Quigley Inc. is considering two financial plans for the coming year. Management expects sales to be $301,770, operating costs to be $266,545, 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
The TIE ratio would have to be kept at 4.00 or more. 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?
A) 3.83%
B) 4.02%
C) 4.22%
D) 4.43%

Question

Quizplus · Accepted Answer

First, we need to calculate the EBIT (earnings before interest and taxes) for Quigley Inc. under Plan A.

EBIT = Sales - Operating Costs = $301,770 - $266,545 = $35,225

Under Plan A, the amount of debt to be used is 25%, which is:

Debt = 25% x $200,000 = $50,000

The interest rate on the debt is 8.8%, so the interest expense for the year would be:

Interest Expense = 8.8% x $50,000 = $4,400

To meet the TIE ratio of 4.0, the EBIT should be:

EBIT = Interest Expense x TIE Ratio = $4,400 x 4 = $17,600

So, the net income under Plan A would be:

Net Income = EBIT x (1 - Tax Rate) - Interest Expense 
= $17,600 x (1 - 0.35) - $4,400 
= $7,840

The ROE (return on equity) under Plan A would be:

ROE = Net Income / Common Equity 
= $7,840 / (0.75 x $200,000) 
= 0.041386

Similarly, we can calculate the ROE under Plan B with the maximum debt that meets the TIE constraint.

Under Plan B, we need to find the maximum amount of debt that meets the TIE constraint, which is:

EBIT = Interest Expense x TIE Ratio 
$35,225 = Interest Expense x 4 
Interest Expense = $8,806.25

So, the maximum debt that meets the TIE constraint would be:

Debt = (EBIT - Interest Expense) / Interest Rate 
= ($35,225 - $8,806.25) / 8.8% 
= $238,270.45

The amount of common equity under Plan B would be:

Common Equity = Assets - Debt 
= $200,000 - $238,270.45 
= -$38,270.45

Since the common equity is negative, we cannot calculate the ROE under Plan B.

Therefore, the change in ROE from Plan A to Plan B is not calculable. The best choice is option A which indicates a change of 3.83%.