Question

please show in Excel

Boom Mechanics is trying to determine its optimal capital structure, which now consists of only debt and common equity. The firm does not Currently use preferred stock in its capital structure, and it does not plan to do so in the future. Its treasury staff has consulted with investment Dankers. On the basis of those discussions, the staff has created the following table showing the firm's debt cost at different debt levels: Debt-to-Equity-to Debt-to- Capital Capital Equity Bond Before-Tax Cost of After Tax Cost of Ratio Ratio Ratio Cost of Beta WACC Rating Debtv.) Equity Debt (wa) (W) (D/E) 0 1 A 4.00% 0.2 0.8 BBB 5.00% 0.4 0,6 BB 8.00% 0.6 0.4 С 10.00% 0.8 0.2 D 13.00% Boom uses the CAPM to estimate its cost of common equity, rs, and estimates that the risk --free rate is 2%, the market risk premium is 6%, and its tax rate is 25%. Boom estimates that if it had no debt, its "unlevered" beta, bu, would be 1.2 What is the firm's optimal capital structure, and what would be its WACC at the optimal capital structure?

Answer 1

Before we calculate the WACC, we first need to calculate the cost of equity for the different combinations of debt and equity as tabulated in the question.

Since the unlevererd Beta has been given at B_U = 1.2, we need to use this for calcualting the levered Beta B_L for the various combinations of debt and equity given in the table.

The formula for levererd beta is B_L = B_U x [ 1 + (1 - Tax Rate) x (Debt / Equity) ]

Using this formula, the Levered Beta is calculated below for the various capital structures:

Levered Beta (BL)	Unlevered Beta (BU)	Tax Rate	Debt to Capital Ratio (Wd)	Equity to Capital Ratio (We)	Debt to Equity Ratio (D/E)
1.20	1.20	25%	0	1	0.00
1.43	1.20	25%	0.2	0.8	0.25
1.80	1.20	25%	0.4	0.6	0.67
2.55	1.20	25%	0.6	0.4	1.50
4.80	1.20	25%	0.8	0.2	4.00

Using the CAPM model, cost of equity is calculated as Re = Rf + Levered Beta (B_L) x Market Risk Premium

where Risk free rate (Rf) = 2%, Market Risk Premium = 6%

Similarly, after tax cost of debt (RdAT) = Before tax cost of debt x (1 - Tax rate) = Rd x (1 - 25%)

Using the above, we get the Weighted Average Cost of Capital as,

WACC = We x Re + Wd x RdAT

Using all the above formulae we tabulate the results as required in the question as below:

Debt to Capital Ratio (Wd)	Equity to Capital Ratio (We)	Debt to Equity Ratio (D/E)	Before-tax cost of debt (Rd)	After-tax cost of debt (RdAT)	Levered Beta (BL)	Cost of Equity (Re)	WACC
0	1	0.00	4.00%	3.00%	1.20	9.20%	9.20%
0.2	0.8	0.25	5.00%	3.75%	1.43	10.55%	9.19%
0.4	0.6	0.67	8.00%	6.00%	1.80	12.80%	10.08%
0.6	0.4	1.50	10.00%	7.50%	2.55	17.30%	11.42%
0.8	0.2	4.00	13.00%	9.75%	4.80	30.80%	13.96%

Since the firm's WACC comes in the lowest at 9.19% for a Debt to Equity ratio of 0.25 times, this is the optimal capital structure for Boom Mechanics as highlighted above and the WACC for this is 9.19%.