11/19/2023
Corporate Finance
Miscellaneous Issues in the WACC
Objectives
• How can we compute the discount rates for international projects?
• How can we set discount rates if the beta is not known?
1
11/19/2023
Miscellaneous Issues in the WACC
Discount Rates for International Projects
Discount Rates for International Projects
• Assume that you are an investor from the United States who has
invested all of his wealth in the local market. Your investment
advisor has recommended that you should invest some of your
wealth in emerging markets.
• Are foreign investments (for instance, investment in emerging
markets) always riskier for you than local investments
(investments in the United States)?
2
11/19/2023
Discount Rates for International Projects
• In order to answer this question, assume that you have the choice
to invest either in the Standard and Poor’s Composite Index (local
investment) or in the Egyptian Stock Market Index (foreign
investment).
• Which one will you consider as a riskier investment?
Discount Rates for International Projects
• If your answer is Egypt, you are right, but only if the risk is defined
as total volatility or variance.
• However, if most of the volatility or variance associated with the
Egyptian Stock Market Index can be eliminated via diversification,
we may need to revise our initial answer that considers Egypt as a
risky investment.
3
11/19/2023
Discount Rates for International Projects
• Therefore, in order to know whether Egyptian Stock Market Index
is a riskier investment or not, we need to answer: Does the
investment in Egypt add to the risk of a portfolio held by you
(the investor who invests all of his wealth in the United
States)?
• If it adds to that risk, only then Egypt is a risky investment.
Discount Rates for International Projects
• The next table shows the estimated betas for the stock market in
Egypt, Poland, Thailand, and Venezuela.
• NOTE: The betas are calculated by regressing the returns of the Egyptian,
Polish, Thai, and Venezuelan stock markets against the returns of the U.S.
market (S&P Composite Index).
4
11/19/2023
Discount Rates for International Projects
• The relationship
between country
indexes and the
S&P Composite
Index is shown
in the next table.
Discount Rates for International Projects
• The table shows that the standard deviations of returns in these
markets were high relative to the standard deviation in the U.S.
market.
• More specifically, the standard deviations of returns in these
markets were two or three times more than the standard
deviations of returns in the U.S. market.
• However, only Thailand had a beta greater than 1.
5
11/19/2023
Discount Rates for International Projects
• Given that beta is the true measure of risk, we can say that
investment in Thailand will add risk to the portfolio of the U.S.
investor. All other markets are not risky for the U.S. investor.
• Therefore, we should always distinguish between the
diversifiable (firm-specific) risk and the market risk while
making a judgment about risk. The opportunity cost of capital
should depend on the market risk.
Discount Rates for International Projects
Example 1
• Consider the following beta estimates. Could this information be
useful to the investors from the United States? Could this be useful
to German investors?
6
11/19/2023
Discount Rates for International Projects
Example 1
• The information could be helpful to a U.S. investor who is
undertaking international capital investment projects. By
examining the beta estimates, such investors can evaluate the
contribution of potential cash flows to the risk.
Discount Rates for International Projects
Example 1
• A German investor would not find this information useful. The
relevant risk depends on the beta of the country relative to the
portfolio held by investors.
• German investors do not invest exclusively, or even primarily, in
the U.S. stocks. They invest the major portion of their portfolios in
German stocks.
7
11/19/2023
Discount Rates for International Projects
• For those international projects that are not riskier than the local
projects, we should discount their cash flows at lower discount
rate.
• HOW MUCH LESS?
• NOTE: We should recognize that most of these projects will be real
projects yet to be undertaken. Therefore, they will have no history of
returns that can be used to compute the discount rate.
Discount Rates for International Projects
• In order to answer this question, assume that the Swiss
pharmaceutical company, Roche, is considering an investment in
the United States.
• Financial manager measures the risk of this investment by its beta
relative to the Swiss Market Index.
• NOTE: Cash flows of this foreign project have to be calculated in Swiss
Francs, if the manager wants to use Swiss Market Index in his analysis.
8
11/19/2023
Discount Rates for International Projects
• The value of Roche’s business in the United States is likely to be
much less closely tied to fluctuations in the Swiss market.
• Therefore, the beta of the U.S. project relative to the Swiss market
is likely to be less than the beta of Roche’s projects in Switzerland.
Discount Rates for International Projects
• The extent of “how much less” is based on the beta of the U.S.
pharmaceutical industry relative to the Swiss Market Index. It
turns out that this beta is 0.36.
• If the expected risk premium on the Swiss Market Index is 6%,
Roche should be discounting the Swiss franc cash flows from its
U.S. project at 0.36 * 6% = 2.20% above the Swiss franc interest
rate.
9
11/19/2023
Discount Rates for International Projects
• Why does Roche’s manager measure the beta of its investments
relative to the Swiss index, whereas her U.S. counterpart measures
the beta relative to the U.S. index?
Discount Rates for International Projects
• The answer lies in the fact that risk cannot be considered in
isolation. It depends on the other securities in investor’s portfolio.
• NOTE: The beta measures risk relative to the investor’s portfolio.
10
11/19/2023
Discount Rates for International Projects
• If the U.S. investors already hold the portfolio in the U.S. market, an
additional dollar invested at home is just the same.
• But, if the Swiss investors hold the portfolio in the Swiss market,
an investment in the United States can reduce their risk.
Discount Rates for International Projects
• That explains why an investment in the United States is likely to
have lower risk for Roche’s shareholders than it has for
shareholders in Merck or Pfizer (the U.S. companies).
• It also explains why Roche’s shareholders are willing to accept a
lower return from such an investment than would the
shareholders in the U.S. companies.
11
11/19/2023
Discount Rates for International Projects
• When Merck measures risk relative to the U.S. market and Roche
measures risk relative to the Swiss market, their managers are
implicitly assuming that the shareholders hold domestic
stocks.
Discount Rates for International Projects
Divergence…
• That’s not a bad approximation, particularly in the case of the
United States.
• Although investors in the United States can reduce their risk by
holding an internationally diversified portfolio of shares, they
generally invest only a small proportion of their money overseas.
• Why??
12
11/19/2023
Miscellaneous Issues in the WACC
Arbitrarily Adjusting Discount Rates
Arbitrarily Adjusting Discount Rates
• People, usually, think of the risks of a project as a list of things that
can go wrong.
• A geologist looking for oil worries about the risk of a dry hole.
• A pharmaceutical manufacturer worries about the risk that a new drug
may not be approved by the regulator.
13
11/19/2023
Arbitrarily Adjusting Discount Rates
• Managers often add fudge factors to discount rates to offset
worries, such as the ones mentioned above. This sort of
adjustment is wrong.
• WHY?
Arbitrarily Adjusting Discount Rates
• First, the bad outcomes we cited appear to reflect unique
(diversifiable) risks that would not affect the expected rate of
return demanded by diversified investors.
• Second, the need for a discount rate adjustment arises because
managers fail to give bad outcomes their due weight in cash flow
forecasts.
14
11/19/2023
Arbitrarily Adjusting Discount Rates
• As an example, consider Project-Z that will produce just one cash
flow, forecasted at $1 million at year 1. It is regarded as an average
risk investment, which is suitable for discounting at a 10% cost of
capital. The value of this project is as follows:
Arbitrarily Adjusting Discount Rates
• However, after a while, you develop some apprehensions
regarding the technology required for the project.
• You are confident that technology will work, but you also realize
that there is a small chance that it will not work. You still believe
that the most likely outcome for cash flows is $1 million, but you
also see some chance that Project-Z will generate zero cash flow
next year.
15
11/19/2023
Arbitrarily Adjusting Discount Rates
• What should you do?
• Should you adjust discount rate for this additional risk?
Arbitrarily Adjusting Discount Rates
• No.
• The correct approach is to adjust the cash flows rather than
discount rate.
• The cash flows in the present value calculation should be unbiased
estimates.
• The discount rate depends on risk relative to the market – not on firmspecific risk as is described in the example.
16
11/19/2023
Arbitrarily Adjusting Discount Rates
Example 1
• An oil company is drilling a series of new wells. About 20% of the
new wells will be dry holes.
• Even if a new well strikes oil, there is still uncertainty about the
amount of oil produced: 40% of new wells that strike oil produce
only 1000 barrels a day and 60% produce 5000 barrels per day.
Arbitrarily Adjusting Discount Rates
Example 1
• Forecast the annual cash revenues from a new well. Use future oil
price of $15 per barrel.
17
11/19/2023
Arbitrarily Adjusting Discount Rates
Example 1
• The expected daily production of the well can be computed as
follows:
• Expected Daily Production = (0.2 * 0) + (0.8) * [(0.4 * 1000) + (0.6 *
5000)] = 2720 barrels
• Therefore, the annual cash revenues are the following:
• Annual Cash Revenues = 2720 * 365 * $15 = $14892000
Arbitrarily Adjusting Discount Rates
Example 1
• A geologist proposes to discount the cash flows of the new well at
30% to offset the risk of dry wells. The oil company’s normal cost
of capital is 10%. Does this proposal make sense? Explain why or
why not?
18
11/19/2023
Arbitrarily Adjusting Discount Rates
Example 1
• No.
• The possibility of a dry well is a diversifiable risk and should not
affect the discount rate. This should affect the forecasted cash
flows.
Arbitrarily Adjusting Discount Rates
Example 2
• Mom and Pop Groceries has just dispatched a year’s supply of
groceries to the government of the Central Antarctic Republic.
Payment of $250000 will be made one year from today when the
shipment arrives by snow train.
• Unfortunately, there is a good chance of a coup in which case the
new government will not pay. Mom and Pop’s controller, therefore,
decides to discount the payment at 40%, rather than at the
company’s 12% cost of capital.
19
11/19/2023
Arbitrarily Adjusting Discount Rates
Example 2
• What is wrong with using a 40% rate to offset political risk?
Arbitrarily Adjusting Discount Rates
Example 2
• The threat of a coup means that the expected cash flow is less than
$250000. Therefore, threat of coup should be adjusted in cash
flows.
• The threat could also increase the discount rate, but only if it
increases market risk.
20
11/19/2023
Arbitrarily Adjusting Discount Rates
Example 2
• How much is the $250000 payment really worth if the odds of a
coup are 25%?
Arbitrarily Adjusting Discount Rates
Example 2
• The expected cash flow is: [(0.25 * 0) + (0.75 * 250000)] =
$187500
• Assuming that the cash flow is about as risky as the rest of the
company’s business: PV = $187500/1.12 = $167411
21
11/19/2023
Miscellaneous Issues in the WACC
Setting Discount Rates When You Cannot Calculate
Beta
Discount Rates in the Absence of Beta
• Suppose a firm wants to analyze the risks of holding a large
inventory of copper. What should be the risk associated with
this investment?
22
11/19/2023
Discount Rates in the Absence of Beta
• In order to answer this question, we must compute the beta of
copper.
• It is important to note that (unlike standard deviation) beta is an
appropriate measure of risk because it indicates the market risk
associated with an investment.
Discount Rates in the Absence of Beta
• Given that copper is a widely traded commodity, the manager can
do the following to compute beta:
• Download the prices of copper
• Calculate the rates of return of copper
• Compute the beta for copper by estimating a regression with market
returns as an independent variable and rates of return of copper as a
dependent variable
23
11/19/2023
Discount Rates in the Absence of Beta
• What should a manager do if the asset he wants to invest in
has no such price record?
Discount Rates in the Absence of Beta
• It calls for judgment.
• However, managers should incorporate observable characteristics
of the project while making any judgment. Often the
characteristics of high and low-beta assets can be observed when
the beta itself cannot be.
24
11/19/2023
Discount Rates in the Absence of Beta
• Some of the factors that can affect beta the beta of a project/asset
are the following:
• Variability in Earnings
• Operating Leverage
Discount Rates in the Absence of Beta
Variability in Earnings
• Many people associate risk with the variability of earnings. But
much of this variability reflects the unique risk.
• In reality, these people should worry about the relationship
between firm’s earnings and the aggregate earnings of all firms
operating in the market.
25
11/19/2023
Discount Rates in the Absence of Beta
Variability in Earnings
• We can measure this variability by:
• Accounting Beta
• Cash Flow Beta
Discount Rates in the Absence of Beta
Variability in Earnings
• Accounting or cash flow betas are similar to a normal beta except
that changes in book earnings or cash flows are used in place of
rates of return on securities.
• Dependent variable will be changes in book earnings or cash flows of a
firm
• Independent variable will be changes in book earnings or cash flows of
entire market
26
11/19/2023
Discount Rates in the Absence of Beta
Variability in Earnings
• It is safe to assume that firms with high accounting or cash-flow
betas should also have high stock betas. These firms are, usually,
cyclical firms.
• NOTE: Revenues and earnings of cyclical firms are strongly dependent on
the state of the business cycle.
• Therefore, investors demand a higher rate of return from
investments whose performance is strongly tied to the
performance of the economy.
Discount Rates in the Absence of Beta
Operating Leverage
• Operating leverage (commitment to fixed production charges) also
increases the beta of a project.
• How??
27
11/19/2023
Discount Rates in the Absence of Beta
Operating Leverage
• Cash flows generated by any asset can be broken down into:
• Revenues
• Fixed Costs
• Variable Costs
• Therefore:
• Cash Flow = Revenue – Fixed Cost – Variable Cost
Discount Rates in the Absence of Beta
Operating Leverage
• Given that the value of asset is equal to the present value of cash
flows generated by it, we can write the following equation:
• PV(Assets)
= PV(Cash Flows)
= PV(Revenues) – PV(Fixed Cost) – PV(Variable Cost)
28
11/19/2023
Discount Rates in the Absence of Beta
Operating Leverage
• A little manipulation of the above equation yields the following:
• PV(Revenues) = PV(Assets) + PV(Fixed Cost) + PV(Variable Cost)
• Above equation indicates that revenues is a portfolio of assets,
fixed costs and variable costs. Beta of this portfolio (βRevenue)
should be equal to the weighted average of the betas of its
components.
Discount Rates in the Absence of Beta
Operating Leverage
• Therefore, beta of our portfolio (βRevenue) can be calculated as
follows:
PV(Fixed Cost)
PV(Variable Cost)
β Fixed Cost 
β Variable Cost
PV(Revenue)
PV(Revenue)
PV(Asset)

β Asset
PV(Revenue)
β Revenue 
29
11/19/2023
Discount Rates in the Absence of Beta
Operating Leverage
• Given that fixed costs do not change (no matter what happens to
the market), beta of fixed cost (βFixed Cost) will be zero.
• Furthermore, the betas of the revenues and variable costs should
be approximately the same. It is because both of them respond to
the same underlying variable – the rate of output. Therefore,
βVariable Cost = βRevenue.
Discount Rates in the Absence of Beta
Operating Leverage
• Given above assumptions, we can reformulate our equation for
βRevenue as follows:
PV(Fixed Cost)
PV(Variable Cost)
PV(Asset)
*0 
β Revenue 
β Asset
PV(Revenue)
PV(Revenue)
PV(Revenue)
PV(Variable Cost)
PV(Asset)

β Revenue 
β Asset
PV(Revenue)
PV(Revenue)
β Revenue 
• In the above expression, βFixed Cost = 0 and βVariable Cost = βRevenue
30
11/19/2023
Discount Rates in the Absence of Beta
Operating Leverage
• A little manipulation of the above equation yields the following:
β Asset 

 PV(Variable Cost) PV(Revenue) 
PV(Revenue)
β Revenue  
*
β Revenue
PV(Asset)
PV(Asset) 
 PV(Revenue)
PV(Revenue)
PV(Variable Cost)
β Revenue 
β Revenue
PV(Asset)
PV(Asset)
 PV(Revenue) - PV(Variable Cost)

PV(Asset)


β Revenue

 PV(Assets)  PV(Fixed Cost)  PV(Variable Cost) - PV(Variable Cost) 

β Revenue
PV(Asset)


 PV(Assets)  PV(Fixed Cost)

PV(Asset)



PV(Fixed Cost)
β Revenue  1 
PV(Asset)



β Revenue

Discount Rates in the Absence of Beta
Operating Leverage
• Thus, the asset beta is proportional to the ratio of the present
value of fixed costs to the present value of the project.
31
11/19/2023
Discount Rates in the Absence of Beta
Operating Leverage
• Now we have a rule of thumb for judging the relative risks of
alternative technologies for producing the same output. Other
things being equal, the alternative with the higher ratio of fixed
costs to project value will have the higher project beta.
Empirical tests confirm that companies with high operating
leverage actually do have high betas.
Miscellaneous Issues in the WACC
Optimal Capital Budget
32
11/19/2023
Optimal Capital Budget
• The optimal capital budget is defined as the set of projects that
maximizes the value of firm.
Optimal Capital Budget
• According to traditional finance theory, all projects with positive
NPVs should be accepted in order to increase the value of firms.
• However, in reality, it may not be possible. Firms may not be able
to accept all projects.
33
11/19/2023
Optimal Capital Budget
• An important complication that arises while accepting all projects
with the positive NPVs pertains to increase in the cost of capital as
the size of capital budget increase.
• Therefore, it makes it hard for analysts to know the proper
discount rate to use when evaluating projects. Without accurate
information about discount rate, it is not possible to compute
accurate NPV.
Optimal Capital Budget
• Taking care of this complication is important because a project
might have a positive NPV if it is part of a $10 million capital
budget, but the same project might have a negative NPV if it is part
of a $20 million capital budget because the cost of capital might
increase.
34
11/19/2023
Optimal Capital Budget
• Therefore, when a rising cost of capital is encountered, we should
proceed in two steps:
• Construct investment opportunity schedule (IOS)
• Construct marginal cost of capital (MCC) schedule
Optimal Capital Budget
• Investment Opportunity Schedule (IOS) can be constructed as
follows:
• Find the IRR (or MIRR) for all potential projects
• Rank them (from highest IRR to lowest IRR) along with their initial costs
• Plot them on a graph with the IRR on the vertical axis and the cumulative
costs on the horizontal axis. The line is called the Investment
Opportunity Schedule (IOS).
35
11/19/2023
Optimal Capital Budget
• As the next step, construct the marginal cost of capital (MCC)
schedule as follows:
• Determine how much capital can be raised before it is necessary to issue
new higher-cost security
• Identify the amounts of higher-cost capital
• Use this information to calculate the WACC (opportunity cost of capital)
that corresponds to different amounts of capital raised
• The increasing WACC represents the marginal cost of capital, and
its graph is called the Marginal Cost of Capital (MCC) schedule.
Optimal Capital Budget
Example 1
• Use the following data to identify the optimal capital budget.
36
11/19/2023
Optimal Capital Budget
Example 1
• The data has already constructed the investment opportunity
schedule (IOS) by ranking the projects according to their IRR.
• The marginal cost of capital (MCC) schedule is also reported by
showing the WACC (opportunity cost of capital) associated with
the rising size of capital budget.
Optimal Capital Budget
Example 1
• Following figure plots the IOS and the MCC for the example.
37
11/19/2023
Optimal Capital Budget
Example 1
• The intersection of the IOS and the MCC schedules indicates the
amount of capital the firm should raise and invest.
• In our example, the firm should have a capital budget of $400. It
will allow the firm to accept projects A, B, C, and D with the WACC
of 10%. The 10% WACC should be used for average-risk projects.
Miscellaneous Issues in the WACC
Final Look at Risk and Discounted Cash Flows
38
11/19/2023
Final Look at Risk and Discounted Cash Flows
Certainty Equivalent
• Usually, managers apply a single discount rate to all future cash
flows. The use of a constant discount rate assumes that project
risk does not change.
• This assumption is faulty because the risks to which companies
are exposed are constantly shifting.
• How should we deal with such faulty assumptions?
Final Look at Risk and Discounted Cash Flows
Certainty Equivalent
• We should convert the expected cash flows to certainty
equivalents.
• How?
39
11/19/2023
Final Look at Risk and Discounted Cash Flows
Certainty Equivalent
• Suppose, you are considering construction of an office building
that you plan to sell after one year for $400000.
• Since that cash flow is uncertain, you discount at a risk-adjusted
discount rate of 12% rather than the 7% risk-free rate of interest.
• This gives a present value of $357143 [= $400000/1.12].
Final Look at Risk and Discounted Cash Flows
Certainty Equivalent
• Suppose that a real estate company approaches you and offers to
fix the price at which it will buy the building from you at the end of
the year.
• This guarantee would remove any uncertainty about the payoff on
your investment. So you would accept a lower figure than the
uncertain payoff of $400000.
40
11/19/2023
Final Look at Risk and Discounted Cash Flows
Certainty Equivalent
• But how much less?
Final Look at Risk and Discounted Cash Flows
Certainty Equivalent
• If the building has a present value of $357143 and the risk-free
interest rate is 7%, then:
Certain Cash Flow
1  0.07 
 Certain Cash Flow  $382143
PV  $357143 
41
11/19/2023
Final Look at Risk and Discounted Cash Flows
Certainty Equivalent
• In other words, a certain cash flow of $382143 has exactly the
same present value as an expected but uncertain cash flow of
$400000. The cash flow of $382143 is, therefore, known as the
certainty-equivalent cash flow.
Final Look at Risk and Discounted Cash Flows
Certainty Equivalent
• Our example illustrates two ways to value a risky cash flow C1.
• Method 1: Discount the risky cash flow at a risk-adjusted discount rate r.
The risk-adjusted discount rate adjusts for both time and risk.
• Method 2: Find the certainty-equivalent cash flow and discount at the
risk-free interest rate. When you use this method, you need to ask, What is
the smallest certain payoff for which I would exchange the risky cash flow
C1?
42
11/19/2023
Final Look at Risk and Discounted Cash Flows
Certainty Equivalent
• Both methods are shown below:
Final Look at Risk and Discounted Cash Flows
Certainty Equivalent
• The above-mentioned methods lead us to the following:
PV 
Ct
CEQ t

1  r t 1  rf t
• In the above expression, CEQ is the certainty equivalent of C. It is
discounted at risk-free rate because there is no risk in it.
43
11/19/2023
Final Look at Risk and Discounted Cash Flows
When to Use a Single Risk-Adjusted Discount Rate
• We are now in a position to examine what is implied when a
constant risk-adjusted discount rate, r, is used to calculate a
present value.
• Consider Project-A with the following uncertain cash flows and
discount rate of 12%.
Final Look at Risk and Discounted Cash Flows
When to Use a Single Risk-Adjusted Discount Rate
• Consider Project-B with the following certain cash flows and riskfree rate of 6%.
• Note that the present value of each year’s cash flow is identical for
the two projects.
44
11/19/2023
Final Look at Risk and Discounted Cash Flows
When to Use a Single Risk-Adjusted Discount Rate
• Year 1: Present value of risky cash flow of $100 from Project-A has
the same present value as the safe cash flow of $94.6 from ProjectB. Therefore $94.6 is the certainty equivalent of $100.
• Since the two cash flows have the same present value, investors
must be willing to give up $5.4 [=$100 - $94.6] in expected income
in year 1 to get rid of the uncertainty.
Final Look at Risk and Discounted Cash Flows
When to Use a Single Risk-Adjusted Discount Rate
• Year 2: Investors are willing to give up $10.4 [=$100 - $89.6] in
expected income in year 2 to get rid of the uncertainty.
• Year 3: Investors are willing to give up $15.2 [=$100 - $84.8] in
expected income in year 3 to get rid of the uncertainty.
45
11/19/2023
Final Look at Risk and Discounted Cash Flows
When to Use a Single Risk-Adjusted Discount Rate
• To value Project-A, you discounted each cash flow at the same riskadjusted discount rate of 12%.
• Now you can see what is implied when you did that. By using a
constant rate, you effectively made a larger deduction for risk from
the later cash flows:
Final Look at Risk and Discounted Cash Flows
When to Use a Single Risk-Adjusted Discount Rate
• The second cash flow is riskier than the first because it is exposed
to two years of market risk. The third cash flow is riskier still
because it is exposed to three years of market risk. This increased
risk is reflected in the steadily declining certainty equivalents:
46
11/19/2023
Final Look at Risk and Discounted Cash Flows
When to Use a Single Risk-Adjusted Discount Rate
• Our example illustrates that if we are to use the same discount rate
for every future cash flow, then the certainty equivalents must
decline steadily as a fraction of the cash flow.
• There’s no law of nature stating that certainty equivalents have to
decrease in this smooth and regular way. It may be a fair
assumption for most projects most of the time, but not all of the
time.
Final Look at Risk and Discounted Cash Flows
Divergence…
• You sometimes hear people say that because distant cash flows are
riskier, they should be discounted at a higher rate than earlier cash
flows. That is quite wrong. We have just seen that using the same
risk-adjusted discount rate for each year’s cash flow implies a
larger deduction for risk from the later cash flows. The reason is
that the discount rate compensates for the risk borne per period.
The more distant the cash flows, the greater the number of periods
and the larger the total risk adjustment.
47
11/19/2023
Final Look at Risk and Discounted Cash Flows
When You Cannot Use a Single Risk-Adjusted Discount Rate
• Sometimes you will encounter problems where risk does change
as time passes, and the use of a single risk-adjusted discount rate
will then get you into trouble.
Final Look at Risk and Discounted Cash Flows
When You Cannot Use a Single Risk-Adjusted Discount Rate
• Example: Vegetron has come up with an electric mop and it is
ready to go ahead with pilot production and test marketing. The
preliminary phase will take one year and cost $125000.
Management feels that there is only a 50% chance that
preliminary phase will be successful. If they are, then Vegetron will
build a $1 million plant that would generate an expected annual
cash flow in perpetuity of $250000 a year after taxes. If they are
not successful, the project will have to be dropped.
48
11/19/2023
Final Look at Risk and Discounted Cash Flows
When You Cannot Use a Single Risk-Adjusted Discount Rate
• The expected cash flows (in thousands of dollars) are:
• Management considers this project extremely risky and discounts
the cash flows at 25%.
Final Look at Risk and Discounted Cash Flows
When You Cannot Use a Single Risk-Adjusted Discount Rate
• Management’s analysis is open to criticism if the first year’s
experiment resolves a high proportion of the risk. If the test phase
is a failure, then there’s no risk at all—the project is certain to be
worthless. If it is a success, there could well be only normal risk
from then on. That means there is a 50% chance that in one year
Vegetron will have the opportunity to invest in a project of normal
risk, for which the normal discount rate of 10 % would be
appropriate.
49
11/19/2023
Final Look at Risk and Discounted Cash Flows
When You Cannot Use a Single Risk-Adjusted Discount Rate
• Thus, the firm has a 50% chance to invest $1 million in a project
with a net present value of $1.5 million:
Final Look at Risk and Discounted Cash Flows
When You Cannot Use a Single Risk-Adjusted Discount Rate
• Thus, we could view the project as offering an expected payoff of
0.5(1500) + 0.5(0) = 750 or $750000 at t = 1 on a $125000
investment at t = 0.
50
11/19/2023
Final Look at Risk and Discounted Cash Flows
When You Cannot Use a Single Risk-Adjusted Discount Rate
• Of course, the certainty equivalent of the payoff is less than
$750000, but the difference would have to be very large to justify
rejecting the project.
• For example, if the certainty equivalent is half the forecasted cash
flow and the risk-free rate is 7%, the project is worth $225500:
Miscellaneous Issues in the WACC
References
51
11/19/2023
References
52