Argo has a current market capitalization of $ $320$ million with $65$ million shares outstanding. The firm has an annual cash flow earnings of $$45$ million, and its cost of capital is $12\%.$ Argo is considering taking over Bylo, which currently has $25$ million shares outstanding with a market capitalization of $ $75$ million and annual cash flow earnings of $$3\mathrm{.}5$ million. The cost of capital for Bylo is $10\%.$ The takeover is expected to result in annual additional cash flow of $ $0\mathrm{.}9$ million in the first year, which is expected to remain constant in perpetuity. The cost of capital for synergies is $12\%.$ Argo is considering two different options to finance the take over $($i$)$ a cash offer with a $45\%$ premium relative to its market price $($ii$)$ a share swap of $3$ shares of Argo for every $4$ shares of Bylo.

Calculate $($i$)$ overall gain $($ii$)$ gain to Argo shareholders and $($iii$)$ gain to Bylo shareholders if the cash offer is made.

Calculate $($i$)$ gain to Argo shareholders and $($ii$)$ gain to Bylo shareholders if the share$-$swap offer is made.

At what cash offer price $($cash offer$)$ would this be a zero NPV investment for Argo Corp?