Question

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		16.2			12.5
Shares outstanding		1,670,000			920,000
Earnings	$	4,609,200		$	1,150,000
Dividends	$	1,067,000		$	487,000

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.

e.	If Plant were to offer 242,000 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., 32.16.)
Plant's outside financial consultants think that the 6 percent growth rate is too optimistic and a 5 percent rate is more realistic.
f-1.	If Plant still offers $30 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., 32.16.)
f-2.	If Plant still offers 242,000 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., 32.16.)

Answer 1

Before we get into answering the questions, let's do some basic cacluations:

Linkage column will help you understand the mathematics:

	Linkage	Plant	Palmer
Price-earnings ratio	A	16	13
Shares outstanding	B	1,670,000	920,000
Earnings	C	4,609,200	1,150,000
Dividends	D	1,067,000	487,000
EPS	E = C/B	2.76	1.25
DPS	F = D/B	0.64	0.53
Price per share	G = A x E	44.71	15.63

Part (e)

If Plant were to offer 242,000 of its shares in exchange for the outstanding stock of Palmer, then the consideration = P x N = 44.71 x 242,000 =  10,820,304.00

Value per share of Palmer:

P0 = D1 / (ke - g) = D0 x (1 + g) / (ke - g)

The price of 15.63 corresponds to a growth rate of 4%

Hence, 15.63 = 0.53 x (1 + 4%) / (ke - 4%)

Hence, ke = 7.52%

Vaue per share if growth rate = 6% wil be:

P = D0 x (1 + g) / (ke - g) = 0.53 x (1 + 6%) / (7.52% - 6%) =  36.83

Hence, valuation of Palmer = P x N =  36.83 x  920,000 =  33,887,398.39

Hence, NPV = - Consideration paid + valuation of Palmer = -10,820,304.00 + 33,887,398.39 =  23,067,094.39

Part (f - 1)

Vaue per share if growth rate = 5% wil be:

P = D0 x (1 + g) / (ke - g) = 0.53 x (1 + 5%) / (7.52% - 5%) =  22.03

Hence, NPV = (- price paid + value per share) x N = (-30 + 22.03) x  920,000 = -7,335,185.26

Part (f - 2)

valuation of Palmer = P x N = 22.03 x  920,000 =   20,264,814.74

Hence, NPV = - Consideration paid + valuation of Palmer = -10,820,304.00 + 20,264,814.74 = 9,444,510.74