Harrods PLC has a market value of $126$ million and $5$ million shares outstanding. Selfridge Department Store has a market value of $36$ million and $2$ million shares outstanding. Harrods is contemplating acquiring Selfridge. Harrods$$s CFO concludes that the combined firm with synergy will be worth $177$ million and Selfridge can be acquired at a premium of $10$ million.

a$.$ If Harrods offers $1\mathrm{.}2$ million shares of its stock in exchange for the $2$ million shares of Selfridge, what will the stock price of Harrods be after the acquisition? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ What exchange ratio between the two stocks would make the value of a stock offer equivalent to a cash offer of $46$ million? $($Do not round intermediate calculations and round your answer to $4$ decimal places, e$.$g$.,32\mathrm{.}1616.)$

a$-$new stock price$=?$

b$-$exchange ratio$=?$