Question

SOS Ltd is currently an all-equity firm and has a market value of $800,000. SOS is evaluating whether a levered capital structure would maximize the wealth of shareholders. The cost of equity is currently 15%. The new capital structure under consideration is an issue of $400,000 new perpetual debt with an 8% interest rate. There are currently 32,000 shares outstanding and a tax rate of 35% applies to this firm. If SOS finally changes to the new levered capital structure,

(a) Calculate the present value of tax shield and explain it briefly. (Show your calculations).

(b) Calculate the firm value and the cost of equity under the levered capital structure. Explain the change in cost of equity briefly. (Show your calculations).

(c) Calculate the WACC under the levered capital structure. (Show your calculations).

(d) What are the stock prices of SOS before and after announcement of the new capital structure? Explain the price change briefly. (Show your calculations).

(e) Suppose the actual stock price of SOS after announcement of the new capital structure is lower than your answer in part (d) above, what could be the possible reasons for this?

Answer 1

According to Modigliani Miller proposition with corporate taxes, value of levered firm = value of unlevered firm + present value of tax shield.

Also, as debt increases, so does the cost of equity.

The equation is Rs= Ro + D/S(1-t)*(Ro-Rd)

Where Rs is new cost of equity taking debt into consideration in capital structure

Ro is the cost of unlevered firms equity

Rd is the cost of debt

D/S is debt equity ratio with new levered equity S

and t is tax

a. Every year tax would be saved when debt is added into capital structure. Annual amount of tax shield by debt is given by

Rd*loan amount*tax rate

= 0.08*400,000*0.35 = 11200

The firm would pay 11200 less taxes every year because of debt inclusion.

This is annual anount of savings. For perpetuity we would save 11200/0.08 = 140,000

Thus present value of tax shield = 140,000

b. Firm value with leverage= Unlevered value + tax shield

Thus, new firm value = 800,000+140,000 = 940,000

Value of levered equity = New firm value- debt amount = 940,000-400,000 = 540,000

New cost of equity = Rs = 15+(400,000/540,000)*(1-0.35)*(15-8) = 15+3.37 = 18.37%

Cost of equity increases as debt increases. This happens as risk for equity holders increases. Debt interest needs to be paid, leaving less for shareholders. The higher the debt, the higher the cost of equity.

c. WACC = (S/V levered)*Rs +( D/V levered)*Rd*(1-t)

Wacc = (540,000/940000)*18.37 + (400,000/940000)*8*(1-0.35) = 10.55+2.21 = 12.76%

d. Stock price before debt announcement= 800,000/32000 = $ 25

Stock price after announcement = Value of Levered firm / shares outstanding = 940,000/32000 = $29.375

Debt has not been issued yet. Therefore, only equity appears on right side of balance sheet. The value of firm increases due to present value of tax shield. If we assume that capital markets efficiently price securities, the increase occurs immediately. That is, rise occurs on date of announcement itself. Equity holders gain as they are owners of the firm.

We can only answer 4 parts in one question. I request you to ask other parts separately. Kindly upvote if you liked it. If you any queries, ask in comments.