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

a. Interest expenses are deducted before tax and that leads to tax savings for a firm. The tax savings each year is given by (tax rate)*(debt amount)*(rate of debt interest) = 0.35*400000*0.08 = 11200

This is the tax shield on an annual basis.

For perpetual savings of this amount every year, we can use formula A/r where A is annual amount and r is rate of interest = 11200/0.08 = 140,000

Thus tax shield present value is $140,000

b. Firm value is equal to value of unlevered firm plus present value of tax shield

Thus levered firm value = 800,000+140,000 = $940,000

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

According to Modigliani Miller proposition with taxes, the cost of equity Rs for levered firm

Rs = Ro + D/S(1-Tax)*(Ro-Rd) = 15+(400,000/540,000)*(1-0.35)*(15-8) = 18.37%

Where Ro is cost of unlevered firms' equity

Rd is cost of debt

S is value of levered equity and D is debt

The cost of equity increased to 18.37% as debt came into picture increasing the risk for equity holders. Regular interest payments need to be served now increasing risk for shareholders.

c. Wacc for levered firm =( Value of levered equity/value of levered firm)*(cost of levered firms' equity) + (value of debt/value of levered firm)*(cost of debt)(1-tax)

= (540000/940000)*(18.37) + (400000/940000)*(8)*(1-0.35) = 12.76%

d. Stock peice before announcement = value of unlevered firm/shares outstanding=800,000/32000 =$ 25

Stock price after announcement = value of levered firm/shares outstanding = $29.375

As soon as announcement is done, the value of firm increases due to present value of tax shield if we assume that capital markets efficiently price securities. This gain is to owners of firm that is shareholders. This rise occurs on date on announcement itself.

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