"refinance" Alpha Corporation, a publicly held company, had issued a "25 year bonds" worth $80 million at interest rate of 10% five years ago. Alpha had paid $5 million in floating cost. Alpha’s CFO is thinking of refinancing their debt since interest rates have declined considerably. To issue new bonds, they have to call the old bonds which have a call premium of 10%. The investments banks will charge $4 million for the floatation cost of the new issue. Alpha will have to issue new bonds one month before the old bonds are called, and the proceeds will be invested for one month in short term securities which pays 3% per year. Alpha’s tax rate is 40%. Should Alpha refinance its old debt

Since the present value of the expenses of issuing new debt is lower than the present value of keeping the old bonds, then the company should issue the new bonds and redeem the old ones.

Explanation:

First of all, we can assume that Alpha is amortizing the flotation costs of the first issuance:

flotation costs = $5,000,000 / 25 years = $200,000 per year and since 5 years have passed, remaining balance of unamortized flotation costs = $4,000,000

when the company redeems its old bonds, it will incur in a $8 (call premium) + $4 (unamortized flotation costs)= $12 million loss

this will yield a tax shield = $12,000,000 x 40% = $4,800,000

total after tax loss = $12,000,000 - $4,800,000 = $7,200,000

current after tax interest + amortization expense = $8,200,000 x (1 - 40%) = $4,920,000

if the company is able to issue 20 year bonds at 8%, its after tax interest + amortization expense (same flotation costs amortization expense) = $6,600,000 x (1 - 40%) = $3,960,000

expenses under current debt:

PV of debt expenses = -$4,920,000 per year x 9.8181 (PV annuity factor, 8%, 20 periods) = -$48,305,052

net expenses if new bonds are issued:

net after tax losses associated to redemption of old bonds = -$7,200,000

PV of debt expenses = $3,960,000 per year x 9.8181 (PV annuity factor, 8%, 20 periods) = -$38,879,676

net proceeds gained from investing $76 million for one month = $76,000,000 x 3% x 1/12 x (1 - 40%) = $114,000

total expenses if new bonds are issued = -$45,965,676

Since the present value of the expenses of issuing new debt is lower than the present value of keeping the old bonds, then the company should issue the new bonds and redeem the old ones.

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