You operate in a perfect capital market in which firms and individuals can borrow or lend as much as they like at 8% p.a. You have currently invested in XYZ Ltd which is unlevered and generates a return of 14% p.a. on average. If XYZ restructured to a 50/50 mix of debt/equity, what return on their investment would equity holders require to invest?A.The return on equity will increase to 20%.B.The return on equity will be unchanged because the amount of debt raised is insufficient to substantially increase the risk of financial distress.C.The return on equity will be 11% since half the firm is financed by equity (which costs 14%) and half is financed by debt (which costs 8%).D.The return on equity is 8%.
Question
You operate in a perfect capital market in which firms and individuals can borrow or lend as much as they like at 8% p.a. You have currently invested in XYZ Ltd which is unlevered and generates a return of 14% p.a. on average. If XYZ restructured to a 50/50 mix of debt/equity, what return on their investment would equity holders require to invest?A.The return on equity will increase to 20%.B.The return on equity will be unchanged because the amount of debt raised is insufficient to substantially increase the risk of financial distress.C.The return on equity will be 11% since half the firm is financed by equity (which costs 14%) and half is financed by debt (which costs 8%).D.The return on equity is 8%.
Solution
In a perfect capital market, the return on equity will increase when a firm takes on debt. This is because equity holders now bear more risk - they are last in line to be paid if the firm goes bankrupt, and they also bear the risk of the firm's operating profits being insufficient to cover the interest payments on the debt.
The return on equity can be calculated using the Modigliani-Miller theorem, which states that the cost of equity increases linearly with the debt-to-equity ratio in a world with no taxes.
The formula to calculate the new return on equity (Re) is:
Re = Ru + (Ru - Rd) * (D/E)
where: Ru = return on unlevered firm = 14% Rd = cost of debt = 8% D/E = debt-to-equity ratio = 50/50 = 1
Substituting these values into the formula gives:
Re = 14% + (14% - 8%) * 1 = 14% + 6% = 20%
So, the return on equity will increase to 20% if XYZ restructures to a 50/50 mix of debt/equity. Therefore, the correct answer is A. The return on equity will increase to 20%.
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