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Week 9

Lecture 9

Ross, Westerfield and Jordan 7e

Chapter 15

Cost of Capital

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Last Week..

• Expected Returns and Variances• Single asset & Portfolios • Using probabilities & Historical returns

• Principle of Diversification• Systematic and Unsystematic Risk• Beta• CAPM• SML• Reward to Risk Ratio

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Chapter 15 Outline

• Cost of Capital: Introduction

• Cost of Equity

• Costs of Debt

• Cost of Preferred Stock

• Weighted Average Cost of Capital

• Divisional and Project Costs of Capital

• Flotation Costs

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Why Cost of Capital Is Important

• The return to an investor is the same as the cost to the company

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

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

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Required Return = Cost of Capital

• The Required Rate of Return = Discount Rate = Hurdle Rate = Cost of Capital

• Need to know the required return for an investment so we can compute the NPV and decide whether or not to take the investment

• Need to earn at least the required return to compensate investors for their financing

• Required return – from the investor’s point of view

• Cost of capital – from the firm’s point of view

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Cost of Capital

• The firm is financed by a mixture of equity and debt

• Cost of Capital is a mix of Cost of Equity and Cost of Debt

• These costs are determined by the market• The firm determines the mix, Debt/Equity (D/E)

reflecting it’s target capital structure.• To calculate cost of capital:

• Calculate cost of equity • Calculate cost of debt• Combine them

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Cost of Equity

• The cost of equity is the return required by equity investors, the shareholders on their investment in the firm

• Since this cost is not directly observable, it must be estimated

• There are two main methods for determining the cost of equity:• Dividend Growth Model• CAPM

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Cost of Equity - DGM Approach

• Start with the dividend growth model formula where g is constant:

• Where: RE is the required return for shareholders, P0 is the current price, D0 is the current/last dividend, D1 is the next dividend

• and rearrange to solve for RE:

• Where D1/P0 is the dividend yield, and g is the growth rate of dividends

gR

D

gR

g)(1DP

E

1

E

00

gP

DR

0

1E

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DGM - Example 1

• Bentex Ltd. recently paid a dividend of 40 cents per share. This dividend is expected to grow at 6% per year indefinitely. If the current market price of Bentex shares is $6 per share, estimate its cost of equity.

• D0 = $0.40, g = 6%, P0 = $6, RE = ?

D1 = D0(1 + g) = $0.40(1.06) = $0.424

RE = (D1 / P0) + g = (0.424/6.00) + 0.06

= 0.1307, and thus the cost of equity is 13.07%.

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DGM – Example 2

• Suppose ABC 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. The current price is $25. What is the cost of equity?

• D1 = $1.50, g = 5.1%, P0 = $25, RE = ?

11.1%.111.05125

1.50g

P

DR

gR

DP

0

1E

E

10

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Example - Estimating the Dividend Growth Rate ‘g’

• One method for estimating the growth rate is to use the historical averageYear Dividend Change Return%• 2000 1.23 -• 2001 1.30 (1.30 – 1.23) / 1.23 = 5.7% • 2002 1.36 (1.36 – 1.30) / 1.30 = 4.6% • 2003 1.43 (1.43 – 1.36) / 1.36 = 5.1% • 2004 1.50 (1.50 – 1.43) / 1.43 = 4.9%

• Average = (5.7 + 4.6 + 5.1 + 4.9) / 4 = 5.1%

• Another way is use analysts’ forecast

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Advantages and Disadvantages of Dividend Growth Model

• Advantage:• easy to understand and use

• Disadvantages• Only applicable to companies currently paying

dividends• Assumes dividend growth is constant• Cost of equity is sensitive to growth estimate• Does not explicitly consider risk

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Cost of Equity - CAPM or SML Approach

• Recall CAPM for any asset i is:

• The CAPM cost of equity is:

• Use the following information to compute our cost of equity• RE = Required return for shareholders

• Rf = Risk-free rate

• E(RM) – Rf = Market risk premium

E = Systematic risk of firm’s equity relative to the market

)R)(E(RβRR fMEfE

)R)(E(RβR)E(R fMifi

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CAPM - Example

• Suppose our ABC company has an equity beta of 0.58 and the current risk-free rate is 6.1%. If the expected market risk premium is 8.6%, what is the cost of equity capital?

• βE = 0.58, Rf = 6.1%, E(RM) – Rf = 8.6%

RE = 0.061 + 0.58(0.086) = 11.1%

• What if the expected market return is 8.6%?

• RE = 0.061 + 0.58(0.086 – 0.061) = 7.55%

)R)(E(RβRR fMEfE

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Advantages and Disadvantages of CAPM

• Advantages• Explicitly adjusts for risk• Applicable to all companies

• Disadvantages• Have to estimate the expected market risk

premium, which does vary over time• Have to estimate beta, which also varies over

time• We are using the past to predict the future,

which is not always reliable

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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%. The market believes our dividends will grow at 6% per year and our last dividend was $2. The stock is currently selling for $15.65. What is the cost of equity?

• Using CAPM: RE = 6% + 1.5(9%) = 19.5%

• Using DGM: RE = [2(1.06) / 15.65] + .06 = 19.55%

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Cost of Preferred Stock

• Reminders• Preferred stock pays a constant dividend • Dividends are expected to be paid forever

• Preferred stock return = Perpetuity RP

• P0 = D/Rp RP = D / P0

• Example:• 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?

• 25 = 3/Rp therefore RP = 3 / 25 = 12%

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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

• The required return is best estimated by computing the yield-to-maturity or YTM

• The cost of debt is NOT the coupon rate• For publicly listed debt use YTM• If the firm has no publicly traded debt, use YTM on

similar debt that is traded.

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YTM of Bond

• In general:

• Where

• C is coupon interest payment,

• RD is required market return or YTM,

• T is the number of periods left until repayment,

• F is face value.

• Need to solve for RD

TDD

TD

0 )R(1

F

R

)R(11

1CP

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Example – Cost of Debt

• Gloss Ltd issued a 20-year, 12% bond 10 years

ago. The bond is currently priced at $860, and

pays interest annually. What is its cost of debt?

• Excel solution gives RD = 0.1476, meaning that

Gloss’s cost of debt is 14.76%.

10DD

10D

)R(1

$1000

R

)R(11

1$120$860

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Example - Cost of Debt

• Suppose a firm has a bond issue currently outstanding that has 25 years left to maturity and pays coupons semiannually. The coupon rate is 9% per year. The bond’s current price is $908.72 per $1000 bond. What is the cost of debt?• t = 25 years x 2 = 50; C = $90/2 = 45; • F = $1000; Bond Price or P = $908.75; • RD or YTM = ?• By trial and error semiannual yield = 5%• YTM = RD = 5% x 2 = 10%

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Weighted Average Cost of Capital

• We can use the individual costs of capital that we have computed to get our “average” cost of capital for the firm.

• WACC is the required return on our 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 we use

WACC = wE*RE + wP*RP + wD*RD

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Capital Structure Weights

• Notation• E = market value of equity = nr. of outstanding shares

times price per share• P = market value of preference shares = nr. of

outstanding preference shares times price per share• D = market value of debt = nr. of outstanding bonds

times bond price• V = market value of the firm = E + P + D

• Weights• wE = E/V = percent financed with equity• wP = P/V = percent financed with preference stock• wD = D/V = percent financed with debt

• wE + wP + wD = 1

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Cost of debt = 5.7 %, Cost of equity = 14.0 %

Cost of preference shares = 9.0 %

Source of Capital M.Value WeightLong term debt $40 m 40%

Pref. shares $10 m 10%

Equity $ 50 m 50%

Total 100 m 100 %

WACC = (E/V)*RE + (P/V)*RP + (D/V)*RD

= (0.5)*0.14 + (0.1)*0.09 + (0.4)*0.057 = 0.1018 WACC = 10.18% (Unadjusted)

Example – Weights & WACC

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WACC – Adjusted

• The company gets a tax deduction for interest on debt, reducing the effective cost of debt.

• If TC is the corporate tax rate then the after tax cost of

debt is RD*(1 TC), and the WACC adjusted for taxation

effects is given by:

• WACC = wE*RE + wP*RPS + wD*RD*(1 TC) or

• WACC = (E/V)*RE + (P/V)*RPS +(D/V)*RD*(1 TC)

• Previous example: If tax rate is 30%, then

WACC = (0.5)*0.14 + (0.1)*0.09 + (0.4)*0.057(0.7)

= 0.0950 or 9.5%.

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WACC - Extended Example (1)

• 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%• Coupon rate = 9%,

semiannual coupons• 15 years to maturity

• Tax rate = 40%

Step 1: Calculate cost of equity and cost of debtStep 2: Calculate the market value of each source of financing and the weightsStep 3: Calculate the WACC adjusting for tax.

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WACC - Extended Example (2)

• What is the cost of equity?• βE = 1.5, Rf = 5%, RM – Rf = 9%, RE = ?

• RE = 5% + 1.15(9%) = 15.35%

• What is the cost of debt?• t = 15y x 2=30; Price = $1100; C = $90/2 = 45;

F = $1000; by trial & error semi yield = 3.9268

• RD = 3.927% x 2 = 7.854%

• What is the after-tax cost of debt?• RD(1-TC) = 7.854(1-0.4) = 4.712%

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WACC - Extended Example (3)

• What are the capital structure weights?• E = 50 million x $80 = $4 billion• D = $1 b x 110% = $1.1 billion Or

$1 b/1000 = 1 million bonds issued

1 m bonds x $1100 = $1.1 billion • V = 4 + 1.1 = 5.1 billion

• wE = E/V = 4 / 5.1 = 0.7843

• wD = D/V = 1.1 / 5.1 = 0.2157

• What is the WACC?• WACC = wE*RE + wD*RD*(1 TC)

• WACC = 0.7843(15.35%) + 0.2157(4.712%) = 13.06%

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Finding the Weights from D/E

• Suppose Belo Corp has a target D/E ratio of 0.33. Cost of Debt is 10% and cost of equity is 20%. If tax is 34%, what is WACC?

• First calculate WE and WD.

• If D/E = 0.33 what is E = ? D = ?

• Assign any value to equity. E = 1

• D/1= 0.33 then D = 0.33 and V = 1.33• E/V = 1/1.33 = 0.7519 and

• D/V = 0.33/1.33 = 0.2481

• WACC = wE*RE + wD*RD*(1 TC)

• WACC = 0.75 x 0.20 + 0.25 x 0.10 x (1-0.34) = 16.65%

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Finding D/E

• If BHP has a WACC of 21.67% and the cost of equity is 29.2%, cost of debt is 10%, what is it’s target D/E ratio? Assume tax is 34%.

• We know that E + D = V or WE + WD = 1

• We express one in terms of another:• WE = 1 - WD

• And insert in WACC equation:• 0.2167 = WE x 0.292 + WD x 0.10 x (1-0.34)

• 0.2167 = (1-WD) x 0.292 + WD x 0.10 x (1-0.34)

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Finding D/E (cont.)

• 0.2167 = (1-WD) x 0.292 + WD x 0.10 x (1-0.34)

• Solve for WD the only unknown variable:

• 0.2167 = 0.292 – WD x 0.292 + WD x 0.066

• 0.2167 – 0.292 = – WD x 0.292 + WD x 0.066

• -0.0753 = -WD x (0.292 - 0.066)

• 0.0753 = WD x 0.226

• WD = 0.0753/0.2260 = 0.333

• Therefore WE = 1 – WD, WE = 1- 0.333 = 0.667

• D/E = 0.333/0.667 = 0.5

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Table 15.1 Cost of Equity & Debt

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Table 15.1 WACC

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Useful Websites

• Yahoo Finance• Share price• Beta• Book value per share• Analysts estimates• T-Bill rate

• www.nasdbondinfo.com• Bond information

• www.sec.gov• Company filings

• www.valuepro.net

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Divisional and Project Costs of Capital

• 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 separatediscount rates

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Using WACC for All Projects - Example

Project Req. Ret. IRR WACCA 20% reject 17% accept 15%B 15% accept 18% accept 15%C 10% accept 12% reject 15%

• Assume the WACC = 15%• If we use the WACC for all projects regardless of

risk• Accept A and B, reject C

• If correct required return based on specific risk is used• Accept B and C, reject A

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Divisional and Project costs of capital

• WACC is the appropriate discount rate only when the project is about the same risk as the firm.

• Other approaches to estimating a discount rate:• divisional cost of capital—used if a company has

more than one division with different levels of risk;• pure play approach—a discount rate that is unique to

a particular project is used;• subjective approach—projects are allocated to

specific risk classes which, in turn, have specified discount rates.

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Other Approaches

• Pure Play Approach:• Look at companies in the same line of business as the

new project• Calculate an average WACC for all the companies and

use this rate as the discount rate of the new project

• Subjective Approach:• Consider the project’s risk relative to the firm overall

risk• If the project risk > firm risk,

use a discount rate > WACC• If the project risk < firm risk,

use a discount rate < WACC

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Flotation Costs

• The required return depends on the risk, not how the money is raised

• However, the cost of issuing new securities should not just be ignored either

• Basic Approach• Compute the weighted average flotation cost• Use the target weights because the firm will issue

securities in these percentages over the long term

fA = (E/V)*fE + (D/V)* fD

• where fA is the weighted average flotation cost, fE is the equity flotation cost proportion, and fD is debt flotation cost proportion.

• True cost of project = Cost/(1-fA)

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Flotation Cost Example

• A firm has a target structure that is 80% equity and 20% debt. The costs for raising equity are 20% and the cost of raising debt are 6%. If the firm needs $65 million for a new facility, what is the true cost after accounting for flotation costs?

fA = (E/V)*fE + (D/V)* fD

= 0.8*0.2 + 0.2*0.06 fA = 0.172 or 17.2% • If the flotation cost is 17.2%, and we need to raise $65

million net, the true cost of the facility would be:

$65/(1 - fA) = 65/0.828 = $78.50 million

• The firm needs to raise $78.5 million to account for flotation costs and to have $65 million left to invest.

• Since 78.5/65 = 1.2077, this suggests that for every dollar required by the project, the firm must raise $1.2077 to finance its projects.

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Quick Quiz

• What are the two approaches for computing the cost of equity?

• What is the cost of debt?

• How do you compute the after-tax cost of debt?

• How do you compute the capital structure weights required for the WACC?

• When is appropriate to use WACC as the discount rate for projects?

• What is the proportion of E and D if we have a D/E ratio of 1.2

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End Chapter 15