Chap14.pdf

CHAPTER 14
COST OF CAPITAL

Chapter 11 – PROJECT ANALYSIS AND
EVALUATION
 Lecture slides posted on blackboard
 For your own reading, will not be on the
exam
11-2

Chapter 14 – Cost of Capital
 The Cost of Capital – Equity, Debt, and Preferred
(Quick Review of DGM & CAPM)
 The Weighted Average Cost of Capital (WACC)
 Project Costs of Capital
 Flotation Costs and the WACC
14-3
– last piece to complete capital budgeting analysis

Cost of Capital
14-4
Banker: The
required return
must be…
CFO: Wow,
that’s my cost!

Cost of Capital
14-5
required return
(for investors)
Cost of capital
(to the firm)
required return = discount rate = cost of capital
more or less interchangeably
=

Cost of Capital
How do we determine the cost of capital/required return?
14-6
required return = discount rate = cost of capital
more or less interchangeably
Key principle – the return required on some asset/project depends on the risk of the asset
Key principle – The cost of capital depends primarily on the use of the funds, not the source of the funds.

14-7
Moscow
❑The cost of capital depends primarily on the
use of the funds (risk), not the source.
Travel agency
Pullman
Higher risk, higher
cost of capital

Importance of cost of capital
❑ Why is it important to determine Cost of Capital ?
Required return = discount rate = cost of capital
❑ How to determine a firm’s overall cost of capital?
– depends on the return required on the firm’s overall assets
14-8
Cost of Equity
Cost of Debt
Capital budgeting decisions (DCF analyses):
We need to know the required return (discount rate) for an
investment before we can compute the NPV and make a decision
about whether or not to take the investment
Corporate policy decisions:
the optimal capital structure (D/E) – minimizes the cost of capital

Cost of Equity
 The cost of equity (RE)
– the return required by equity investors, given the
risk of (the cash flows from) the firm
 There are two major methods for determining the
cost of equity
▪ Dividend growth model (DGM)
▪ CAPM (or SML)
14-9
Covered in FIN325
A quick review here
Chapter 13

The Dividend Growth Model Approach – Quick
Review
 Start with the dividend growth model (DGM)
(with constant growth)
14-10
D1 = D0(1+g)
RE = dividend yield (D1 / P0) + capital gains yield (g)
Rearrange, solve for RE

Example: Dividend Growth Model
Example – Suppose that your company is expected
to pay a dividend of $1.50 per share next year.
There has been a steady growth in dividends of
5.1% per year and the market expects that to
continue.
The current price is $25. What is the cost of
equity?
14-11

The Dividend Growth Model Approach
The dividend growth model (DGM) formula
14-12
D1 = D0(1+g)
❑ To use DGM, we need 3 pieces of information: D0 , P0 , and g.
❑ Which one is most difficult to get?
▪ the expected g for dividends, must be estimated.
❑ To estimate g:
▪ Use analysts’ forecasts of future growth rates -available
from a variety of sources, e.g. at yahoo.com, or zacks.com.
▪ Use historical growth rates

Advantages and Disadvantages of Dividend
Growth Model
Advantages and disadvantages of DGM:
 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
▪ Extremely sensitive to the estimated g —
an overestimation of g by 1% → an overestimation of RE by 1%
▪ Does not explicitly consider risk
14-13

Chapter 14 – Cost of Capital
 The Cost of Capital – Equity
(Quick Review of DGM & CAPM)
14-14

The CAPM (or SML) Approach
14-15
What is risk premium?
Risk premium = Expected return – risk-free rate
E(RE) – Rf = E (E(RM) – Rf)
CAPM (or SML) Approach: Link Expected Return to Risk
The risk premium on individual assets depends on:
▪ risk premium on the market portfolio (M)
▪ risk – the beta coefficient with respect to M
Nobel Prize
Wining Theory
E(RE) = Rf + E (E(RM) – Rf)

Expected Return and Risk
 According to CAPM, what type risk should matter for E(R)?
 Still remember Systematic vs. Unsystematic risk?
❑ Systematic risk – inflation, recession, interest rate
❑ Unsystematic risk – lighting strike, CEO heart attack, unexpected big order
Systematic !Unsystematic risk can be diversified away, not priced
Recession Lighting strike

Expected Return and Risk
❑According to CAPM, only Systematic risk matters in
determining E(R), unsystematic risk can be diversified away,
you will not be paid if you hold it.
❑How to measure systematic risk? – by Beta:
i =[COV(ri,rM)] / σ2
M
 measures: How individual security is correlated with market
portfolio.
❑An individual security’s total risk (2i) can be partitioned into
systematic and unsystematic risk:
What is the beta of the market? M = ?
2i = sys. risk + unsys. risk
= i2 M
2 + 2(ei)
M = 1

Expected Return and Risk (Basic Logic)
 In equilibrium, return-to-risk ratio should be the same for all assets.
 The ratio of risk premium to beta should be the same for any two securities, and to that of the market portfolio:
M
fM
i
firrErrE

−=
− )()(
CAPM
j
j
i
i
risk
Return
risk
Return=
Systematic risk ()
Risk premium
M = 1
Professor William Sharpe, Stanford
University, won the Nobel Prize in 1990

Sample Calculations for SML
βx = 1.25
E(rx) =3% + 1.25 (8%) = 13%
βy = .6
E(ry) =3% + 0.6 (8%) = 7.8%
Equation of the CAPM
E(ri) = rf + βi[E(rM) – rf]
If β = 1?
If β = 0?
Can we plot the return-risk
relation of these stocks?
E(rm) – rf = 8% – Market risk premium – Return per unit of sys. risk
rf = 3% – Risk-free rate
E(rm) – rf = 8% – Market risk premium (Return per unit of sys. Risk)
E(rm) = 11% – Market return
rf = 3% – Risk-free rate

E(r)
SML
ß
ßM1.0
RM=11%
3%
Rx=13%
ßx1.25
Ry=7.8%
ßy.6
8%
Graph of Sample Calculations
7-20
▪ =0 , ERriskfree=3%
▪ =0.6 , ER=7.8%
▪ =1, ERMkt=11%
▪ =1.25, ER=13%
Market risk premium
Equation of the CAPM
E(ri) = rf + bi [E(rM) – rf]
If all securities are correctly
priced (CAPM), they should plot
on SML.

Question 1
Southern Home Cookin’ just paid its annual dividend
of $0.65 a share. The stock has a market price of $13
and a beta of 1.2. The return on the U.S. Treasury bill
is 2.5 percent and the market return is 10.5 percent.
What is the cost of equity?
A. 9.60 percent
B. 12.10 percent
C. 12.60 percent
D. 15.10 percent
Answer: B – Not D
Re = 2.5% + 1.2  (10.5% – 2.5%)
= 12.10 percent
Wrong answer:
Re = 2.5% + 1.2  10.5%
= 2.5% + 12.60% =15.10 percent
Equation of the CAPM
E(ri) = rf + bi [E(rM) – rf]

The CAPM or SML Approach – A quick review
14-22
CAPM (or SML) Approach:
The risk premium on individual assets depends on:
▪ risk premium of market
▪ sys. risk (β)
Higher beta, higher return
High beta stock? Low beta stock?

E(r)
SML
ß
ERLVS
ßLVS2.0
ERMCD
ßMCD.38
Graph of Sample Calculations
7-23
Using past 10
years data:
E(R)LVS=28%
E(R)MCD=12%

 = +2% Positive  is good, Plot above SML
+  gives the buyer a positive abnormal return
E(rE(r))
15%15%
SMLSML
ßß1.01.0
RRmm=11%=11%
rrff=3%=3%
1.251.25
Disequilibrium Example
Suppose a security Q with β Q of ____ is offering an expected return of ____
According to the SML, the E(r) should be
___?__
1.25
15%
Underpriced: too cheap – offers too high of a return for its level of risk
The difference between the actual return and the return required for the risk
level as measured by the CAPM is called the stock’s alpha. What is the α in
this case?
E(r) = rf + β Q [E(rM) – rf]
=
Is the security under or overpriced?
13%
7-24
Q
3% + 1.25 (8%) = 13%
Mispricing

More on alpha and beta
E(rM) = 14%
βS = 1.5
rf = 5%
Required return(s) = rf + β S [E(rM) – rf]
=
If you believe the stock will actually provide a return of ____,
what is the implied alpha? Is the stock overpriced or
underpriced?
 =
5 + 1.5 [14 – 5] = 18.5%
17%
17% – 18.5% = – 1.5%, the stock is overpriced (too expensive)
A stock with a negative alpha plots below the SML & gives
the buyer a negative abnormal return

Measuring Beta
 Concept:
 Method
We need to estimate the relationship between the
security and the “Market” portfolio.
▪ using historical data of excess returns of the
security and the Market portfolio
▪ Use regression analysis to calculate the Security
Characteristic Line (SCL) and estimate beta
How to measure beta?

Security Characteristic Line (SCL)
Excess Returns (i)
.
.
…
.
. .
. ..
. .
.
. .
. ..
.
..
. .
. ..
. ..
. .
. .
.
. ..
. .
.
. … .. .. .
Excess returns
on market (M)
Ri =  i + ßiRM + ei
Slope = 
 – abnormal returnWhat should  be?
SCL
Dispersion of the points
around the line measures
__________________.Unsys. risk (e)
7-27
SCL equation:
E(ri) – rf = i + βi[E(rM) – rf]

Advantages and Disadvantages of
CAPM
 Advantages
▪ Explicitly adjusts for systematic risk
▪ Applicable to all companies, even companies that do not pay dividends! – as long as we can estimate beta.
 Disadvantages
▪ Have to estimate beta, which also varies over time
▪ Have to estimate the expected market risk premium, which does vary over time
▪ We are using the past to predict the future, which is not always reliable
14-28

Advantages and Disadvantages of CAPM
Takeaways or what to do – When estimate Beta?
❑ Looking at analyst forecasts may NOT be reliable
▪ especially if you have the skill to estimate beta yourself
❑ If you notice that there are business strategy changes
▪ you probably want to use the most recent data to estimate
beta
❑ On the other hand, if the company has been stable
▪ you should use as long a time period as possible.
▪ Because, statistically, the more the observations, the more
accurate the estimation

Chapter Outline
 The Cost of Capital
 The Weighted Average Cost of Capital (WACC)
▪ The Cost of Equity
▪ The Costs of Debt and Preferred Stock
 Divisional and Project Costs of Capital
 Flotation Costs and the WACC
14-30

Cost of Debt – Chap 7
❑The cost of debt – required return (YTM) on a
company’s debt.
❑How to estimate Cost of Debt for a company?
▪ Computing the YTM on the existing debt
▪ Use current YTM based on the credit rating
❖If the firm is rated as BBB, we can find YTM (or the
interest rate) on newly issued BBB bonds.
14-31

Cost of Preferred Stock
 Reminders
▪ Preferred stock generally pays a constant dividend each
period forever
 Preferred stock is a perpetuity:
 RP = D / P0
14-32
• perpetuity formula: P0= D / RP ,
• rearrange and solve for RPIf a company has preferred stock with an
annual dividend of $3. Current price is
$25, then cost of preferred stock is:
RP = 3 / 25 = 12%

The Weighted Average Cost of Capital
14-33
Cost of
equity
Cost of
debt
Weighted Ave.
Cost of Capital
(WACC)
The weights are determined by
market value of each asset

Capital Structure Weights
 Notations
▪ E = market value of equity
= # of outstanding shares x price per share
▪ D = market value of debt
= # of outstanding bonds x bond price
▪ V = market value of the firm
= D + E
 Weights (capital structure weights)
▪ wE = E/V = percent financed with equity
▪ wD = D/V = percent financed with debt
14-34

Taxes and the WACC
 Effect of taxes
❑ Interest expense (on bonds) reduces firms’ tax liability, therefore
reduces the cost of debt
After-tax cost of debt = RD(1-TC)
❑ Dividends (on stocks) are not tax deductible, so there is no tax
impact on the cost of equity
 Therefore:
WACC = wE RE + wD RD (1-TC)
14-35

Extended Example: WACC
 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 price = 1,100
▪ Coupon rate = 9%,
semiannual coupons
▪ 15 years to maturity
 Tax rate = 40%
14-36

Extended Example: WACC
 What is the cost of equity?
▪ RE = 5 + 1.15(9) = 15.35%
 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(1-40%) = 4.712%
14-37
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
Current price = 1100
Coupon rate = 9%, semiannual;
15 years to maturity
Tax rate = 40%

Extended Example: WACC
 What are the capital structure weights?
▪ E = 50 million ($80) = $4 billion
▪ # of outstanding bonds
=$ 1billion FV/$1,000 =1 mil units of bonds
▪ D = 1 mil x ($1,100) = $1.1 billion
▪ V = 4 billion + 1.1billion = $ 5.1 billion
▪ wE = E/V = 4 / 5.1 = 78.43%
▪ wD = D/V = 1.1 / 5.1 = 21.57%
 What is the WACC?
▪ WACC = .7843 x (15.35%) + .2157 x (4.712%) = 13.06%
14-38
Equity Information
50 million shares
$80 per share
Debt Information
$1 billion in outstanding debt
(FV)
Current price = $1100
RE = 15.35%; RD(1-TC) = 4.712%

Practice Question 8
Kelso’s has a debt-equity ratio of 0.55. The firm does not issue
preferred stock. The cost of equity is 14.5 percent and the cost of
debt is 8% and tax rate is 40%. What is the weighted average
cost of capital?
A. 10.46 percent
B. 10.67 percent
C. 11.06 percent
D. 11.38 percent
E. 12.19 percent
Answer – C
D/E=0.55; D=0.55; E=1; V=0.55+1=1.55
E/V =1 / 1.55 =64.52%;
D/V = 0.55 /1.55 =35.48%
WACC= (64.52%) (14.5%) + (35.48%) x 8% x (1-0.4)
= 11.06%

❑ How to estimate WACC
❑ First, Cost of Equity
❑ Go to Yahoo! Finance
to get information on Eastman Chemical (EMN)
◼ Under Profile and Key Statistics, you can find:
▪ # of shares outstanding; Price; Beta
◼ Under analysts estimates:
▪ estimates of earnings growth (g)
◼ The Bonds section : T-bill rate
❑ Use CAPM and DGM to estimate the cost of equity
14-40
Eastman Chemical (EMN)–
is an American Fortune 500 company, it
is a global chemical company with
Market cap about 13 billion
A Real Example
– WACC

Eastman Chemical (EMN) – Cost of Equity
Yahoo.finance
Summary of EMN
Price=85
Beta=1.24
D1=2.04
Find other information
under: statistics and
analysis (such as g,
D/E)
85
1.24
2.04 Forward dividend
EMN
2018-9-14
Estimate beta yourself

Eastman Chemical (EMN) – Cost of Equity
Growth
EstimatesEMN Industry Sector S&P 500
Current Qtr. 13.70% N/A N/A 0.34
Next Qtr. 12.10% N/A N/A 0.40
Current Year 10.90% N/A N/A 0.17
Next Year 8.80% N/A N/A 0.12
Next 5 Years
(per annum)8.00% N/A N/A 0.12
Past 5 Years
(per annum)4.06% N/A N/A N/A
g=8%

Eastman Chemical (EMN) – Cost of Equity
140 D/E=140%
(mrq-most recent Q)

Eastman Chemical – Cost of Equity
 Use CAPM and DGM to estimate the cost of equity
 (1) Use DGM:
RE= D1 / P0 + g
= 2.04/85 + 8%= 2.4%+ 8% =10.4%
 (2) Use CAPM:
RE=riskfree +Beta*(RM – riskfree)
RE=1%+1.24* (14% – 1%)=17.12%
14-44
Price = $85
Beta = 1.24
g = 8%
D1= $2.04
Last 3 years, average market return was about 14% (market index, e.g.
S&P500), Risk-free rate 1% (3-month T bill)
Average these two = 13. 76%

Eastman Chemical (EMN) – Cost of Debt
14-45
 Various websites for bond information:
▪ Government website: FINRA, or morningstar.com
▪ Bloomberg terminal
 Enter “EMN” to find bond information▪ Note that you may not be able to find information on all bond issues due to
the illiquidity of the bond market
7 bond issues currently outstanding
Do a weighted average YTM of all EMN bonds
Cost of debt = 3.29 %

Eastman Chemical (EMN) – WACC
 Find the weighted average cost of the debt (WACC)
▪ Use market values if you were able to get the information
▪ Use the book values (only) if market information was not available
▪ They are often very close
 Compute Eastman’s WACC (Assuming a tax rate of 35%)
14-46
WACC = 13.76% * 0.42 + 3.29% * (1-T) *0.58 = 7.02 %
Type Percentage
D/E ratio 140%
Debt 58%
Equity 42%
D/E = 140%
D=140; E=100
V= D + E =240
D/V=140/240 = 58%
E/V=100/240 = 42%
Cost of Equity= 13.76%; Cost of Debt = 3.29%; T=35%
find WACC
with just a
Name!

Chapter Outline
 The Cost of Capital
 The Weighted Average Cost of Capital (WACC)
 Flotation Costs and the WACC
 Divisional and Project Costs of Capital
14-47

Flotation Costs and WACC
 If a company accepts a new project, it may be required to
issue, or float, new bonds and stocks. This means that the
firm will incur some costs, which we call flotation costs.
 Flotation costs is NOT included in WACC (i.e. discount rate)
– included directly in the Initial Cost of a project.
 Basic Approach
▪ Compute the weighted average flotation cost, use it to
adjust the overall initial cost properly
14-48

Example: Flotation costs
 The Marcus company uses both debt and equity. The
firm’s target capital structure is 60 percent equity, 40
percent debt. The flotation costs associated with equity
are 10 percent and with debt are 5 percent.
 The firm is contemplating a large-scale, $100 million
expansion of its existing operations, which will be
financed by issuing both debt and equity.
 When flotation costs are considered, what is the cost of
the expansion?

Example: Flotation costs
 First, the weighted average flotation cost, fA
fA= E/V * fE + D/V *fD= 60% x 0.1 + 40% x 0.05 = 8%
Important principal –
▪ Although we may not know how much equity/debt the firm issued to get the
$100 mil.
▪ We should always use the target capital structure weights because the firm
will issue securities in target weights over the long term
▪ Target capital structure is 60% equity, 40% debt.
▪ The flotation costs of equity are10% and of debt are 5%.
▪ New project costs $100 million and will be financed by issuing both debt and equity.
When flotation costs are considered, what is the cost of the expansion?
E=60%
D=40%

Example: Flotation costs
 The weighted average flotation cost, fA
 Incorporate flotation cost in the initial cost:
Amount raised excluding flotation costs = amount needed for the project
Amount raised x (1-8%) = 100 million
Total Amount raised = $100 million/(1 − 8%)
= $108.7 million.
fA= 8%
▪ Target capital structure is 60% equity, 40% debt.
▪ The flotation costs of equity are10% and of debt are 5%.
▪ New project costs $100 million and will be financed by issuing both debt and equity.
When flotation costs are considered, what is the cost of the expansion?
Total amount raised including flotation costs = the true cost of the project

FLOTATION COSTS AND NPV
 Suppose the Tripleday Printing Company is currently at its target
debt−equity ratio of 100 %. It is considering building a new
$500,000 printing plant in Kansas. This new plant is expected to
generate aftertax cash flows of $73,150 per year forever. The tax
rate is 34 %. There are two financing options:
 A $500,000 new issue of common stock: The issuance costs is 10
% of the amount raised. The required return on equity is 20 %.
 A $500,000 issue of 30-year bonds: The issuance costs is 2 % of
the proceeds. The company can raise new debt at 10 %.
 What is the NPV of the new printing plant?

FLOTATION COSTS AND NPV
What is the NPV of the new printing plant?
❑The company’s cost of capital:
WACC =50% x 20 + 50% x 10 x (1-0.34)
= 13.3%
❑ OCF= $73,150 per year forever:
PV of perpetuity = OCF / WACC
= $73,150/0.133=$550,000
❑If we ignore flotation costs, the project can generate:
NPV=$550,000 – 500,000 = $50,000
❑ common stock: require
return = 20 %
❑ bonds: required return
= 10 %
❑ Tax rate = 34%
❑ D/E=1
❑ Initial cost = 500,000

FLOTATION COSTS AND NPV
What is the NPV of the new printing plant,
considering flotation costs?
Compute weighted average flotation cost:
The true cost (amount raised) including
flotation costs:Amount raised (1-f)= $500,000
Amount raised = $500,000/(1 − fA)
= $500,000/.94 = $531,915.
With flotation costs, the project can generate:
NPV=$550,000 – 531,915 = $18,085Without flotation costs, NPV= $50,000
❑ common stock: The
issuance costs= 10 %
❑ bonds: The issuance
costs = 2 %
❑ D/E=1
❑ Initial cost = 500,000
❑ PV of CFs
=$73,150/0.133
=$550,000
%6%250.0%1050.0
)/()/(
=+=
+=DEA
fVDfVEf

Divisional and Project Costs of Capital
 We use WACC to value the entire firm
 For an individual project, can we use
WACC of the firm?
▪ Yes, if it has the same risk as the firm’s
current operations
▪ If a project does NOT have the same risk as
the firm ➔ need to determine the
appropriate discount rate for that project
 Same is true for different divisions –
company has more than one line of
business.
14-55
Entire Firm
WACC
(discount rate)
Division
(project)
Division
(project)
Cost of
capital
Cost of
capital

14-56
Moscow Travel agency
Smart Cougs !
Offers R=16%
βB=1.2
E(R)= 7% +1.2×8% = 16.6%
Offers R=14%
βA=0.6
E(R)= 7% +0.6×8% =11.8%
Rf = 7%
RM – Rf=8%
• 14% >11.8%, positive α, Accept! • 16% < 16.6%, negative α, Reject! Pullman Ice Cream & Deli 14-57 Moscow Travel agency Smart Cougs ! Offers R=16% negative α & NPV Offers R=14% Positive α &NPV ❑Wrong decision! Using WACC for all projects without considering risk:Accept risky projects Reject less risky but profitable projects ❑if the company does this on a consistent basis The firm will become riskier. The overall WACC will increase!Cutoff =15% Pullman Ice Cream & DeliWACC=15% Solutions? – The Pure Play Approach Pure Play Approach 14-58 From this example, we learn: ❑ Estimate cost of capital for individual project (based on risk) is important! ❑ However, in this example, Beta is given: ▪ ICE Cream Beta =0.6; Travel agency Beta = 1.2 ❑ But, how do we get these? ▪ The company has not started the projects yet? – No data/information Solutions? – The Pure Play Approach  Find pure play companies – companies that specialize in the product or service that we are considering  Use beta & CAPM to find the appropriate required rate of return for each pure play company ◼ use for the project we’re considering ◼ Assumption – the project has the same risk as the pure play company  Disadvantage – Often difficult to find pure play companies ◼ need to find companies that focus as exclusively as possible on the type of project in which we are interested. 14-59 Solutions? – Subjective Approach Subjective approach:  Consider the project’s risk relative to the firm overall risk ◼ If the project risk > the firm, use a discount rate
greater than the WACC
◼ If the project risk < the firm, use a discount rate less than the WACC 14-60 Example – Subjective Approach Category ExamplesAdjustment FactorDiscount Rate High risk New products +6% 20% Moderate riskExpansion of existing lines, cost savings+0 14% Low riskReplacement of existing equipment−4% 10% WACC of the firm = 14% Which one to choose if using WACC=14%? Which one to choose if putting them into proper risk categories? B A A =12% B =16% Correct decision! Example – Subjective Approach Category ExamplesAdjustment FactorDiscount Rate High risk New products +6% 20% Moderate riskExpansion of existing lines, cost savings+0 14% Low riskReplacement of existing equipment−4% 10% WACC of the firm = 14% Summary: ❑Not as precise as CAPM – do not compute the exact E(R) ❑But the error rate should be lower than not considering subjective approach at all – especially useful when it’s hard to find pure play companies