Lecture3.pdf

FINS3625 Applied Corporate Finance

Lecture 3 (Chapter 13) Jared Stanfield March 14, 2012

Figure 13.2 Two Capital Structures

13.1 A First Look at the Weighted Average Cost of Capital

•  Opportunity Cost and the Overall Cost of Capital

•  Weighted Averages and the Overall Cost of Capital – Weighted Average Cost of Capital (WACC) – Market-‐Value Balance Sheet Market Value of Equity + Market Value of Debt = Market Value of Assets (Eq. 13.1)


•  Weighted Average Cost of Capital CalculaWons – Leverage

•  Unlevered •  Levered


•  Weighted Average Cost of Capital CalculaWons – The Weighted Average Cost of Capital: Unlevered Firm

•  rWACC = Equity Cost of Capital


•  Weighted Average Cost of Capital CalculaWons – The Weighted Average Cost of Capital: Levered Firm

(Eq. 13.2)

13.2 The Firm’s Costs of Debt and Equity Capital

•  Cost of Debt Capital – Yield to Maturity and the Cost of Debt

•  The Yield to Maturity is the yield that investors demand to hold the firm’s debt (new or exisWng).

– Taxes and the Cost of Debt •  EffecWve Cost of Debt rD (1 -‐ TC) (Eq. 13.3)

where TC is the corporate tax rate.

EffecWve Cost of Debt

Problem: •  By using yield to maturity on Gap Inc.’s debt, we find that its pre-‐tax cost

of debt is 7.13%. If Gap Inc.’s tax rate is 40%, what is its effecWve cost of debt?


SoluWon: Plan: •  We can use Eq. 13.3 to calculate GAP’s effecWve cost of debt:

rD =7.13%% (pre-‐tax cost of debt) TC =40% (corporate tax rate)


Execute: •  Gap Inc.’s effecWve cost of debt is

0.0713 (1-‐0.40)= .0428 = 4.28%


Evaluate: •  For every $1000 it borrows, Gap Inc. pays its bondholders

0.0713($1000) = $71.30 in interest every year. Because it can deduct that $71.30 in interest from its income, every dollar in interest saves Gap Inc. 40 cents in taxes, so the interest tax deducWon reduces the firm’s tax payment to the government by 0.40($71.30) =$28.52. Thus Gap Inc.’s net cost of debt is the $71.30 it pays minus the $28.52 in reduced tax payments, which is $42.78 per $1,000 or 4.28%.


•  Cost of Preferred Stock Capital

•  Assume DuPont’s class A preferred stock has a price of $66.67 and an annual dividend of $3.50. Its cost of preferred stock, therefore, is $3.50 ÷ $66.67 = 5.25%

Prefered DividendCost of Preferred Stock Capital =

Preferred Stock Pricepfd

pfd

DivP

=(Eq. 13.4)


•  Cost of Common Stock Capital – Capital Asset Pricing Model

•  From Chapter 12 1.  EsWmate the firm’s beta of equity, typically by regressing

60 months of the company’s returns against 60 months of returns for a market proxy such as the S&P 500.

2.  Determine the risk-‐free rate, typically by using the yield on Treasury bills or bonds.



•  From Chapter 12 3.  EsWmate the market risk premium, typically by comparing

historical returns on a market proxy to contemporaneous risk-‐free rates.

4.  Apply the CAPM:

Cost of Equity = Risk-‐Free Rate + Equity Beta × Market Risk Premium

Return CalculaWon Reminder

No Stock Split Returns: Rt = (Pt – Pt-‐1 + Dt)/Pt-‐1

X for Y Stock Split Returns: Rt = ((X/Y)*Pt – Pt-‐1 + (X/Y)*Dt)/Pt-‐1



•  Assume the equity beta of DuPont is 1.37, the yield on ten-‐year Treasury notes is 3%, and you esWmate the market risk premium to be 6%. DuPont’s cost of equity is 3% + 1.37 × 6% = 11.22%


•  Cost of Common Stock Capital – Constant Dividend Growth Model

• 

(Eq. 13.5)


•  Cost of Common Stock Capital – Constant Dividend Growth Model

•  Assume in mid-‐2010, the average forecast for DuPont’s long-‐run earnings growth rate was 6.2%. With an expected dividend in one year of $1.64 and a price of $36.99, the CDGM esWmates DuPont’s cost of equity as follows (using Eq. 13.5):

1 $1.64Cost of Equity = 0.062 0.106 or 10.6%

$36.99E

Div gP

+ = + =

Table 13.1 EsWmaWng the Cost of Equity

13.3 A Second Look at the Weighted Average Cost of Capital

•  WACC EquaWon rwacc = rEE% + rpfd P% + rD(1 -‐ TC)D%

– For a company that does not have preferred stock, the WACC condenses to:

rwacc = rEE% + rD(1 -‐ TC)D%

(Eq. 13.6)

(Eq. 13.7)


•  WACC EquaWon –  In mid-‐2010, the market values of DuPont’s common stock, preferred stock, and debt were $30,860 million, $187 million, and $9543 million, respecWvely. Its total value was, therefore, $30,860 million + $187 million + $9543 million = $40,590. Given the costs of common stock, preferred stock, and debt we have already computed, DuPont’s WACC in late 2010 was:


•  WACC EquaWon

( )30,860 187 9,54311.22% 5.25% 1 0.35 3.66%40,590 40,590 40,590

9.11%

WACC ! " ! " ! "= + + −$ % $ % $ %

& ' & ' & '=

CompuWng the WACC

Problem: •  The expected return on Macy’s equity is 10.8%, and the firm has a yield to

maturity on its debt of 8%. Debt accounts for 16% and equity for 84% of Macy’s total market value. If its tax rate is 40%, what is this firm’s WACC?

CompuWng the WACC

SoluWon: Plan: •  We can compute the WACC using Eq. 13.7. To do so, we need to know the

costs of equity and debt, their proporWons in Macy’s capital structure, and the firm’s tax rate. We have all that informaWon, so we are ready to proceed.

CompuWng the WACC Execute: rwacc = rEE% + rD (1 -‐TC)D% = (0.108)(0.84) + (0.08)(1 -‐0.40)(0.16) = .0984 or 9.84%

CompuWng the WACC

Evaluate: •  Even though we cannot observe the expected return of Macy’s

investments directly, we can use the expected return on its equity and debt and the WACC formula to esWmate it, adjusWng for the tax advantage of debt. Macy’s needs to earn at least a 9.84% return on its investment in current and new stores to saWsfy both its debt and equity holders.

Figure 13.3 WACCs for Real Companies


•  Methods in PracWce – Net Debt

•  Net Debt = Debt – Cash and Risk-‐Free SecuriWes

(Eq. 13.8)

WACC E D CMarket Value of Equity Net Debt

r = r r (1 T )Enterprise Value Enterprise Value

! " ! "+ −$ % $ %

& ' & '


•  Methods in PracWce – The Risk-‐Free Interest Rate

•  Most firms use the yields on long-‐term treasury bonds

– The Market-‐Risk Premium •  Since 1926, the S&P 500 has produced an average return of 7.1% above the rate for one-‐year Treasury securiWes

•  Since 1959, the S&P 500 has shown an excess return of only 4.7% over the rate for one-‐year Treasury securiWes

Table 13.2 Historical Excess Returns of the S&P 500 Compared to One-‐Year Treasury Bills and Ten-‐Year U.S. Treasury SecuriWes

13.4 Using the WACC to Value a Project

•  Levered Value – The value of an investment, including the benefit of the interest tax deducWon, given the firm’s leverage policy

•  WACC ValuaWon Method – DiscounWng future incremental free cash flows using the firm’s WACC, which produces the levered value of a project


•  Levered Value

( ) ( )31 2

0 2 3 ...1 1 1

L

WACC WACC WACC

FCFFCF FCFVr r r

= + + ++ + +

(Eq. 13.9)

The WACC Method

Problem: •  Suppose Starbucks is considering introducing a new

Frappuccino that is orange to be called Orange Mocha Frappuccino. The firm believes that the coffee’s flavor, color, and appeal to ridiculously good-‐looking male models will make it a success.

The WACC Method

Problem: •  The risk of the project is judged to be similar to the risk of the

company. The cost of bringing the Orange Mocha Frappuccino to market is $280 million, but Starbucks expects first-‐year incremental free cash flows from Orange Mocha Frappuccino to be $80 million and to grow at 5% per year thereaqer. Should Starbucks go ahead with the project?

The WACC Method

SoluWon: Plan: •  We can use the WACC method shown in Eq. 13.9 to value OMF and then

subtract the upfront cost of $280 million. We will need Starbucks’ WACC, which was esWmated in Figure 13.3 as 11.0%.

The WACC Method

Execute: •  The cash flows for OMF are a growing perpetuity. Applying the growing

perpetuity formula with the WACC method, we have:

L 10 0

WACC

FCF $80millionV FCF 280 $1,053.33million ($1.05billion)r g 0.11 .05

= + = − + =− −

The WACC Method

Evaluate: •  The OMF project has a posiWve NPV because it is expected to generate a

return on the $280 million far in excess of Starbucks’ WACC of 11.0%. As discussed in Chapter 3, taking posiWve-‐NPV projects adds value to the firm. Here, we can see that the value is created by exceeding the required return of the firm’s investors.


•  Key AssumpWons – Average Risk

• We assume iniWally that the market risk of the project is equivalent to the average market risk of the firm’s investments

– Constant Debt-‐Equity RaWo • We assume that the firm adjusts its leverage conWnuously to maintain a constant raWo of the market value of debt to the market value of equity


•  Key AssumpWons (cont’d) – Limited Leverage Effects

• We assume iniWally that the main effect of leverage on valuaWon follows from the interest tax deducWon and that any other factors are not significant at the level of debt chosen


•  WACC Method ApplicaWon: Extending the Life of a DuPont Facility –  Suppose DuPont is considering an investment that would extend the life of one of its chemical faciliWes for four years

–  The project would require upfront costs of $6.67 million plus a $24 million investment in equipment

–  The equipment will be obsolete in four years and will be depreciated via straight-‐line over that period


•  WACC Method ApplicaWon: Extending the Life of a DuPont Facility – During the next four years, however, DuPont expects annual sales of $60 million per year from this facility

– Material costs and operaWng expenses are expected to total $25 million and $9 million, respecWvely, per year

– DuPont expects no net working capital requirements for the project, and it pays a tax rate of 35%.

Table 13.3 Expected Free Cash Flow from DuPont’s Facility Project


•  WACC Method ApplicaWon: Extending the Life of a DuPont Facility

•  NPV = $61.41 million -‐ $28.34 million = $33.07 million

0 2 3 4

19 19 19 19$61.41 million

1.0911 1.0911 1.0911 1.0911LV = + + + =


•  Summary of WACC Method 1.  Determine the incremental free cash flow of the

investment 2.  Compute the weighted average cost of capital

using Eq. 13.6 3.  Compute the value of the investment, including

the tax benefit of leverage, by discounWng the incremental free cash flow of the investment using the WACC

13.5 Project-‐Based Costs of Capital

•  Cost of Capital of a New AcquisiWon – Suppose DuPont is considering acquiring Weyerhaeuser, a company that is focused on Wmber, paper, and other forest products

– Weyerhaeuser faces different market risks than DuPont does in its chemicals business

– What cost of capital should DuPont use to value a possible acquisiWon of Weyerhaeuser?


•  Cost of Capital of a New AcquisiWon – Because the risks are different, DuPont’s WACC would be inappropriate for valuing Weyerhaeuser

–  Instead, DuPont should calculate and use Weyerhaeuser’s WACC of 8.8% when assessing the acquisiWon


•  Divisional Costs of Capital – Now assume DuPont decides to create a forest products division internally, rather than buying Weyerhaeuser

– What should the cost of capital for the new division be?

•  If DuPont plans to finance the division with the same proporWon of debt as is used by Weyerhaeuser, then DuPont would use Weyerhaeuser’s WACC as the WACC for its new division

Walker, Texas Yogurt •  Suppose you are the financial planning

director for Martial Arts Australia. After watching an Activia Yogurt commercial, you think that yogurt that helps you go to the bathroom is a good product, but needs to toughen up its image

•  You decide Martial Arts Australia will introduce a new Chuck Norris yogurt that roundhouses anyone that makes fun of you for eating fiber-filled yogurt. The firm believes that the new yogurt will make it less embarrassing to consume this type of yogurt in public

•  How would you come up with the required rate of return?

•  MAA’s WACC is 6.6%, the risk-free rate is 3.0% and the market risk premium is 5.4%

A Project in a New Line of Business

SoluWon: Plan: •  The first step is to idenWfy a company operaWng in MAA’s

targeted line of business. Danone SA is a well-‐known marketer of yogurt. In fact, that is almost all Danone does. Thus the cost of capital for Danone would be a good esWmate of the cost of capital for MAA’s proposed yogurt business.


SoluWon: Plan (cont’d): •  Suppose you find that the beta of Danone is 0.4. With this beta, the risk-‐

free rate, and the market risk premium, you can use the CAPM to esWmate the cost of equity for Danone. Danone has a market value debt/assets raWo of .58, and its cost of debt is 3.8%. Its tax rate is 28%.


Execute: •  Using the CAPM, we have:

•  To get Danone’s WACC, we use equaWon 13.6. Danone has no preferred stock, so the WACC is:

' '3% .4 5.4% 5.8%

Coca Cola s cost of equity Risk free rate Coca Cola s beta Market Risk Premium− = − + − ×

= + × =

%02.4)58.0)(28.1%(8.3)42.0%(8.5%D)T1(r%Err CDEWACC

=−+=

−+=


Evaluate: •  The correct cost of capital for evaluaWng a beverage investment

opportunity is 4.02%. If we had used the 6.6% cost of capital that is associated with MAA’s exisWng business, we would have mistakenly used too high of a cost of capital. That could lead us to reject the investment, even if it truly had a posiWve NPV.

13.6 When Raising External Capital Is Costly

•  Issuing new equity or bonds carries a number of costs –  Issuing costs should be treated as cash outlows that are necessary to the project

– They can be incorporated as addiWonal costs (negaWve cash flows) in the NPV analysis

Transforming βequity into βasset

•  The assets of a firm are equal to its liabilities (debt) + equity: – Assets = Debt + Equity

•  The β of a portfolio of securities is a weighted average of the β’s of the securities

Transforming βequity into βasset

•  Since the assets of a firm are claimed by a portfolio of debt and equity we can write:

DebtThe assumption that = 0 is often made:

Assets Equity Debt

Assets Equity

Equity DebtDebt Equity Debt Equity

Equity

β β β

β

β β

= ⋅ + ⋅+ +

= ⋅

Thus, the firm's asset beta is a weighted average of the debt and equity betas.

Debt Equity+

Transforming βequity into βasset •  We can rewrite the formula for the asset beta to get an

expression for the equity beta (equity risk):

•  What does this equation say about where equity risk

comes from?

EquityDebt

:that means whichEquityDebt

Equity

AssetsAssetsEquity

EquityAssets

⋅+=

+⋅=

βββ

ββ ,

Asset Beta Example

•  Your company has two divisions. One sells beverages and the other manufactures and sells fancy candy bars through a direct retail channel

•  You feel that Rocky Mountain Chocolate Factory is a comparable publicly traded company for your candy bars division. If RMCF’s beta for its common stock is 0.96 and its debt is 10% of its capital structure

•  What is the appropriate discount rate for projects in your candy bar division? Assume a risk free rate of 3% and a risk premium (market return minus risk free rate) of 8%

Solution

•  We can use RMCF’s Beta of equity to solve for RMCF’s Beta of Assets to obtain a measure of the project risk of your division:

( )( ) ( )( )( ) ( )

0.96 .90 0.86

0.03 0.86 0.08 0.0988

Assets Equity

Assets

f Assets M f

EquityDebt Equity

E R r E R r

E R

β β

β

β

= ⋅+

= =

= + −

= + =

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