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 transactions needed and the amount of
profit to be made.
d. What is the optimal capital structure in MM perfect capital markets with no taxes?

Answer 1

Under MM Proposition 1, Aussie Ltd's stock price should be the same as Kiwi Ltd's at $24 per share. If Aussie's equity is valued at $10 million, there is an opportunity for arbitrage. The optimal capital structure in MM perfect capital markets with no taxes is considered irrelevant.

Step-by-step explanation:

According to MM Proposition 1, the stock price for Aussie Ltd should remain the same as Kiwi Ltd, as the value of the firm is not affected by the financing mix used, given perfect capital markets with no taxes. Therefore, with 1 million shares outstanding and a share price of $24 per share, the equity value in both firms would be $24 million.

If the equity of Aussie Ltd was valued at $10 million, it would suggest the market is not adhering to MM Proposition 1. An investor should be indifferent about investing in either firm, as per MM's theory; however, if Aussie Ltd's equity is undervalued, there might be an opportunity for arbitrage. To achieve a 10% ownership stake in Aussie Ltd with mispriced equity, one could sell short 100,000 shares of Kiwi Ltd for $2.4 million, buy 100,000 shares of Aussie Ltd for $1 million, and lend out the remaining $1.4 million at the 5% interest rate, which would result in a riskless arbitrage profit.

In MM perfect capital markets with no taxes, the optimal capital structure is irrelevant since a firm's value is unaffected by how it is financed.