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: $0\mathrm{.}12$

$[6$ marks$]$

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.

$(3$ marks$)$

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.