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**CHAPTER 13 The Cost of Capital**

Sources of capital Component costs WACC

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Cost of Capital The cost of capital represents the overall cost of financing to the firm The cost of capital is normally the relevant discount rate to use in analyzing an investment The overall cost of capital is a weighted average of the various sources, including debt, preferred stock, and common equity: WACC = Weighted Average Cost of Capital WACC = After-tax costs x weights

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**What sources of long-term capital do firms use?**

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**Calculating the weighted average cost of capital**

WACC = xd(pretax kd)(1-Tax rate) + xpskps + xcskcs The x’s refer to the firm’s capital structure weights. The k’s refer to the cost of each component.

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**Should our analysis focus on before-tax or after-tax costs?**

Stockholders focus on After-Tax CFs. Therefore, we should focus on A-Tax capital costs. Only cost of debt needs adjustment, because interest is tax deductible.

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**Should our analysis focus on historical costs or new (marginal) costs?**

The cost of capital is used primarily to make decisions that involve raising new capital. So, focus on today’s marginal costs (for WACC).

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**How are the weights determined?**

WACC = xd(pretax kd)(1-Tax rate) + xpkp + xcskcs As a percentage of total financing

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Weighting example Bonds 40 Pref. Stock 100 Common 100 Ret. Earn. 160 Total L & E 400 What is weight of each component?

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Weighting example Bonds 40 Pref. Stock 100 Common 100 Ret. Earn. 160 Total L & E 400 Bonds = 40/400 = 10% Pref. Stock = 100/400 = 25%

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**Component cost of debt WACC = xd(pretax kd)(1-T) + xpkp + xcskcs**

kd is the marginal cost of debt capital. The yield to maturity on outstanding L-T debt is often used as a measure of kd. Why tax-adjust, i.e. why kd(1-Tax rate)?

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**If tax rate is 40% then 10% before tax = 6% after tax**

Sales 1,000 Interest 100* EBT 900 Tax 40% 360 400 EAT 540 600 60 difference

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**Component cost of debt Interest is tax deductible, so**

aftertax kd = pretax kd (1-T) = 10% ( ) = 6% T = tax rate = 40%

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Cost of debt What is the current cost of debt for a firm that has a 9% coupon bond with 5 years to maturity and a current price of $962? What is the after tax cost if it is in the 40% tax bracket?

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**Component cost of preferred stock**

WACC = xdkd(1-T) + xpkp + xcskcs kp is the marginal cost of preferred stock. The rate of return investors require on the firm’s preferred stock.

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**What is the cost of preferred stock?**

The cost of preferred stock can be solved by using this formula: kp = Dp / Pp = $8 / $111 = 7.2%

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**Component cost of preferred stock**

Preferred dividends are not tax-deductible, so no tax adjustments necessary.

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**Component cost of equity**

WACC = xd(pretax kd)(1-T) + xpkp + xcskcs kcs is the marginal cost of common equity

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**Why is there a cost for retained earnings?**

Earnings can be reinvested or paid out as dividends. Investors could buy other securities, earn a return. If earnings are retained, there is an opportunity cost (the return that stockholders could earn on alternative investments of equal risk). Investors could buy similar stocks and earn kcs. Firm could repurchase its own stock and earn kcs. Therefore, kcs is the cost of retained earnings.

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**Two ways to determine the cost of common equity, kcs**

1. CAPM: kcs = RRF + β x (Mkt. risk premium [E(RM)– RRF]) RRF = Risk Free Rate (now around 2.7%) RM = Return on the market β = Beta - the relation of its returns with that of the stock market e.g. 0 – not correlated 1 - moves with the market 2 – twice as volatile

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**Two ways to determine the cost of common equity, kcs**

2. DCF: P0 = (D1 / r - g) r = kcs kcs = (D1 / P0)+ g

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**If the market premium is 6%, risk-free rate is 2**

If the market premium is 6%, risk-free rate is 2.7% and the firm’s beta is 1.48, what’s the cost of common equity based upon the CAPM? kcs = RRF + β(mkt premium) = 2.7% (6.0%) = 11.58%

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**If D0 = $1.72, P0 = $43, and g = 5%, what’s the cost of common equity based upon the DCF approach?**

D1 = D0 (1+g) D1 = $1.72 ( ) D1 = $1.81 kcs = (D1 / P0)+ g = ($1.81 / $43) = 9.2%

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**What is a reasonable final estimate of kcs?**

Method Estimate CAPM 11.58% DCF 9.2% Average 10.4%

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Calculate WACC If 40% of your financing is from debt at an after tax cost of 8% and 60% is from pref. stock at 10%, what is the WACC? It will be between what two numbers?

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40% (.08) + 60% (.10) = .092 9.2%

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**Balance Sheet use costs that were just calculated**

Cash 5,000 LT Debt 3,000 Equipment Pref. Stock 1,000 Stock 6,000 Tot. Assets 10,000 Tot. Debt & Eq. Market values

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**Ignoring issuance costs, what is the firm’s WACC?**

WACC = xd(pretax kd)(1-Tax) + xpkp + xcskcs = .3(10%)(0.6) + .1(7.2%) + .6(10.4%) = 1.8% % + 6.2% = 8.7%

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WACC You are analyzing the cost of capital for a firm that is financed with 60 percent equity and 40 percent debt. The after-tax cost of debt capital is 10 percent, while the cost of equity capital is 20 percent for the firm. What is the overall cost of capital for the firm? (.6 x .2) + (.4 x .1) = 16% Equity + Debt

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Cardinal Health has bonds outstanding with 15 years to maturity and are currently priced at $800. If the bonds have a coupon rate of 8.5 percent, then what is the after-tax cost of debt for Beckham if its marginal tax rate is 30%? 7.9%

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**Should the company use the composite WACC as the hurdle rate for each of its projects?**

NO! The composite WACC reflects the risk of an average project undertaken by the firm. Therefore, the WACC only represents the “hurdle rate” for a typical project with average risk. Different projects have different risks. The project’s WACC should be adjusted to reflect the project’s risk.

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**Optimum Capital Structure**

The optimal (best) situation is associated with the minimum overall cost of capital: Optimum capital structure means the lowest WACC Usually occurs with 30-50% debt in a firm’s capital structure WACC is also referred to as the required rate of return or the discount rate

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**Optimal Capital Structure**

Cost (After-tax) Weights Weighted Cost Financial Plan A: Debt………………………… % % % Equity……………………… 10.9% Financial Plan B: Debt………………………… % % % Equity……………………… 10.3% Financial Plan C: Debt………………………… % % % Equity……………………… 11.4%

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Cost of capital curve

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