Answer:
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.
