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 (which is equal to its total invested capital) to be $200,000, and its tax rate to be 35%. Under Plan A it would finance the firm using 25% debt and 75% common equity. The interest rate on the debt would be 8.8%,but under a contract with existing bondholders the TIE ratio would have to be maintained at or above 5.0. Under Plan B, the maximum debt that met the TIE constraint would be employed. Assuming that sales, operating costs, assets, total invested capital, 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

%Change in ROE =  1.85%

Hence, The ROE change in response to the change in the capital structure will be 1.85%

Explanation:

Data Given:

Sales = 300,000

Operating Cost = 265,000

EBIT = Earnings Before Interests and Taxes = Sales - Operating Costs

EBIT =  300,000 - 265,000

EBIT = 35000

So,

For PLAN A, we have TIE = 5

We know that,

TIE = EBIT/Interest

Interest = EBIT/TIE

Interest = 35000/5

Interest = 7000

Now, we need to find out the maximum amount of Debt:

Maximum amount of debt = Interest/Rate of Interest

We know that,

Rate of Interest = 8.8%

Interest = 7000

So,

Maximum amount of debt = 7000/0.088

Maximum amount of debt = 79,545.45

For PLAN A:

Assets = 200,000

Debt (25%) = 50,000

Equity (75%) = 150,000

Interest Rate = 8.8%

For PLAN B:

Assets = 200,000

Debt (25%) = 79,545.45

Equity (75%) = 120,454.54   (200,000 - 79545.45)

Interest Rate = 8.8%

Income Statement:

For Plan A:

Sales = 300,000

Operating Cost = 265,000

EBIT = 35000

Interest = 4400  (50,000 x 8.8%)

EBT = 30,600     (35000 - 4400)

Tax (35%) = 10710  (35% x 30,600)

Net Income After Tax = 19890

Similarly, For Plan B:

Sales = 300,000

Operating Cost = 265,000

EBIT = 35000

Interest = 7000     (79,545.45 x 8.8%)

EBT = 28,000    (35000 - 4400)

Tax (35%) = 9800      (35% x 28000)

Net Income After Tax = 18200

ROE = Net income / Equity

ROE For Plan A = 19890/ 150,000 x 100

ROE for Plan A = 13.26 %

Similarly,

ROE for Plan B = Net income / Equity  

ROE for Plan B = 18200/ 120,454.54

ROE for Plan B = 15.109%

%Change in ROE =  15.11% - 13.26%

%Change in ROE =  1.85%

Hence, The ROE change in response to the change in the capital structure will be 1.85%

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