An unlevered firm with a market value of $1 million has 50,000 shares outstanding

please see the attached file.

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.

Cash flows received from sale of bonds = 200*1000=$200,000
Market value of equity shares = 1,000,000/50,000=$20
Number of shares repurchased = 200,000/20=10000
The break-even EBIT is the level of EBIT at which unlevered and levered firms yield the same EPS. Suppose the breakeven EBIT is X, then we have

Levered Unlevered
Earnings before interest and taxes X X
Less: Interest expense @8% =200*1000*8%
=16000 0
Earnings before taxes X-16000 X
Less: Taxes - No taxes $ - $ -
Earnings after taxes X-16000 X
Number of Outstanding Shares =50000-10000
=40000 50000
Earnings per share (X-16000)/40000 X/50000

Equating the two EPS we get

X/50000 = (X - $16,000)/40000
Solving we get X = $80,000