Final answer:
After a $5 drop in the underlying stock price, with a conversion ratio of 40 and a delta of 0.50, the convertible bond's value is approximately reduced by $100, leading to a new approximate value of $800.
Step-by-step explanation:
If the price of the underlying stock drops $5 per share and the conversion ratio is 40, the value of the conversion option drops by 40 shares × $5 = $200. Given the delta of the convertible bond is 0.50, the bond's price will decrease approximately by 0.50 × $200 = $100. Therefore, the new approximate value of the convertible bond will be $900 (original price) - $100 (decrease due to stock price drop) = $800.