$5.$ ABC stock is trading at $$100,$ its annualized standard deviation is $\backslash$sigma A $=0\mathrm{.}3,$ its mean is zero, and its continuous annual dividend yield is $5\%.$ The annual risk$-$free rate is $2\mathrm{.}5\%.$

a$.$ Determine the equilibrium prices of ABC American and European $100$ call and put options expiring in $180$ days using the BOPM Excel program. Subdivided your tree into n $=100$ sub$-$periods. Comment on what explains the differences you observe between the European and American call prices and the European and American put prices.

b$.$ Using the BOPM Excel program, determine the equilibrium prices of ABC American and European $100$ call and put options expiring in $180$ days given there are no dividends. Subdivided your tree into n $=100$ sub$-$periods.

c$.$ Explain the impact dividends have on American and European call and put prices.