recent market performance?
How to Choose RM in the CAPM
RM needs to be the expected rate of return on the market
portfolio in the future, on average, over a long time. How do we
know that?
Base it on recent market performance?
No. Recent past performance is a very poor predictor of longterm future performance. (See the link on our website for
annual stock returns.)
How to Choose RM in the CAPM
RM needs to be the expected rate of return on the market
portfolio in the future, on average, over a long time. How do we
know that?
Base it on past long-term performance? The average annual
return on the market over the last 74 years is about 11.6%.
How to Choose RM in the CAPM
RM needs to be the expected rate of return on the market
portfolio in the future, on average, over a long time. How do we
know that?
Base it on past long-term performance? The average annual
return on the market over the last 74 years is about 11.6%.
If you always use 11.6% as RM, you lock the SML to that
point so it decreases slope as Rf rises and increases slope
as Rf falls. This is just about opposite of what you would
expect to happen.
How to Choose RM in the CAPM
RM needs to be the expected rate of return on the market
portfolio in the future, on average, over a long time. How do we
know that?
Base it on market risk premium? On average over a long
time, this has been about 5.6%.
How to Choose RM in the CAPM
RM needs to the expected rate of return on the market portfolio
in the future, on average, over a long time. How do we know
that?
Base it on market risk premium? On average over a long
time, this has been about 5.6%.
This method has the best economic basis for what we are
doing, and it is very simple.
Using this method, the CAPM is used simply as:
E(Re ) = Adjusted Rf +  ( 5.6% )
Finding All Leather’s Cost of Equity (Cont)
• Other operating factors impact beta:
– Cost structure and production process
– Mix of variable and fixed costs
• Volatility of operating cash flow (EBIT) will rise with fixed
operating costs
• Substituting fixed for variable costs increases profits
more than proportionally when sales increase, but hurts
more if sales fall
Finding All Leather’s Cost of Equity (Cont)
Define degree of operating leverage (DOL) as the expected
% in EBIT divided by the expected % in sales.
DOL 
ΔEBIT ΔSales

EBIT
Sales
(Eq 9.2)
Estimate DOL as DOL = (Sales – Total VC)/EBIT
= Total Contribution Margin / EBIT
High DOL: small change in sales  large change in EBIT
– 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
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
Financial Data for All Leather Inc. and
Microfiber Corp.
All Leather
Sales is Units
36,000
40,000
Sales
- Variable Costs
Gross Profit
- Fixed Op Costs
Operating Profit (EBIT)
34.2
(21.6)
12.6
(10.0)
2.6
38.0
(24.0)
14.0
(10.0)
4.0
Calcualted DOL
Actual % Change
4.8
-35%
3.5
Microfiber
44,000
36,000
40,000
41.8
(26.4)
15.4
(10.0)
5.4
34.2
(28.8)
5.4
(2.0)
3.4
38.0
(32.0)
6.0
(2.0)
4.0
2.9
35%
1.6
-15%
1.5
44,000
41.8
(35.2)
6.6
(2.0)
4.6
1.4
15%
All Leather’s additional operating leverage results in a larger
percentage change in EBIT for a change in sales than Microfiber.
- Larger volatility of cash flows to support debt
- Larger volatility of cash flows to shareholders
Operating Leverage for All Leather and
Microfiber
EBIT
All Leather
Microfiber
Sales
Operating Leverage for All Leather and
Microfiber
30,000
25,000
All Leather
20,000
Sales (000)
15,000
10,000
5,000
Microfiber
0
-5,000
-10,000
-15,000
100,000
90,000
80,000
70,000
60,000
50,000
40,000
30,000
20,000
10,000
-
EBIT (000)
Impact of Operating Leverage
on Costs of Debt and Equity
• QUESTION: Does an increase in operating leverage result
in an increase in the cost of debt, other things equal?
Impact of Operating Leverage
on Costs of Debt and Equity
• QUESTION: Does an increase in operating leverage result
in an increase in the cost of debt, other things equal?
– YES (in general) because it increases the volatility of cash
flows that are needed to pay the interest payments on the
debt.
Impact of Operating Leverage
on Costs of Debt and Equity
• QUESTION: Does an increase in operating leverage result
in an increase in the cost of debt, other things equal?
– YES (in general) because it increases the volatility of cash
flows that are needed to pay the interest payments on the
debt.
• QUESTION: Does an increase in operating leverage result
in an increase in the cost of equity, other things equal?
Impact of Operating Leverage
on Costs of Debt and Equity
• QUESTION: Does an increase in operating leverage result
in an increase in the cost of debt, other things equal?
– YES (in general) because it increases the volatility of cash
flows that are needed to pay the interest payments on the
debt.
• QUESTION: Does an increase in operating leverage result
in an increase in the cost of equity, other things equal?
– IT DEPENDS on how closely variations in sales are linked to
changes in general economic conditions. In other words, it
depends of whether the sales volatility is due to systematic
or unsystematic risk.
Measuring Financial Leverage and its Impact
on Firm’s Stock Beta
• Firms also use fixed cost financing (debt and preferred
stock) to magnify the effect of a given change in EBIT on
net income. This is called financial leverage.
– Measured as the degree of financial leverage (DFL)
DFL 
ΔNI ΔEBIT

NI
EBIT
• Estimate DFL as DFL = EBIT / EBT
• Financial leverage can increase expected net profits, but it
also increases risk
– Thus, an increase in financial leverage can also increase a
firm’s stock beta, and therefore its cost of equity.
Measuring Financial Leverage and its Impact
on Firm’s Stock Beta
All Leather - No Debt
Sales is Units
Sales
- Variable Costs
Gross Profit
- Fixed Op Costs
Operating Profit (EBIT)
- Less Interest
36,000
40,000
All Leather - With Debt
44,000
36,000
40,000
44,000
34.2
(21.6)
12.6
(10.0)
2.6
-
38.0
(24.0)
14.0
(10.0)
4.0
-
41.8
(26.4)
15.4
(10.0)
5.4
-
34.2
(21.6)
12.6
(10.0)
2.6
(2.0)
38.0
(24.0)
14.0
(10.0)
4.0
(2.0)
41.8
(26.4)
15.4
(10.0)
5.4
(2.0)
Taxable Income
- Less Taxes (34%)
Net Income
2.6
(0.9)
1.7
4.0
(1.4)
2.6
5.4
(1.8)
3.6
0.6
(0.2)
0.4
2.0
(0.7)
1.3
3.4
(1.2)
2.2
% Change in Sales
DOL
% Change in EBIT
DFL
% Change in NI
DTL=DOL*DFL
-10%
10%
-10%
3.50
-35%
3.50
35%
-35%
1.00
-35%
35%
2.00
35%
3.50
10%
-70%
70%
7.00
Measuring Financial Leverage and its Impact
on Firm’s Stock Beta
All Leather - No Debt
Sales is Units
36,000
40,000
44,000
All Leather - With Debt
36,000
40,000
44,000
Sales
- Variable Costs
Gross Profit
- Fixed Op Costs
Operating Profit (EBIT)
- Less Interest
Taxable Income
- Less Taxes (34%)
Net Income
34.2
(21.6)
12.6
(10.0)
2.6
2.6
(0.9)
1.7
38.0
(24.0)
14.0
(10.0)
4.0
4.0
(1.4)
2.6
41.8
(26.4)
15.4
(10.0)
5.4
5.4
(1.8)
3.6
34.2
(21.6)
12.6
(10.0)
2.6
(2.0)
0.6
(0.2)
0.4
38.0
(24.0)
14.0
(10.0)
4.0
(2.0)
2.0
(0.7)
1.3
41.8
(26.4)
15.4
(10.0)
5.4
(2.0)
3.4
(1.2)
2.2
Debt Financing
Equity Financing
Total Capital
Return on Equity
Return on Capital
Total Cash to Investors
$
$ 50.00
$ 50.00
3.43%
3.43%
$
1.72
$
$ 50.00
$ 50.00
5.28%
5.28%
$
2.64
$
$ 50.00
$ 50.00
7.13%
7.13%
$
3.56
$ 25.00
$ 25.00
$ 50.00
1.58%
0.79%
$
2.40
$ 25.00
$ 25.00
$ 50.00
5.28%
2.64%
$
3.32
$ 25.00
$ 25.00
$ 50.00
8.98%
4.49%
$
4.24
The Weighted Average Cost of Capital
(WACC)
For firm’s that have both equity and debt in the capital
structure, use the weighted avg cost of capital (WACC) as
the discount rate.
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) outstanding worth $50mn, with rd = 6.5%
Calculate WACC = 11% as follows:
 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 the return he/she would earn.
– Second way: Suppose the firm invests in a project earning 11% and
distributes its return to the investors. Will they be satisfied?
The following table shows that the cash flows generated and
distributed satisfy the investors’ claims:
Cash distributions to Comfy investors
Total CF available to distribute ($200m x 11%)
Interest owed on bonds ($50m x 6.5%)
Cash available to shareholders ($22m - $3.25m)
Rate of return earned by S/Hs ($18.75m ÷ $150m)
$22.00 million
$3.25 million
$18.75 million
12.5%
Finding WACC for Firms with Complex
Capital Structures
How do you estimate the WACC if a firm has long-term (LT)
debt as well as preferred (P) and common stock (E)?
Find weighted average of the individual capital costs:
E
LT
P






WACC  
re  
rd  
rp
E  D P
E  D P
E  D P
Finding WACC for Firms with Complex
Capital Structures
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, $2 annual dividend, $25 price, $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
Although they were developed separately, WACC is consistent
with the CAPM. In fact, you can use the CAPM to estimate the
cost of any security.
– To calculate the beta for bonds of a large corporation:
• First find covariance between the bonds and the stock
market, then
• Plug computed debt beta (d), Rf & Rm into CAPM to find rd
– The debt beta is typically quite low for healthy, low-debt firms
– The debt beta rises with leverage, and approaches the equity
beta in high-debt companies.
If Comfy’s debt beta is 0.1, then the CAPM estimate of its cost
of debt is:
rd  Rf  d ( RM  Rf )  4%  0.1  (12.5%  4%)  4.85%
Calculating Asset Betas and Equity Betas
• The CAPM establishes a direct link between the required
return and the betas of securities.
• The firms ASSET Beta equals the weighted average of the
debt and equity betas:
D
E
βA  (
) βd  (
) βe
(Eq 9.4)
DE
DE
• A firm’s asset beta thus equals the covariance of the firm’s
CFs with RM, divided the variance the market’s return.
– For an all-equity firm, the asset beta = equity beta
– For a levered firm, the asset beta will be less than equity beta
• If the asset beta is known and the debt beta is assumed to
be 0, the equity beta can be computed directly from A
D
βE  β A (1  )
E
(Eq 9.5)
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 
Finding Equity Betas from Asset Betas, and
Vice Versa (Cont)
• Can now state decision rule for determining the discount
rate to use for projects with asset betas similar to the firm’s
own:
– For an all equity firm, use the cost of equity given by the
CAPM
– For a levered firm, use the WACC computed using the
CAPM and the betas of the 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 the firm’s WACC to evaluate an individual
project would be inappropriate. Instead, use the project’s
asset beta adjusted for desired leverage.
Finding the Discount Rate to Use for
Projects Unrelated to Firm’s Industry
Assume GE is evaluating an investment in the oil & gas
industry. This is much different from any of GE’s existing
businesses.
– GE should examine existing firms that are pure plays (public
firms operating only in the O&G industry).
Say GE selects Berry Petroleum and Forest Oil as pure plays:
– They are operationally similar firms, but Berry Petroleum’s E =
0.65 and Forest Oil’s E = 0.90. Why so different?
• Forest uses debt for 39% of its financing, while Berry has
only 14% debt in its capital structure. Even if the core
businesses have the same risk (A equal), E will differ
because of the differences in financial leverage.
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 the correct A to use as discount rate for GE’s
O&G project, convert the pure play E to the A, then average.
– The previous table lists the data needed to compute the
unlevered equity beta for each of the surrogates.
– The unlevered equity beta (same as A) strips out the effect of
financial leverage, so it’s always less than or equal to the equity
beta for a company.
– Berry’s A = 0.56, Forest’s A = 0.55, so average A = 0.55
• GE’s capital structure consists of 20% debt and 80% equity
(D/E ratio = 0.25). So, compute the relevered equity beta for
GE as follows:


 GE   A 1 
D
  0.551  0.25  0.69
E
Converting Equity Betas to Asset Betas for
Two Pure Play Firms (Continued)
• Now assume that the risk-free rate of interest is 6% and the
expected risk premium on the market is 7%
– Using the CAPM equation, compute the rate of return GE
shareholders require for the oil and gas investment:
E(R) = 6% + 0.69(7%) = 10.83%
• The final step to find the right discount rate for GE’s
investment in this industry is to calculate the project’s 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
•
We have thus far assumed away taxes, but taxes (or the exclusion
of taxes on interest payments0 are ften important.
– Tax deductibility of interest payments favors use of debt
– Accounting for interest tax shields yields the after-tax WACC
 D 
 E 
WACC  
(
1

T
)
r



re
d
DE
DE
(Eq 9.6)
• From Eq. 9.6, we can likewise present a method for
computing the after-tax equity beta from the asset beta. Again
assuming debt beta = 0, the equity beta is given by:


 E   A 1  (1  T )
D

E
(Eq 9.7)
A Closer Look at Risk
Break-Even Analysis
A key component in assessing operating risk is finding the
break-even point (BEP).
– BEP is the level of output (units of product sold) where all
operating costs (fixed and variable) are covered.
– BEP is found by dividing Fixed Operating Costs (FC) by the
the contribution margin per unit (CM)

 
Fixed Costs
FC

  
BEP  

Contributi
on
m
arg
in
Pr
ice
/
unit

VC
/
unit




A Closer Look at Risk
Break-Even Analysis
Use this to find the BEP for All Leather and Microfiber
– All Leather: FC = $10,000,000; Pr = $950/un; VC = $600/unit
– Microfiber: FC = $2,000,000; Pr = $950/un; VC = $800/unit
 $10,000,000   $10,000,000 
BEPAllLeather  

  28,572 sofas
$350
 $950  $600  

BEPMicrofiber
 $2,000,000   $2,000,000 


  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 the importance of
each assumption underlying a forecast.
Best Electronics Inc (BEI) has a new DVD player project. Base
case assumptions (below) yield E(NPV) = $1,139,715
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–
–
–
–
–
–
–
–
–
–
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
Pessimistic
Assumption
Optimistic
$43,000,000
Initial investment
$39,000,000
+2,727,745
2,800,000 units
Market size in year 1
3,200,000 units
+3,386,004
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
-$545,002
62% of sales
Variable costs
58% of sales
+2,824,432
-$2,064,260
-10% per yr
Annual price change
0% per year
+4,688,951
16%
Discount rate
12%
+3,348,720
-$448,315
-$1,106,574
-$640,727
-$899,413
NPV
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 and nationwide roll-out
– Very hard to evaluate in standard capital budgeting
framework
• Decision trees allow managers to break investment
analysis into distinct phases
– Forces managers to perform extended “if-then” analysis
Using Decision Trees to Make Multi-Step
Investment Decisions
Assume Trinkle Foods (Canada) has invented a new salt
substitute, Odessa. Market testing will take place in Vancouver.
– Market test will cost $5 million, but no new facilities are needed
– If the test is successful, Trinkle will spend an additional $50mn to
build a factory and launch nationwide one year later, after which
Trinkle predicts $12mn NCF per year for 10 years
– If the test is unsuccessful, Trinkle expects full product launch to
generate only $2 mn NCF per year for 10 years.
If Trinkle’s WACC=15% should Trinkle invest? If so, in what?
Using Decision Trees (Cont)
• 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, the project’s NPV equals -$39.96 mn and the
firm should walk away -- not fund nationwide roll-out.
– Note that in this case the $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
Using Decision Trees (Cont)
Now we have a set of simple “if-then” decision rules from
the decision tree:
– If the test successful (50% prob), launch nationwide and get
E(NPV) = $10.23 mn
– If the test is unsuccessful (50% prob), don’t invest $50 mn for
national launch but the $5 mn cost of the test is a sunk cost.
Using Decision Trees (Cont)
Now must decide (at t=0) whether to spend $5 mn for the
test:
– Must discount the NPVs computed at t=1 and take the
weighted average of the two possible outcomes using the
probability of a successful test as the weights
 10.23 
 0 
NPV  5  0.5

0
.
5


  0.55
 1.15 
 1.15 
So, it seems unwise to invest in the market test
– But, the decision is very sensitive to discounting the future
CF’s at 15% rate
– Since test results known t=1, may use lower rate afterwards