Understanding the cost of capital
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The Cost of Capital is defined as the rate of return that a company must offer on its securities in order to maintain its market value.

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Understanding the Cost of Capital

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Understanding the Cost of Capital

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Cost of Capital

  • The Cost of Capital is defined as the rate of return that a company must offer on its securities in order to maintain its market value.

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Cost of Capital

  • Financial managers must know the cost of capital in order to

  • Make capital budgeting decisions,

  • Help establish the optimal capital structure and

  • Make decisions concerning leasing, bond refunding and working capital management.

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Cost of Capital

  • The cost of capital is computed as a weighted average of the various capital components, items on the right hand side of the balance sheet such as debt, preferred stock, common stock and retained earnings.

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Weighted Average Cost of Capital

  • Each element of capital has a component cost that is identified by the following:

  • ki = before tax cost of debt

  • k­d = ki (1-t) = after tax cost of debt, where t = tax rate

  • kp = cost of preferred stock

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Weighted Average Cost of Capital

  • ks = cost of retained earnings (or internal equity)

  • ke = cost of external equity, or cost of issuing new common stock

  • ko = company’s overall cost of capital , or a weighted average cost of capital

  • The after tax weighted average cost of capital (WACC) is given by the following formula:

  • WACC = ka = ke = (S/V) + kd (1-t) (D/V)

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An Example of Cost of Capital

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Formula for Cost of Capital

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An Example of Cost of Capital

  • Suppose this firm faces a corporate tax rate of 40%, has variable expenses equal to 30% of sales, and has fixed costs of $158.

  • Working back from these requirements we can forecast the level of sales the firm must earn in order to achieve these operating results…thereby setting a sales performance target for management.

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An Example of Cost of Capital

  • Working backwards, we get:

  • SalesX

  • Variable Costs0.3X

  • Fixed Costs158

  • EBIT

  • Interest42

  • Taxes (40%)

  • Net Income:300

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An Example of Cost of Capital

  • If sales = X, then VC = .3X and X - .3X – 158 = EBIT

  • (EBIT – I)(1-T) = NI so (EBIT – 42)(1-.4) = 300 => EBIT = 542 which => X = 1000, and so VC = 300 and also Taxes = (542-42)(.4) = 200, so:

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An Example of Cost of Capital

  • Sales1000

  • Variable costs300

  • Fixed costs158

  • EBIT542

  • Interest42

  • Taxes (40%)200

  • Net Income:300

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An Example of Cost of Capital

  • This working backwards process is the approach taken by regulators to set pricing for rate of return regulated industries, like utilities. So cost of capital drives utility rate increases!

  • Assuming earnings are a perpetuity, we have

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An Example of Cost of Capital

  • P = EPS/Ke = ROE* BVPS/Ke

  • Firm ABC has:

  • Debt D of 8% annual coupon bonds with 10 years to maturity and book value of $1 m.

  • Preferred shares P with 10% annual dividend and book value of $1 m.

  • 100,000 Common shares originally issued at $15/share for a value of $1.5 m.

  • Retained earnings of $0.5

  • Total of $4 m.

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An Example of Cost of Capital

  • Market values:

  • The present market rate of similar risk 10 year bonds is 6% so the market value of the bonds is given by 80,000PVIFA(10 years, 6%) = [80000/.06](1-1/1.06^10) + 1,000,000/1.06^10 = $1,147,202.

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An Example of Cost of Capital

  • Similar risk preferred shares are providing yields of 8%, so the market value of the preferred shares is 100,000/.08 = $1,250,000.

  • The market value of the common shares is currently $25/share, so the total market value of the shares is $2,500,000.

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An Example of Cost of Capital

  • The market value of the firm’s balance sheet V = D + P + SE = $1,147,202 + $1,250,000 + $2,500,000 = $4,897,202 and D/V = .234, P/V = .255 and SE/V = .511.

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