Quigley Inc. is considering two financial plans for the coming year. Management
ID: 2755716 • Letter: Q
Question
Quigley 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 the TIE ratio would have to be kept at 3.2 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?
Explanation / Answer
The assets are financed with 25% debt and 75% equity.
Debt = $50,000 (25% out of $200,000)
Equity = $150,000 (75% out of $200,000)
Interest rate on debt = 8.8% x $50,000 = $4,400
Under the terms of Plan A
TIE/ Times Interest Earned ratio under Plan A:
The formula for calculating TIE is
TIE = EBIT / Interest = (Sales - Operating costs) / Interest = ($300,000 - $265,000) / $4,400 = $35,000 / $4,400 = 7.95
ROE/Return on Equity under Plan A:
ROE = Net income / Total equity = (EBIT - Interest expense – Tax amount) / Total Equity = (($35,000 - $4,400 - $10,710) / $150,000 = $19,890
ROE = $19,890 / $150,000= 0.1326 or 13.26%
Under the terms of Plan B
TIE ratio should be 3.2 and the capital structure should be identified according to the TIE ratio.
TIE = EBIT / Interest
Since we don’t know the capital structure in Plan B, we don’t know the interest expense also.
3.2 = $35,000 / Interest
Interest = $35,000 / 3.2 = $10,937.50
Therefore, the interest expense under Plan B is $10,937.50
Total debt = $10,937.50 / 8.8% = $124,290
Therefore, the total debt = $124,290
Total equity = $200,000 - $124,290 = $75,710
ROE = Net income / Total equity = (EBIT - Interest expense – Tax amount) / Total Equity
= ($35,000 - $10,937.50 - $8,421.88 ) / $75,710 = 20.94%
Percentage change in ROE = 20.94% - 13.26% = 7.68%
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