All-4-One is an all-equity firm with a market capitalization of $300 million. Its equity cost of...

All-4-One is an all-equity firm with a market capitalization of $300 million. Its equity cost of capital is 22.5%. Assume that there are no taxes or costs of financial distress, so the Modigliani-Miller Propositions hold. The company decides to issue $100 million in debt and use the proceeds to pay a special dividend to its shareholders. The cost of debt at the new capital structure will be 5%.

What is the value of the firm after the change in capital structure?
How does the change in capital structure affect the wealth of the shareholders?
What is the equity cost of capital after the change in capital structure?

Solutions

Expert Solution

(a.) In the arrangement adopted by the firm, where the firm issues debt and uses it to pay special dividend, is just a change in the capital structure of the firm. $100mn debt is issued and same is used to pay dividends to shareholders.

As per Modiliani-Miller approach, change in capital structure does not changes the valuation of the firm. Therefore, even after issue of debt and releasing dividend, value of the firm will be $300mn.

(b.) In the new capital structure, Value of Equity is $200mn (300mn - 200mn) and value of debt is $100mn. Also, $100 mn is given to shareholders as special dividends. So, current change in capital structure does not effect the wealth of the shareholders, as still they have $300mn value of assets as $200mn being value of equity in firm and $100mn of cash received in the form of special dividends.

(c.) With the introduction of debt in the firm, the shareholders of the firm perceive higher risk than before, so the equity cost of capital will increase. When Modigliani-Miller proposition hold, cost of capital of the firm remain constant, indifferent to the different capital structures. And cost of capital is weighted average cost of capital of the firm.

Therefore, before introduction of debt, when the it was an all equity firm, cost of capital of the firm would be 22.5%. After, introduction of debt with K_d=5%, the new cost of equity being K_e,

22.5 = (2/3)K_e + (1/3)5

=> K_e = 31.25

Therefore, the equity cost of capital after the change in capital structure is 31.25%.

ekkarill92 answered 10 months ago

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