# Jacob Cornwall has a business in which he’s invested \$250,000 of his own money. Jacob Cornwall has a business in which he’s invested \$250,000 of his own money, which is the firm’s only capital. (There are no other equity investors and no debt.) In a recent year the firm had net income of \$20,000 for a return on equity of 8% (\$20,000/\$250,000). What will the firm’s return on equity be next year if net income from business operations remains the same but it borrows \$150,000 returning the same amount to Jake from the equity account ifThe after tax interest rate is 6%.The after tax interest rate is 10%.Comment on the difference between the results of a and b.

Question

Jacob Cornwall has a business in which he’s invested \$250,000 of his own money. Jacob Cornwall has a business in which he’s invested \$250,000 of his own money, which is the firm’s only capital. (There are no other equity investors and no debt.) In a recent year the firm had net income of \$20,000 for a return on equity of 8% (\$20,000/\$250,000). What will the firm’s return on equity be next year if net income from business operations remains the same but it borrows \$150,000 returning the same amount to Jake from the equity account if

1. The after tax interest rate is 6%.
2. The after tax interest rate is 10%.
3. Comment on the difference between the results of a and b.
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Step 1

Net income from business operations = NOPAT = \$ 20,000

Part (1)

Post tax interest rate = 6%

Debt = \$ 150,000

Post tax interest expense= 6% x 150,000 = \$ 9,000

Hence net income = NOPAT - post tax interest expense = \$ 20,000 - 9,000 = \$ 11,000

Equity = Initial equity capital - equity capital returned = \$ 250,000 - \$ 150,000 = \$ 100,000

ROE = Net income / Equity capital = 11,000 / 100,000 = 11%

Step 2

Part (2)

Post tax interest rate = 10%

Debt = \$ 150,000

Post tax interest expense= 10% x 150,000 = \$ 15,000

Hence net income = NOPAT - post tax interest expense = \$ 20,000 - 15,000 = \$ 5,00...

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