Principles of Corporate Finance_ 12th Edition

504 Part Five Payout Policy and Capital Structure

bre44380_ch19_491-524.indd 504 09/30/15 12:07 PM

because of financial risk, but notice that WACC declines. The decline is not caused by use of

“cheap” debt in place of “expensive” equity. It falls because of the tax shields on debt inter-

est payments. If there were no corporate income taxes, the weighted-average cost of capital

would be constant, and equal to the opportunity cost of capital, at all debt ratios. We showed

this in Chapter 17.

Figure 19.1 shows the shape of the relationship between financing and WACC, but initially

we have numbers only for Sangria’s current 40% debt ratio. We want to recalculate WACC at

a 20% ratio.

Here is the simplest way to do it. There are three steps.

Step 1 Calculate the opportunity cost of capital. In other words, calculate WACC and the

cost of equity at zero debt. This step is called unlevering the WACC. The simplest unlevering

formula is

Opportunity cost of capital = r = rDD/V + rEE/V

This formula comes directly from Modigliani and Miller’s proposition 1 (see Section 17-1).

If taxes are left out, the weighted-average cost of capital equals the opportunity cost of capital

and is independent of leverage.

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 Modigliani and Miller’s proposition 2 (see Section 17-2). It calls for D/E, the

ratio of debt to equity, not debt to value.

Step 3 Recalculate the weighted-average cost of capital at the new financing weights.

Let’s do the numbers for Sangria at D/V = .20, or 20%.

◗ FIGURE 19.1

This plot shows WACC for the Sangria

Corporation at debt-to-equity ratios of 25%

and 67%. The corresponding debt-to-value

ratios are 20% and 40%.

0.25

(D/V = 0.2)

0.67

(D/V = 0.4)

10.8

9.42

6.0

12.4

9.0

6.0

Cost of equity (rE )

Cost of debt (rD )

Opportunity cost of capital (r = 9.84)

WACC

9.84

6

Debt–equity ratio (D/E )

Rates of return, %

BEYOND THE PAGE

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Try it!

Figure 19.1:

Sangria’s WACC