Reference no: EM131886578

Omnicom wants to issue $100 million worth of convertible debentures (100,000 bonds issued at par value of $1,000 per bond). They would like the coupon rate to be very low to save on cash interest. Their investment banker tells them that zero coupon convertibles might be the right thing for them. (A zero coupon convertible is just a convertible bond with the coupon rate set to zero.) Suppose that Omnicom was considering a maturity of five years. Given Omnicom’s credit quality, if they issued straight (i.e., non-convertible) zero coupon debt with five years to maturity, they would have to pay an annual yield of 8%. The stock price of Omnicom is $25 per share. a. Assuming the bond is initially priced at par, calculate the value of the option to buy the stock by exchanging the bond for the shares. b. Assume that there is a market for five-year to maturity call options on Omnicom stock for different strike prices. These calls have the following prices: Exercise price 30 29 28 27 26 25 24 Call price 6.70 7.06 7.43 7.82 8.24 8.66 9.13 For a zero coupon convertible, the face value divided by the conversion ratio equals the exercise price of the option to buy the shares. The conversion ratio is also the number of shares you have the right to buy using the convertible bond. Using your answer to a and the information on the above call prices, what is approximately the conversion ratio of the convertible bond. (Hint: which of these strike prices gives a call value which, multiplied by the conversion ratio, yields a number closest to your answer of part a.