Question

In: Finance

Abdul Inc., wants to raise $1 million by issuing six-year zero coupon bonds with a face...

  1. Abdul Inc., wants to raise $1 million by issuing six-year zero coupon bonds with a face value of $1,000. Its investment banker states that investors would use an 11.4 percent discount rate to value such bonds. At what price would these bonds sell in the marketplace? How many bonds would the firm have to issue to raise $1 million? Assume semi-annual interest payments.

(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.

Solutions

Expert Solution

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.

  • Interest rate risk is the risk that the value of bonds may fall as a result of change in interest risk.
  • Bonds always have a fixed interest rate.
  • If the interest rate rise above that fixed interest rate then investor want to switch its investment to earn higher return.
  • In this situation Bond having Long Life is more risky because if they invest in alternative opportunity then they will earn more and they will troubling in selling the bond because any new investor can earn more than that easily in the open market.

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 %.


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