You buy a 5-year XYZ convertible bond with a coupon of 2% at a price of $1000. Interest is paid semi-annually. The bond is convertible into 20 shares of XYZ stock. The stock price today is $40. Currently, 5-year XYZ bonds are trading with a yield of 4%. Also, the following XYZ 5-year call options are trading at the following prices:

$20 strike trades at $21

$25 strike trades at $18

$40 strike trades at $10

$50 strike trades at $4.50



QUESTION: SHOW THAT THE $1,000 PURCHASE PRICE IS FAIR.