Question

1. A 3% coupon, $1,000 face amount, 5-year bond is convertible into 25 shares of company stock. The current stock price is $30. At maturity, the stock price is $50. Assuming the bond is bought at issuance for $1,000, i.e. par, and interest is paid semi-annually, the total annual return for the investor will be:

Answer 1

Given,

Coupon rate = 3%

Value of 5 year convertible Bond=$1000(bought at par)

The fact that interest is paid semi annually is not of any relevance for the purpose of this question.

So interest income per year = $1000*3%=$30

Interest amount of $30 will be paid every year for a period of 5 years

At the end of 5th year, investor will receive 25 shares ($50 each) along with interest = $30+(25*50)

=$30+$1250= $1280

But as per the question we have to calculate annual return on the bond. So from the $1250 received on conversion of bond we have to deduct investment in bond i.e., $1000

So the actual return (in $) at the end of 5th year is $1280-$1000=$280

The formula for calulating annual return is Return(in $)/Investment*100

We can get a better idea by referring the below given table

Year	Return(In $)	Annual Return
1	30	3%
2	30	3%
3	30	3%
4	30	3%
5	280	28%

As per the above table, annual return for first 4 years is 3% and annual return for the 5th year is 28%

So the average annual return on the bond over the period of 5 years = 3+3+3+3+28/5

=40/5 =8%