Question

Your firm currently unlevered and has an equity value of $2 million. EBIT is projected to be $100,000 under normal market conditions. If there is an economic boom, EBIT is expected to be 25% higher. If there is an economic recession, EBIT is expected to be 30% lower. Your firm is planning to restructure by issuing $500,000 of debt to buy back stock. The cost of debt is 5% and there are currently 250,000 shares outstanding. Ignore taxes.

If your firm does not restructure, calculate the EPS for the recession.
If your firm does restructure, calculate the ROE for the boom.
How many shares of stock will the company buy back from the public?
At what EBIT would your firm have the same EPS under both plans?

Answer 1

The EPS for the firm in a recession without restructuring is $0.28. After restructuring during a boom, the ROE is 6.67%, and the firm can buy back 62,500 shares. The firm would have the same EPS under both plans at an EBIT of $83,333.33.

Step-by-step explanation:

To calculate the EPS for the firm if it does not restructure during a recession, we must use the lower EBIT projection. A 30% reduction from the normal EBIT of $100,000 gives us $70,000. Therefore, the EPS in a recession without restructuring = EBIT / Number of Shares = $70,000 / 250,000 shares = $0.28 per share.

If the firm undergoes restructuring and experiences an economic boom, EBIT is expected to increase by 25%, resulting in EBIT of $125,000. Post-restructuring, the firm will have additional interest expenses of 5% of the $500,000 debt, which is $25,000. Thus, the profit available to equity holders = $125,000 - $25,000 (interest) = $100,000. The ROE for the boom = (Profit available to Equity Holders / Equity Value after Restructuring) * 100. After buying back stock with $500,000, the new equity value is $1.5 million. Therefore, the ROE = ($100,000 / $1.5 million) * 100 = 6.67%.

For the stock buyback, if the firm uses $500,000 to buy back stock, we divide this amount by the number of shares to get the price per share. The price per share is calculated as Equity Value / Number of Shares = $2,000,000 / 250,000 shares = $8 per share. Hence, the firm can buy back $500,000 / $8 = 62,500 shares.

To determine the EBIT at which the firm would have the same EPS under both plans, we take the original number of shares, less the number bought back, to find the new number of shares, which is 250,000 - 62,500 = 187,500 shares. The EPS under the unlevered plan is EBIT / 250,000 shares, and the EPS under the levered plan would be (EBIT - Interest) / 187,500 shares. If we set these two expressions equal to each other to solve for EBIT, we get EBIT / 250,000 = (EBIT - $25,000) / 187,500. Solving for EBIT yields the same EBIT of $83,333.33 under both plans.