Consider an American call option on one company A share. The current company A stock price is $105 and the stock is expected to pay a dividend of $7.74 per share in 1 year's time. The strike price of the option is $110. the risk-free rate is 10% per annum, the volatility is 40% per annum and there is 2 year to maturity.

(a) Calculate the current value of the option using Black's American Option Pricing Model.

(b) We know that Black's American Option Pricing Model only gives an approximate value for the option. What does your answer in (a) imply about the exact value of the option.