Question

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Alpha has 10 million shares outstanding with a market price of $5 per share and no...

Alpha has 10 million shares outstanding with a market price of $5 per share and no debt. The company generates consistently stable earnings and pays a corporate tax rate of 35%. The firm just announces it will issue a consol (or perpetuity) bond with a par value of $10 million at a coupon rate of 5%. The company will use the borrowed funds to repurchase outstanding shares.

i. What is the stock price of Alpha On the announcement date?

ii.What is the stock price of Alpha On the date when the consol bond is issued but before the share repurchase?

iii. What is the stock price of Alpha After the share repurchase?

Expert Solution

i

share price of alpha on announcement date is $5.

ii.

value before bond issue

total value of equity = 10 million share * $ 5 = $50 million

total value of asset = value of equity + value of debt = $50 million + $ 0 = $50 M

debt = bond value

total value of equity after bond issue = asset - debt = $50 M - $10 M = $ 40 M

value of bond = $10 M

market value of perpetual bond is equal to par value

share price = total equity value / no of share outstanding = $40 M / 10 M = $4

hence share price after bond issue is $4

iii

no of share repurchase = total amount used in repurchase / share price = $10 M / $4 = 2.5 M share

share outstanding after repurchase = 10 M - 2.5 M = 7.5 M

total value of asset = value of equity + value of debt - amount paid to shareholder in repurchase = $40 M + $ 10 M - $10 M = $40 M

value of equity after repurchase = Asset - debt = $40 M - $10 M = $30 M

share price after repurchase = total equity value / no of share outstanding = $30 M / 7.5 M = $4

hence share price after repurchase is $4

jeff jeffy answered 5 months ago

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