Question $6[6$ marks$]$

Consider Barrack Industries, for which the following financial data is provided:

$$ Current Share Price: R$150$

$$ Strike Price of the Option: R$150$

$$ Risk$-$Free Rate: $6\%$

$$ Variance of Share Returns: $0\mathrm{.}12$

a$)$ Use the given data to calculate the values of d$1$ and d$2$ using the Black$-$Scholes model. Please detail your calculations for full credit. $(3)$

b$)$ Given that N$($d$1)=0\mathrm{.}59675$ and N$($d$2)=0\mathrm{.}50000,$ calculate the value of a European call option on Barrack Industries' shares. Clearly state any assumptions you make and explain how they affect the option's value. $(3)$

Hint: The Black$-$Scholes model requires the assumption of European options $($which can only be exercised at expiration$),$ no dividends, constant risk$-$free interest rate, and log$-$normal distribution of asset prices.