In: Finance
(b) Investor A holds a 15-year bond, while investor B has an 7-year bond. If interest rate increases by 1 percent, which investor will have the higher interest rate risk? Explain.
(c) Investor A holds a 10-year bond paying 8 percent a year, while investor B also has a 10-year bond that pays a 6 percent coupon. Which investor will have the higher interest rate risk? Explain.
A.
Face Value - $ 1000
Bond value - $ 1 million
Discount Rate = 11.4 %
Life of Bond = 6 years
Semi annual interest payment
Price at which these Zero coupon bonds sell in the market place
=Redemption Value * PVF ( rate, No. of years)
= 1000 * PVF ( 11.4%, 6)
= $ 523.23
No. of bond to be issue to raise $ 1 million
Issue price = 523.23
Amount to be raised = $ 1million
No. of bonds to be issued = 1million / 523.23 = 1912
B. Investor A holds a 15-year bond
Investor B hold a 7-year bond.
If the interest Rate increase by 1%, then Investor A has higher interest rate risk, because Investor A is holding bond of 15 years and Investor B is holding for 7 years. Investor A has to sacrifice additional opportunity cost and have more trouble for selling these bonds because their life is more.
C. Investor A holds a 10-year bond paying 8 percent a year, while investor B also has a 10-year bond that pays a 6 percent coupon.
Interest Rate risk is more in case of lower coupon rate.
If the Life of the bonds are same, but coupon rate is difference, then Bond paying less Coupon amount has high risk than bond paying high risk amount, because in this situation Bond with Low Coupon Rate will be very difficult to sale in the open market because no new investor want to purchase Bond giving very low coupon as compare to market.
Therefore in the given question, Investor B have more risk because coupon rate is low i.e 6 % in comparison to Investor A with coupon rate 8 %.