Question

Zippy Corporation just sold $30 million of convertible bonds with a conversion ratio of 40. Each $1,000 bond is convertible into 25 shares of Zippy's stock. (a) What is the conversion price of Zippy's stock? (b) If the current price of Zippy's stock is $15 and the company's annual stock return is normally distributed with a standard deviation of $5, what is the probability that investors will find it attractive to convert the bond into Zippy stock in the next year?

Answer 1

.(a) Price of each bond=$1000

Conversion Ratio=40

Conversion price=(Price of bond)/(Conversion ratio)=1000/40=$25

Note: “Conversion ratio of 40” and” $1,000 bond is convertible into 25 shares of Zippy's stock” are not matching statements. If one is true, the other one cannot be true.

We are assuming : “Conversion ratio of 40” to be true.

.(b) Current Price =$15

Standard deviation =$5

Assuming current price is the mean price,

Investors will find it attractive to convert if the price is greater than $25

(price –Mean)=(25-15)=10=2*Standard Deviation(2 Sigma)

+ or - 2 sigma value has probability of0.9545

Probability of Value being greater than 2 sigma=(1-0.9545)/2=0.0228

Hence ,

Probability that investors will find it attractive to convert the bond into Zippy stock in the next year=0.0228

Calculating more accurately by using, Statistical Table

Value of z=(Price- Mean price)/(Standard Deviation)=(25-15)/5=2

Investors will find it attractive if value of z >2

Using “Cumulative Area Under the Standard Normal Distribution “ table:

When D=2, N(d)=0.9772

Hence ,

Probability that investors will find it attractive to convert the bond into Zippy stock in the next year=1-0.09772=1-0.09772=0.0228

Probability that investor will find it attractive to convert

0.0228