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.

Slide 14

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

12-18

• 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.)

Slide 21

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

Slide 22

12-22

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

12-32

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

12-33

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.