Cookie Monster Inc. $($a $$15$ billion snack food company$)$ is considering acquiring Keebler Elves but is unsure of how much is should be willing to pay for the target firm. At the moment, Keebler$$s $44$ million shares are trading in the market for $$67\mathrm{.}54$ but Cookie Monster$$s managers are convinced that its managers could tease out more value from their operations. Specifically, they expect to be able to decrease corporate overhead and thus increase the growth rate of Keebler$$s dividends by $1\%$ per year. In order to capture these gains, Cookie Monster will also have to incur $$65$ million worth of after$-$tax restructuring costs at the end of the first year and another $$40$ million $($after$-$tax$)$ at the end of year $2.$ Keebler$$s dividend this year was $$3\mathrm{.}80$ and the appropriate discount rate is $13\%.$

a$)$ Assuming they can purchase the company for its current share price, how much would the Keebler acquisition be worth to Cookie Monster?

b$)$ After consulting with their investment bankers, Cookie Monster$$s managers believe they will need to offer Keebler$$s shareholders a $10\%$ premium above its current market price in order to secure its sale. Furthermore, there is some uncertainty about how successful the integration of the new firm will be with the worst$-$case scenario $(20\%$ chance of occurring$)$ resulting in no change in Keebler$$s dividend growth. Assuming a $100\%$ cash deal, what is the maximum loss Cookie$$s shareholders can incur?