Question

Kiwi Ltd is an all-equity firm, with 1 million shares outstanding that trade for a price of $24 per share. Aussie Ltd is identical in all respects to Kiwi Ltd, except that it has $12 million in debt at an interest rate of 5% p.a. Both firms generate a cash flow of $10 million annually. Suppose that there are no taxes, and after paying any interest on debt, both companies use all remaining cash free cash flows to pay dividends each year.

Assume Miller and Modigliani (MM) perfect capital markets with no taxes and that both firms and individuals can borrow and lend at the same 5% rate as Aussie Ltd.
A)According to MM Proposition 1, what is the stock price for Aussie Ltd?
B)According to MM Proposition 1, which firm would you invest in if the equity of Aussie Ltd was valued at $10 million? Briefly justify your choice.
C)Given your answer to part (b), show how you could make a riskless arbitrage profit if you wanted a 10% ownership stake of the firm. Give a full explanation of the D)transactions needed and the amount of profit to be made.
What is the optimal capital structure in MM perfect capital markets with no taxes?

Answer 1

According to MM Proposition I, the stock price for Aussie Ltd should be equal to Kiwi Ltd, since capital structure does not influence firm value in perfect capital markets with no taxes. Investing in Aussie Ltd, which is undervalued at $10 million, provides an opportunity for arbitrage. To exploit this opportunity, one would purchase shares in Aussie Ltd and short-sell shares in Kiwi Ltd to make a riskless profit.

Step-by-step explanation:

The question refers to two firms, Kiwi Ltd and Aussie Ltd, with different capital structures, and discusses valuation according to Miller and Modigliani's Proposition I (MM Proposition 1). Since both firms have identical cash flows and we're assuming perfect capital markets with no taxes, per MM Proposition 1, the market value of both firms should be the same because the value of the firm is not affected by its capital structure, only by its assets and earnings.

A) The stock price for Aussie Ltd, when considering MM Proposition 1, would remain the same as that of Kiwi Ltd because the capital structure does not affect firm value. Thus, Aussie Ltd's total firm value would be 1 million shares at $24 each, totaling $24 million, minus the $12 million debt, resulting in $12 million equity value. Since the equity of Aussie Ltd is valued at $10 million, which is lower than the value calculated using MM Proposition 1 ($12 million), there is an arbitrage opportunity.

B) You would invest in Aussie Ltd if the equity is undervalued at $10 million since it indicates that the shares are trading at a discount compared to their theoretical value in these perfect market conditions.

C) To execute a riskless arbitrage for a 10% ownership stake in Aussie Ltd, you could purchase 10% of Aussie Ltd's undervalued equity at $10 million, which would cost you $1 million. Simultaneously, you could short-sell 10% of Kiwi Ltd's overvalued equity for $2.4 million. With no taxes and the ability to borrow at the same interest rate, you could use the proceeds from the short sale to pay for the purchase and also repay any borrowed amount. The profit from this arbitrage would be the difference between the two values.

Optimal Capital Structure in MM Perfect Capital Markets with No Taxes:

In perfect capital markets with no taxes, as per Modigliani and Miller, the optimal capital structure is irrelevant because the firm's value is determined entirely by its assets and operation, not by the mixture of debt and equity it employs.