Question

CAPITAL STRUCTURE PROBLEM The following data reflect a firm's condition. current financial Value of debt (book value=market value) $ 5,000,000 Market value of equity (P. x shares) $ 25,000,000 Total value of firm $ 30,000,000 EBIT $ 5,500,000 Tax Rate (T) 40% At the current level of debt, the cost of debt (k) is 100 and the firm's beta = 1.5. The firm is questioning the possibility of issuing $1,500,000 of additional debt and using the proceeds to repurchase stock. If it does, the interest on new debt would rise to 12t and beta would rise to 2.0. (The old 10debt would remain outstanding.) E[R] = 10% and R, = 63. (1) Calculate the value of the firm at the higher level of debt and decide if the firn should increase its debt to $6,500,000. The market price of the firm's stock was originally $25.00. Calculate the new stock price (P') at a debt level of $6,500,000. Calculate the value of EPS under the original debt level of $5,000,000 and its value under the higher debt level of $6,500,000. (4) How does your answer to (3) influence the decision you made in answering (1)? EXPLAIN! (5) Calculate the WACC, ka, at the original debt level of $5,000,000. (6) Calculate the WACC, ka $6,500,000 at the new debt level of (7) Do the results of (5) and (6) above contradict or support the decision you made in answering (1)? EXPLAIN!

Answer 1

(1)

Value of the firm with additional debt = Value of the firm before additional debt + Additional Tax shield

30,000,000 + 0.40 * 1,500,000 = $30,600,000  

Based on the value of the firm, additional debit can be issued.

(2) To arrive at new share price p^,

First calculate the new equity value i.e Firm value after additional debt - Current Debt

= $ 30,600,000 - $ 6,500,000 = $ 24,100,000

Second check the no. of shares outstanding after repurchase.

Originally $25,000,000 equity @ $ 25 per share gives us 1000,000 shares outstanding.

No. of shares repurchased with additional debt of $1,500,000 = 1,500,000 / 25 = 60,000

So the no. of shares outstanding after repurchase = 1,000,000 - 60,000 = 940,000

Finally, new share price = Equity value / No. of shares outstanding = 24,100,000 /940,000 = 25.64

(3 )

Originally with 1 Million shares and a debt of 5 Million
EBIT	5,500,000.00
Interest @ 10% on 5 Million	500,000.00
EBT	5,000,000.00
Tax @ 40%	2,000,000.00
Net Income	3,000,000.00
EPS = NI / No of outstanding shares	3.00
Higher debt level of 6.5 Million and 940000 shares
EBIT	5,500,000.00
Interest @12%	780,000.00
EBT	4,720,000.00
Tax @40%	1,888,000.00
Net Income	2,832,000.00
EPS = NI / No of outstanding shares	3.01

(4) It is clear now that apart from tax shield savings additional debt also increased the earning per share. Increase in EPS is seen as a positive sign. A share repurchase signals that the company believes in a strong future and the stock is currently undervalued. So it it beneficial to raise additional debt.

(5) Before calculating WACC let us arrive at the cost of equity. We use CAPM for this.

R_{e =} R_{f +} Beta ( R_{m -} R_f) = 0.06 + 1.5 ( .10-.06) = .12 or 12%

WACC = D / V * r_d * (1-t) + E /V * r_e = 5000,000/30,000,000 * .10 (1-.4) + 25,000,000/30,000,000 *.12 = 0.11 or 11%

(6) WACC at new debt level

Cost of equity using CAPM  R_{e =} R_{f +} Beta ( R_{m -} R_f) = 0.06 + 2 ( .10-.06) = .14 or 14%

WACC = D / V * r_d * (1-t) + E /V * r_e = 6,500,000/30,600,000 * .12 (1-.4) + 24,100,000/30,600,000 *.14 = 0.1256 or 12.56%

(7) As per Modigiliani Miller propositions with taxes the important point to be noted is that debt maximizes the value of the company and minimizes the WACC. This means the following

a. An all equity firm value is less than the value of the firm with debt due to savings from tax shield.

b. The cost of equity increases with increase in borrowing but at a slower rate because of the tax component.

An all equity firm cost of equity is represented as R_e= r₀ + ( r_{0 -} r_d) D/ E where r_{0 is cost of all equity.}

A firm with debt cost of equity is represented as R_e= r₀ + ( r_{0 -} r_d) (1-) D/ E

So clearly the cost of equity increases but at a slower rate minimizing the WACC.

It is advisable to borrow additional 1.5 million.