(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.