# Answer to Question #11714 in Other Management for John

Question #11714
5. 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% e. 4.65%
Correct answer is (a) - the change will be by 3.83 %.

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

TIE/ Times Interest Earned ratio under Plan A:
The formula for calculating TIE is
TIE = EBIT / Interest = (Sales - Operating costs) / Interest = (\$301,770 - \$266,545) / \$4,400 = \$35,225 / \$4,400 = 8.00
ROE/Return on Equity under Plan A:
ROE = Net income / Total equity = (EBIT &ndash; Interest expense - Taxable amount) / Total Equity = ((\$35,225 &ndash; \$4,400 - \$10,789) / \$150,000 = \$20,036
ROE = \$20,036 / \$150,000= 0.1336 or 13.36%

Under the terms of Plan B

TIE ratio should be 4.00 and the capital structure should be identified according to the TIE ratio.
TIE = EBIT / Interest
Since we don&rsquo;t know the capital structure in Plan B, we don&rsquo;t know the interest expense also.
4.00 = \$35,225 / Interest

Interest = \$35,225 / 4.00 = \$8,806.25
Therefore, the interest expense under Plan B is \$8,806.25

8.8% - \$8,806.25
100% - ?
Total debt = (100% x \$8,806.25) / 8.8% = \$100,071
Therefore, the total debt = \$100,071
Total equity = \$200,000 - \$100,071 = \$99,929
ROE = Net income / Total equity
But net income changes with the change of Interest expense.

[table]EBIT35225INTEREST8806.25EBT26418.75TAX RATE9247NET INCOME17173[/table]
ROE under Plan B is = \$17,173 / \$99,929= 0.17185 or 17.19%
Percentage change in ROE = 17.19% - 13.36% = 3.83%

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