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**CHAPTER 09 Cost of Capital**

Outline Sources of capital Component costs WACC Adjusting for flotation costs Adjusting for risk

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**Overview of the Cost of Capital**

The cost of capital represents the firm’s cost of financing, and is the minimum rate of return that a project must earn to increase firm value. Financial managers are ethically bound to only invest in projects that they expect to exceed the cost of capital. The cost of capital reflects the entirety of the firm’s financing activities. Most firms attempt to maintain an optimal mix of debt and equity financing. To capture all of the relevant financing costs, assuming some desired mix of financing, we need to look at the overall cost of capital rather than just the cost of any single source of financing.

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**Overview of the Cost of Capital (cont.)**

A firm is currently faced with an investment opportunity. Assume the following: Best project available today Cost = $100,000 Life = 20 years Expected Return = 7% Least costly financing source available Debt = 6% Because it can earn 7% on the investment of funds costing only 6%, the firm undertakes the opportunity.

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**Overview of the Cost of Capital (cont.)**

Imagine that 1 week later a new investment opportunity is available: Best project available 1 week later Cost = $100,000 Life = 20 years Expected Return = 12% Least costly financing source available Equity = 14% In this instance, the firm rejects the opportunity, because the 14% financing cost is greater than the 12% expected return.

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**Overview of the Cost of Capital (cont.)**

What if instead the firm used a combined cost of financing? Assuming that a 50–50 mix of debt and equity is targeted, the weighted average cost here would be: (0.50 6% debt) + (0.50 14% equity) = 10% With this average cost of financing, the first opportunity would have been rejected (7% expected return < 10% weighted average cost), and the second would have been accepted (12% expected return > 10% weighted average cost).

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

Long-Term Debt Preferred Stock Common Stock Retained Earnings New Common Stock

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**Weighted Average Cost of Capital (WACC)**

The weighted average of the component costs of debt, preferred stock and common equity. The w’s are all weights of different components. The r’s are all the rate of return to be paid to the investors. T is the tax rate.

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**Should our analysis focus on historical (embedded) 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). The relevant cost of capital for a firm is the marginal cost of capital necessary to raise the next marginal dollar of financing the firm’s future investment opportunities. A firm’s future investment opportunities in expectation will be required to exceed the firm’s cost of capital.

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Cost of debt, rd The quoted interest rate the firm must pay on new debt. But, the interest payments paid to bondholders are tax deductable for the firm, so the interest expense on debt reduces the firm’s taxable income and, therefore, the firm’s tax liability. Thus the tax advantage is taken into account while calculating the cost of debt. After tax cost of debt is used, rd(1-T).

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**Cost of Preferred Stock, rp**

Preferred stock gives preferred stockholders the right to receive their stated dividends before the firm can distribute any earnings to common stockholders. rp is the rate of return investors require on firm’s preferred stocks. rp = Dp/Pp Preferred dividends are not tax-deductible, so no tax adjustments necessary.

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**Cost of Common Stock (rs)**

The cost of common stock is the return required on the stock by investors in the marketplace. There are two forms of common stock financing: retained earnings new issues of common stock The cost of common stock equity, rs, is the rate at which investors discount the expected dividends of the firm to determine its share value.

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**Cost of Common Stock (cont.)**

Equity has two components: Retained earnings & common stocks Cost of retained earnings = opportunity cost of investing in more stocks i.e. required rate of return Cost of common stocks = required rate of return and flotation cost of the firm’s shares.

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**Cost of Common Stock (cont.)**

The capital asset pricing model (CAPM) describes the relationship between the required return, rs, and the nondiversifiable risk of the firm as measured by the beta coefficient, b. rs = RF + [b (rm – RF)] where RF = risk-free rate of return rm = market return; return on the market portfolio of assets

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**Methods of calculating rs**

CAPM approach, r = rRF + (rM - rRF)b Dividend yield plus expected growth rate, r = (D1/P0) + g Final estimate of rs is the average of all the alternative estimates

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Flotation costs The percentage cost of issuing new common stock given to investment bankers or brokers. It is usually adjusted with the required rate of return to find the cost of equity. Flotation costs depend on the risk of the firm and the type of capital being raised. The flotation costs are highest for common equity. However, since most firms issue equity infrequently, the per-project cost is fairly small. We will frequently ignore flotation costs when calculating the WACC.

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**Flotation Cost Adjustment**

The amount that must be added to estimated rs to account for floatation cost. F = Floatation cost per share

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

The weighted average cost of capital (WACC), ra, reflects the expected average future cost of capital over the long run; found by weighting the cost of each specific type of capital by its proportion in the firm’s capital structure. WACC, ka = wdkd(1-T) + wpkp + wsks = 0.3(10%)(0.6) + 0.1(9%) + 0.6(14%) = 1.8% + 0.9% + 8.4% = 11.1% Where, wd + wp + ws=1.0

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**Weighted Average Cost of Capital (cont.)**

Three important points should be noted in the equation for WACC: For computational convenience, it is best to convert the weights into decimal form and leave the individual costs in percentage terms. The weights must be non-negative and sum to 1.0. Simply stated, WACC must account for all financing costs within the firm’s capital structure. The firm’s common stock equity weight, ws, is multiplied by either the cost of retained earnings, rr, or the cost of new common stock, rn. Which cost is used depends on whether the firm’s common stock equity will be financed using retained earnings, rr, or new common stock, rn.

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**Weighted Average Cost of Capital (cont.)**

The costs of the various types of capital for Duchess Corporation to be as follows: Cost of debt, rd = 5.6% Cost of preferred stock, rp = 10.6% Cost of retained earnings, rr = 13.0% Cost of new common stock, rn= 14.0% The company uses the following weights in calculating its weighted average cost of capital: Long-term debt = 40% Preferred stock = 10% Common stock equity = 50%

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**Table 9.1 Calculation of the Weighted Average Cost of Capital for Dutchess Corporation**

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**Factors affecting WACC**

Factors firm cannot control Interest rates in the economy General level of stock prices Tax rates Factors that firm controls Capital Structure Dividend payout ratio Capital Budgeting decisions: Firms with riskier projects generally have a higher WACC.

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