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