Covent Gardens Inc. is considering two financial plans for the coming year. Management expects sales to be $300,000, operating costs to be $265,000, assets to be $200,000, and its tax rate to be 35%. Under Plan A it would use 25% debt and 75% common equity. The interest rate on the debt would be 8.8%, but under a contract with existing bondholders the Times Interest Earned (TIE) ratio would have to be maintained at or above 4.5. Under Plan B, the maximum debt that met the TIE constraint would be employed. Assuming that sales, operating costs, assets, the interest rate, and the tax rate would all remain constant, by how much would the ROE change in response to the change in the capital structure?

Question

Quizplus · Accepted Answer

First, we need to calculate the elements needed to determine ROE:

Net income = Sales - Operating Costs - Interest Expense*(1-tax rate)
Under Plan A, Interest Expense = 0.25*200,000*0.088 = $4,400
Net income = 300,000 - 265,000 - 4,400*(0.35) = $31,680

ROE under Plan A = Net Income / Common Equity
Common equity = 0.75*200,000 = $150,000
ROE (Plan A) = 31,680 / 150,000 = 0.2112 = 21.12%

For Plan B, we need to find the maximum amount of debt allowed to maintain the TIE ratio:

TIE ratio = EBIT / Interest Expense
TIE ratio = (Sales - Operating Costs) / Interest Expense
4.5 = (300,000 - 265,000) / Interest Expense
Interest Expense = $7,778
Debt = Interest Expense / Interest Rate
Debt = 7,778 / 0.088 = $88,352

So, under Plan B, the capital structure would be 44.18% debt (88,352/200,000) and 55.82% common equity (1-0.4418).

Net income (Plan B) = 300,000 - 265,000 - 7,778*(0.35) = $34,926

ROE (Plan B) = Net Income / Common Equity
Common equity (Plan B) = 0.5582*200,000 = $111,640
ROE (Plan B) = 34,926 / 111,640 = 0.3127 = 31.27%

Therefore, the change in ROE is 31.27% - 21.12% = 10.15%, which is a 2.59% increase (10.15%/0.3912). The best choice is B.