Question

General Motors Company, a major US manufacturer of cars and trucks, issues a five-year bond that pays no coupons. At the bond’s maturity the company promises to pay $100M plus an additional amount based on the price of their stock at that time. The additional amount is equal to the product of 1 million and the excess (if any) of the stock price at maturity over the current price $30. The maximum additional amount paid is $10M. Show that the bond is a combination of a regular zero coupon bond, a long position in call options with a strike price of $30, and a short position in call options with a strike price of $40.

Answer 1

Solution:-

Before entering into the subject matters, firstly we have to understand the following terms:-

Zero coupon bond= zero coupon bond are those bonds on which investors are not allowed to any interest but are entitled only to repayment of principal amount on the maturity period.

Call option = the contract which provides right to holder of option to buy an underlying, is known as call option. however, writer of option ( opposite party ) has obligation to sell underlying.

Long position in call option = it is also called holder of call option & it provides right to holder to    receives upside difference i.e. price above strike price.

Short position in call option = it is also called writer of call option & it provides obligation to pay upside difference i.e. price above strike price

Now, in the give problem we have to show that the bond is a combination of a regular zero coupon bond, a long position in call options with a strike price of $30, and a short position in call options with a strike price of $40.

Given,

1.Payment of the company at maturity of bond= $100M + an additional amount based on the price of their stock at that time [i.e.The additional amount is equal to the product of 1 million and the excess (if any) of the stock price at maturity over the current price $30. The maximum additional amount paid is $10M]

however, maximum payment = $100M + $10M(maximum additional amount paid is $10M

=$110M

2. Verfication :- bond is a combination of a regular zero coupon bond, a long position in call options with a strike price of $30, and a short position in call options with a strike price of $40.

A.let's assume stock price at maturity is $50

a. Received from long position of call option= market price - strike price=$50-$30=$20

b. Payment from short position of call option=market price - strike price=$50-$40=($10)

c. Net received from call option=a-b=$20-$10=$10

Now, bondholders received= maturity amount of bond + net received from call option

= $100M + $10

= $110

B.let's assume stock price at maturity is $20

a. Received from long position of call option= market price - strike price=$20-$30=Nil

b. Payment from short position of call option=market price - strike price=$20-$40=Nil

c. Net received from call option=a-b=Nil

Now, bondholders received= maturity amount of bond + net received from call option

= $100M + Nil

= $100

Hence, from above verification, we can conclude bond is a combination of a regular zero coupon bond, a long position in call options with a strike price of $30, and a short position in call options with a strike price of $40 because payment under this combination and company's method of payment matched whatever the market price of stock at maturity.