# Convertible Bond Problem

Consider a Convertible Bond with Par value of $1,000, Coupon rate of 9.5%. The Market price of the convertible bond is $1,000, the Conversion ratio is 37.383, the estimated straight value of bond is $510 and the Yield to maturity of straight bond is 18.7%. Assume that the price of the common stock is $23 and that the dividend per share is $0.75 per year.

(a) Calculate each of the following:

(i) Conversion value, (ii) Market conversion price, (iii), Conversion premium per share, (iv) Conversion premium ratio, (v) Premium over straight value, (vi) Favorable income differential per share, and (vii) Premium payback period.

(b) Suppose that the price of the common stock increases from $23 to $46. Answer the following:

(i) What will be the approximate return realized from investing in the convertible bond?

(ii) What would be the return realized if $23 had been invested in the common stock?

(iii) Why would the return on investing in the common stock directly be higher than investing in the convertible bond?

(c) Suppose that the price of the common stock declines from $23 to $8. Answer the following questions:

(i) What will be the approximate return realized from investing in the convertible bond?

(ii) What would be the return realized if $23 had been invested in the common stock?

(iii) Why would the return on investing in the convertible bond be higher than investing in the common stock directly?

#### Solution Preview

a) Calculate each of the following:

(i) Conversion value = (market price of common stock)( conversion ratio)

= $23(37.383) = $859.809 or about $859.81.

(ii) Market conversion price = (market price of convertible bond) / (conversion ratio)

= $1,000 / 37.383 = $26.750127 or about $26.57.

(iii) Conversion premium per share = market conversion price - current market price

= $26.5701127 - $23 = $3.5701127 or about $3.57.

(iv) Conversion premium ratio = (conversion premium per share) / (current market price)

= $3.57 / $23 = 0.163049 or about 16.305%.

(v) Premium over straight value= (market price of convertible bond / straight value) - 1

= ($1,000 / $510) - 1 = 1.96078 - 1 = 0.96078 or about 96.08%.

(vi) Favorable income differential per share =

[(coupon interest from bond) - (conversion ratio)(dividend per share)] / conversion ratio.

Coupon interest from bond = coupon ...

#### Solution Summary

This posting answers a set of questions based on a convertible bond.