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Cost of Capital

Chapter 14

Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

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Chapter Outline

•The Cost of Capital – Overview•The Cost of Equity•The Cost of Debt•The Cost of Preferred Stock•The Weighted Average Cost of Capital (WACC)•Divisional and Project Costs of Capital•Floatation Costs relative to WACC

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Why the Cost of Capital

Is Important1. We know that the return

earned on assets depends on the risk of those assets

2. The return to an investor is the same as the cost to the company

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Why the Cost of Capital

Is Important

3. Our cost of capital provides us with an indication of how the market views the risk of our assets

4. Knowing our cost of capital can also help us determine our required return for capital budgeting projects

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The Cost of Equity

The cost of equity is the return required by equity investors given the risk of the cash flows from the firm:

•Business risk•Financial risk

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The Cost of Equity

There are two major methods for determining the cost of equity:

1. Dividend growth model (aka: the Gordon Model)

2. SML, or the CAPM

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The Dividend Growth Model

(The Gordon Model)

Start with the dividend growth model formula and rearrange to solve for RE

gP

DR

gR

DP

E

E

0

1

10

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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?%1.11111.051.25

50.1ER

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Example: Estimating the Dividend Growth

RateOne method for estimating the growth rate is to use the historical average:

Year Dividend Percent Change2005 1.232006 1.302007 1.362008 1.432009 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%

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The SML ApproachUse the following information to compute our cost of equity:

Risk-free rate, Rf

Market risk premium, E(RM) – Rf

Systematic risk of asset, ))(( fMEfE RRERR

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Example - SMLSuppose your company has:

• an equity beta of .58

• the current risk-free rate is 6.1%

• the expected market risk premium is 8.6%

What is the cost of equity using the SML valuation technique?

RE = 6.1 + .58(8.6) = 11.1%

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How Did We Do?Since we came up with similar numbers using both the dividend growth model (11.1%) and the SML approach (11.1%), we should feel good about our estimate!

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Example – Cost of Equity

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 the SML?

RE = 6% + 1.5(9%) = 19.5%

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Example – Cost of Equity

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 the DGM?

RE= [2(1.06) / 15.65] + .06 = 19.55%

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Cost of Debt

The cost of debt is the required return on our company’s debt

We usually focus on the cost of long-term debt or bonds (as opposed to short-term debt like notes payable)

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Cost of DebtThe required return is best estimated by computing the yield-to-maturity on the existing long-term debt (the YTM).

The computation of the YTM was presented in the chapter on Bond Valuation

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Example: Cost of Debt: computing the

YTMSuppose we have a corporate bond issue currently outstanding that has 25 years left to maturity.

The coupon rate is 9%, and coupons are paid semiannually.

The bond is currently selling for $908.72 per $1,000 bond.

What is the cost of debt?

$1,000 = FV

25 years/2 = 50 periods = N

$90/2 = $45 = Payment (PMT)$-908.72 = PV

YTM = i = ?

5.00 (x2 = 10%)

HP 12-C

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25 yrs/2 = 50 payments = N

$ -908.72 = PV

$90/2 = $45 (PMT)

$1,000 = FV

YTM = I/Y = ?

5%(5 x 2 = 10%

1st2nd

TI BA II Plus

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Capital Structure Weights

To compute the WACC, we first need the weights of each source of funds: namely debt, preferred stock and equity

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Capital Structure Weights

Let’s simplify with an example of just debt and equity.

We often use the market value of both debt and equity

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Capital Structure Valuation

Debt’s Market Value = (# of outstanding bonds ) x (the market price of one bond)

Equity’s Market Value = (# shares of outstanding common stock) x (the market price of one share of common stock)

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Capital Structure Valuation

A firm’s market value is simply the added value of both the debt and the equity:

V = D + E

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Capital Structure Weights

WD = D/V

This is the % financed with debt

WE = E/VThis is the % financed with equity

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Student Alert!The capital structure weights must always add up to 100%

WD + WE = 100% orWD + WPS + WE = 100%

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Example: Capital Structure Weights

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%

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Taxes and the WACC

Wait a minute!

Debt and Equity are not equal in the eyes of the firm.

Debt gets a tax advantage and Equity does not.

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Taxes and the WACC• Interest expense reduces our tax liability

• This reduction in taxes reduces our cost of debt

Thus, our real cost of debt is actually the AFTER-TAX cost of debt or …

After-tax cost of debt = RD(1-TC)

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Taxes and the WACC•Our new equation for the WACC is:

WACC = WDRD(1-TC) + WE RE

This is one of the most powerful relationships in finance.

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Putting All the Pieces Together – WACC

ExampleEquity 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

• Coupon rate = 9%,• semiannual coupons

• 15 years to maturityThe firm’s tax rate is 40%

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WACC Example

2. What is the cost of equity (using the CAPM)?RE = 5 + 1.15(9) = 15.35%

1. What is the cost of debt?N = 30; PV = -1,100; PMT = 45; FV = 1,000; CPT I/Y = 3.9268RD = 3.927(2)

= 7.854%

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WACC Example3. What is the AFTER-TAX cost of debt?

RD (1 – TC) = 7.854 (1 - .40) = 4.712%

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WACC Example4. What are the capital structure weights?

Debt = 1 billion ($1.10) = $1.1 billionEquity = 50 million ($80) = $4 billionValue of the Firm = 4 + 1.1 = $5.1 billion

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WACC Example (Plug and Chug)

5. Compute the Weighted Average Cost of Capital (the WACC)

WACC = .2157 (4.712%) + .7843 (15.35%)

= 13.06%

WACC = WDRD(1-TC) + WE RE

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Formulas

gP

DR

gR

DP

E

E

0

1

10

))(( fMEfE RRERR

Cost of Equity (Dividend Growth Model)

Cost of Equity (CAPM)

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Formulas (continued)

Rps = D_ P0

WACC = WDRD(1-TC) + WE RE

After-tax cost of debt = RD(1-TC)

Cost of Preferred Stock