Meta$15.$Calculating NPVPlant, Inc., is considering making an offer to purchase Palmer Corp. Plant$$s vice president of finance has collected the following information:

$$ Plant Palmer

Price$-$earnings ratio $14\mathrm{.}510$

Shares outstanding $1,500,000750,000$

Earnings $$4,200,000$ $$960,000$

Dividends $1,050,000470,000$

Plant also knows that securities analysts expect the earnings and dividends of Palmer to grow at a constant rate of $4$ percent each year. Plant management believes that the acquisition of Palmer will provide the firm with some economies of scale that will increase this growth rate to $6$ percent per year.

a$.$What is the value of Palmer to Plant?

b$.$What would Plant$$s gain be from this acquisition?

c$.$If Plant were to offer $$20$ in cash for each share of Palmer, what would the NPV of the acquisition be$?$

d$.$What is the most Plant should be willing to pay in cash per share for the stock of Palmer?

e$.$If Plant were to offer $225,000$ of its shares in exchange for the outstanding stock of Palmer, what would the NPV be$?$

f$.$Should the acquisition be attempted? If so$,$ should it be as in $($c$)$ or as in $($e$)?$

g$.$Plant$$s outside financial consultants think that the $6$ percent growth rate is too optimistic and a $5$ percent rate is more realistic. How does this change your previous answers?