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%

Expert's answer

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 – Interest expense - Taxable amount) / Total Equity = (($35,225 – $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’t know the capital structure in Plan B, we don’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%**

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

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 = Net income / Total equity = (EBIT – Interest expense - Taxable amount) / Total Equity = (($35,225 – $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’t know the capital structure in Plan B, we don’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%

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