Q2 has $2 million 12%, 20-year callable bonds outstanding. Coupons are paid annu

Question

Q2 has $2 million 12%, 20-year callable bonds outstanding. Coupons are paid annually. Currently, the bond is trading at 168.82 (you should know this is % of par). The call price is 125 (% of par). Q2 is considering calling the bonds and replacing it with new bonds issued at par. The administrative costs of calling the old bonds are 1% of the market value of old bonds and the flotation cost for the new issue is $60,000. There is a 30-day overlap period and Q2 will invest the proceeds from the new issue in 30-day T-bills that yield 2% (you should know this is 2% per year). Q2 pays 25% tax.

a. Should Q2 call the old bonds?
b. At what call price (% of par) will make the NPV of calling the old bond zero?

Explanation / Answer

Answer to the question (a) : Should Q2 call the old bonds?

Yes, because it will make a net cash inflow of $411,575 if the old bonds are called.

Calculations for the above conclusion are given below:

a. Cost of calling old bonds = 125% of $2 mn = $2.5 mn

b. Gross proceed of new issue = $ 2.00mn
Less: Floatation costs $60000 = $ 0.06mn
Net proceeds of new issue = $ 1.94mn

c. Tax savings on call premium & administrative cost on outstanding bonds = 0.25($0.5mn + $2mn*168.82%)
= $ 0.9541mn

d. Tax savings on floatation cost of new bonds = 0.25($0.06mn) = $0.015 mn

e. Post-tax earnings on investing proceeds of new bonds into 30-day T-Bills
Earnings = $2mn*2%*30/365 = $0.0033mn
Tax on earnings = $0.0033mn*25% = $0.000825mn
Post-tax earnings = $0.002475mn

f. NPV of calling old bonds = b-a+c+d+e = $0.411575 mn

Answer to the question (b): At what call price (% of par) will make the NPV of calling the old bond zero?

In order to make the NPV of calling old bond zero, we shall find the call price which increase the Post-tax cost of calling old bonds $411,575.

So, Post-tax premium on old bond = Premium on redemption (1-Tax%)
$411575 = Premium on redemption (1-0.25)
Premium on redemption = 411575/0.75 = $548,767

Call Price = Par value + Premium on redemption
   = $2mn + $548,767
   = $2,548,767

Call price (% of par) = $2,548,767/$2,000,000 = 127,44% (rounded-off to 2 decimals)

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