Question

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%

Answer 1

Answer:

b. 4.02%

$$TIE = \frac{EBIT}{\text{Interest charges}}$$ $$TIE_1 = \frac{\$301,770 - \$266,545}{0,088 * 0,25 * y} \geq 4$$ $$TIE_2 = \frac{\$301,770 - \$266,545}{0,088 * x * y} \geq 2,5$$ $$y = 440312,5$$

$x = 0,4$ – is a part of debt equity

$$ROE = \frac{\text{Net income}}{\text{Shareholders equity}}$$ $$ROE_1 = \frac{16599,98}{0,75 * 440312,5} = 0,05$$ $$ROE_2 = \frac{13737,75}{0,6 * 440312,5} = 0,052$$ $$\frac{ROE_2}{ROE_1} = \frac{0,052}{0,05} = 1,0402$$