ADVANCED CORPORATE FINANCE
LECTURE 6
Risk
and
Cost of Capital
Learning Outcomes
▪ Calculating the cost of equity
▪ Discuss and explain how Beta is and should be determined
▪ Explain debt and asset Beta
▪ Evaluate the appropriate way to measure asset Betas in
the face of different types of risk.
▪ Calculating NPV of projects with multiple discount rates
▪ Explain and calculate Certainty Equivalent Cash Flows
Cost of Equity
▪ Capital Asset Pricing Model (CAPM):
requity = rf + β equity (rm − rf )
▪ Equity beta (ßequity) measures market risk →
Undiversifiable risk.
▪ ßequity measures how much the company returns
change for every 1% change in market return.
Example : Disney
Source : http://www.reuters.com/finance/stocks/overview?symbol=DBMS.KL accessed 9 Sept 2011
Estimating beta
▪ Future beta is usually not far off from past beta as
the beta of most stocks is quite stable over time
▪ By running a regression of four to five years of
monthly rates of return on a stock against the returns
on the market for the same months, the slope of the
regression line is an estimate of beta
▪ Beta tells us how much on average the stock price
changed for each additional one percent change in
the market index
Example : Campbell Soup
Example : CitiGroup
Estimating beta continued
▪ Total equity risk = Market risk + Unique risk
▪ Market risk is measured by R-squared (R2)
▪ Example: From 2008 to 2009 the R2 for Disney is 0.67. In
other words 67% of Disney’s risk was market risk and
33% was diversifiable risk (unique risk)
▪ Proportion of the total variance that can
be measured by market movements
▪ How well scatter point align on the “best
fit line”
▪ Unique risk is reflected in the scatter of points
around the regression line
Estimating beta continued
▪ Based on a 95% confidence interval, the equity beta
lies between:
▪ - 2 + 2
▪ Estimation errors of individual betas tend to cancel
out when you estimate beta of a portfolio e.g.
industry betas
▪ Industry betas which have lower standard errors
Issues in estimating beta
▪ Adjustment for thin trading
▪ Infrequently traded shares are underestimated
in the regression
▪ Adjustment for or mean reversion
▪ Betas tend to mean value of (1) over time
▪ It is always useful to check on the cost of
equity estimate using the dividend growth
formula or arbitrage pricing theory
What determines asset beta?
PV(fixed cost)
β assets = β revenue 1 +
PV(asset)
1. Cyclicality
• Lone prospectors in search of gold look
forward to extremely uncertain future
earnings
• Whether they strike it rich does not depend
on the performance of the market portfolio
• Therefore an investment in gold has a high
standard deviation but a relatively low beta
What determines asset beta? cont’d
o What really counts is the strength of
the relationship between the firm’s
earnings and the aggregate earnings
on all real assets
o Cyclical firms, firms whose revenues
and earnings are strongly dependent
on the state of the business cycle, tend
to be high-beta firms.
o You should demand a higher rate of
return from cyclical investments
What determines asset beta? cont’d
2. Operating leverage
o A production facility with high fixed cost,
relative to variable costs has high operating
leverage;
o Given the cyclicality of revenues (reflected in
βrevenue), the asset beta is proportional to the
ratio of the present value of fixed costs to the
present value of the project;
o Other things being equal, the alternative
with higher fixed costs relative to variable
costs or with the higher ratio of fixed costs to
project value is said to have higher operating
leverage and thus higher project beta.
Debt and asset beta
▪ Asset beta measures the average risk of the
firm’s existing business
▪ The firm’s asset beta is the beta of a portfolio of
all the firm’s debt and equity securities:
debt equity
β assets = β portfolio = β debt + β equity
debt + equity debt + equity
Debt and asset beta continued
• When a firm issues more debt to replace part of its
outstanding equity while holding the same assets,
asset beta (reflecting asset risk) does not change
• However the change of the debt ratio affects the
risk and thus the expected returns on the firm’s
existing debt and equity securities
Debt and asset beta (continued….)
▪ A higher debt ratio increases the default risk
and debt beta, so debtholders will demand a
higher interest rate;
▪ A higher debt ratio also increases the financial
risk to shareholders resulting in a higher equity
beta and a higher required return demanded by
shareholders;
Setting discount rate when you don’t have a beta
Three pieces of advice
1. Avoid adding fudge factors to the
discount rate to offset worries about
bad outcomes; adjust cash-flow
forecasts first
2. Think about the determinants of
asset betas; often the characteristics
of high-beta and low-beta assets can
be observed when the beta itself
cannot be
3. Don’t be fooled by diversifiable
project risk
Avoiding fudge factors
▪ People think of the risks of a
project as a list of things that
can go wrong
▪ For example, a geologist looking
for oil worries about the risk of a
dry hole or a pharmaceutical
manufacturer worries about the
risk that a new drug may not be
approved by the regulatory
authority
▪ Managers often add fudge factors
to offset worries such as these.
Avoid fudge factors (continued…)
▪ The bad outcomes reflect
unique risks that can be
diversified away in
shareholders’ portfolios and
would not increase the
expected return demanded
by shareholders
▪ If managers have given bad
outcomes their due weight
in cash-flow forecasts,
there is no need for a
discount rate adjustment
Adjust cash-flow forecast first
• Project cash flows are supposed to be unbiased
forecasts, which give due weight to all good and bad
outcomes
• The unbiased forecast is the sum of the probability-
weighted cash flows
Adjust cash-flow forecast first cont’d
Possible cash Probability Probability-weighted
flow ($M) Cash Flow ($M)
1.2 0.25 .3
1.0 0.50 .5
0.8 0.25 .2
Unbiased Forecast 1.0
At a 10% cost of capital, the present value is 1M/1.1 = $909,091
Adjust cash-flow forecast first cont’d
• If we introduce a 10% chance of a zero cash flow:
Possible cash Probability Probability-weighted
flow ($M) Cash Flow ($M)
1.2 .225 .27
1.0 .45 .45
0.8 .225 .18
0.0 .10 .00
Unbiased Forecast .90
• The present value is .90/1.1 = $818,182
Adjust cash-flow forecast first cont’d
• Now you can figure out the right fudge factor to add to
the discount rate to apply to the original $1 million
forecast to get the correct present value:
1,000,000
PV = = 818,182 Solve for r = 22.22%
(1 + r)
• If you have thought through possible cash flows to
make unbiased forecasts, you don’t need the fudge
factor of 12.22% here
When to use multiple discount rates
• Most projects produce cash flows for several years
• Firms generally assume that project risk (project beta)
is the same in every future period and use the same
risk-adjusted rate to discount each of these cash flows
• Distant cash flows are riskier and are discounted by a
greater number of periods
Multiple discount rates continued
Year Cash Flow PV at 10%
1 100 90.9
2 100 82.6
3 100 75.1
• The more distant the cash flows, the larger the total risk
adjustment as reflected in the steadily declining present values
Multiple discount rates continued
• For projects where risk and beta change as time
passes, you should break the project into segments
within which the same discount rate can be
reasonably used
Multiple discount rates example
• A firm is ready to go ahead with pilot production and
test marketing of a new product. The preliminary
phase will take one year and cost $125,000. There
is a 50 percent chance that pilot production and
market tests will be successful. If they are, the firm
will build a $1 million plant that would generate an
expected annual cash flow in perpetuity of $250,000
a year. The project will be dropped otherwise.
• The test phase requires a return of 25% while the
discount rate for normal risk is 10%.
Multiple Discount Rate Example continued
• Year 1: Two possible outcomes
Success NPVt=1 = -1M + 250,000/.10
= +$1.5M (50% chance)
Failure NPVt=1 = 0 (50% chance)
• Year 0: discount the expected payoff at 25%
NPVt=0 = -125,000 + [.5(1.5M)+.5(0)]/1.25
= +$475,000
Certainty Equivalent Cash Flows (CEQ)
Ct CEQt
PV = =
(1 + r ) t
(1 + rf ) t
The value of risk free cash flow that would make the
investor indifferent as to the choice between this
safe cash flow or an alternative risky cash flow.
Certainty Equivalent Method
Working Example
Project A is expected to produce CF = $100 mil for each of
three years. Given a risk free rate of 6%, a market premium
of 8%, and beta of .75, what is the PV of the project?
Project A
Year Cash Flow PV @ 12%
r = r f + B ( rm − r f )
1 100 89.3
= 6 + .75(8)
2 100 79.7
= 12%
3 100 71.2
Total PV 240.2
Now assume that the cash flows change, but are RISK FREE. What is
the new PV?
Certainty Equivalent Method
Project A Project B
Year Cash Flow PV @ 12% Year Cash Flow PV @ 6%
1 100 89.3 1 94.6 89.3
2 100 79.7 2 89.6 79.7
3 100 71.2 3 84.8 71.2
Total PV 240.2 Total PV 240.2
Since the 94.6 is risk free, we call it a Certainty Equivalent of the 100.
The difference between the 100 and the certainty equivalent (94.6) is 5.4%…this % can be
considered the annual premium on a risky cash flow
Risky cash flow
= certainty equivalent cash flow
1.054
Certainty Equivalent Method
100
Deduction Year 1 = = 94.6
Year Cash Flow CEQ 1.054
for risk
1 100 94.6 5.4 100
Year 2 = 2
= 89.6
2 100 89.6 10.4 1.054
3 100 84.8 15.2
100
Year 3 = 3
= 84.8
1.054
QUIZ 6
http://gg.gg/ACFQuiz6_March2020
