Case Study 2: S&S Air Goes Public
Slide 1
12-1
Cost of Capital
Slide 2
12-2
Key Concepts and Skills
• Know how to determine:
– A firm’s cost of equity capital
– A firm’s cost of debt
– A firm’s overall cost of capital
• Understand pitfalls of overall cost of capital and how to manage them
From our modules on capital budgeting, we learn that the discount rate, or required return, on an investment
is a critical input. However, we haven’t discussed how to come up with that particular number. This module
brings together many of our earlier discussions dealing with stocks and bonds, capital budgeting, and risk
and return. Our goal is to illustrate how firms go about determining the required return on a proposed
investment. Understanding required returns is important to everyone because all proposed projects must
offer returns in excess of their required returns to be acceptable.
In this module, we learn how to compute a firm’s cost of capital and find out what it means to the firm and
its investors. We will also learn when to use the firm’s cost of capital and, perhaps more important, when
not to use it.
Why is it important? A good estimate is required for:
• good capital budgeting decisions—neither the NPV rule nor the IRR rule can be implemented without knowledge of the appropriate discount rate
• financing decisions—the optimal/target capital structure minimizes the cost of capital • operating decisions—cost of capital is used by regulatory agencies in order to determine the “fair”
return in some regulated industries (e.g. utilities)
Slide 3
12-3
Chapter Outline
• The Cost of Capital: Some Preliminaries
• The Cost of Equity (RE)
• The Costs of Debt (RD) and Preferred Stock (RP)
• The Weighted Average Cost of Capital (WACC)
• Divisional and Project Costs of Capital
Slide 4
12-4
Cost of Capital Basics
• The cost to a firm for capital funding = the return to the providers of those funds – The return earned on assets depends on the
risk of those assets
– A firm’s cost of capital indicates how the market views the risk of the firm’s assets
– A firm must earn at least the required return to compensate investors for the financing they have provided
– The required return is the same as the appropriate discount rate
Cost of capital, required return, and appropriate discount rate are different phrases that all refer to the
opportunity cost of using capital in one way as opposed to alternative financial market investments of the
same systematic risk.
• Required return is from an investor’s point of view.
• Cost of capital is the same return from the firm’s point of view.
• Appropriate discount rate is the same return used in a PV calculation.
Slide 5
12-5
Cost of Equity
• The cost of equity is the return required by equity investors given the risk of the cash flows from the firm
• Two major methods for determining the cost of equity
▪Dividend growth model
▪SML or CAPM
The Cost of Equity = Return required by shareholders.
✓ Dividend Growth Model (or called Gordon Growth Model)
• RE = (D1 / P0) + g
✓ Capital Asset Pricing Model (CAPM - derived from the Security Market Line ((SML))
• RE = Rf + [E(RM) - Rf]
12-6
The Dividend Growth Model Approach
Start with the dividend growth model formula and rearrange to solve for RE
g P
D R
gR
D P
0
1 E
E
1 0
+=
− =
According to the dividend growth model,
P0 = D1 ⁄ (RE − g)
Rearranging and solving for the cost of equity gives:
RE = (D1 ⁄ P0) + g
which is equal to the dividend yield (D1 / P0) plus the capital gains yield, g (growth rate).
Note that D1 = D0(1+g).
Implementing the Approach
• Price and latest dividend are directly observed; g must be estimated. • Estimating g – typically use historical growth rates or analysts’ forecasts.
Slide 7
12-7
Example: Dividend Growth Model
• Your company is expected to pay a dividend of $4.40 per share next year. (D1)
• Dividends have grown at a steady rate of 5.1% per year and the market expects that to continue. (g)
• The current stock price is $50. (P0)
• What is the cost of equity?
139.051. 50
40.4 RE =+=
Slide 8
12-8
Example: Estimating the Dividend Growth Rate
• One method for estimating the growth rate is to use the historical average
Year Dividend Percent Change
2009 1.23
2010 1.30
2011 1.36
2012 1.43
2013 1.50
(1.30 – 1.23) / 1.23 = 5.7%
(1.36 – 1.30) / 1.30 = 4.6%
(1.43 – 1.36) / 1.36 = 5.1%
(1.50 – 1.43) / 1.43 = 4.9%
Average = (5.7 + 4.6 + 5.1 + 4.9) / 4 = 5.1%
g can be estimated using the historical average.
Our historical growth rates are fairly close, so we could feel reasonably comfortable that the market will
expect our dividend to grow at around 5.1%. Note that when we are computing our cost of equity, it is
important to consider what the market expects our growth rate to be, not what we may know it to be
internally. The market price is based on market expectations, not our private information. So, another way
to estimate the market consensus estimate is to look at analysts’ forecasts and take an average.
Slide 9
12-9
Advantages and Disadvantages of Dividend Growth Model
• Advantage – easy to understand and use
• Disadvantages
– Only applicable to companies currently paying dividends
– Not applicable if dividends aren’t growing at a reasonably constant rate (eg. 5.7->10.5->2.4->8.6)
– RE is extremely sensitive to the estimated growth rate
– Does not explicitly consider risk
Advantages and Disadvantages of the Approach
-Approach only works for dividend paying firms
-RE is very sensitive to the estimate of g.
-Historical growth rates may not reliably predict future growth rates.
-Risk is only indirectly accounted for by the use of the price.
You may question how you value the stock for a firm that doesn’t pay dividends. In the case of growth-
oriented, non-dividend-paying firms, analysts often look at the trend in earnings or use similar firms to
project the future date of the first expected dividend and its future growth rate. However, such processes
are subject to greater estimation error, and when companies fail to meet (or even exceed) estimates, the
stock price can experience a high degree of variability. It should also be pointed out that no firm pays zero
dividends forever – at some point, every going concern will pay dividends. Microsoft is a good example.
Many people believed that Microsoft would never pay dividends, but even it ran out of investments for all
of the cash that it generated and began paying dividends in 2003.
Slide 10
12-10
The SML Approach
• Use the following information to compute the cost of equity
▪ Risk-free rate, Rf ▪ Market risk premium, E(RM) – Rf ▪ Systematic risk of asset,
)R)R(E(RR fMEfE −+=
Another method for determining the cost of equity (RE)
You will often hear this referred to as the Capital Asset Pricing Model Approach as well. Betas are widely
available and T-bill rates are often used for Rf. The S&P 500 returns are usually used for the required return
on the market E(RM).
Visit finance.yahoo.com. Both betas and 3-month T-bills are available on this site. To get betas, enter a
ticker symbol to get the stock quote, then choose Key Statistics. To get the T-bill rates, click on “Bonds”
under Investing on the home page.
Slide 11
12-11
Example: SML
• Company’s equity beta = 1.2
• Current risk-free rate = 7%
• Expected market risk premium = 6%
• What is the cost of equity capital?
%2.14)6(2.17RE =+=
Slide 12
12-12
Advantages and Disadvantages of SML
• Advantages
– Explicitly adjusts for systematic risk
– Applicable to all companies, as long as beta is available
• Disadvantages
– Must estimate the expected market risk premium,
which does vary over time
– Must estimate beta, which also varies over time
– Relies on the past to predict the future, which is not
always reliable
Advantages and Disadvantages of the Approach
-This approach explicitly adjusts for risk in a fashion that is consistent with capital market history.
-It is applicable to virtually all publicly traded stocks.
-The main disadvantage is that the past is not a perfect predictor of the future, and both beta and the
market risk premium vary through time.
The two approaches may result in slightly different estimates. Why?
The underlying assumptions of the two approaches are very different. The constant (dividend) growth
model is a variant of a growing perpetuity model and requires that dividends are expected to grow at a
constant rate forever and that the discount rate is greater than the growth rate. The SML approach requires
assumptions of normality of returns and/or quadratic utility functions. It also requires the absence of
taxes, transaction costs, and other market imperfections.
Slide 13
12-13
Example: Cost of Equity
• Suppose our company has a beta of 1.5. The market risk premium is expected to be 9%, and the current risk-free rate is 6%.
• We have used analysts’ estimates to determine that the market believes our dividends will grow at 6% per year and our last dividend was $2.
• Our stock is currently selling for $15.65. What is our cost of equity?
▪ Using SML: RE = 6% + 1.5(9%) = 19.5%
▪ Using DGM: RE = [2(1.06) / 15.65] + .06 = 19.55%
Since the two models are reasonably close, we can assume that our cost of equity is probably around 19.5%.
Again, though, this similarity is a function of the inputs selected and is not indicative of the true similarity
that could be expected.
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12-14
Cost of Debt
• The cost of debt (RD) = the required return on a company’s debt
• Method 1 = Compute the yield to maturity on existing debt
• Method 2 = Use estimates of current rates based on the bond rating expected on new debt
• The cost of debt is NOT the coupon rate
Cost of debt (RD) – the interest rate on new debt can easily be estimated using the yield to maturity on
outstanding debt or by knowing the bond rating and looking up rates on new issues with the same rating.
We usually focus on the cost of long-term debt or bonds. The required return is best estimated by computing
the yield-to-maturity on the existing debt. We may also use estimates of current rates based on the bond
rating we expect when we issue new debt.
The cost of debt is equal to the yield to maturity because it is the market rate of interest that would be
required on new debt issues. The coupon rate, on the other hand, is the firm’s promised interest payments
on existing debt.
The coupon rate was the cost of debt for the company when the bond was issued. We are interested in the
rate we would have to pay on newly issued debt, which could be very different from past rates.
Slide 15
12-15
• Suppose we have a bond issue currently outstanding that has 15 years left to maturity.
• The coupon rate is 12%, and coupons are paid semiannually.
• The bond is currently selling for $1,253.72 per $1,000 bond.
• What is the cost of debt?
Example: Cost of Debt
Slide 16
12-16
Example: Cost of Debt
Current bond issue:
– 15 years to maturity
– Coupon rate = 12%
– Coupons paid semiannually
– Currently bond price
= $1,253.72
30 N
-1253.72 PV
1000 FV
60 PMT
CPT I/Y 4.45%
YTM = 4.45%*2 = 8.9%
N = 30; PMT = 60; FV = 1000; PV = -1,253.72; CPT I/Y = 4.45%; YTM = 4.45(2) = 8.9%
Slide 17
12-17
Cost of Preferred Stock
• Preferred pays a constant dividend every period
• Dividends expected to be paid forever
• Preferred stock is a perpetuity
0
P P
D R =
Preferred stock is generally considered to be a perpetuity, so you rearrange the perpetuity equation to get
the cost of preferred, RP
RP = D ⁄ P0
Slide 18
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• Your company has preferred stock that has an annual dividend of $3.
• If the current price is $25, what is the cost of preferred stock?
• RP = 3 / 25 = 12%
Example: Cost of Preferred Stock
Slide 19
12-19
Weighted Average Cost of Capital
• We can use the individual costs of capital (RE, RP, RD) to compute a weighted “average” cost of capital for the firm
• This “average” is the required return on the firm’s assets, based on the market’s perception of the risk of those assets
• The weights are determined by how much of each type of financing is used
One of the most important concepts we develop is that of the weighted average cost of capital (WACC).
This is the cost of capital for the firm as a whole, and it can be interpreted as the required return on the
overall firm.
The WACC is the minimum return a company needs to earn to satisfy all of its investors, including
stockholders, bondholders, and preferred stockholders.
Slide 20
12-20
Capital Structure Weights
• Notation
E = market value of equity
= # outstanding shares X price per share
D = market value of debt
= # outstanding bonds X bond price
V = market value of the firm = D + E
• Weights
wE = E/V = percent financed with equity
wD = D/V = percent financed with debt
Note that for bonds we would find the market value of each bond issue and then add them together. Also
note that preferred stock would just become another component of the equation if the firm has issued it.
Finally, we generally ignore current liabilities in our computations. However, if a company finances a
substantial portion of its assets with current liabilities, it should be included in the process.
E = market value of the firm’s equity = # of outstanding shares times stock price per share
D = market value of the firm’s debt = # of bonds times price per bond or take bond quote as percent of par
value and multiply by total par value
V = combined market value of the firm’s equity and debt = E + D (Assuming that there is no preferred
stock and current liabilities are negligible. If this is not the case, then you need to include these components
as well. This is really just the market value version of the balance sheet identity. The market value of the
firm’s assets = market value of liabilities + market value of equity.)
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12-21
• Suppose you have a market value of equity equal to $500 million and a market value of debt equal to $475 million.
▪ What are the capital structure weights? • V = 500 million + 475 million = 975 million
• wE = E/V = 500 / 975 = .5128 = 51.28%
• wD = D/V = 475 / 975 = .4872 = 48.72%
Example: Capital Structure Weights
Assuming that there is no preferred stock
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Taxes and the WACC
• We are concerned with after-tax cash flows, so we also need to consider the effect of taxes on the various costs of capital
• Interest expense reduces our tax liability ▪ This reduction in taxes reduces our cost of debt
▪ After-tax cost of debt = RD(1-TC)
• Dividends are not tax deductible, so there is no tax impact on the cost of equity
• WACC = wERE + wDRD(1-TC)
• wE = E/V = percent financed with equity
• wD = D/V = percent financed with debt 14-22
Assuming that there is no preferred stock
After-tax cash flows require an after-tax discount rate. Let TC denote the firm’s marginal tax rate. Then,
the weighted average cost of capital is:
WACC = (E⁄V)RE + (D⁄V)RD(1−TC)
With preferred stock:
WACC = (E⁄V)RE + (D⁄V)RD(1−TC) + (P⁄V)RP
The Tax Cuts and Jobs Act of 2017 placed limitations on the amount of interest that can be deducted in
certain situations. If there is no deduction, then the pretax and aftertax cost of debt would be equal. If any
deduction is allowed, then the aftertax cost would be lower.
With a lower tax rate and/or less deductibility, the overall WACC would be higher, which would reduce
project/firm value. However, the lower tax rate also increases cash flows, which would increase
project/firm value. The latter seems to be the dominant impact.
Slide 23
12-23
WACC
WACC = [(E/V) x RE ] + [(P/V) x RP ] + [(D/V) x RD x (1- TC)]
Where:
(E/V) = % of common equity in capital structure
(P/V) = % of preferred stock in capital structure
(D/V) = % of debt in capital structure
RE = firm’s cost of equity
RP = firm’s cost of preferred stock
RD = firm’s cost of debt
TC = firm’s corporate tax rate
Weights
Component
costs
WACC—overall return the firm must earn on its assets to maintain the value of its stock. It is a market
rate that is based on the market’s perception of the risk of the firm’s assets.
Without preferred stock:
WACC = (E ⁄ V)RE + (D ⁄ V)RD(1 − TC)
Slide 24
12-24
Extended Example: WACC - I
• Equity Information
▪ 50 million shares
▪ $80 per share
▪ Beta = 1.15
▪ Market risk premium = 9%
▪ Risk-free rate = 5%
• Debt Information
▪ $1 billion in outstanding debt (face value)
▪ Current quote = 110% of face value
▪ Coupon rate = 9%, semiannual coupons
▪ 15 years to maturity
• Tax rate = 40% 14-24
Assuming that there is no preferred stock.
Note that bond prices are quoted as a percent of par value.
Slide 25
12-25
Extended Example: WACC - II
• What is the cost of equity?
▪ RE = 5 + 1.15(9) = 15.35% (Using CAPM)
• What is the cost of debt?
▪ N = 30; PV = -1,100; PMT = 45; FV = 1,000; CPT I/Y = 3.9268
▪ RD = 3.927(2) = 7.854%
• What is the after-tax cost of debt?
▪ RD(1-TC) = 7.854(1-.4) = 4.712%
14-25
Dividend growth model cannot be used since no information is provided in this example. Let’s use
CAPM (SML) to estimate RE.
We assume that the interest expense remains fully deductible.
Slide 26
12-26
Extended Example: WACC - III
• What are the capital structure weights?
▪ E = 50 million (80) = 4 billion
▪ D = 1 billion (1.10) = 1.1 billion
▪ V = 4 + 1.1 = 5.1 billion
▪ wE = E/V = 4 / 5.1 = .7843
▪ wD = D/V = 1.1 / 5.1 = .2157
• What is the WACC?
▪ WACC = .7843(15.35%) + .2157(4.712%) = 13.06%
14-26
WACC – overall return the firm must earn on its assets to maintain the value of its stock. It is a market
rate that is based on the market’s perception of the risk of the firm’s assets.
Slide 27
12-27
Extended Example: WACC I, II, III - Summary
Cost of capital:
RE = 5 + 1.15 x (9) = 15.35%
RD = 3.927 x (2) = 7.854%
RD x (1-TC) = 7.854 x (1-.4) = 4.712% Weights:
•WE = E/V = 4/ 5.1 = 0.7843
•WD = D/V = 1.1 / 5.1 = 0.2157
Component Values:
• E = 50 million x (80) = 4 billion
• D = 1 billion x (1.10) = 1.1 billion
• V = 4 + 1.1 = 5.1 billion
WACC = [(E/V) x RE ] + [(P/V) x RP ] + [(D/V) x RD x (1- TC)]
Component W R
Debt (after tax) 0.2157 4.712%
Common equity 0.7843 15.35%
WACC = .7843 x (15.35%) + .2157 x (4.712%) = 13.06%
Assume that there is no preferred stock.
WACC = .7843 x (15.35%) + .2157 x (4.712%) = 13.06%
If the firm issues preferred stock, WACC will be computed as:
E.g., Preferred Stock Information
• 5 million shares
• Annual dividend of $3
• Current price is $25
Cost of Preferred Stock = RP = 3 / 25 = 12%
Component Values:
E = 50 million x (80) = 4 billion
D = 1 billion x (1.10) = 1.1 billion
P = 5 million x (25) = 0.512 billion
V = 4 + 1.1 + 0.512= 5.612 billion
Weights:
WE = E/V = 4/ 5.612 = 0.7128
WD = D/V = 1.1 / 5.612 = 0.196
Wp = P/V = 0.512 / 5.612 = 0.0912
WACC = .7128 x (15.35%) + .196 x (4.712%) + 0.0912 x (12%)
= 10.94% + 0.924% + 1.094% = 12.96%
Slide 28
12-28
Factors that Influence a Company’s WACC
• Market conditions, especially interest rates, tax rates and the market risk premium
• The firm’s capital structure and dividend policy
• The firm’s investment policy – Firms with riskier projects generally have a
higher WACC
If market interest rates rise, then both the cost of equity and debt will rise.
If the market risk premium increases, then the cost of equity increases.
The firm’s capital structure affects the division between debt and equity and the weights in the WAC
equation.
Dividend policy affects the amount of retained earnings available for internal use and thus the amount of
external funding required.
Slide 29
3:11PM (EST), 2012
12-29
Eastman Chemical Equity Data
Source: http://finance.yahoo.com
Several web sites are utilized to find the information required to compute the WACC.
Go to Yahoo! Finance to get information on Eastman Chemical (EMN).
Under Profile and Key Statistics, you can find the following information:
• # of shares outstanding
• Book value per share
• Price per share
• Beta
Stock price: 53.74
Beta: 2.31
Last year dividend: 1.04
Slide 30
12-30
Eastman Chemical -
Beta and Shares
Outstanding
Source: http://finance.yahoo.com
Under Key Statistics
Number of share outstanding: 136.92 mil
Slide 31
12-31
Source: http://finance.yahoo.com
Eastman Chemical Dividend Growth
Under analysts estimates, you can find analysts’ estimates of earnings growth (use as a proxy for dividend
growth)
Analyst’s estimated dividend growth rate: 7.67
Slide 32
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Eastman Chemical Cost of Equity - SML
• Beta: Yahoo Finance 2.31
Reuters.com 1.25
(1.25 is a more reasonable value)
• T-Bill rate = 0.05% (Yahoo Finance bonds section)
• Market Risk Premium = 7% (assumed)
• Cost of Equity (SML) = 0.05% + (7%)(1.25) = 8.80%
Estimates at 3:11PM (EST), 2012
)R)R(E(RR fMEfE −+=
Eastman’s beta on Yahoo! is 2.31, which is much higher than the beta of the average stock. To check this
number, we went to www.reuters.com. The beta estimates we found there was 1.25. This estimate is more
realistic, and some financial judgment is required here. Because the beta estimate from Yahoo! is so much
higher, we will ignore it and use the beta of 1.25. Thus, the beta estimate we will use is 1.25.
The Bonds section at Yahoo! Finance can provide the T-bill rate.
Use this information, along with the CAPM and DGM, to estimate the cost of equity.
Alternatively, we can use an average of betas from three four sources (finance.yahoo.com,
finance.google.com, www.reuters.com, and www.valueline.com).
Why do four Web sites report four different betas for the same stock?
There is more than one way to calculate betas. One of the variables in the beta calculation is how far
back you go with the calculation. Some calculations are based on three or four years of data, while others
are based on five or six years of numbers. These variables and others can make a difference in the beta
that is reported. Most sites don’t provide information on how many of their numbers were calculated –
many sites buy the data from vendors. Your best bet is to stick with names you know and trust and if you
want to compare companies, use the same web site since the numbers should be consistent that way.
https://www.thebalance.com/betas-aid-in-stock-trading-but-which-beta-do-you-use-3141356
https://www.wallstreetoasis.com/forums/where-to-find-stocks-beta
Slide 33
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Eastman Chemical Cost of Equity - DCF
• Growth rate 7.67%
• Last dividend $1.04
• Stock price $53.74
• Cost of Equity (DCF) =
%75.9
0767. 74.53
)0767.1(04.1$
0
1
=
+=
+=
E
E
E
R
R
g P
D R
Use this information, along with the CAPM and DGM, to estimate the cost of equity.
Slide 34
12-34
Eastman Chemical - 7 Cost of Equity
Cost of Equity Method Estimated Value
SML 8.80%
DCF 9.75%
Average (RE) 9.28%
Slide 35
12-35
Eastman Chemical Bond Data
Source: http://www.sec.gov
Go to the SEC website to get book value information from the firm’s most recent 10Q
Slide 36
12-36
Eastman Chemical Cost of Debt
• For Eastman, the cost of debt is similar when using either
book values or market values.
Avg. of YTM = RD
Go to FINRA's Market Data Center at http://finra-markets.morningstar.com/MarketData/ to get market
information on Eastman Chemical’s bond issues.
✓ Enter “Eastman Ch” to find the bond information. ✓ Note that you may not be able to find information on all bond issues due to the illiquidity of the bond
market.
Go to the SEC website to get book value information from the firm’s most recent 10Q.
Market values of debts: 1661 mil
The average YTM is the weighted average of the yields on the bond issues, weighted by the percent of
each issue’s market value on the total market value of outstanding debt.
Slide 37
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Capital structure weights (market values):
E = 136.92 million x $53.74 = $7.358 billion
D = 1.661 billion
V = $7.358 + 1.661 = 9.019 billion
E/V = 7.358 / 9.019 = .82
D/V = 1.661 / 9.019 = .18
3.81 = RD 9.28 = RE Tax rate (assumed) = 35%
WACC = .82(9.28%) + .18(3.81%)(1-.35)
= 8.02%
Eastman Chemical - 10 WACC
Slide 38
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Risk-Adjusted WACC
• Using the WACC as our discount rate is only appropriate for projects that have the same risk as the firm’s current operations.
• If we are looking at a project that does NOT have the same risk as the firm, then we need to determine the appropriate discount rate for that project.
• Divisions also often require separate discount rates.
It is important to know that a single corporate WACC is not very useful for companies that have several
disparate divisions.
A firm’s WACC is an average applicable only to projects with the same risk.
If a proposed project has a risk significantly different from the firm’s average projects, then the WACC
should be adjusted to reflect that additional risk.
Eg. GE
If GE’s WACC was used for every division, then the riskier divisions would get more investment capital
and the less risky divisions would lose the opportunity to invest in positive NPV projects.
Slide 39
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Using WACC for All Projects
• What would happen if we use the WACC for all projects regardless of risk?
• Assume the WACC = 15%
Project Required Return IRR
A 20% 17%
B 15% 18%
C 10% 12%
If you use the firm’s WACC across divisions, then riskier divisions will receive more funding and less
risky divisions will have to forgo what would be good projects if the appropriate discount rate were used.
This will lead to an increase in risk for the overall firm.
Which projects would be accepted if you used the WACC for the discount rate? Compare 15% to IRR and
accept projects A and B.
Which projects should be accepted if you use the required return based on the risk of the project? Accept
B and C.
So, what happened when we used the WACC? We accepted a risky project that we shouldn’t have and
rejected a less risky project that we should have accepted. What will happen to the overall risk of the firm
if the company does this on a consistent basis? The firm will become riskier. What will happen to the
firm’s cost of capital as the firm becomes riskier? It will increase (adjusting for changes in market returns
in general) as well.
Slide 40
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Pure Play Approach
• Find one or more companies that specialize in the product or service being considered
• Compute the beta for each company
• Take an average
• Use that beta along with the CAPM to find the appropriate return for a project of that risk
• Pure play companies can be difficult to find
It is easy to find company betas; however, divisional betas are not readily available. The pure play
approach can be used to find divisional betas.
Basically, find a company that has a single line of business that is the same as the project under
consideration. If there is more than one pure play company, you can take an average of the betas to
determine the divisional beta.
Pure play – a company that has a single line of business. The idea is to find the required return on a near
substitute investment.
Slide 41
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Subjective Approach
• Consider the project’s risk relative to the firm overall
– If the project is riskier than the firm, use a discount rate greater than the WACC
– If the project is less risky than the firm, use a discount rate less than the WACC
– You may still accept projects that you shouldn’t and reject projects you should accept, but your error rate should be lower than not considering differential risk at all.
Subjective Approach - Assigns investment to “risk” categories that have higher or lower risk premiums
than the firm as a whole.
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Subjective Approach - Example
Risk Level Discount Rate
Very Low Risk WACC – 8% 6%
Low Risk WACC – 4% 10%
Same Risk as Firm WACC 14%
High Risk WACC + 6% 20%
Very High Risk WACC + 10% 24%
WACC = 14%