- 15 Marks
FM – L2 – Q40 – Capital structure
Question
A company has estimated that its cost of debt capital varies according to the level of gearing, as follows:
| Gearing | Cost of debt |
|---|---|
| 20 | 5.0 |
| 30 | 5.4 |
| 40 | 5.8 |
| 50 | 6.5 |
| 60 | 7.2 |
Gearing is measured as the market value of the company’s debt as a proportion of the total market value of its equity plus debt.
The rate of tax is 30%. The ungeared equity beta factor for the company is 0.90. The risk-free rate of return is 4% and the return on the market portfolio is 9%.
Required:
Identify the optimal gearing level and WACC.
Answer
The optimal WACC is the lowest WACC, because this will maximise the value of the company and the wealth of shareholders.
Step 1
Calculate the geared beta for equity at each level of gearing.
| Gearing | Geared beta |
|---|---|
| 20% | 0.90 × [80 + 20(1 – 0.30)] / 80 = 1.057 |
| 30% | 0.90 × [70 + 30(1 – 0.30)] / 70 = 1.170 |
| 40% | 0.90 × [60 + 40(1 – 0.30)] / 60 = 1.320 |
| 50% | 0.90 × [50 + 50(1 – 0.30)] / 50 = 1.530 |
| 60% | 0.90 × [40 + 60(1 – 0.30)] / 40 = 1.845 |
Step 2
Use the geared beta value and the CAPM to calculate a cost of equity at each gearing level.
| Gearing | Cost of equity (4% + β(9 – 4)%) |
|---|---|
| 20% | 4 + 1.057 × 5 = 7.17% |
| 30% | 4 + 1.170 × 5 = 7.51% |
| 40% | 4 + 1.320 × 5 = 7.96% |
| 50% | 4 + 1.530 × 5 = 8.59% |
| 60% | 4 + 1.845 × 5 = 9.54% |
Step 3
Calculate the WACC at each level of gearing, and identify the gearing level with the lowest WACC.
| Gearing | WACC |
|---|---|
| 20% | [20% × 5.0(1 – 0.30)] + [80% × 7.17] = 6.44% |
| 30% | [30% × 5.4(1 – 0.30)] + [70% × 7.51] = 6.39% |
| 40% | [40% × 5.8(1 – 0.30)] + [60% × 7.96] = 6.40% |
| 50% | [50% × 6.5(1 – 0.30)] + [50% × 8.59] = 6.59% |
| 60% | [60% × 7.2(1 – 0.30)] + [40% × 9.54] = 6.84% |
Conclusion
The optimal gearing level is 30%, because the WACC is lowest at this gearing level. However, the WACC is almost as low at a gearing level of 40%.
- Topic: Capital structure
- Uploader: Samuel Duah