Quigley inc. is considering two financial plans for the coming year. management expects sales to be $300,000, operating costs to be $265,000, 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 under a contract with existing bondholders the tie ratio would have to be maintained at or above 4.5. 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. 2.72%b. 2.59%c. 2.96%d. 3.22%e. 3.14%

b. 2.59%

Explanation:

The assets are 200,000

For Plan A

it will be 25% debt  = 200,000 x 25% = 50,000

and 75% equity      = 200,000 x 75% = 150,000

The debt will generate 8.8% interest expense

50,000 x 8.8% = 4,400

Income for the expected project under Plan A

sales revenue 300,000

operating cost 265,000

EBIT                     35,000

interest expense  4,400

EBT                      30,600

income tax            10,710

Net income          19,890

TE = times interest earned = EBIT /interest expense

35,000 / 4,400 = 7,95 It achieve the requirement of 4.5 or above

ROE for plan A  net income / equity

19,890/150,000 = 0,1326 = 13.26%

Under Plan B

We will take as much debt as we can until TIE = 4.5

so:

EBIT / interest expense = TIE

35,000/interest expense = 4.5

35,000/4.5 = 7.777,78

This will be the interest expense for plan B

Now we calculate net income:

(EBIT - interest) x (1- tax-rate) = net income

(35,000 - 7,777.78) x (1-35%) = 17.694,443

and for the ROE for plan B first, we need to check the capital structure:

The interest expense are the 8.8% of the debt so

debt x rate = interest expense

interest expense / rate = debt

7,777.78/0.088 = 88.383,86

Asset = debt + equty

200,000 = 88,383.86 + equity

200,000 - 88,383.86 = equity = 111,616.14‬

Now, we got the capital structure

debt 88,383.86

equity 111,616.14

ROE for Plan B

17,694.443 / 111,616.14 = 0,15852943 = 15.85%

now we compare both ROE

Plan A 13.26%

Plan B 15.85%

Difference 2.59%

Using Plan B will increase the ROE for 2.59%

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