Question

On January 1 the total market value of DOS Company was $50 million. During the year, the company plans to raise and invest $10 million in new assets. The firm's present market value, optimal capital structure is $10 million debt and $40 million equity. Up to $1 million in new bonds can be sold for $975 each if the maturity is 10 years, the face value is $1000 and the annually paid coupon rate is 11%. Selling any bonds beyond that point will raise only $950 each. Assume that there is no short-term debt. The common stock is currently selling at $45 per share and new shares can be sold with a 9% floatation costs. The beta of the firm is 1.5 and the risk-free rate is 8% while the return on the market is 12%. The dividend is $3.38 to be paid next year, and the firm has an annual expected growth rate of 7.5% which is expected to be continuous for the foreseeable future. The bond yields plus risk premium approach assumes that stock earn at least 4% more than the initial rate on debt issued by the company. Retained earnings are projected to be $5 million and the marginal tax rate is 40%.

A. How much of the $10 million capital budget must be financed by equity to maintain the optimal capital structure? How much of the new funds are generated by new debt? How much will come from new stock?

B. Calculate the two costs of debt.

C. Estimate the current cost of equity by taking an average of the three different methods of estimation.

D. What is the cost of equity after flotation costs?

E. Are there any breakpoints in this WACC, where are they located, and what caused them to occur?

F. Calculate the WACC both before and after the breakpoints.

Answer 1

A). Optimal capital structure is debt (D) to equity (E) of 10:40 so out of the required 10 million capital, 4/5*10 = 8 million will be equity and 2 million will be debt, if optimal capital structure is to be maintained.

DSO needs to raise 10 million so out of the 8 million, 5 million can come from retained earnings and the remaining 3, from new stock issue. 2 million will be raised through new debt.

B). Cost for bonds sold at $975:

PV = -975; FV = 1,000; PMT = coupon rate*par value = 11%*1,000 = 110; N = 10; solve for RATE. YTM = 11.43%

After-tax cost of debt = YTM*(1-tax rate) = 11.43%*(1-40%) = 6.86%

Cost for bonds sold at $950:

PV = -950; FV =1,000; PMT = 110; N = 10; solve for RATE. YTM = 11.88%

After-tax cost of debt = 11.88%*(1-40%) = 7.13%

C). Cost of equity (using CAPM) = risk-free rate + beta*(market return - risk-free rate) = 8% + 1.5*(12%-8%) = 14%

Cost of equity (using DDM) = Expected dividend/current price + growth rate

= (3.38/45) + 7.5% = 15.01%

Cost of equity (using bond yield plus premium) = Initial rate on debt + 4% = 11.43% + 4% = 15.43%

Average cost of equity = (14% + 15.01% + 15.43%)/3 = 14.81%

D). Cost of equity (after flotation costs) = 14.81%/(1-f) = 14.81%/(1-9%) = 16.28%

E). First break point will occur at 5 million capital (1 million debt and 4 million equity from retained earnings). 2nd break point will occur at 10 million capital (next 1 million debt, 1 million from retained earnings and 3 million from new stock). Beyond that, (after 2 million of debt) debt cost will remain constant and equity will be solely raised from new stock as retained earnings will be exhausted.

F).

Debt amount	Debt (kd)	Equity amount	Equity (ke)	Debt weight (wd)	Equity weight (we)	WACC (kd*wd) + (ke*we)
1 million debt	6.86%	4 million	14.81%	0.20	0.80	13.22%
1 million debt	7.13%	4 million	15.91%	0.20	0.80	14.16%
Over 2 million	7.13%	Over 8 million	16.28%	0.20	0.80	14.45%

ke of 15.91% is a mix of cost of retained earnings and cost of new stock issue computed as,

(1/4*14.81%) + (3/4*16.28%) = 15.91%