Homework Answers
- The value of the firm is governed by the weighted average cost of capital (WACC).
- WACC is weighted average of post tax cost of debt and cost of equity and is calculated as = Proportion of debt, Wd x cost of debt, Kd x (1 - Tax rate) + Proportion of equity, We x Cost of equity, Ke
- It's true that as proportion of debt, Wd in capital structure increases, cost of equity, Ke increase. But cost of debt, Kd usually (excluding the situation of financial distress or bankruptcy) is far lower than cost of equity Ke. Further, once we make it post tax, cost of debt, Kd x (1 - T) is further lower than Ke.
- As Wd increases,
- proportion of WACC contributed by debt [i.e. Wd x Kd x (1 - T)] increases;
- Proportion of equity, We = (1 - Wd) decreases
- Hence, proportion of WACC contributed by We x Ke decreases
- And hence on overall basis WACC decreases and firm's value increases.
- This decreases takes place till the time capital structure hits an optimal debt ratio.
- Any further increase in leverage will now lead to increase in WACC and firm value will start decreasing.
Let me illustrate by an example below. Please see the table below. Please be guided by the second row to understand the mathematics. I have also given you the plot after the table.
| Debt Ratio | Cost of debt | Tax rate | Part of WACC contributed by Debt | Equity ratio | Cost of equity | Part of WACC contributed by Equity | WACC |
| Wd | Kd | T | Wd x Kd x (1 - T) | We = 1- Wd | Ke | WeKe | Wd x Kd x (1-T) + We x Ke |
| 0% | 0% | 30% | 0.00% | 100% | 12.00% | 12.00% | 12.00% |
| 15% | 7.70% | 30% | 0.81% | 85% | 13.00% | 11.05% | 11.86% |
| 30% | 8.80% | 30% | 1.85% | 70% | 14.00% | 9.80% | 11.65% |
| 45% | 11.90% | 30% | 3.75% | 55% | 16.00% | 8.80% | 12.55% |
| 60% | 14.80% | 30% | 6.22% | 40% | 18.00% | 7.20% | 13.42% |
| 75% | 17.50% | 30% | 9.19% | 25% | 20.00% | 5.00% | 14.19% |
| 90% | 20.00% | 30% | 12.60% | 10% | 23.00% | 2.30% | 14.90% |
Hence, as debt increases, even though cost of equity increases, WACC decreases till the time we hit the optimal capital structure and hence value of the firm first increases and then decreases once leverage exceeds the optimal level.
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right hand or bottom"
Blank #2 "then we know our current ... , or the proportion"
(equity capacity / debt capacity)
Blank #3 "the ... capital structure is" ( target / optimal)
Blank #4 "while an ... capital structure" (optimal / actual)
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According to the trade-off theory, a firm's optimal capital structure: is the debt-equity ratio that exists at the point where the firm's weighted after- tax cost of debt is minimized. is the debt-equity ratio that results in the lowest possible weighted average cost of capital. exists when the debt-equity ratio is 0.50. is found by locating the mix of debt and equity which causes the earnings per share...
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Please
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(equity capacity / debt capacity)
Blank #3 "the ... capital structure is" ( target / optimal)
Blank #4 "while an ... capital structure" (optimal / actual)
If correct I will thumbs up, thank you!
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