Reacher Technology has consulted with investment bankers and determined the interest rate it would pay for different capital structures, as shown below. Data for the risk-free rate, the market risk premium, an estimate of Reacher’s unlevered beta, and the tax rate are also shown below. Based on this information, what is the firm’s optimal capital structure and what is the weighted average cost of capital at the optimal structure?
| Percent Financed with Debt (wd) | Before-tax Cost Debt (rd) | |
| 0% | 6.0% | |
| 10% | 6.1% | |
| 20% | 7.0% | |
| 30% | 8.0% | |
| 40% | 10.0% | |
| 50% | 12.5% | |
| 60% | 15.5% | |
| 70% | 18.0% |
| Fill in formulas in the yellow cells to find the optimum capital structure. | ||||||
| Debt/Value | Equity/Value | Debt/Equity | A-T Cost of | Levered | Cost of | |
| Ratio (wd) | Ratio (ws) | Ratio (wd/ws) | Debt (rd) | Beta | Equity | WACC |
| 0% | 1.0 | 0.00 | ||||
| 10% | 0.9 | 0.11 | ||||
| 20% | 0.8 | 0.25 | ||||
| 30% | 0.7 | 0.43 | ||||
| 40% | 0.6 | 0.67 | ||||
| 50% | 0.5 | 1.00 | ||||
| 60% | 0.4 | 1.50 | ||||
| 70% | 0.3 | 2.33 | ||||
| WACC at optimum debt ratio = | ||||||
| Optimum debt ratio = | ||||||
WACC Optimal Debt Ratio Answer
| Debt/Value | Equity/Value | Debt/Equity | A-T Cost of | Levered | Cost of | D/A at min. WACC | ||
| Ratio (wd) | Ratio (ws) | Ratio (wd/ws) | Debt (rd) | Beta(bL) | Equity (rs) | WACC | ||
| 0% | 1.0 | 0.00 | 3.60% | 0.80 | 5.30% | 5.30% | 0 | |
| 10% | 0.9 | 0.11 | 3.66% | 0.85 | 5.35% | 5.04% | 0 | |
| 20% | 0.8 | 0.25 | 4.20% | 0.92 | 5.42% | 4.84% | 0 | |
| 30% | 0.7 | 0.43 | 4.80% | 1.01 | 5.51% | 4.72% | 0.3 | |
| 40% | 0.6 | 0.67 | 6.00% | 1.12 | 5.62% | 4.81% | 0 | |
| 50% | 0.5 | 1.00 | 7.50% | 1.28 | 5.78% | 5.14% | 0 | |
| 60% | 0.4 | 1.50 | 9.30% | 1.52 | 6.02% | 5.76% | 0 | |
| 70% | 0.3 | 2.33 | 10.80% | 1.92 | 6.42% | 6.46% | 0 | |
| Calculation: | ||||||||
| Working Note: Following calculations are only for first value, remaining values will be calculated in same manner. | ||||||||
| After Tax Cost of Debt: | ||||||||
| A-T rd = rd(1-T) | After tax cost of debt for 0% debt ratio = 6%*(1-40%) = 3.60% | |||||||
| Levered Beta: | ||||||||
| bL = bU [1+ (1-T)(D/S)] | Levered Beta for 0% debt ratio = 0.8[1+(1-40%)(0) = 0.8 | |||||||
| Cost of Equity: | ||||||||
| rs = rRF + b(rM-rRF) | Cost of equity for 0% debt ratio = 4.5%+0.8(5.5%-4.5%) = 5.30% | |||||||
| WACC: | ||||||||
| WACC = wd(rd)(1-T) + ws(rs) | WACC = 0*3.60%*(1-40%)+1*5.30% = 5.30% | |||||||
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