Question

You own a bond with the following features: Face value of $1000, Coupon rate of 7% (annual) 10 years to maturity. The bond is callable after 6 years with the call price of $1,054. If the market interest rate is 3.59% in 6 years when the bond can be called, if the firm calls the bond, how much will it save or lose by calling the bond? State your answer to the nearest penny (e.g., 84.25) If there would be a loss, state your answer as a negative (e.g., -37.51)

Answer 1

Given market reate of interest after 6 years= 3.59%

Number of years till maturity after 6th year = 10-6=4 years

Given Coupon rate =7%

Hence coupun payment = 7% of 1000=70

Hence cash flow in Year 7-10 is given as

Cashflow at year 7= Coupun =70

Cashflow at year 8= Coupun =70

Cashflow at year 9= Coupun =70

Cashflow at year 10= Coupun+ principal =70+1000=1070

Present value of Cashflows at year 6 = 70/(1+ Interest rate)^ Time till cashflow of 7th year from 6th year+70/(1+ Interest rate)^ Time till cashflow of 8th year from 6th year+70/(1+ Interest rate)^ Time till cashflow of 9th year from 6th year+1070/(1+ Interest rate)^ Time till cashflow of 10th year from 6th year

=70/(1.0359)^1+70/(1.0359)^2+70/(1.0359)^3+1070/(1.0359)^4

=70/1.039+70/1.073088+70/1.1116127+1070/1.1515196

=67.57+65.23+62.97+929.21

=1124.98

Hence if the bond was not callable in nature the price of the bond should have been 1124.98 at 3.59% market rate of interest.

However since the bond will be called at 1054 (As the call price is less than the market price, it will be benefecial for the bond issuer to call) hence the amount of loss due to call= Call price - Bond price if it is not called= 1054-1124.98

=-70.98

Hence you will lose 70.98 if the bond is called

Hence answer = -70.98