(a)  (i) Conversion Value

Conversion Value = Conversion Ratio * Stock Price

                = 22*$40 = $880

(ii) Market Conversion Price

Market Conversion Price = Market Value/Conversion ratio

Market Value = 105% of par value = $1050

Market conversion price = $1050/22 = $47.73

(iii) Premium Payback period

Premium payback period = (Market Conversion price - stock price)/(Bond interest - (Conversion ratio * Dividends per share))/Conversion Ratio

Premium payback period = (47.73 - 40)/($65 - (22*$1.20))/22 = 4.4 years

(b)  (i) Stock price volatility is positively related to the value of the call option, according to the Black-Scholes-Merton option pricing model. The value of a callable convertible bond can be written as follows.

Value of bond = Straight value of bond + Value of call option on stock - value of call option on bond

Hence as stock price volatility increases, the value of the callable convertible bond also increases, because the increase in stock price volatility will increase the value of the call option on stock.

(ii) As seen above,

Value of bond = Straight value of bond + Value of call option on stock - value of call option on bond

As interest rate volatility increases, there will be an increase in the value of the call option on bond. Hence the value of the callable convertible bond decreases with increase in interest rate volatility.