An unlevered firm with a market value of $1 million has 50,000 shares outstanding. The firm restructures itself by issuing 200 new par bonds with face value of $1,000 and an 8% coupon. The firm uses the proceeds to repurchase outstanding stock. In considering the newly levered versus formerly unlevered firm, what is the breakeven EBIT? Ignore Taxes
To calculate the breakeven EBIT (Earnings Before Interest and Taxes), we need to compare the earnings of the newly levered firm to the earnings of the formerly unlevered firm. Let's break down the steps to find the breakeven EBIT.
1. Find the total amount of debt issued:
- The firm issued 200 par bonds with a face value of $1,000 each.
- Therefore, the total debt issued is 200 * $1,000 = $200,000.
2. Calculate the interest expense:
- The coupon rate is 8%, so the annual interest expense is $200,000 * 8% = $16,000.
3. Determine the change in earnings due to the repurchase of stock:
- The firm repurchased its outstanding stock using the proceeds from the bond issuance.
- The number of shares outstanding before the repurchase was 50,000.
- Let's assume the repurchase resulted in x number of shares remaining.
- Therefore, the change in shares is 50,000 - x.
4. Calculate the change in earnings:
- The earnings per share (EPS) can be found by dividing the earnings by the number of shares outstanding.
- For the formerly unlevered firm, the EPS is the same as the earnings since there is no debt.
- Let's assume the earnings are E and the EPS is E / 50,000 = E / (50,000 - x).
- For the newly levered firm, the earnings will be reduced due to interest expense. Therefore, the EPS becomes:
- (E - $16,000) / x
5. Set up the breakeven equation:
- The breakeven point occurs when the EPS of the formerly unlevered firm is equal to the EPS of the newly levered firm.
- Therefore, we have the equation: E / (50,000 - x) = (E - $16,000) / x.
6. Solve for the breakeven EBIT:
- Rearrange and simplify the equation to solve for x:
- Ex * x = (50,000 - x) * (E - $16,000)
- Ex = 50,000E - $16,000 * 50,000 - Ex * x + $16,000 * x
- Ex * x + Ex * x = 50,000E - $16,000 * 50,000 + $16,000 * x
- 2Ex * x = 50,000E - $16,000 * 50,000 + $16,000 * x
- 2Ex * x - $16,000 * x = 50,000E - $16,000 * 50,000
- x(2Ex - $16,000) = 50,000E - $16,000 * 50,000
- x = (50,000E - $16,000 * 50,000) / (2Ex - $16,000)
- Now substitute x back into the earnings formula to find the breakeven EBIT:
- E / (50,000 - [(50,000E - $16,000 * 50,000) / (2Ex - $16,000)]) = (E - $16,000) / [(50,000E - $16,000 * 50,000) / (2Ex - $16,000)]
- Simplify the equation and solve for EBIT
Please note that the above steps involve a complex equation, and the exact breakeven EBIT value cannot be determined without knowing the specific earnings (E) of the firm.