Plant, 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 $15\mathrm{.}210\mathrm{.}7$

Shares outstanding $1,570,000820,000$

Earnings $ $4,505,900$ $ $1,107,000$

Dividends $ $1,057,000$ $ $477,000$

Plant also knows that securities analysts expect the earnings and dividends of Palmer to grow at a constant rate of $7$ 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 $9$ percent per year.

a$.$

What is the value of Palmer to Plant? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ What would Plant$$s gain be from this acquisition? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$.$ If Plant were to offer $$27$ in cash for each share of Palmer, what would the NPV of the acquisition be$?($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

d$.$ What is the most Plant should be willing to pay in cash per share for the stock of Palmer? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

e$.$ If Plant were to offer $232,000$ of its shares in exchange for the outstanding stock of Palmer, what would the NPV be$?($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

Plant's outside financial consultants think that the $9$ percent growth rate is too optimistic and a $8$ percent rate is more realistic.

f$-1.$ If Plant still offers $$27$ per share, what is the NPV with this new growth rate? $($A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

f$-2.$ If Plant still offers $232,000$ shares, what is the NPV with this new growth rate? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$