Question

Lomholt Manufacturing Limited is a small listed company which has a strategy of maintaining a $1 million book-value capital structure. Lomholt Manufacturing Limited currently earns $250,000 per year before corporate taxes of 50%, has an all-equity capital structure of 100,000 shares and distributes all of its earnings as dividends. The company is considering issuing debt and using the proceeds to repurchase shares. The company is able to repurchase shares at the current price of $10 per share. The Chief Financial Officer (CFO) of the company has provided the following estimates for the cost of debt and resulting share price for the company’s equity at various potential debt levels:

Amount of Debt	Debt-to-Total Assets Ratio	Average Pre-tax Cost of Debt	Resulting Share Price
$0	0.00	-	$10.00
$200,000	0.20	10.00%	$10.50
$400,000	0.40	11.00%	$11.00
$600,000	0.60	14.00%	$9.50

Provide answers to the following questions:

1. By observation, what do you think is the firm’s optimal capital structure? Why?
2. Determine the after-tax cost of debt (R_D), the after-tax cost of equity (R_S) and the weighted average cost of capital (WACC) at each potential leverage position for the firm. Construct a graph which relates the computed after-tax capital costs to the respective leverage (debt-to-total asset) ratios.

Do the figures and/or the graph from question 2) confirm your answer provided in question 1)?

Answer 1

1. option no. 3 in the above table i.e. $400,000 debt & $600,000 equity is the optimal capital structure for the company. As the resulting share price is highest for the company in this case of debt to total asset ratio of 0.4. The other cases aren't optimal although they increase Earning Per Share for the company but shareholders stand to loose as share price is lower.

2. Formula

After tax cost of debt = Pre-tax cost of debt * (1 - tax rate)

after tax cost of equity = dividend/ market capitalisation of company (derieved from dividend discount model - price = dividend/ cost of equity).

debt to total asset	Profit before tax	interest cost	adjusted PBT	tax (@50%)	profit after tax	dividend	market cap.	cost of equity
0	250,000	0	250,000	125000	125,000	125,000	10*100,000= 1,000,000	12.5%
0.2	250,000	20,000	230,000	115,000	115,000	115,000	10.5*100,000= 1,050,000	10.95%
0.4	250,000	44,000	206,000	103,000	103,000	103,000	11*100,000= 1,100,000	9.36%
0.6	250,000	84000	166,000	83,000	83,000	83,000	9.5*100,000= 950,000	8.74%

amount of debt	after tax cost of debt [a]	after tax cost of equity[b]	WACC[a+b]
0	0% * 0 = 0%	12.5% * 1.0 = 12.5%	12.5%
0.2	{10% * 0.5} * 0.2 = 1%	10.95% * 0.8 = 8.76%	9.76%
0.4	{11% * 0.5} * 0.4 = 2.2%	9.36% * 0.6 = 5.62%	7.82%
0.6	{14% * 0.5} * 0.6 = 4.2%	8.74% * 0.4 = 3.5%	7.7%

Overall view - even though the lowest WACC is seen in scenario 4 where debt-to-total asset is at 0.6 but the maximum share price is seen in scenario 3 where debt-to-total asset is at 0.4 - one of the reason is that excess debt in the total capital is considered dangerous for the company as interest on debt is a fixed cost needs to be paid regardless whether company is in profit or loss. Here, the company should choose scenario 3 even though WACC is marginally higher but shareholders should make money in the long run.