公司金融理论Lecture 7 Estimating the firm's cost of capital, WACC(4)

Step 3: Recalculate the WACC at the new financing weights
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3-Step adjustment example
Step 1: The firm’s current debt ratio is .4, so r = rDD/V + rEE/V = 0.06(.4) + 0.124(.6) =0.0984 Step 2: We will assume that the debt cost stays at 6% when the debt ratio is 20%, then rE = r + (r – rD)D/E = 0.0984 + (0.0984 -0.06)(.2/.8) =0.108 Cost of equity decreases because of lower financial risk Step 3: Recalculate WACC at the new debt ratio WACC = 0.06(1 - 0.35)(.2) + 0.108(.8) = 0.0942 WACC increases only because of the lower tax shields on reduced interest payments
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Valuing businesses
Do not deduct interest and calculate taxes as if the company were all-equity financed Usually forecast each year’s FCF out to an arbitrary medium-term valuation horizon (H) and add a terminal value to the cash flows in the horizon year
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Adjusted discount rate
As interest is a tax-deductible expense, the value of interest tax shield on debt supported by a project has to be incorporated into the
The terminal value (or horizon value) is the present value at the horizon of all subsequent cash flows (PVH)
valuation The adjustment is usually to calculate NPV by discounting after-tax cash flows at an adjusted discount rate, the after-tax weighted average cost of capital (WACC)
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WACC
D = market value of the firm’s debt E = market value of the firm’s equity V = D + E is the total market value of the firm rD = current cost of debt rE = current cost of equity TC = marginal corporate tax rate The after-tax cost of debt, rD(1 - TC), is used to
D E rE V V
Step 2: Estimate the cost of debt, rD, at the new debt ratio and calculate the new cost of equity: rE = r + (r – rD)D/E

This formula is MM’s proposition 2 in lecture 8
Lsinesses
You can use WACC to value an entire company or business as long as the debt ratio is to remain approximately constant
Treat the company as it were one big project and forecast the firm’s free cash flow (FCF) FCF = profit after tax + depreciation – investment in fixed assets – investment in working capital
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Review of assumptions
Users of WACC need not worry about small or temporary fluctuations in debt ratios that do not change the firm’s long-term financing policy Suppose that the firm borrows $12.5M but the project supports only $5M of debt capacity, then
expected equity income Expected equity return rE equity value $1.125 [(0.06)(1 0.35)($5)] 0.124 $7.5
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Review of assumptions
If a project has different business risk to the firm’s
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3 Steps to adjust WACC when debt ratios differ
Step 1: Calculate the opportunity cost of capital
This step is called unlevering the WACC:
Opportunity cost of capital = r rD
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Example:
A $12.5 million project, funded by $5M debt and $7.5M equity, is expected to generate a perpetual stream of cash flow of $1.731 million
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Learning objectives
Explain the after-tax weighted average cost of capital, WACC Use the WACC to value a project or business How to adjust WACC when business risk or capital structure changes Estimate the WACC in practice with helpful hints
ii. the project will be financed to maintain the firm’s
current, market-value debt ratio
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Example: BMA pp480-481
Cost of debt (rD)
0.06 Cost of equity (rE) 0.124 Marginal tax rate (TC) 0.35 Debt ratio (D/V) $500/$1250 = 0.4 Equity ratio (E/V) $750/$1250 = 0.6 WACC = rD(1 – TC)(D/V) + rE(E/V) = (0.06)(1 - 0.35)(0.4) + (0.124)(0.6) = 0.09 or 9.0%
per year pretax
The project is average risk, so we can use WACC to discount its after-tax cash flow of (1 - 0.35)($1.731)=$1.125 million NPV = -$12.5 + ($1.125/0.09) = 0
other assets, or if its acceptance would lead to a permanent, material change in the firm’s debt ratio, the firm can use WACC as a benchmark rate to be adjusted for differences in business risk or debt ratios Discounting cash flows by the WACC is only approximately correct if the firm does not adjust its borrowing (rebalance its capital structure) to maintain a constant debt ratio over time
D E WACC rD (1 TC ) rE V V
capture the value of interest tax shields