FM – L2 – Q40 – Capital structure

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.

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%.