Gatwick Ltd. has after tax profits (net income) of $500,000 and no debt. The owners have a $6 million investment in the business. If they borrow $2 million at 10% and use it to retire stock, how will the return on their investment (equity) change if earnings before interest and taxes remains the same

Return on equity would increase from 8.33%  to 9.50%

Explanation:

The tax rate of 40% is missing from the question.

Return on equity prior to share repurchase=$500,000/$6,000,000

Return on equity prior to share repurchase=8.33%

With the issue of debt finance of $2,000,000, the after-tax interest expense is computed thus:

after-tax interest expense=$2,000,000*10%*(1-40%)=120000

adjusted net income=$500,000-$120,000=$380,000

new common stock=$6,000,000-$2,000,000=$4,000,000

adjusted return on equity=$380,000/$4,000,000=9.50%

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