You would like to be holding a protective put position on the stock of XYZ Company to lock in a guaranteed minimum value of $$180$ at year$-$end. XYZ currently sells for $$180.$ Over the next year, the stock price will either increase by $8\%$ or decrease by $8\%.$ The $T-$bill rate is $6\%.$ Unfortunately, no put options are traded on XYZ Company.

Required:

a$.$ How much would it cost to purchase if the desired put option were traded? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

b$.$ What would be the cost of the protective put portfolio? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Cost of the protective put portfolio