Question

Consider two firms L and U which are identical in all aspects except for capital structure. The EBIT and cost of capital for each firm is Sh. 900,000 and 10% respectively. U is an all-equity financed firm while L has 7.5% of Sh.4, 000,000 debt.

a. Estimate the value of levered firm (L) and Unlevered firm (U) using Net Income (NI) approach;

b. Establish whether there is an arbitrage opportunity

c. Estimate the arbitrage profits if any by considering an investor who holds 10% of the stock of overvalued firm

Answer 1

a)As per Net Income approach, the cost of equity will remain the same for both Levered and unlevered firms.

Value of Unlevered Firm U = EBIT / Cost of equity = Sh900000/0.1 = Sh. 9,000,000

In case of Levered firm,

EBIT = Sh.900000

Less Interest = Sh.400000 *7.5% =Sh.300000

EBT = Sh. 600000

PAT = Sh. 600000 (as there is no tax)

So, Value of Equity = Sh. 600000/0.1 =Sh. 6,000,000

Value Of Levered Firm L = Value of Equity + Value of Debt = Sh. 6000000 + Sh. 4000000 =Sh. 10,000,000

b)As per MM approach, the value of Levered firm and Unlevered firm should be the same in the absence of Taxes.  As the value of Levered firm is higher than Unlevered firm, there is an arbitrage opportunity by selling the Levered firm and purchasing the Unlevered firm.

c) The arbitrage process works as below :

1) Sell 10% stock in the overvalued ie. Levered firm for Sh.600,000

2) Borrow 10% of Firm L's Debt i.e. Sh 400.000 at 7.5%,  thus have a total of Sh. 1,000,000

3) Purchase 10% stock in the unlevered firm for Sh 900,000 and invest the remaining Sh 100,000 can be lent at 7.5%

Income resulting from the above = 10% of Firm U's earnings - interest on Sh400000 + interest on Sh 100000

= Sh 90000- Sh30000 + Sh7500 = Sh.67500

The 10% stock in Firm L provides annual earnings of Sh. 60,000

Thus, the investor is better off by an amount of Sh.7500 every year by the above arbitraage strategy which is the arbitrage profit