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) PV of Tax Shield = Debt x tax rate = 400,000 x 35% = 140,000

It is the value addition to the company if they increase their debt.

b) Firm Value = Unlevered value + PV of tax shield = 940,000

Equity Value = 940,000 - 400,000 = 540,000

Cost of levered (re) equity can be calculated as below

re = ru + D/E x (1 - tax) x (ru - rd)

= 15% + 400,000 / 540,000 x (1 - 35%) x (15% - 8%)

= 18.37% is the new cost of equity

There is an increase in cost of equity due to increase in risk (due to leverage).

c) WACC = wd x rd x (1 - tax) + we x re

= 400/940 x 8% x (1 - 35%) + 540/940 x 15%

= 12.77%

d) Stock Price before = 800,000 / 32,000 = $25

With 400,000 in debt, shares repurchased = 400,000 / 25 = 16,000

New shares = 16,000

New Stock Price = 540,000 / 16,000 = $33.75

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