Coupon: 0% Call Date: 1 July 2012 Call Price: 104.32% Maturity: 1 July 2019 A firm issues the convertible debt shown above. The price of stock in this company on 1 July 2012 is $28.20. What is the minimum conversion ratio that would make a bondholder prefer to convert rather than accept the call price?

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The conversion ratio is the number of shares of stock that a bondholder receives in exchange for each $1,000 of principal. The minimum conversion ratio that would make a bondholder prefer to convert rather than accept the call price is the ratio that would give the bondholder the same number of shares of stock as they would receive if they accepted the call price. In this case, the call price is $104.32 per $1000 of principal. The price of stock on July 1, 2012 is $28.20. Therefore, the minimum conversion ratio that would make a bondholder prefer to convert rather than accept the call price is $104.32/$28.20 = 37 shares per $1000 principal amount.