Build-a-Model: WACC and Optimal Capital Structure - Spreadsheet Problem 15-12, R

Question

Build-a-Model: WACC and Optimal Capital Structure - Spreadsheet Problem 15-12, Reacher Technology has consulted with investment bankers and determined the interest rate it would pay for different capital structures, as shown in the following table. Data for the risk-free rate, the market risk premium, an estimate of Reacher's unlevered beta, and the tax rate are shown. Based on this information, what's the firm optimal structure, and what is the weighted average cost of capital at optimal structure?

Percent Financed with Debt

0%

10

20

30

40

50

60

70

Before -Tax Cost Debt

6.0%

6.1

7.0

8.0

10.0

12.5

15.5

18.0

Input Data

Risk-free rate 4.5%

Market risk premium 5.5%

Unlevered Data 0.8

Tax rate 40.0%

Explanation / Answer

Where:
BL is the firm's beta with leverage.
Tc is the corporate tax rate.
D/E is the company's debt/equity ratio.

cost of equity= riskfree rate+(levered beta x Market risk premium)



Before -Tax Cost Debt After -Tax Cost Debt levered beta Cost of Equity

6.0% 3.6% .8x[1+(.6x0)]= .8 4.5+(5.5x.8)=8.9%
6.1 3.66% .8x[1+(.6x.11)]= .8528 4.5+(5.5x.8528)=9.19%
7.0 4.2% .8x[1+(.6x.25)]= .92 4.5+(5.5x.92)= 9.56%

8.0 4.8% .8x[1+(.6x.43)]= 1.0064 4.5+(5.5x1.0064)= 10.04%

10.0 6% .8x[1+(.6x.67)]= 1.1216 4.5+(5.5x1.1216)= 10.67%

12.5 7.5% .8x[1+(.6x1)]= 1.28 4.5+(5.5x 1.28)= 11.54%
15.5 9.3% .8x[1+(.6x1.5)]= 1.52 4.5+(5.5x1.52)= 12.86%
18.0 10.8% .8x[1+(.6x2.33)]=1.9184 4.5+(5.5x1.9184)= 15.05%



WACC

(0x3.6 )+ (1x 8.9)= 8.9%

.1x3.66 +.9x 9.19%= 8.637%
.2x4.2+ .8x9.56%= 8.488%
.3x4.8+.7x 10.04%=8.468%

.4x6+.6x10.67%= 8.802%

.5x7.5+.5x 11.54%=9.52%
.6x9.3+ .4x12.86%=10.724%
.7x10.8+.3x 15.05%=12.075%

WACC at optimum debt ratio =8.47%

Optimum debt ratio =.3 or 30%

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