Problem on Stock per share value

Question

ABC Company plans to buy back 1 million shares of its own stock from its cash reserves at $50 a share. This will raise the bankruptcy costs by $10 million, and the debt/assets ratio from 35% to 40%. The income tax rate of the company is 30%. Determine the value of the stock per share after this buyback. Is the company making the correct move?

Answer 1

Shares repurchased = 1 million*$50 = $50 million

Increase in bankruptcy costs = $10 million

Assume the total value is $1000 million. Since the debt-to-assets ratio is 35% initially, the value of debt is $350 million and that of equity is $650 million. Assuming that the after-tax cost of debt is 5.6%

Value of firm after buy back = 1000 + 50*.3 – (10*.3)/0.056 = 961.43 million
Value of equity = 0.6*961.43 = 576.88
Share price before buy back = 650/50 =13 million shares
Since 1 million is bought back,
Share price after buyback = 576.88/12 = $48.07

Hence the company is not making the right move.