A 1-year option is offered on a non-dividend-paying stock. The stock price is $85. The exercise price of the option is $90 and the volatility is 18% per annum. The continuously compounded risk-free rate is 6% per annum. When the Black-Scholes-Merton model is used

a) What is the value of d_{1}?

b) What is the value of d_{2}?

c) What is the price of a call option, c?

d) What is the price of a put option, p?

Now, assume that the stock pays a dividend after 3-months and 9-months of $1.50.

e) What is the present value of the dividends?

f) What is the new value of d_{1} with dividends?

g) What is the new value of d_{2} with dividends?

h) What is the value of a call option?