Question

You buy a $2,000 bond on August 15, 2014, paying bond interest at j₂ = 6% and redeemable at par on August 15, 2024.

a) How much did you pay for the bond if your desired yield rate is j₂ = 7%?

b) After exactly 5 years you sell the bond. Interest rates have dropped and the bond is sold to a buyer to yield at j₁ = 4%. Determine the sale price.

c) Determine the approximate value of the yield rate j₂ to the maturity using the method of average if the bond is quoted at 109.50 on August 15, 2019.

Answer 1

1. The price to be paid for the Bond is the future value of expected cash flows discounted at rate of interest hence periodic cash flows $ 6 per year, expected rate of interest =7%, terminal cash flows $ 100+$6=106$. (Refer table below -)

Hence for $ 2,000 Bond (i.e 20 Bonds investor shall pay 92.98$*20) = $ 1859.53

2. After exactly 5 years, Aug 15, 2019 the bond is sold when expected rate is 4% then the price received on sale would be the PV of Bond future cash flows discounted at 4% for 5 years -

3. In case the Bond is quoted at $ 109.5 on August 15, 2019 then the rate of interest would be such a rate at which PV of Inflows=PV of Outflows hence j2=3.87% using IRR formula, alternatively IRR can be calculated using trial & error method also considering 2 discount rates

Using Trial & Error method-