$510.88 is the value of the convertible bond.
a). Current price of the zero coupon bond = par value/(1+9%)^11 = 387.53
If a bond is converted then the converted value is the number of shares upon conversion*current share price = 10*63 = 630
Gain, if converted = 630-387.53 = $242.47
The decision should be to convert the bond.
b). Fair price of the bond = 387.53
Bond price = 476
Value of the option to buy the shares = 476-387.53 = $88.47
c). Fair price of the bond after one year = 1,000/(1+9%)^10 = 422.41
Value of convertible bond = fair price + value of conversion option = 422.41 + 88.47 = $510.88.
A convertible bond is a fixed-income commercial debt security that yields interest payments but can be converted into a destined number of common stock or equity shares. The conversion from the bond to stock can be done at certain times during the bond's life and is generally at the discretion of the bondholder.
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