The Investment Principle
Aswath Damodaran
Stern School of Business
Aswath Damodaran
1
First Principles

Invest in projects that yield a return greater than the minimum
acceptable hurdle rate.
• The hurdle rate should be higher for riskier projects and reflect the
financing mix used - owners’ funds (equity) or borrowed money (debt)
• Returns on projects should be measured based on cash flows
generated and the timing of these cash flows; they should also
consider both positive and negative side effects of these projects.


Choose a financing mix that minimizes the hurdle rate and matches the
assets being financed.
If there are not enough investments that earn the hurdle rate, return the
cash to stockholders.
•
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The form of returns - dividends and stock buybacks - will depend upon
the stockholders’ characteristics.
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What is a investment or a project?


Any decision that requires the use of resources (financial or otherwise)
is a project.
Broad strategic decisions
• Entering new areas of business
• Entering new markets
• Acquiring other companies


Tactical decisions
Management decisions
• The product mix to carry
• The level of inventory and credit terms

Decisions on delivering a needed service
• Lease or buy a distribution system
• Creating and delivering a management information system
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Measuring Returns Right: The Basic Principles



Use cash flows rather than earnings. You cannot spend earnings.
Use “incremental” cash flows relating to the investment decision, i.e.,
cashflows that occur as a consequence of the decision, rather than total
cash flows.
Use “time weighted” returns, i.e., value cash flows that occur earlier
more than cash flows that occur later.
The Return Mantra: “Time-weighted, Incremental Cash Flow
Return”
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Steps in Investment Analysis


Estimate a hurdle rate for the project, based upon the riskiness of the
investment
Estimate revenues and accounting earnings on the investment.
• Measure the accounting return to see if the investment measures up to the
hurdle rate.

Convert accounting earnings into cash flows
• Use the cash flows to evaluate whether the investment is a good
investment.

Time weight the cash flows
• Use the time-weighted cash flows to evaluate whether the investment is a
good investment.

Consider all side-costs and side-benefits when analyzing project.
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I. Estimating Discount Rates
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The Essence of Discount Rates: The notion of
a benchmark




Since financial resources are finite, there is a hurdle that projects have
to cross before being deemed acceptable.
This hurdle will be higher for riskier projects than for safer projects.
A simple representation of the hurdle rate is as follows:
Hurdle rate = Riskless Rate + Risk Premium
The two basic questions that every risk and return model in finance
tries to answer are:
• How do you measure risk?
• How do you translate this risk measure into a risk premium?
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1. The Nominal versus Real Choice & A
Currency for your analysis


A project can be analyzed in nominal terms (in which case inflation is
incorporated into both your cashflows and your discount rate) or in
real terms. When inflation is high and volatile, analysts may find it
easier to do everything in real terms.
If an analysis is nominal, you have to pick the currency to do the
analysis is. Any project can be analyzed in any currency. In choosing a
currency to do the analysis, you should consider:
• Where the project will be located and what currency its costs and
revenues will be in. (The costs may be in one currency and the revenues
may be in another or more than one currency)
• How easy it will be to obtain fundamental information on risk free rates
and risk premiums in that currency.
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2. Risk Free Rate

For an investment to be risk free, it has to fulfill two conditions:
• There can have no default risk
• There can be no reinvestment risk

Using this principle strictly, there can be no one risk free rate for any
investment that delivers cash flows at different points in time. The
right risk free rate for each cash flow will be the interest rate on a zerocoupon default free government bond maturity on the same date as the
cash flow.
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Some common sense rules on risk free rates


Currency with default free entity: If you are working with a currency where a
default free entity exists ($ or Euro), use the interest rate on a government
bond with roughly the same duration as the project as the riskfree rate for all
cashflows.
Currency with no default free entity: There are two solutions when there is no
default free entity:
• Approach 1: Subtract default spread from local government bond rate:
Government bond rate in local currency terms - Default spread for Government in
local currency
• Approach 2: Use forward rates and the riskless rate in an index currency (say Euros
or dollars) to estimate the riskless rate in the local currency.

Real Risk free rate: To obtain a real riskfree rate, you can try the following:
•
•
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from an inflation-indexed government bond, if one exists
set equal, approximately, to the long term real growth rate of the economy in which
the valuation is being done.
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3. Determine a debt ratio and a cost of debt for
the project


Most projects do not carry debt on their own. Instead, the parent
company borrows money, using its general assets as collateral, and
uses this money to fund the projects.
Some projects are large enough and have assets that are separable from
the firm. These projects sometimes borrow on their own assets, with
no recourse against the parent company.
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What debt ratio should you use for a project?
Case 1: Single business company with several, small and similar projects
Company’s cost of debt and debt ratio
Case 2: Diverse company with large projects with different risk exposures
Average debt ratio for the industry in which the project is and the cost of
debt for the company
Case 3: Large project which carries its own debt (with no or limited
recourse to parent company assets)
Estimated debt ratio for the project and cost of debt for the project
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What is debt?

General Rule: Debt generally has the following characteristics:
• Commitment to make fixed payments in the future
• The fixed payments are tax deductible
• Failure to make the payments can lead to either default or loss of control
of the firm to the party to whom payments are due.

As a consequence, debt should include
• Any interest-bearing liability, whether short term or long term.
• Any lease obligation, whether operating or capital.
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Estimating the Cost of Debt



If the firm has bonds outstanding, and the bonds are traded, the yield
to maturity on a long-term, straight (no special features) bond can be
used as the interest rate.
If the firm is rated, use the rating and a typical default spread on bonds
with that rating to estimate the cost of debt.
If the firm is not rated,
• and it has recently borrowed long term from a bank, use the interest rate
on the borrowing or
• estimate a synthetic rating for the company, and use the synthetic rating to
arrive at a default spread and a cost of debt


If you are estimating the cost of debt for a project, you usually have to
use a synthetic rating.
The cost of debt has to be estimated in the same currency as the cost of
equity and the cash flows in the valuation.
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Estimating Synthetic Ratings


The rating for a firm can be estimated using the financial
characteristics of the firm. In its simplest form, the rating can be
estimated from the interest coverage ratio
Interest Coverage Ratio = EBIT / Interest Expenses
Consider InfoSoft, a private firm with EBIT of $2000 million and
interest expenses of $ 315 million
Interest Coverage Ratio = 2,000/315= 6.15
• Based upon the relationship between interest coverage ratios and ratings,
we would estimate a rating of A for the firm.

You can estimate synthetic ratings for individual projects that will be
carrying their own debt.
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Interest Coverage Ratios, Ratings and Default
Spreads
Interest Coverage Ratio
> 12.5
9.50 - 12.50
7.50 – 9.50
6.00 – 7.50
4.50 – 6.00
3.50 – 4.50
3.00 – 3.50
2.50 – 3.00
2.00 - 2.50
1.50 – 2.00
1.25 – 1.50
0.80 – 1.25
0.50 – 0.80
Rating
AAA
AA
A+
A
ABBB
BB
B+
B
BCCC
CC
C
Default Spread
0.20%
0.50%
0.80%
1.00%
1.25%
1.50%
2.00%
2.50%
3.25%
4.25%
5.00%
6.00%
7.50%
< 0.65
D
10.00%
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Costs of Debt for Boeing, the Home Depot and
InfoSoft
Bond Rating
Rating is
Default Spread over treasury
Market Interest Rate
Marginal tax rate
Cost of Debt
The treasury bond rate is 5%.
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Boeing
AA
Actual
0.50%
5.50%
35%
3.58%
Home Depot
A+
Actual
0.80%
5.80%
35%
3.77%
InfoSoft
A
Synthetic
1.00%
6.00%
42%
3.48%
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4. Cost of Equity
Preferably, a bottom-up beta,
based upon other firms in the
business, and firm’s own financial
leverage
Cost of Equity =
Riskfree Rate
Has to be in the same
currency as cash flows,
and defined in same terms
(real or nominal) as the
cash flows
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+
Beta *
(Risk Premium)
Historical Premium
1. Mature Equity Market Premium:
Average premium earned by
stocks over T.Bonds in U.S.
2. Country risk premium =
Country Default Spread* ( Equity /Country bond )
or
Implied Premium
Based on how equity
market is priced today
and a simple valuation
model
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Risk Premium
Equity Risk Premium
Premium for investing in equity versus riskless asset
Look at the past: Historical Premium
For mature markets, you can estimate the
premium by looking at a very long time
period of history.
- In the US: Average premium from 19282004 was 4.84%
- Across mature markets: Average
premium was about 4%
For developed markets, you can add a
premium for country risk to this mature
market premium.
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Look to the market: Implied Premium
Back out the equity risk premium that is
implied in current stock prices. This
premium will be a function of
- the level of stock prices today
- dividends & buybacks
- the expected growth
- the riskfree rate
The premium will by dynamic and shift
as markets shift.
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Everyone uses historical premiums, but..


The historical premium is the premium that stocks have historically earned
over riskless securities.
Practitioners never seem to agree on the premium; it is sensitive to
•
•
•
How far back you go in history…
Whether you use T.bill rates or T.Bond rates
Whether you use geometric or arithmetic averages.
For instance, looking at the US:
Arithmetic average Geometric Average
Stocks - Stocks - Stocks - Stocks Historical Period T.Bills T.Bonds T.Bills T.Bonds
1928-2002
7.67% 6.25% 5.73% 4.53%
1962-2002
5.17% 3.66% 3.90% 2.76%
1992-2002
6.32% 2.15% 4.69% 0.95%

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Two Ways of Estimating Country Risk
Premiums…

Default spread on Country Bond: In this approach, the country risk premium is
based upon the default spread of the bond issued by the country (but only if it
is denominated in a currency where a default free entity exists.
•

Brazil was rated B2 by Moody’s and the default spread on the Brazilian dollar
denominated C.Bond at the end of September 2003 was 6.01%. (10.18%-4.17%)
Relative Equity Market approach: The country risk premium is based upon the
volatility of the market in question relative to U.S market.
Country risk premium = Risk PremiumUS* Country Equity / US Equity
Using a 4.53% premium for the US, this approach would yield:
Total risk premium for Brazil = 4.53% (33.37%/18.59%) = 8.13%
Country risk premium for Brazil = 8.13% - 4.53% = 3.60%
(The standard deviation in weekly returns from 2001 to 2003 for the Bovespa was
33.37% whereas the standard deviation in the S&P 500 was 18.59%)
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And a third approach


Country ratings measure default risk. While default risk premiums and
equity risk premiums are highly correlated, one would expect equity
spreads to be higher than debt spreads.
Another is to multiply the bond default spread by the relative volatility
of stock and bond prices in that market. In this approach:
• Country risk premium = Default spread on country bond* Country Equity /
Country Bond
– Standard Deviation in Bovespa (Equity) = 33.37%
– Standard Deviation in Brazil C-Bond = 26.15%
– Default spread on C-Bond = 6.01%
• Country Risk Premium for Brazil = 6.01% (33.37%/26.15%) = 7.67%%
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Implied Equity Risk Premiums

An implied equity risk premium is a forward looking estimate, based upon how stocks
are priced today and expected cashflows in the future.

On January 1, 2003, the S&P was trading at 879.82.
•
•
•
•
Treasury bond rate = 3.81%
Expected Growth rate in earnings (next 5 years) = 8% (Consensus estimate for
S&P 500 earnings)
Expected growth rate after year 5 = 3.81%
Dividends + stock buybacks = 3.29% of index (in latest year)
Year 1
$31.25
Year 2
$33.75
Year 3
$36.45
Year 4
$39.37
Year 5
$42.52
Expected Dividends =
+ Stock Buybacks
Expected dividends + buybacks in year 6 = 42.52 (1.0381) = $ 44.14
879.82 = 31.25/(1+r) + 33.75/(1+r)2+ + 36.45/(1+r)3 + 39.37/(1+r)4 + (42.52+(44.14/(r-.0381))/(1+r)5
Solving for r, r = 7.91%. (Only way to do this is trial and error)
Implied risk premium = 7.91% - 3.81% = 4.10%
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4. Measuring Project Risk: Risk and Return
Models
Step 1: Defining Risk
T he risk in an investment can be measured by the variance in actual returns around an
expected return
Riskless Investment
Low Risk Investment
High Risk Investment
E(R)
E(R)
E(R)
Step 2: Differentiating between Rewarded and Unrewarded Risk
Risk that is specific to investment (Firm Specific)
Risk that affects all investments (Market Risk)
Can be diversified away in a diversified portfolio
Cannot be diversified away since most assets
1. each investment is a small proportion of portfolio
are affected by it.
2. risk averages out across investments in portfolio
T he marginal investor is assumed to hold a “diversified” portfolio. Thus, only market risk will
be rewarded and priced.
Step 3: Measuring Market Risk
T he CAPM
If there is
1. no private information
2. no transactions cost
the optimal diversified
portfolio includes every
traded asset. Everyone
will hold this market portfolio
Market Risk = Risk
added by any investment
to the market portfolio:
Beta of asset relative to
Market portfolio (from
a regression)
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T he APM
If there are no
arbitrage opportunities
then the market risk of
any asset must be
captured by betas
relative to factors that
affect all investments.
Market Risk = Risk
exposures of any
asset to market
factors
Multi-Factor Models
Since market risk affects
most or all investments,
it must come from
macro economic factors.
Market Risk = Risk
exposures of any
asset to macro
economic factors.
Betas of asset relative
to unspecified market
factors (from a factor
analysis)
Betas of assets relative
to specified macro
economic factors (from
a regression)
Proxy Models
In an efficient market,
differences in returns
across long periods must
be due to market risk
differences. Looking for
variables correlated with
returns should then give
us proxies for this risk.
Market Risk =
Captured by the
Proxy Variable(s)
Equation relating
returns to proxy
variables (from a
regression)
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Estimating Beta
Beta of Equity
Rj
Top-Down
R2:
Proportion of
risk that is not
diversifiable
Slope = Beta
Bottom-up
1. Identify businesses that firm is in.
2. Take weighted average of the
unlevered betas of other firms in the
business
3. Compute the levered beta using the
firm’s current debt to equity ratio:
 l =  u [1 + (1-tax rate) (Debt/Equity)]
Intercept - R f (1-Beta) = Jensen’s Alpha
Rm
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Decomposing Boeing’s Beta
Segment
Commercial Aircraft
ISDS $ 18,125
Firm



Revenues
$ 26,929
$ 12,688
$ 42,848
Estimated Value
$ 30,160
0.80
unlevered
Weight
0.91
70.39%
29.61% 0.2369
100.00% 0.88
Weighted 
0.6405
0.93
1.01
Levered Beta
1.06
The values were estimated based upon the revenues in each business and the typical
multiple of revenues that other firms in that business trade for.
The unlevered betas for each business were estimated by looking at other publicly
traded firms in each business, averaging across the betas estimated for these firms, and
then unlevering the beta using the average debt to equity ratio for firms in that business.
Unlevered Beta = Average Beta / (1 + (1-tax rate) (Average D/E))
Using Boeing’s current market debt to equity ratio of 25%
Boeing’s Beta = = 0.88 (1+(1-.35)(.25)) = 1.014
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The Home Depot’s Comparable Firms
Compa ny Na me
Buil ding Materi als
Catal ina Ligh ting
Cont'l Material s Corp
Eagl e Hardware
Emco Li mite d
Fas tena l Co.
HomeBa se Inc.
Hughe s Sup ply
Lowe's Cos .
Waxma n In dustries
Wes tburn e In c.
Wol ohan Lum ber
Sum
Averag e
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Beta Market Cap $ (Mil)
1.0 5
$13 6
1
$16
0.5 5
$32
0.9 5
$61 2
0.6 5
$18 7
1.2 5
$1,157
1.1
$22 7
1
$61 0
1.2
$12 ,554
1.2 5
$18
0.6 5
$60 7
0.5 5
$76
$16 ,232
0.9 3
Deb t Due 1-Yr Ou t
$1
$7
$2
$6
$39
$16
$1
$11 1
$6
$9
$2
$20 0
Lon g-Term Deb t
$11 3
$19
$7
$14 6
$11 9
$
$11 6
$33 5
$1,046
$12 1
$34
$20
$2,076
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Estimating The Home Depot’s Bottom-up Beta



Average Beta of comparable firms = 0.93
D/E ratio of comparable firms = (200+2076)/16,232 = 14.01%
Unlevered Beta for comparable firms = 0.93/(1+(1-.35)(.1401))
= 0.86
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Beta for InfoSoft, a Private Software Firm
The following table summarizes the unlevered betas for publicly traded
software firms.
Grouping
Number of Beta
D/E Ratio Unlevered
Firms
Beta
All Software
264
1.45
3.70%
1.42
Small-cap Software
125
1.54
10.12% 1.45
Entertainment Software 31
1.50
7.09%
1.43
 We will use the beta of entertainment software firms as the unlevered
beta for InfoSoft.
 We will also assume that InfoSoft’s D/E ratio will be similar to that of
these publicly traded firms (D/E = 7.09%)
 Beta for InfoSoft = 1.43 (1 + (1-.42) (.0709)) = 1.49
(We used a tax rate of 42% for the private firm)
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Total Risk versus Market Risk

Adjust the beta to reflect total risk rather than market risk. This
adjustment is a relatively simple one, since the R squared of the
regression measures the proportion of the risk that is market risk.
Total Beta = Market Beta / √R squared

In the InfoSoft example, where the market beta is 1.10 and the
average R-squared of the comparable publicly traded firms is 16%,
• Total Beta = 1.49/√0.16 = 3.725
• Total Cost of Equity = 5% + 3.725 (5.5%)= 25.49%

This cost of equity is much higher than the cost of equity based upon
the market beta because the owners of the firm are not diversified.
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Estimating a beta for a project
Case 1: Single business company with several, small and similar projects
Company’s levered beta
Case 2: Diverse company with large projects with different risk exposures
Levered beta for the industry in which the project operates. (Alternatively,
you can use an unlevered beta for the industry in which the project
operates and use the company’s debt to equity ratio to lever up)
Case 3: Large project which carries its own debt (with no or limited
recourse to parent company assets)
Levered beta estimated using unlevered beta for publicly traded firms
comparable to the project and the debt to equity ratio for project.
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5. Cost of Capital
Cost of borrowing should be based upon
(1) synthetic or actual bond rating
(2) default spread
Cost of Borrowing = Riskfree rate + Default spread
Cost of Capital =
Cost of Equity (Equity/(Debt + Equity))
Cost of equity
based upon bottom-up
beta
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+
Cost of Borrowing
(1-t)
Marginal tax rate, reflecting
tax benefits of debt
(Debt/(Debt + Equity))
Weights should be market value weights
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Estimating Cost of Capital: Boeing

Equity
• Cost of Equity = 5% + 1.01 (5.5%) =
• Market Value of Equity =
• Equity/(Debt+Equity ) =

Debt
• After-tax Cost of debt =
• Market Value of Debt =
• Debt/(Debt +Equity) =

10.58%
$32.60 Billion
82%
5.50% (1-.35) =
3.58%
$ 8.2 Billion
18%
Cost of Capital = 10.58%(.80)+3.58%(.20) = 9.17%
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Boeing’s Divisional Costs of Capital
Cost of Equity
Equity/(Debt + Equity)
Cost of Debt
Debt/(Debt + Equity)
Cost of Capital
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Boeing
10.58%
79.91%
3.58%
20.09%
9.17%
Aerospace
10.77%
79.91%
3.58%
20.09%
9.32%
Defense
10.07%
79.91%
3.58%
20.09%
8.76%
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Cost of Capital: InfoSoft and The Home Depot
Cost of Equity
Equity/(Debt + Equity)
Cost of Debt
Debt/(Debt + Equity)
Cost of Capital
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The Home Depot
9.78%
95.45%
3.77%
4.55%
9.51%
InfoSoft
25.49%
93.38%
3.48%
6.62%
24.03%
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In summary: Estimating cost of capital for a
project

If a firm is in only one business, and all of its investments are
homogeneous:
• Use the company’s costs of equity and capital to evaluate its investments.

If the firm is in more than one business, but investments within each of
business are similar:
• Use the divisional costs of equity and capital to evaluate investments
made by that division

If a firm is planning on entering a new business:
• Estimate a cost of equity for the investment, based upon the riskiness of
the investment
• Estimate a cost of debt and debt ratio for the investment based upon the
costs of debt and debt ratios of other firms in the business
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Analyzing Project Risk: Three Examples

The Home Depot: A New Store
• The Home Depot is a firm in a single business, with homogeneous
investments (another store).
• We will use The Home Depot’s cost of equity (9.78%) and capital (9.51%)
to analyze this investment.

Boeing: A Super Jumbo Jet (capable of carrying 400+ people)
• We will use the cost of capital of 9.32% that we estimated for the
aerospace division of Boeing.

InfoSoft: An Online Software Store
• We will estimate the cost of equity based upon the total beta for online
retailers (5.25). We will also assume that the online software company
will not borrow any money (reflecting industry practices)
• Cost of capital = Cost of equity = 33.875%
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Current Practices in the US: Costs of Capital
Cost of capital item
Cost of Equit y




Cost of Debt

Weights for Deb t
and Equ it y

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Current Practices
81% of firms used the capit al asset pricing model to estim ate
the cost of equit y, 4% used a modified capit al asset pricing
model and 15% were unce rtain about how they e stim ated the
cost of equtiy.
70% of firms used 10-year treasuries or longe r as the riskless
rate, 7% used 3 to 5-yea r treasuries and 4% used the treasury
bill rate.
52% used a publi shed source for a beta estim ate, whil e 30%
estima ted it t hems elves.
Ther e was wide va riation in the market ris k premi um used,
wit h 37 % using a premi um between 5 and 6%.
52% of firms used a marginal borrowing rate and a marginal
tax rate, while 37% used the current ave rage borrowing rate
and the e ffective tax rate.
59% used market value weight s for debt and equity in the cost
of capital, 15% used book va lue weights and 19% were
unce rtain about wha t weights they u sed.
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Choosing a Hurdle Rate



Either the cost of equity or the cost of capital can be used as a hurdle
rate, depending upon whether the returns measured are to equity
investors or to all claimholders on the firm (capital)
If returns are measured to equity investors, the appropriate hurdle rate
is the cost of equity.
If returns are measured to capital (or the firm), the appropriate hurdle
rate is the cost of capital.
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39
II. The Estimation Process: Sources of
Information/ Estimation




Experience and History: If a firm has invested in similar projects in
the past, it can use this experience to estimate revenues and earnings
on the project being analyzed.
Market Testing: If the investment is in a new market or business, you
can use market testing to get a sense of the size of the market and
potential profitability.
Macro economic/ Sector forecasters: There are services that provide
forecasts of varying accuracy/ reliability on what they think will
happen to the economy or a particular sector.
Market Data: There are some cases where market prices provide
information that can be used in forecasts. This is especially the case
when you are forecasting interest rates, exchange rates and commodity
prices.
Aswath Damodaran
40
Three approaches to estimation



Expected value approach: In this approach, we estimate the expected
revenues and earnings of a project. While these are point estimates,
they presumably incorporate all the information you have on other
scenarios.
Simulation: In this approach, we estimate a statistical distribution (and
the parameters of the distribution) for each variable. We then run
simulations drawing from the distribution and compute the return on
each simulation. The output is a distribution of the decision variable
(NPV, IRR, ROC etc.)
Scenario Analysis: In this approach, we define scenarios for key
variables and probabilities of each occurring. We then compute the
revenues and earnings under scenario. The output is the decision
variable under each scenario.
Aswath Damodaran
41
The Home Depot’s New Store: Experience and
History


The Home Depot has 700+ stores in existence, at difference stages in
their life cycles, yielding valuable information on how much revenue
can be expected at each store and expected margins.
At the end of 1999, for instance, each existing store had revenues of $
44 million, with revenues starting at about $ 40 million in the first year
of a store’s life, climbing until year 5 and then declining until year 10.
Aswath Damodaran
42
The Margins at Existing Stores
Aswath Damodaran
43
Projections for The Home Depot’s New Store Expected Value Analysis

For revenues, we will assume
 that the new store being considered by the Home Depot will have
expected revenues of $ 40 million in year 1 (which is the approximately
the average revenue per store at existing stores after one year in operation)
 that these revenues to grow 5% a year
• that our analysis will cover 10 years (since revenues start dropping at
existing stores after the 10th year).

For operating margins, we will assume
• The operating expenses of the new store will be 90% of the revenues
(based upon the median for existing stores)
Aswath Damodaran
44
The Simulation Alternative


Instead of using the expected values for each variable and arriving at a set of
expected cashflows for the analysis, we could have enriched the analysis by
assuming a distribution for each of the key variables - revenues, margins and
growth, for instance.
Steps in a simulation
•
•
•
•
•
Aswath Damodaran
Step 1: Determine the variables that you will be estimating distributions/parameters
for.
Step 2: Choose the statistical distribution for each of the variables and esitmate the
parameters of the distribution.
Step 3: Run your first simulation, drawing one outcome from each distribution.
Step 4: Repeat process. The number of simulations run will depend upon how
many variables are being simulated and the range of outcomes.
Step 5: Compute your decision variable (NPV, IRR, ROIC) for each simulation and
report the findings in a distribution.
45
What simulations do and what they do not…

Simulations do
• Provide richer information about a project’s outcomes to decision makers.
• Provide information about potentially dangerous outcomes (for the firm),
in terms of worst case scenarios. (Violation of lending covenants, Failure
to make interest payments etc.)
• A measure of “outcome variability” that can be compared across mutually
exclusive investments

Simulations do not
• Adjust cash flows for risk (They generate expected cashflows)
• Provide better estimates of the expected value or NPV of an investment.
Aswath Damodaran
46
When simulations make sense and when they
do not..

Simulations make sense
• When there is sufficient information to estimate the correct statistical
distributions for each variables and the parameters of those distributions.
This is most likely to be the case for firms that
– Take the same kind of investment over and over again (like the Home Depot)
– Have done extensive market testing of a product or service and generated
output from the testing which can be used in the distribution
• When there is a lower bound constraint, which if violated, can lead to the
project ending. (An example would be capital ratio constraints at banks…)

Simulations don’t make sense
• When the distributions chosen and the parameters used are arbitrary. It is
garbage in, garbage out.
Aswath Damodaran
47
Scenario Analysis: Boeing Super Jumbo

We consider two factors:
• Actions of Airbus (the competition): Produces new large capacity plane to
match Boeing’s new jet, Improves its existing large capacity plane (A300) or abandons this market entirely.
• Much of the growth from this market will come from whether Asia. We
look at a high growth, average growth and low growth scenario.

In each scenario,
• We estimate the number of planes that Boeing will sell under each
scenario.
• We estimate the probability of each scenario.
Aswath Damodaran
48
Scenario Analysis

The following table lists the number of planes that Boeing will sell
under each scenario, with the probabilities listed below each number.
High Growth in Asia
Airbus New
large plane
120
(0.125)
Average Growth in Asia 100
Low Growth in Asia
(0.15)
75
Airbus A-300
150
Airbus abandons
large airplane
200
(0.125)
(0.00)
135
160
(0.25)
(0.10)
110
120
(0.05)
(0.10)
(0.10)
Expected Value = 120*0.125+150*.125+200*0+100*.15+135*.25
+160*.10+ 75*.05+110*.10+120*10 = 125 planes
Aswath Damodaran
49
III. Measures of return: Accounting Earnings

Principles Governing Accounting Earnings Measurement
• Accrual Accounting: Show revenues when products and services are sold
or provided, not when they are paid for. Show expenses associated with
these revenues rather than cash expenses.
• Operating versus Capital Expenditures: Only expenses associated with
creating revenues in the current period should be treated as operating
expenses. Expenses that create benefits over several periods are written
off over multiple periods (as depreciation or amortization)
Aswath Damodaran
50
From Forecasts to Accounting Earnings




Separate projected expenses into operating and capital expenses:
Operating expenses, in accounting, are expenses designed to generate
benefits only in the current period, while capital expenses generate
benefits over multiple periods.
Depreciate or amortize the capital expenses over time: Once expenses
have been categorized as capital expenses, they have to be depreciated
or amortized over time.
Allocate fixed expenses that cannot be traced to specific projects:
Expenses that are not directly traceable to a project get allocated to
projects, based upon a measure such as revenues generated by the
project; projects that are expected to make more revenues will have
proportionately more of the expense allocated to them.
Consider the tax effect: Consider the tax liability that would be created
by the operating income we have estimated
Aswath Damodaran
51
Boeing Super Jumbo Jet: Investment
Assumptions


Boeing has already spent $ 2.5 billion in research expenditures,
developing the Super Jumbo. (These expenses have been capitalized)
If Boeing decides to proceed with the commercial introduction of the
new plane, the firm will have to spend an additional $ 5.5 billion
building a new plant and equipping it for production.
Year
Now
1
2
3
4

Investment Needed
$ 500 million
$ 1,000 million
$ 1,500 million
$ 1,500 million
$ 1,000 million
After year 4, there will be a capital maintenance expenditure required
of $ 250 million each year from years 5 through 15.
Aswath Damodaran
52
Operating Assumptions



The sale and delivery of the planes is expected to begin in the fifth year, when
50 planes will be sold. For the next 15 years (from year 6-20), Boeing expects
to sell 125 planes a year. In the last five years of the project (from year 21-25),
the sales are expected to decline to 100 planes a year. While the planes
delivered in year 5 will be priced at $ 200 million each, this price is expected
to grow at the same rate as inflation (which is assumed to be 3%) each year
after that.
Based upon past experience, Boeing anticipates that its cost of production, not
including depreciation or General, Sales and Administrative (GS&A)
expenses, will be 90% of the revenue
Boeing allocates general, selling and administrative expenses (G,S & A) to
projects based upon projected revenues, and this project will be assessed a
charge equal to 4% of revenues. (One-third of these expenses will be a direct
result of this project and can be treated as variable. The remaining two-thirds
are fixed expenses that would be generated even if this project were not
accepted.)
Aswath Damodaran
53
Other Assumptions



The project is expected to have a useful life of 25 years.
The corporate tax rate is 35%.
Boeing uses a variant of double-declining balance depreciation to
estimate the depreciation each year. Based upon a typical depreciable
life of 20 years, the depreciation is computed to be 10% of the book
value of the assets (other than working capital) at the end of the
previous year. We begin depreciating the capital investment
immediately, rather than waiting for the revenues to commence in year
5.
Aswath Damodaran
54
Revenues: By Year
Ye ar
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Aswath Damodaran
Numb er of Plan es
50
12 5
12 5
12 5
12 5
12 5
12 5
12 5
12 5
12 5
12 5
12 5
12 5
12 5
12 5
12 5
10 0
10 0
10 0
10 0
10 0
Price p er pl ane
$
20 0.00
$
20 6.00
$
21 2.18
$
21 8.55
$
22 5.10
$
23 1.85
$
23 8.81
$
24 5.97
$
25 3.35
$
26 0.95
$
26 8.78
$
27 6.85
$
28 5.15
$
29 3.71
$
30 2.52
$
31 1.59
$
32 0.94
$
33 0.57
$
34 0.49
$
35 0.70
$
36 1.22
Expected Revenue s
$
10 ,000 .00
$
25 ,750 .00
$
26 ,522 .50
$
27 ,318 .18
$
28 ,137 .72
$
28 ,981 .85
$
29 ,851 .31
$
30 ,746 .85
$
31 ,669 .25
$
32 ,619 .33
$
33 ,597 .91
$
34 ,605 .85
$
35 ,644 .02
$
36 ,713 .34
$
37 ,814 .74
$
38 ,949 .19
$
32 ,094 .13
$
33 ,056 .95
$
34 ,048 .66
$
35 ,070 .12
$
36 ,122 .22
55
Operating Expenses & S,G & A: By Year
Yea r
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Aswath Damodaran
Revenue s
$ 10,000
$ 25,750
$ 26,523
$ 27,318
$ 28,138
$ 28,982
$ 29,851
$ 30,747
$ 31,669
$ 32,619
$ 33,598
$ 34,606
$ 35,644
$ 36,713
$ 37,815
$ 38,949
$ 32,094
$ 33,057
$ 34,049
$ 35,070
$ 36,122
COGS
$ 9,0 00
$ 23,175
$ 23,870
$ 24,586
$ 25,324
$ 26,084
$ 26,866
$ 27,672
$ 28,502
$ 29,357
$ 30,238
$ 31,145
$ 32,080
$ 33,042
$ 34,033
$ 35,054
$ 28,885
$ 29,751
$ 30,644
$ 31,563
$ 32,510
GS&A Expen se
$
400
$
1,0 30
$
1,0 61
$
1,0 93
$
1,1 26
$
1,1 59
$
1,1 94
$
1,2 30
$
1,2 67
$
1,3 05
$
1,3 44
$
1,3 84
$
1,4 26
$
1,4 69
$
1,5 13
$
1,5 58
$
1,2 84
$
1,3 22
$
1,3 62
$
1,4 03
$
1,4 45
56
Depreciation and Amortization: By Year
Year Capital
Depreciaton Book Value R&D
Amortization Ending Value Deprecn &
Expenditures
Investment
of R&D
Amortization
0 $
500
$
500
2500
0
2500
1
$
1,000 $
50 $
1,450 $
2,500 $
167 $
2,333
$217
2
$
1,500 $
145 $
2,805 $
2,333 $
167 $
2,167
$312
3
$
1,500 $
281 $
4,025 $
2,167 $
167 $
2,000
$447
4
$
1,000 $
402 $
4,622 $
2,000 $
167 $
1,833
$569
5 $
250 $
462 $
4,410 $
1,833 $
167 $
1,667
$629
6 $
250 $
441 $
4,219 $
1,667 $
167 $
1,500
$608
7 $
250 $
422 $
4,047 $
1,500 $
167 $
1,333
$589
8 $
250 $
405 $
3,892 $
1,333 $
167 $
1,167
$571
9 $
250 $
389 $
3,753 $
1,167 $
167 $
1,000
$556
10 $
250 $
375 $
3,628 $
1,000 $
167 $
833
$542
11 $
250 $
363 $
3,515 $
833 $
167 $
667
$529
12 $
250 $
351 $
3,413 $
667 $
167 $
500
$518
13 $
250 $
341 $
3,322 $
500 $
167 $
333
$508
14 $
250 $
332 $
3,240 $
333 $
167 $
167
$499
15 $
250 $
324 $
3,166 $
167 $
167 $
$491
16
$
- $
317 $
2,849
$317
17
$
- $
285 $
2,564
$285
18
$
- $
256 $
2,308
$256
19
$
- $
231 $
2,077
$231
20
$
- $
208 $
1,869
$208
21
$
- $
187 $
1,683
$187
22
$
- $
168 $
1,514
$168
23
$
- $
151 $
1,363
$151
24
$
- $
136 $
1,227
$136
25
$
- $
123 $
1,104
$123
Aswath Damodaran
57
Earnings on Project
Yea r
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Aswath Damodaran
Revenue s
$0
$0
$0
$0
$10 ,000
$25 ,750
$26 ,523
$27 ,318
$28 ,138
$28 ,982
$29 ,851
$30 ,747
$31 ,669
$32 ,619
$33 ,598
$34 ,606
$35 ,644
$36 ,713
$37 ,815
$38 ,949
$32 ,094
$33 ,057
$34 ,049
$35 ,070
$36 ,122
COGS
$0
$0
$0
$0
$9,000
$23 ,175
$23 ,870
$24 ,586
$25 ,324
$26 ,084
$26 ,866
$27 ,672
$28 ,502
$29 ,357
$30 ,238
$31 ,145
$32 ,080
$33 ,042
$34 ,033
$35 ,054
$28 ,885
$29 ,751
$30 ,644
$31 ,563
$32 ,510
GS&A Expen se Deprecn & Amortizatio
EBIT n
$0
$0
$0
$0
$40 0
$1,030
$1,061
$1,093
$1,126
$1,159
$1,194
$1,230
$1,267
$1,305
$1,344
$1,384
$1,426
$1,469
$1,513
$1,558
$1,284
$1,322
$1,362
$1,403
$1,445
$21 7
$31 2
$44 7
$56 9
$62 9
$60 8
$58 9
$57 1
$55 6
$54 2
$52 9
$51 8
$50 8
$49 9
$49 1
$31 7
$28 5
$25 6
$23 1
$20 8
$18 7
$16 8
$15 1
$13 6
$12 3
($21 7)
($31 2)
($44 7)
($56 9)
($29 )
$93 7
$1,003
$1,068
$1,132
$1,197
$1,262
$1,327
$1,392
$1,458
$1,525
$1,760
$1,854
$1,946
$2,038
$2,129
$1,739
$1,815
$1,891
$1,968
$2,045
EBIT(1 -t)
($14 1)
($20 3)
($29 1)
($37 0)
($19 )
$60 9
$65 2
$69 4
$73 6
$77 8
$82 0
$86 2
$90 5
$94 8
$99 1
$1,144
$1,205
$1,265
$1,325
$1,384
$1,130
$1,180
$1,229
$1,279
$1,329
58
And the Accounting View of Return
Yea r
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
EBIT(1 -t)
($1 40.8 3)
($2 02.5 8)
($2 90.6 6)
($3 69.9 3)
($1 8.77 )
$6 09.2 8
$6 51.8 2
$6 94.0 2
$7 36.0 4
$7 78.0 1
$8 20.0 6
$8 62.3 2
$9 04.8 9
$9 47.8 8
$9 91.3 9
$1 ,143 .84
$1 ,204 .91
$1 ,265 .13
$1 ,324 .76
$1 ,384 .00
$1 ,130 .16
$1 ,179 .86
$1 ,229 .47
$1 ,279 .15
$1 ,329 .04
Avera ge
$7 77.7 3
Aswath Damodaran
Beg inni ng BV Capi tal Exp
$3 ,000 .00
$1 ,000 .00
$3 ,783 .33
$1 ,500 .00
$4 ,971 .67
$1 ,500 .00
$6 ,024 .50
$1 ,000 .00
$6 ,455 .38
$2 50.0 0
$6 ,076 .51
$2 50.0 0
$5 ,718 .86
$2 50.0 0
$5 ,380 .31
$2 50.0 0
$5 ,058 .94
$2 50.0 0
$4 ,753 .05
$2 50.0 0
$4 ,461 .08
$2 50.0 0
$4 ,181 .64
$2 50.0 0
$3 ,913 .47
$2 50.0 0
$3 ,655 .46
$2 50.0 0
$3 ,406 .58
$2 50.0 0
$3 ,165 .92
$0 .00
$2 ,849 .33
$0 .00
$2 ,564 .40
$0 .00
$2 ,307 .96
$0 .00
$2 ,077 .16
$0 .00
$1 ,869 .45
$0 .00
$1 ,682 .50
$0 .00
$1 ,514 .25
$0 .00
$1 ,362 .83
$0 .00
$1 ,226 .54
$0 .00
Depre cia tion
$2 16.6 7
$3 11.6 7
$4 47.1 7
$5 69.1 2
$6 28.8 7
$6 07.6 5
$5 88.5 5
$5 71.3 6
$5 55.8 9
$5 41.9 7
$5 29.4 4
$5 18.1 6
$5 08.0 1
$4 98.8 8
$4 90.6 6
$3 16.5 9
$2 84.9 3
$2 56.4 4
$2 30.8 0
$2 07.7 2
$1 86.9 4
$1 68.2 5
$1 51.4 3
$1 36.2 8
$1 22.6 5
End ing BV
$3 ,783 .33
$4 ,971 .67
$6 ,024 .50
$6 ,455 .38
$6 ,076 .51
$5 ,718 .86
$5 ,380 .31
$5 ,058 .94
$4 ,753 .05
$4 ,461 .08
$4 ,181 .64
$3 ,913 .47
$3 ,655 .46
$3 ,406 .58
$3 ,165 .92
$2 ,849 .33
$2 ,564 .40
$2 ,307 .96
$2 ,077 .16
$1 ,869 .45
$1 ,682 .50
$1 ,514 .25
$1 ,362 .83
$1 ,226 .54
$1 ,103 .89
Average BV
$3 ,391 .67
$4 ,377 .50
$5 ,498 .08
$6 ,239 .94
$6 ,265 .95
$5 ,897 .69
$5 ,549 .58
$5 ,219 .63
$4 ,906 .00
$4 ,607 .06
$4 ,321 .36
$4 ,047 .55
$3 ,784 .47
$3 ,531 .02
$3 ,286 .25
$3 ,007 .63
$2 ,706 .86
$2 ,436 .18
$2 ,192 .56
$1 ,973 .30
$1 ,775 .97
$1 ,598 .38
$1 ,438 .54
$1 ,294 .68
$1 ,165 .22
Wo rking Capital
$0 .00
$0 .00
$0 .00
$0 .00
$1 ,000 .00
$2 ,575 .00
$2 ,652 .25
$2 ,731 .82
$2 ,813 .77
$2 ,898 .19
$2 ,985 .13
$3 ,074 .68
$3 ,166 .93
$3 ,261 .93
$3 ,359 .79
$3 ,460 .58
$3 ,564 .40
$3 ,671 .33
$3 ,781 .47
$3 ,894 .92
$3 ,209 .41
$3 ,305 .70
$3 ,404 .87
$3 ,507 .01
$3 ,612 .22
Retu rn on Capital
-4.15%
-4.63%
-5.29%
-5.93%
-0.26%
7.19%
7.95%
8.73%
9.53%
10 .37%
11 .22%
12 .11%
13 .02%
13 .95%
14 .92%
17 .68%
19 .21%
20 .71%
22 .18%
23 .58%
22 .67%
24 .06%
25 .38%
26 .64%
27 .82%
$3 ,620 .52
$2 ,637 .26
12 .75%
59
Would lead use to conclude that...

Invest in the Super Jumbo Jet The return on capital of 12.75% is
greater than the cost of capital for aerospace of 9.32%; This would
suggest that the project should not be taken.
Aswath Damodaran
60
An extension to existing projects: Return
Spreads and EVA
How good are the collective investments that a firm has already made? One
way, albeit a limited one, is to compute the collective return on capital for the
entire company and compare it to the cost of capital for the entire company.
This is a return spread.
 Extending this approach, you can convert the return spread (which is a
percentage value) into an absolute value by multiplying the return spread by
the capital invested in the firm (which generates an economic value added)
 EVA = (Return on capital - Cost of capital) (Capital invested)
Where
Return on capital = EBIT (1-t)/ Invested Capital
Cost of capital = Hurdle rate for investments of equivalend risk at the start of the
period of analysis
Capital invested = Book value + Book Value Cash - Debt

Aswath Damodaran
61
EVAs and project quality

The EVA for a project is good measure of project quality when
• Project earnings closely resemble cashflows.
• Project earnings are measured consistently and the annual cashflows are
fairly uniform over time.
• The firm using its is a mature firm with most of its assets already in place
with little or no investment needed for long term grosth.

The EVA for a project is a poor measures of project quality when
• Project earnings are being manipulated by questionable accounting
practices.
• Project are volatile and change over time.
• The firm is a growth firm with most of its value from growth assets.
Aswath Damodaran
62
From Project to Firm Return on Capital
Just as a comparison of project return on capital to the cost of capital
yields a measure of whether the project is acceptable, a comparison
can be made at the firm level, to judge whether the existing projects of
the firm are adding or destroying value.
Boeing
Home Depot
InfoSoft
Return on Capital
5.82%
16.37%
23.67%
Cost of Capital
9.17%
9.51%
12.55%
ROC - Cost of Capital
-3.35%
6.87%
11.13%

Aswath Damodaran
63
IV. From Earnings to Cash Flows

To get from accounting earnings to cash flows:
• you have to add back non-cash expenses (like depreciation and
amortization)
• you have to subtract out cash outflows which are not expensed (such as
capital expenditures)
• you have to make accrual revenues and expenses into cash revenues and
expenses (by considering changes in working capital).

For the Boeing Super Jumbo, we will assume that
• The depreciation used for operating expense purposes is also the tax
depreciation.
• Working capital will be 10% of revenues, and the investment has to be
made at the beginning of each year.
Aswath Damodaran
64
Estimating Cash Flows: The Boeing Super
Jumbo
Yea r
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Aswath Damodaran
EBIT(1 -t)
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
(141 )
(203 )
(291 )
(370 )
(19)
609
652
694
736
778
820
862
905
948
991
1,1 44
1,2 05
1,2 65
1,3 25
1,3 84
1,1 30
1,1 80
1,2 29
1,2 79
1,3 29
Depreciation
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
217
312
447
569
629
608
589
571
556
542
529
518
508
499
491
317
285
256
231
208
187
168
151
136
123
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
Cap Ex
3,0 00
1,0 00
1,5 00
1,5 00
1,0 00
250
250
250
250
250
250
250
250
250
250
250
-
Chang e in WC Salvag e Va lue
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
1,0 00
1,5 75
77
80
82
84
87
90
92
95
98
101
104
107
110
113
(686 )
96
99
102
105
-
$
4,7 16
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
FCFF
(3,0 00)
(924 )
(1,3 91)
(1,3 43)
(1,8 01)
(1,2 15)
890
911
933
958
983
1,0 10
1,0 38
1,0 68
1,0 99
1,1 31
1,3 57
1,3 83
1,4 11
1,4 42
2,2 77
1,2 21
1,2 49
1,2 79
1,3 10
6,1 68
65
The Depreciation Tax Benefit





While depreciation reduces taxable income and taxes, it does not
reduce the cash flows.
The benefit of depreciation is therefore the tax benefit. In general, the
tax benefit from depreciation can be written as:
Tax Benefit = Depreciation * Tax Rate
For example, in year 2, the tax benefit from depreciation to Boeing
from this project can be written as:
Tax Benefit in year 2 = $ 217 million (.35) = $ 76 million
Proposition 1: The tax benefit from depreciation and other non-cash
charges is greater, the higher your tax rate.
Proposition 2: Non-cash charges that are not tax deductible (such as
amortization of goodwill) and thus provide no tax benefits have no
effect on cash flows.
Aswath Damodaran
66
The Capital Expenditures Effect


Capital expenditures are not treated as accounting expenses but they
do cause cash outflows.
Capital expenditures can generally be categorized into two groups
• New (or Growth) capital expenditures are capital expenditures designed to
create new assets and future growth
• Maintenance capital expenditures refer to capital expenditures designed to
keep existing assets.


Both initial and maintenance capital expenditures reduce cash flows
The need for maintenance capital expenditures will increase with the
life of the project. In other words, a 25-year project will require more
maintenance capital expenditures than a 2-year asset.
Aswath Damodaran
67
The Working Capital Effect




Intuitively, money invested in inventory or in accounts receivable
cannot be used elsewhere. It, thus, represents a drain on cash flows.
To the degree that some of these investments can be financed using
suppliers credit (accounts payable) the cash flow drain is reduced.
Assets that earn a fair market return should not be counted as part of
working capital for cash flow purposes. Since cash is usually invested
to earn a fair market return in marketable securities, it should generally
not be considered as part of working capital.
Investments in working capital are thus cash outflows
• Any increase in working capital reduces cash flows in that year
• Any decrease in working capital increases cash flows in that year

To provide closure, working capital investments need to be salvaged at
the end of the project life.
Aswath Damodaran
68
NPV of Boeing Super Jumbo and Working
Capital as % of Revenues
Aswath Damodaran
69
V. From Cash Flows to Incremental Cash Flows


The incremental cash flows of a project are the difference between the
cash flows that the firm would have had, if it accepts the investment,
and the cash flows that the firm would have had, if it does not accept
the investment.
The Key Questions to determine whether a cash flow is incremental:
• What will happen to this cash flow item if I accept the investment?
• What will happen to this cash flow item if I do not accept the investment?

If the cash flow will occur whether you take this investment or reject
it, it is not an incremental cash flow.
Aswath Damodaran
70
Sunk Costs



Any expenditure that has already been incurred, and cannot be
recovered (even if a project is rejected) is called a sunk cost
When analyzing a project, sunk costs should not be considered since
they are incremental
By this definition, market testing expenses and R&D expenses are
both likely to be sunk costs before the projects that are based upon
them are analyzed. If sunk costs are not considered in project analysis,
how can a firm ensure that these costs are covered?
Aswath Damodaran
71
Allocated Costs



Firms allocate costs to individual projects from a centralized pool
(such as general and administrative expenses) based upon some
characteristic of the project (sales is a common choice)
For large firms, these allocated costs can result in the rejection of
projects
To the degree that these costs are not incremental (and would exist
anyway), this makes the firm worse off.
• Thus, it is only the incremental component of allocated costs that should
show up in project analysis.

How, looking at these pooled expenses, do we know how much of the
costs are fixed and how much are variable?
Aswath Damodaran
72
Boeing: Super Jumbo Jet


The $2.5 billion already expended on the jet is a sunk cost, as is the
amortization related that expense. (Boeing has spent the first, and it is
entitled to the latter even if the investment is rejected)
Two-thirds of the S,G&A expenses are fixed expenses and would exist
even if this project is not accepted.
Aswath Damodaran
73
The Incremental Cash Flows: Boeing Super
Jumbo
Ye ar
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Aswath Damodaran
EBIT(1-t)
$0
($3 3)
($9 4)
($1 82)
($2 62)
$9 0
$7 18
$7 60
$8 02
$8 44
$8 86
$9 28
$9 71
$1 ,013
$1 ,056
$1 ,100
$1 ,144
$1 ,205
$1 ,265
$1 ,325
$1 ,384
$1 ,130
$1 ,180
$1 ,229
$1 ,279
$1 ,329
Depre cia tion
$0
$5 0
$1 45
$2 81
$4 02
$4 62
$4 41
$4 22
$4 05
$3 89
$3 75
$3 63
$3 51
$3 41
$3 32
$3 24
$3 17
$2 85
$2 56
$2 31
$2 08
$1 87
$1 68
$1 51
$1 36
$1 23
Cap Ex
$3 ,000
$1 ,000
$1 ,500
$1 ,500
$1 ,000
$2 50
$2 50
$2 50
$2 50
$2 50
$2 50
$2 50
$2 50
$2 50
$2 50
$2 50
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
Chan ge i n WC Sal va ge Value
$0
$0
$0
$0
$0
$0
$0
$0
$1 ,000
$0
$1 ,575
$0
$7 7
$0
$8 0
$0
$8 2
$0
$8 4
$0
$8 7
$0
$9 0
$0
$9 2
$0
$9 5
$0
$9 8
$0
$1 01
$0
$1 04
$0
$1 07
$0
$1 10
$0
$1 13
$0
($6 86)
$0
$9 6
$0
$9 9
$0
$1 02
$0
$1 05
$0
$0
$4 ,716
FCFF
($3 ,000 )
($9 83)
($1 ,449 )
($1 ,402 )
($1 ,859 )
($1 ,273 )
$8 31
$8 52
$8 75
$8 99
$9 25
$9 52
$9 80
$1 ,010
$1 ,041
$1 ,073
$1 ,357
$1 ,383
$1 ,411
$1 ,442
$2 ,277
$1 ,221
$1 ,249
$1 ,279
$1 ,310
$6 ,168
Sun k Cos t
($2 ,500 )
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
Fi xe d GS&A(1-t)
$0
$0
$0
$0
$1 73
$4 46
$4 60
$4 74
$4 88
$5 02
$5 17
$5 33
$5 49
$5 65
$5 82
$6 00
$6 18
$6 36
$6 55
$6 75
$5 56
$5 73
$5 90
$6 08
$6 26
In crem enta l FCFF
($5 00)
($9 83)
($1 ,449 )
($1 ,402 )
($1 ,859 )
($1 ,100 )
$1 ,278
$1 ,312
$1 ,349
$1 ,387
$1 ,427
$1 ,469
$1 ,513
$1 ,558
$1 ,606
$1 ,655
$1 ,956
$2 ,001
$2 ,048
$2 ,098
$2 ,952
$1 ,777
$1 ,822
$1 ,869
$1 ,918
$6 ,794
74
VI. To Time-Weighted Cash Flows



Incremental cash flows in the earlier years are worth more than
incremental cash flows in later years.
In fact, cash flows across time cannot be added up. They have to be
brought to the same point in time before aggregation.
This process of moving cash flows through time is
• discounting, when future cash flows are brought to the present
• compounding, when present cash flows are taken to the future

The discount rate is the mechanism that determines how cash flows
across time will be weighted.
Aswath Damodaran
75
Discounted cash flow measures of return

Net Present Value (NPV): The net present value is the sum of the
present values of all cash flows from the project (including initial
investment).
NPV = Sum of the present values of all cash flows on the project, including
the initial investment, with the cash flows being discounted at the
appropriate hurdle rate (cost of capital, if cash flow is cash flow to the
firm, and cost of equity, if cash flow is to equity investors)
• Decision Rule: Accept if NPV > 0

Internal Rate of Return (IRR): The internal rate of return is the
discount rate that sets the net present value equal to zero. It is the
percentage rate of return, based upon incremental time-weighted cash
flows.
• Decision Rule: Accept if IRR > hurdle rate
Aswath Damodaran
76
Closure on Cash Flows


In a project with a finite and short life, you would need to compute a
salvage value, which is the expected proceeds from selling all of the
investment in the project at the end of the project life. It is usually set
equal to book value of fixed assets and working capital
In a project with an infinite or very long life, we compute cash flows
for a reasonable period, and then compute a terminal value for this
project, which is the present value of all cash flows that occur after the
estimation period ends..
Aswath Damodaran
77
Salvage Value on Boeing Super Jumbo
We will assume that the salvage value for this investment at the end of
year 25 will be the book value of the investment.
Book value of capital investments at end of year 25 = $1,104 million
Book value of working capital investments: yr 25 = $3,612 million
Salvage Value at end of year 25 =
$4,716 million

Aswath Damodaran
78
Considering all of the Cashflows… The NPV
Yea r
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
FCFF
$ (500 )
$ (983 )
$ (1,4 49)
$ (1,4 02)
$ (1,8 59)
$ (1,1 00)
$ 1,2 78
$ 1,3 12
$ 1,3 49
$ 1,3 87
$ 1,4 27
$ 1,4 69
$ 1,5 13
$ 1,5 58
$ 1,6 06
$ 1,6 55
$ 1,9 56
$ 2,0 01
$ 2,0 48
$ 2,0 98
$ 2,9 52
$ 1,7 77
$ 1,8 22
$ 1,8 69
$ 1,9 18
$ 2,0 78
Salvag e Va lue
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
4,7 16
FCFF + Sal va ge
$
(500 )
$
(983 )
$
(1,4 49)
$
(1,4 02)
$
(1,8 59)
$
(1,1 00)
$
1,2 78
$
1,3 12
$
1,3 49
$
1,3 87
$
1,4 27
$
1,4 69
$
1,5 13
$
1,5 58
$
1,6 06
$
1,6 55
$
1,9 56
$
2,0 01
$
2,0 48
$
2,0 98
$
2,9 52
$
1,7 77
$
1,8 22
$
1,8 69
$
1,9 18
$
6,7 94
Net Pre sent Val ue =
Aswath Damodaran
Prese nt Value (@9.3 2%)
$
(500 )
$
(899 )
$
(1,2 13)
$
(1,0 73)
$
(1,3 02)
$
(704 )
$
749
$
703
$
661
$
622
$
585
$
551
$
519
$
489
$
461
$
435
$
470
$
440
$
412
$
386
$
497
$
274
$
257
$
241
$
226
$
732
$
4,0 19
79
Which makes the argument that..


The project should be accepted. The positive net present value
suggests that the project will add value to the firm, and earn a return in
excess of the cost of capital.
By taking the project, Boeing will increase its value as a firm by
$4,019 million.
Aswath Damodaran
80
The IRR of this project
Internal Rate of Return
Aswath Damodaran
81
The IRR suggests..


The project is a good one. Using time-weighted, incremental cash
flows, this project provides a return of 14.88%. This is greater than the
cost of capital of 9.32%.
The IRR and the NPV will yield similar results most of the time,
though there are differences between the two approaches that may
cause project rankings to vary depending upon the approach used.
Aswath Damodaran
82
An IRR-based Approach to analyzing existing
investments - CFROI


The CFROI is the internal rate of return that you generate by looking
collectively at the investment in all of your assets and the cashflows
you expect to generate from them. CFROI is usually done in real
terms and should generally be compared to a real cost of capital.
In terms of inputs, CFROI is usually computed using the following:
• Gross investment in plant and equipment, which is obtained by adding
back accumulated depreciation to net plant and equipment, is used as the
equivalent of the initial investment.
• The annual cashflow is computed by adding back depreciation to after-tax
operating income.
• The life of the asset, at the time of the original purchase, is used as the life
of the assets
Aswath Damodaran
83
Equity Analysis: The Parallels


The investment analysis can be done entirely in equity terms, as well.
The returns, cashflows and hurdle rates will all be defined from the
perspective of equity investors.
If using accounting returns,
• Return will be Return on Equity (ROE) = Net Income/BV of Equity
• ROE has to be greater than cost of equity

If using discounted cashflow models,
• Cashflows will be cashflows after debt payments to equity investors
• Hurdle rate will be cost of equity
Aswath Damodaran
84
A New Store for the Home Depot





It will require an initial investment of $20 million in land, building and
fixtures.
The Home Depot plans to borrow $ 5 million, at an interest rate of
5.80%, using a 10-year term loan.
The store will have a life of 10 years. During that period, the store
investment will be depreciated using straight line depreciation. At the
end of the tenth year, the investments are expected to have a salvage
value of $ 7.5 million.
The store is expected to generate revenues of $40 million in year 1,
and these revenues are expected to grow 5% a year for the remaining 9
years of the store’s life.
The pre-tax operating margin, at the store prior to depreciation, is
expected to be 10% for the entire period.
Aswath Damodaran
85
Interest and Principal Payments
Year
1
2
3
4
5
6
7
8
9
10
Aswath Damodaran
Outstanding debt
Interest Expense
Total Payment
Principal Repaid Remaining Principal
$5,000,000.00
$290,000.00
$672,917.36
$382,917.36
$4,617,082.64
$4,617,082.64
$267,790.79
$672,917.36
$405,126.57
$4,211,956.08
$4,211,956.08
$244,293.45
$672,917.36
$428,623.91
$3,783,332.17
$3,783,332.17
$219,433.27
$672,917.36
$453,484.09
$3,329,848.08
$3,329,848.08
$193,131.19
$672,917.36
$479,786.17
$2,850,061.91
$2,850,061.91
$165,303.59
$672,917.36
$507,613.77
$2,342,448.14
$2,342,448.14
$135,861.99
$672,917.36
$537,055.37
$1,805,392.77
$1,805,392.77
$104,712.78
$672,917.36
$568,204.58
$1,237,188.19
$1,237,188.19
$71,756.92
$672,917.36
$601,160.44
$636,027.75
$636,027.75
$36,889.61
$672,917.36
$636,027.75
$0.00
86
Net Income on The Home Depot Store
Year
1
2
3
4
5
6
7
8
9
10
Revenues
$40,000,000
$42,000,000
$44,100,000
$46,305,000
$48,620,250
$51,051,263
$53,603,826
$56,284,017
$59,098,218
$62,053,129
Aswath Damodaran
Operating Expens es
$36,000,000
$37,800,000
$39,690,000
$41,674,500
$43,758,225
$45,946,136
$48,243,443
$50,655,615
$53,188,396
$55,847,816
Depreciation
$1,250,000
$1,250,000
$1,250,000
$1,250,000
$1,250,000
$1,250,000
$1,250,000
$1,250,000
$1,250,000
$1,250,000
EBIT
$2,750,000
$2,950,000
$3,160,000
$3,380,500
$3,612,025
$3,855,126
$4,110,383
$4,378,402
$4,659,822
$4,955,313
Interes t Expens e Taxable Income
$290,000
$2,460,000
$267,791
$2,682,209
$244,293
$2,915,707
$219,433
$3,161,067
$193,131
$3,418,894
$165,304
$3,689,823
$135,862
$3,974,521
$104,713
$4,273,689
$71,757
$4,588,065
$36,890
$4,918,423
Taxes
$861,000
$938,773
$1,020,497
$1,106,373
$1,196,613
$1,291,438
$1,391,082
$1,495,791
$1,605,823
$1,721,448
Net Income
$1,599,000
$1,743,436
$1,895,209
$2,054,693
$2,222,281
$2,398,385
$2,583,438
$2,777,898
$2,982,242
$3,196,975
87
The Hurdle Rate


The analysis is done in equity terms. Thus, the hurdle rate has to be a
cost of equity
The cost of equity for the Home Depot is 9.78%. Since the Home
Depot’s investments are assumed to be homogeneous, the cost of
equity for this project is also assumed to be 9.78%.
Aswath Damodaran
88
An Incremental CF Analysis
Year
0
1
2
3
4
5
6
7
8
9
10
Aswath Damodaran
Net Income
Depreciation
$1,599,000
$1,743,436
$1,895,209
$2,054,693
$2,222,281
$2,398,385
$2,583,438
$2,777,898
$2,982,242
$3,196,975
$1,250,000
$1,250,000
$1,250,000
$1,250,000
$1,250,000
$1,250,000
$1,250,000
$1,250,000
$1,250,000
$1,250,000
Capital Expenditures
Debt Iss ued/PrincipalChange
Repayment
in Working Capital
Salvage Value
($20,000,000)
$5,000,000
($3,200,000)
($382,917)
($160,000)
($405,127)
($168,000)
($428,624)
($176,400)
($453,484)
($185,220)
($479,786)
($194,481)
($507,614)
($204,205)
($537,055)
($214,415)
($568,205)
($225,136)
($601,160)
($236,393)
($636,028)
$4,964,250
$7,500,000
FCFE
($18,200,000)
$2,306,083
$2,420,309
$2,540,185
$2,665,989
$2,798,014
$2,936,566
$3,081,968
$3,234,557
$3,394,689
$16,275,198
89
NPV of the Store
Year
0
1
2
3
4
5
6
7
8
9
10
Aswath Damodaran
FCFE
($18,200,000)
$2,306,083
$2,420,309
$2,540,185
$2,665,989
$2,798,014
$2,936,566
$3,081,968
$3,234,557
$3,394,689
$16,275,198
PV at Cost of Equity
($18,200,000)
$2,100,640
$2,008,281
$1,919,976
$1,835,547
$1,754,825
$1,677,646
$1,603,856
$1,533,307
$1,465,855
$6,401,681
$4,101,613
90
Internal Rate of Return: The Home Depot Store
Aswath Damodaran
91
The ‘‘Consistency Rule” for Cash Flows

The cash flows on a project and the discount rate used should be
defined in the same terms.
• If cash flows are in one currency, the discount rate has to be a dollar
(baht) discount rate
• If the cash flows are nominal (real), the discount rate has to be nominal
(real).

If consistency is maintained, the project conclusions should be
identical, no matter what cash flows are used.
Aswath Damodaran
92
The Home Depot: A New Store in Chile





It will require an initial investment of 4700 million pesos for land,
building and fixtures. The Home Depot plans to borrow 1880 million
pesos, at an interest rate of 12.02%, using a 10-year term loan.
The store will have a life of 10 years. During that period, the store will
be depreciated using straight line depreciation. At the end of the tenth
year, the investments are expected to have a salvage value of 2,350
million pesos.
The store is expected to generate revenues of 7,050 million pesos in
year 1, and these revenues are expected to grow 12% a year for the
remaining 9 years.
The pre-tax operating margin at the store, prior to depreciation, is
expected to be 6% for the entire period.
The working capital requirements are estimated to be 10% of total
revenues, and investments will be made at the beginning of each year.
Aswath Damodaran
93
The Home Depot Chile Store: Cashflows in
Pesos
Year Net Income Depreciation Capital Expenditures Debt Iss ued/Principal Repayment Change in Working Capital Salvage Value
FCFE
0
(4,700.00)
1,880.00
(705.00)
(3,525.00)
1
(22.83)
235.00
(107.01)
(84.60)
20.57
2
15.35
235.00
(119.87)
(94.75)
35.72
3
58.11
235.00
(134.29)
(106.12)
52.70
4
106.00
235.00
(150.43)
(118.86)
71.71
5
159.64
235.00
(168.52)
(133.12)
93.00
6
219.72
235.00
(188.78)
(149.09)
116.84
7
287.01
235.00
(211.48)
(166.99)
143.55
8
362.39
235.00
(236.91)
(187.02)
173.45
9
446.81
235.00
(265.39)
(209.47)
206.94
10
541.36
235.00
(297.30)
1,955.02
2,350.00
4,784.08
Aswath Damodaran
94
The Home Depot Chile Store: Cost of Equity in
Pesos


Cost of Equity for a U.S. store = 9.78%
Estimating the Country Risk Premium for Chile
• Default spread based on Chilean Bond rating = 1.1%
• Relative Volatility of Chilean Equity to Bond Market = 2.2
• Country risk premium for Chile = 1.1% * 2.2 = 2.42%
Cost of Equity for a Chilean Store (in U.S. $)
= 5% + 0.87 (5.5% + 2.42%) = 11.88%
 Assume that the expected inflation rate in Chile is 8% and the
expected inflation rate in the U.S. is 2%.
 Cost of Equity for a Chilean Store (in Pesos)
= [(1 + Cost of Equity in $)* (1 + inflationChile)/ (1 + inflationUS)] - 1
=[ 1.1188* (1.08/1.02)] -1 = 18.46%

Aswath Damodaran
95
NPV in Pesos
Year
0
1
2
3
4
5
6
7
8
9
10
Aswath Damodaran
FCFE in pesos (millions ) PV at Pes o Cos t of Equity
-3,525.00
-3,525.00
20.57
17.36
35.72
25.46
52.70
31.70
71.71
36.41
93.00
39.86
116.84
42.28
143.55
43.84
173.45
44.72
206.94
45.04
4,784.08
878.90
-2,319
96
Converting Pesos to U.S. dollars


This entire analysis can be done in dollars, if we convert the peso cash
flows into U.S. dollars.
If you want the analysis to yield consistent conclusions, expected
exchange rates have to be estimated based upon expected inflation
rates:
• Current Exchange Rate = 470 pesos
• Expected Ratet = Exchange Rate* (1 + inflationChile)/ (1 + inflationUS)]
• Expected Exchange Rate in year 1 = 470 pesos * (1.08/1.02) = 497.65
Aswath Damodaran
97
Analyzing the Project: U.S. Dollars
Ye ar
0
1
2
3
4
5
6
7
8
9
10
Aswath Damodaran
FCFE in p esos (mil lion s)
-35 25
21
36
53
72
93
11 7
14 4
17 3
20 7
47 84
Expected Excha nge Ra te
47 0.00
49 7.65
52 6.92
55 7.92
59 0.73
62 5.48
66 2.28
70 1.23
74 2.48
78 6.16
83 2.40
FCFE in $
$ (7,500,000)
$
41 ,327
$
67 ,797
$
94 ,457
$
12 1,39 1
$
14 8,68 6
$
17 6,42 8
$
20 4,70 7
$
23 3,61 2
$
26 3,23 5
$ 5,747,306
98
NPV in U.S. Dollars
Ye ar
0
1
2
3
4
5
6
7
8
9
10
Aswath Damodaran
FCFE in $
$
(7,500,000)
$
41 ,327
$
67 ,797
$
94 ,457
$
12 1,39 1
$
14 8,68 6
$
17 6,42 8
$
20 4,70 7
$
23 3,61 2
$
26 3,23 5
$
5,747,306
NPV (i n U.S. $)
In Peso s
PV at $ co st o f eq uity
$
(7,500,000)
$
36 ,938
$
54 ,161
$
67 ,445
$
77 ,471
$
84 ,812
$
89 ,949
$
93 ,282
$
95 ,148
$
95 ,826
$
1,870,008
$
(4,934,960)
-23 19
99
The Role of Sensitivity Analysis



Our conclusions on a project are clearly conditioned on a large number
of assumptions about revenues, costs and other variables over very
long time periods.
To the degree that these assumptions are wrong, our conclusions can
also be wrong.
One way to gain confidence in the conclusions is to check to see how
sensitive the decision measure (NPV, IRR..) is to changes in key
assumptions.
Aswath Damodaran
100
Viability of New Store: Sensitivity to Operating
Margin
Aswath Damodaran
101
What does sensitivity analysis tell us?
Assume that the manager at The Home Depot who has to decide on
whether to take this plant is very conservative. She looks at the
sensitivity analysis and decides not to take the project because the
NPV would turn negative if the operating margin drops below 8%. Is
this the right thing to do?
 Yes
 No
Explain.
Aswath Damodaran
102
Dealing with Inflation




In our analysis, we used nominal dollars and pesos. Would the NPV
have been different if we had used real cash flows instead of nominal
cash flows?
It would be much lower, since real cash flows are lower than nominal
cash flows
It would be much higher
It should be unaffected
Aswath Damodaran
103
From Nominal to Real : The Home Depot

To do a real analysis, you need a real cost of equity or capital
• Nominal cost of equity for The Home Depot = 9.78%
• Expected Inflation rate = 2%
• Real Cost of Equity = (1.0978/1.02)-1 = 7.59%

To estimate cash flows in real terms
• Real Cash flowt = Nominal Cash flowt / (1+ Expected Inflation rate)t
Aswath Damodaran
104
Nominal versus Real
Year
0
1
2
3
4
5
6
7
8
9
10
NPV
Aswath Damodaran
FCFE (nominal)
($18,200,000)
$2,826,083
$2,966,309
$3,113,485
$3,267,954
$3,430,077
$3,600,232
$3,778,817
$3,966,249
$4,162,966
$17,081,888
PV (nominal)
($18,200,000)
$2,574,315
$2,461,331
$2,353,299
$2,250,003
$2,151,234
$2,056,796
$1,966,497
$1,880,157
$1,797,603
$6,718,984
$8,010,219
Deflation factor FCFE (Real)
1.0000
0.9801
0.9606
0.9415
0.9227
0.9044
0.8864
0.8687
0.8514
0.8345
0.8179
($18,200,000)
$2,769,830
$2,849,397
$2,931,242
$3,015,429
$3,102,025
$3,191,098
$3,282,720
$3,376,963
$3,473,900
$13,970,716
PV (Real)
$
$
$
$
$
$
$
$
$
$
$
$
(18,200,000)
2,574,315
2,461,331
2,353,299
2,250,003
2,151,234
2,056,796
1,966,497
1,880,157
1,797,603
6,718,984
8,010,219
105
Side Costs and Benefits




Most projects considered by any business create side costs and benefits
for that business.
The side costs include the costs created by the use of resources that the
business already owns (opportunity costs) and lost revenues for other
projects that the firm may have.
The benefits that may not be captured in the traditional capital
budgeting analysis include project synergies (where cash flow benefits
may accrue to other projects) and options embedded in projects
(including the options to delay, expand or abandon a project).
The returns on a project should incorporate these costs and benefits.
Aswath Damodaran
106
Opportunity Cost


An opportunity cost arises when a project uses a resource that may
already have been paid for by the firm.
When a resource that is already owned by a firm is being considered
for use in a project, this resource has to be priced on its next best
alternative use, which may be
• a sale of the asset, in which case the opportunity cost is the expected
proceeds from the sale, net of any capital gains taxes
• renting or leasing the asset out, in which case the opportunity cost is the
expected present value of the after-tax rental or lease revenues.
• use elsewhere in the business, in which case the opportunity cost is the
cost of replacing it.
Aswath Damodaran
107
Project Synergies


A project may provide benefits for other projects within the firm. If
this is the case, these benefits have to be valued and shown in the
initial project analysis.
For instance, the Home Depot, when it considers opening a new
restaurant at one of its stores, will have to examine the additional
revenues that may accrue to this store from people who come to the
restaurant.
Aswath Damodaran
108
Project Options

One of the limitations of traditional investment analysis is that it is
static and does not do a good job of capturing the options embedded in
investment.
• The first of these options is the option to delay taking a project, when a
firm has exclusive rights to it, until a later date.
• The second of these options is taking one project may allow us to take
advantage of other opportunities (projects) in the future
• The last option that is embedded in projects is the option to abandon a
project, if the cash flows do not measure up.

These options all add value to projects and may make a “bad” project
(from traditional analysis) into a good one.
Aswath Damodaran
109
The Option to Delay



When a firm has exclusive rights to a project or product for a specific
period, it can delay taking this project or product until a later date.
A traditional investment analysis just answers the question of whether
the project is a “good” one if taken today.
Thus, the fact that a project does not pass muster today (because its
NPV is negative, or its IRR is less than its hurdle rate) does not mean
that the rights to this project are not valuable.
Aswath Damodaran
110
Valuing the Option to Delay a Project
PV of Cash Flows
from Project
Initial Investment in
Project
Present Value of Expected
Cash Flows on Product
Project has negative
NPV in this section
Aswath Damodaran
Project's NPV turns
positive in this section
111
Insights for Investment Analyses



Having the exclusive rights to a product or project is valuable, even if
the product or project is not viable today.
The value of these rights increases with the volatility of the underlying
business.
The cost of acquiring these rights (by buying them or spending money
on development - R&D, for instance) has to be weighed off against
these benefits.
Aswath Damodaran
112
The Option to Expand/Take Other Projects



Taking a project today may allow a firm to consider and take other
valuable projects in the future.
Thus, even though a project may have a negative NPV, it may be a
project worth taking if the option it provides the firm (to take other
projects in the future) provides a more-than-compensating value.
These are the options that firms often call “strategic options” and use
as a rationale for taking on “negative NPV” or even “negative return”
projects.
Aswath Damodaran
113
The Option to Expand
PV of Cash Flows
from Expansion
Additional Investment
to Expand
Present Value of Expected
Cash Flows on Expansion
Firm will not expand in
this section
Aswath Damodaran
Expansion becomes
attractive in this section
114
An Example of an Expansion Option


Assume that The Home Depot is considering opening a small store in
France. The store will cost 100 million French Francs (FF) to build,
and the present value of the expected cash flows from the store is 120
million FF. Thje store has a negative NPV of 20 million FF.
Assume, however, that by opening this store, the Home Depot will
acquire the option to expand its operations any time over the next 5
years. The cost of expansion will be 200 million FF, and it will be
undertaken only if the present value of the expected cash flows from
expansion exceeds 200 million FF. At the moment, this present value is
believed to be only 150 million FF. The Home Depot still does not
know much about the market for home improvement products in
France, and there is considerable uncertainty about this estimate. The
variance in the estimate is 0.08.
Aswath Damodaran
115
Valuing the Expansion Option
Value of the Underlying Asset (S) = PV of Cash Flows from
Expansion, if done now =150 million FF
 Strike Price (K) =Cost of Expansion = 200 million FF
 Variance in Underlying Asset’s Value = 0.08
 Time to expiration = Period for which expansion option applies = 5
years
Call Value= 150 (0.6314) -200 (exp(-0.06)(20) (0.3833)= 37.91 million FF

Aswath Damodaran
116
Considering the Project with Expansion Option



NPV of Store = 80 million FF - 100 million FF = -20 million
Value of Option to Expand = 37.91 million FF
NPV of store with option to expand = -20 million + 37.91 million =
17.91 mil FF
Accept the project
Aswath Damodaran
117
The Option to Abandon


A firm may sometimes have the option to abandon a project, if the
cash flows do not measure up to expectations.
If abandoning the project allows the firm to save itself from further
losses, this option can make a project more valuable.
PV of Cash Flows
from Project
Cost of Abandonment
Present Value of Expected
Cash Flows on Project
Aswath Damodaran
118
Valuing the Option to Abandon


Assume that the Home Depot is considering a new store that requires a
net initial investment of $ 9.5 million and generates cash flows with a
present value of $8.563 million. The net present value of -$937,287
would lead us to reject this project.
To illustrate the effect of the option to abandon, assume that the Home
Depot has the option to close the store any time over the next 10 years
and sell the land back to the original owner for $ 5 million. In addition,
assume that the standard deviation in the present value of the cash
flows is 22%.
Aswath Damodaran
119
Project with Option to Abandon






Value of the Underlying Asset (S) = PV of Cash Flows from Project
= $ 8,562,713
Strike Price (K) = Salvage Value from Abandonment = $ 5 million
Variance in Underlying Asset’s Value = 0.222 = 0.0484
Time to expiration = Life of the Project = 10 years
Dividend Yield = 1/Life of the Project = 1/10 = 0.10 (We are assuming
that the project’s present value will drop by roughly 1/n each year into
the project)
The riskless rate is 5%.
Aswath Damodaran
120
Should The Home Depot take this project?
Value of Put = 5,000,000 exp(-0.05)(10) (1-0.4977) - -8,562,713
exp(0.10)(10) (1-0.7548) = $ 474,831
 The value of this abandonment option has to be added to the net
present value of the project of -$ 937,287, yielding a total net present
value that remains negative.
NPV without abandonment option =
-$937,287
Value of abandonment option =
+$474,831
NPV with abandonment option =
-$462,456

Notwithstanding the abandonment option, this store should not be opened.
Aswath Damodaran
121
First Principles

Invest in projects that yield a return greater than the minimum
acceptable hurdle rate.
• The hurdle rate should be higher for riskier projects and reflect the
financing mix used - owners’ funds (equity) or borrowed money (debt)
• Returns on projects should be measured based on cash flows
generated and the timing of these cash flows; they should also
consider both positive and negative side effects of these projects.


Choose a financing mix that minimizes the hurdle rate and matches the
assets being financed.
If there are not enough investments that earn the hurdle rate, return the
cash to stockholders.
•
Aswath Damodaran
The form of returns - dividends and stock buybacks - will depend upon
the stockholders’ characteristics.
122