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

Only 4 parts can be answered in one question. Kindly ask separately mentioning other parts required in a separate question.

a. Present value of perpetuity is given by the formula A/r where A is annual perpetual cash flow and r is rate of interest

The value of annual tax shield is given ( tax rate*loan amouny*rate of interest of debt) = (0.35*0.08*400,000) = 11200

This is net savings in tax due to interest payments. This advantage is tax shield. Thus, present value of tax shield will be

annual tax shield amount/rate of interest on debt

= 11200/0.08 =$ 140,000

b. Firm value new ( levered) = unlevered firm value+ present value of tax shield

Levered Firm value = 800,000+140,000 = $940,000

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

Cost of equity According to Modigliani Miller proposition with tax is given by

Rs = Ro+(D/S)*(1-tax)*(Ro-Rd)

Where Rs is cost of levered firms' equity

Ro is cost of equity of unlevered firm

Rd ia cost of debt

D is debt amount and S is value of levered equity

Thus Rs = 15+(400,000/540,000)*(1-0.35)*(15-8) = 18.37%

Thus cost of equity for levered firm is 18.37%. It increases with debt as risk increases with addition of debt as interest payments need to be done before paying shareholders.

c. Wacc = Rs*(S/Value of levered firm) + Rd*(D/Value of levered firm)*(1-tax)

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

Wacc = 12.76%

d. Stock price before announcement = value of unlevered firm/shares outstanding = 800,000/32000= $35

After announcement stock price = Value of levered firm/shares outstanding=940,000/32000 = $29.375

Value increases after announcement as the present value of tax shield is added to firm value. This increase in value leada to gain of shareholders. Assuming capital markets to efficiently price stocks, as soon as announcement is made, this change happens.

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