ABC has $1\mathrm{.}00$ million shares$$ outstanding, each of which has a price of $ $18.$ It has made a takeover offer of XYZ$$ Corporation, which has $1\mathrm{.}00$ million shares$$ outstanding, and a price per share of $ $2\mathrm{.}32.$ Assume that the takeover will occur with certainty and all market participants know this.$$ Furthermore, there are no synergies to merging the two firms.

a$.$ Assume ABC made a cash offer to purchase XYZ for $ $3\mathrm{.}55$ million. What happens to the price of ABC and XYZ on the$$ announcement? What premium over the current market price does this offer$$ represent?

b$.$ Assume ABC makes a stock offer with an exchange ratio of $0\mathrm{.}13.$ What happens to the price of ABC and XYZ this$$ time? What premium over the current market price does this offer$$ represent?

c$.$ At current market$$ prices, both offers are offers to purchase XYZ for $ $3\mathrm{.}55$ million. Does that mean that your answers to parts $($a$)$ and $($b$)$ must be$$ identical? Explain.