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%
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