Question

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%

Answer 1

Under Plan-A

Sales = $301,770

Operating costs = $266,545

Assets = $200,000

Tax rate = 35%

Debt = 25%($200,000)

= $50,000

Equity = 75%($200,000)

= $150,000

Interest rate on debt = 8.8%

Calculating the amount of interest expense:

Interest expense = 8.8%($50,000)

= $4,400

Computing the TIE ratio under Plan-A:

$$\text{TIE ratio} = \frac{\text{EBIT}}{\text{Interest expense}} = \frac{(\text{Sales} - \text{Operating costs})}{4,400} \times [\text{Since EBIT} = \text{Sales} - \text{Operating costs}]$$ $$= \frac{(\$301,770 - \$266,545)}{4,400}$$ $$= \frac{\$35,225}{\$4,400}$$ $$= 8.00$$

Under Plan-A the value of TIE ratio comes to 8.00

Under Plan-B the TIE ratio should be kept at 4.00 to know the amount of debt employed in the capital structure.

Computing the ROE ratio under Plan-A:

$$\text{ROE} = \frac{\text{Net income}}{\text{Total equity}}$$

But Net income is obtained by deducting the interest expense and taxable amount from EBIT.

$$\text{ROE} = \frac{(\text{EBIT} - \text{Interest expense} - \text{Taxable amount})}{\text{Total equity}}$$ $$\text{ROE} = \frac{(\$35,225 - \$4,400 - \$10,789)}{\$150,000}$$

Taxable amount is calculated as

$$\text{Taxable amount} = 35\% \times (\$35,225 - \$4,400) = \$10,789$$ $$\text{ROE} = \frac{\$20,036}{\$150,000} = 0.1336 \text{ or } 13.36\%$$

Therefore, the **ROE under Plan-A is 13.36%**

Computing the TIE ratio under Plan-A:

Here, we know the amount of debt and equity. To know this let us calculate the value of interest expense using the TIE ratio 4.00

$$\text{TIE ratio} = \frac{\text{EBIT}}{\text{Interest expense}}$$ $$\text{TIE ratio} = \frac{(\text{Sales} - \text{Operating costs})}{\text{Interest expense}} \times [\text{Since EBIT} = \text{Sales} - \text{Operating costs}]$$ $$4.00 = \frac{(\$301,770 - \$266,545)}{\text{Interest expense}}$$ $$\text{Interest expense} = \frac{\$35,225}{4.00} = \$8,806.25$$

Therefore, the value of **interest expense comes to \$8,806.25**

This value is 8.8% on Total debt.

If the value of interest expense is 8.8% on debt, then the value of total debt is calculated as

$$8.8\% = \$8,806.25$$ $$100\% = ?$$ $$\text{Total debt} = \frac{\$8,806.25 \times 100\%}{8.8\%} = \$100,071$$

Therefore, the **total amount of debt is \$100,071**

Calculating the total amount of equity under Plan-B:

$$\text{Total equity} = \text{Total assets} - \text{Total debt} = \$200,000 - \$100,071 = \$99,929$$

Therefore, the value of **total equity comes to \$99,929**

Computing the change in ROE:

$$\text{ROE} = \frac{(\text{EBIT - Interest expense - Taxable amount})}{\text{Total equity}}$$ $$\text{ROE} = \frac{(\$35,225 - \$8,806.25 - \$9,246.5)}{\$99,929}$$

Taxable amount is calculated as

$$\text{Taxable amount} = 35\% \text{ (\$35,225 - \$8,806.25)} = \$9,246.5$$ $$\text{ROE} = \frac{\$17,172.25}{\$99,929} = 0.1718 \text{ or } 17.18\%$$

Therefore, the value of ROE under Plan-B is 17.18%

Hence, the ROE change by [17.18% - 13.36% = 3.82%]

Therefore, the ROE changes by 3.82% with the change in the capital structure.