BREALEY & MYERS MERGER EVALUATION APPROACH



ANALYSIS OF A POTENTIAL BUSINESS ACQUISITION

The presentation below follows the definitions and analysis in Brealey & Myers, Chapter 33.

DEFINITION OF TERMS

Define the following terms.

[pic] = value of firm A stock if firm A is a stand-alone company (not merged with B)

[pic] = value of firm B stock if firm B is a stand-alone company (not merged with A)

[pic]= value of firm A stock after merger with firm B (before deducting any cash paid by

A to buy B)

Gain = total economic gain to shareholders from merger = [pic] ( ([pic]+ [pic])

Cost = portion of Gain going to the firm B shareholders = value of the payment to the firm B shareholders for their firm B shares minus what the firm B shareholders give up ([pic]).

Cash-for-stock acquisition:

Cost = [Cash paid by firm A to the firm B shareholders] ( [pic]

Stock-for-stock acquisition:

Cost = [Value of firm A stock paid by firm A to firm B shareholders] ( [pic]

Cash and stock paid in acquisition:

Cost = [Cash paid by firm A to the firm B shareholders]

+ [Value of firm A stock paid by firm A to firm B shareholders] ( [pic]

NPV = portion of Gain going to the firm A shareholders

= Gain ( Cost

= Gain ( portion of Gain going to firm B shareholders

= [value of the firm A shares held by the firm A shareholders after the merger] minus [value of the firm A shares held by the firm A shareholders before the merger]

Estimating [pic], [pic] and [pic]:

[pic]: If the market price of the stock is judged to be a good estimate of firm A’s stand-alone equity intrinsic value, use market value prevailing before the merger is publicly known. Otherwise, estimate the intrinsic value of the equity using the method in TBV.

[pic]: Same approach as in estimating [pic].

[pic]: There are two approaches: [a] Estimate the intrinsic value the proposed firm AB to be created by the merger ([pic]) using the method in TBV. [b] Estimate the value of the synergies due to the merger and add that amount to [[pic] + [pic]].

ANALYZING A POTENTIAL ACQUISITION

Purchase for Cash (Brealey & Myers Example) - Firm A buys Firm B equity for $65 million in cash (dollar amounts below in $million)

[pic] = $200

[pic] = $50

[pic]= $275

Gain = [pic] ( ([pic]+ [pic]) = $25

Cost = portion of Gain going to the firm B shareholders.

= cash paid to firm B shareholders ( [pic]

= $65 ( $50 = $15

NPV = portion of Gain going to the firm A shareholders.

= Gain ( Cost

= $25 ( $15

= $10

Purchase for Cash if the Market Value of Firm B’s Stock Reflects the Possibility of the Merger with Firm A (Brealey & Myers Example)

A key goal of the above analysis is to determine the total value impact of the merger between A and B. In the analysis, [pic]and [pic] are the stand-alone values of the shares of firms A and B, respectively. The stand-alone values of the firm A and firm B shares are the values that the market would place on the shares if investors believed that there was no chance of the merger between A and B. Now suppose that, before the merger agreement, the market learns that the merger might occur; in this case, the equity market values of firms A and B might reflect the merger possibility, e.g., the firm B shares might have a market value of $50 million rather than a stand-alone value [pic] of $44 million. It is stand-alone values [pic] and [pic] that should be used in the analysis. So, it is the $44 million ([pic]), rather than the $50 million that would be relevant to the analysis. To estimate stand-alone value, one could directly value (using DCF analysis) the two firms’ shares assuming that firms A and B are stand-alone companies; or could look at the most recent firm A and firm B equity market values prevailing before the rumor of the merger started (this date depends on how the merger negotiations unfolded).

Brealey and Myers example: Firm A purchases firm B’s stock for $65 million. The stand-alone value of the firm B shares is $44 million, but the market value of the firm B stock is $50 million because the market factors in the possibility of a merger with firm A. Suppose that the stand-alone value of the firm A shares is $200 million, and the economic gain from the merger is $25 million. Therefore we have the following (all amounts in $million).

[pic] = $200, [pic] = $44 and [pic]= $269 ($200 + $44 + $25, where $25 = Gain)

Gain = [pic] ( ([pic]+ [pic]) = $25

Cost = portion of Gain going to the firm B shareholders

= cash paid to firm B shareholders ( [pic]

= $65 ( $44 = $21

NPV = portion of Gain going to the firm A shareholders

= Gain ( Cost

= $25 ( $21

= $4

Purchase for Stock (Brealey & Myers Example) - Firm A buys Firm B equity for .325 million shares of firm A stock; A has 1.0 million shares outstanding before the merger (dollar amounts below in $million)

[pic] = $200, [pic] = $50 and [pic]= $275

Gain = [pic] ( ([pic]+ [pic]) = $25

X = the fraction of the firm A shares that will be owned by the firm B shareholders after the merger = [.325/1.325] since firm A pays .325 million shares to the firm B shareholders and has 1.325 million shares outstanding after the merger.

Cost = portion of Gain going to the firm B shareholders

= [Value of firm A stock paid to firm B shareholders] ( [pic]

= X ([pic]) ( [pic]

= [.325/1.325] $275 ( $50

= $17.45

NPV = portion of Gain going to the firm A shareholders

= Gain ( Cost

= $25 ( $17.45

= $7.55

ADDITIONAL PROBLEMS

Purchase for Cash - Firm A buys Firm B equity for $130 million in cash (dollar amounts below in $million)

[pic] = $300

[pic] = $70

[pic]= $460

Gain = [pic] ( ([pic]+ [pic]) = $90

Cost = portion of Gain going to the firm B shareholders

= cash paid to firm B shareholders ( [pic]

= $130 ( $70 = $60

NPV = portion of Gain going to the firm A shareholders.

= Gain ( Cost

= $90 ( $60

= $30

Purchase for Cash - Firm A buys Firm B equity for $150 million in cash (dollar amounts below in $million)

[pic] = $450

[pic] = $90

[pic]= $650

Gain = [pic] ( ([pic]+ [pic]) = $110

Cost = portion of Gain going to the firm B shareholders

= cash paid to firm B shareholders ( [pic]

= $150 ( $90 = $60

NPV = portion of Gain going to the firm A shareholders

= Gain ( Cost

= $110 ( $60

= $50

Purchase for Stock - Firm A buys Firm B equity for .4 million shares of firm A stock; A has 2.0 million shares outstanding before the merger (dollar amounts below in $million)

[pic] = $385

[pic] = $45

[pic]= $480

Gain = [pic] ( ([pic]+ [pic]) = $50

X = the fraction of the firm A shares that will be owned by the firm B shareholders after the merger = [.4/2.4] since firm A pays .4 million shares to the firm B shareholders and has 2.4 million shares outstanding after the merger.

Cost = portion of Gain going to the firm B shareholders

= [Value of firm A stock paid to firm B shareholders] ( [pic]

= X ([pic]) ( [pic]

= [.4/2.4] $480 ( $45

= $35

NPV = portion of Gain going to the firm A shareholders

= Gain ( Cost

= $50 ( $35

= $15

Purchase for Stock - Firm A buys Firm B equity for .7 million shares of firm A stock; A has 3.0 million shares outstanding before the merger (dollar amounts below in $million)

[pic] = $580

[pic] = $100

[pic]= $740

Gain = [pic] ( ([pic]+ [pic]) = $60

X = the fraction of the firm A shares that will be owned by the firm B shareholders after the merger = [.7/3.7] since firm A pays .7 million shares to the firm B shareholders and has 3.7 million shares outstanding after the merger.

Cost = portion of Gain going to the firm B shareholders

= [Value of firm A stock paid to firm B shareholders] ( [pic]

= X ([pic]) ( [pic]

= [.7/3.7] $740 ( $100

= $40

NPV = portion of Gain going to the firm A shareholders

= Gain ( Cost

= $60 ( $40

= $20

Purchase for Cash and Stock - Firm A buys Firm B equity for $10 million in cash and .25 million shares of firm A stock; A has 1.0 million shares outstanding before the merger (dollar amount below in $million)

[pic] = $200

[pic] = $50

[pic]= $275

Gain = [pic] ( ([pic]+ [pic]) = $25

X = the fraction of the firm A shares that will be owned by the firm B shareholders after the merger = [.25/1.25] since firm A pays .25 million shares to the firm B shareholders and has 1.25 million shares outstanding after the merger.

Cost = portion of Gain going to the firm B shareholders

= [Cash paid to firm B shareholders] + [Value of firm A stock paid to firm B shareholders] ( [pic]

= $10 + X ([pic]( Cash paid to firm B shareholders) ( [pic]

= $10 + [.25/1.25] ($275 ( $10) ( $50

= $13

The above quantity ([pic]( Cash paid to firm B shareholders) is the post-merger value of the firm A shares after deducting the share value impact of the $10 cash payment to the firm B shareholders.

NPV = portion of Gain going to the firm A shareholders

= Gain ( Cost

= $25 ( $13

= $12

Purchase for Cash and Stock - Firm A buys Firm B equity for $60 million in cash and 1.0 million shares of firm A stock; A has 3.0 million shares outstanding before the merger (dollar amounts below in $million)

[pic] = $290

[pic] = $90

[pic]= $460

Gain = [pic] ( ([pic]+ [pic]) = $80

X = the fraction of the firm A shares that will be owned by the firm B shareholders after the merger = [1/4] since firm A pays 1 million shares to the firm B shareholders and has 4 million shares outstanding after the merger.

Cost = portion of Gain going to the firm B shareholders

= [Cash paid to firm B shareholders] + [Value of firm A stock paid to firm B shareholders] ( [pic]

= $60 + X ([pic]( Cash paid to firm B shareholders) ( [pic]

= $60 + [1/4] ($460 ( $60) ( $90

= $70

The above quantity ([pic]( Cash paid to firm B shareholders) is the post-merger value of the firm A shares after deducting the share value impact of the $60 cash payment to the firm B shareholders.

NPV = portion of Gain going to the firm A shareholders

= $80 ( Cost

= Gain ( $70

= $10

Purchase for Cash and Stock - Firm A buys Firm B equity for $40 million in cash and .8 million shares of firm A stock; A has 4.0 million shares outstanding before the merger (dollar amounts below in $million)

[pic] = $530

[pic] = $100

[pic]= $700

Gain = [pic] ( ([pic]+ [pic]) = $70

X = the fraction of the firm A shares that will be owned by the firm B shareholders after the merger = [1/6] since firm A pays .8 million shares to the firm B shareholders and has 4.8 million shares outstanding after the merger.

Cost = portion of Gain going to the firm B shareholders

= [Cash paid to firm B shareholders] + [Value of firm A stock paid to firm B shareholders] ( [pic]

= $40 + X ([pic]( Cash paid to firm B shareholders) ( [pic]

= $40 + [1/6] ($700 ( $40) ( $100

= $50

The above quantity ([pic]( Cash paid to firm B shareholders) is the post-merger value of the firm A shares after deducting the share value impact of the $40 cash payment to the firm B shareholders.

NPV = portion of Gain going to the firm A shareholders

= Gain ( Cost

= $70 ( $50

= $20

NEGOTIATING THE TERMS: Acquiring another firm requires setting terms for the transaction. Both the buyer and the seller have to be happy with the merger or it will not happen. Let’s see how terms are set if firm A is purchasing all the shares of firm B.

Purchase for Cash: The firm A shareholders want to gain at least $10 from the merger, and the firm B shareholders want to gain at least $8 from the merger. If the shareholders of both A and B assign the following valuations (dollar amounts below in $million), are there terms that will satisfy both groups of shareholders? If so, what are those terms?

[pic] = $200

[pic] = $50

[pic]= $275

Gain = [pic] ( [pic]( [pic] = $25

Solution: By definition, NPV is the gain to firm A shareholders, and Cost is the gain to the firm B shareholders. Let “Cash” be the cash paid by firm A to the firm B shareholders for the firm B stock.

To satisfy the firm B shareholders (who want a gain of at least $8), it must be that:

[pic] = Cost = Cash ( [pic] = Cash ( $50 ( $8 (1)

which implies that, to satisfy the firm B shareholders, the payment to the firm B shareholders must satisfy:

Cash ( $58 (2)

To satisfy the firm A shareholders (who want a gain of at least $10), it must be that:

[pic] = NPV = Gain ( Cost = $25 ( (Cash ( [pic])

= $25 ( (Cash ($50)

= $75 ( Cash ( $10 (3)

Therefore, to satisfy the firm A shareholders, $75 ( Cash ( $10, which implies that:

Cash ( $65 (4)

Putting (2) and (4) together we have:

$58 ( Cash ( $65 (5)

Any payment of cash fulfilling (5) will meet the requirements of both the firm A and the firm B shareholders. The outcome will depend on the negotiating effectiveness of both sides.

Purchase for Stock: As in the previous problem, the shareholders of A and B assign the valuations stated below (dollar amounts in $million). Assume that, before the merger, firm A has 2 million shares outstanding and firm B has 1 million shares outstanding. As before, the firm A shareholders want to gain at least $10 from the merger, and the firm B shareholders want to gain at least $8 from the merger. Are there terms that will satisfy both groups of shareholders, and what are they? How many shares must firm A offer to satisfy these terms?

[pic] = $200

[pic] = $50

[pic]= $275

Gain = [pic] ( [pic]( [pic] = $25.

Solution:

n = number of firm A shares paid to the firm B shareholders

X = fraction of firm A shares that will be owned by the firm B shareholders after the merger

= [n/(2,000,000 + n)]

To satisfy the firm A shareholders:

NPV = portion of Gain going to the firm A shareholders

= Gain ( Cost

= Gain ( [X ([pic]) ( [pic]]

= $25 ( X ($275) + $50

( $10 (6)

Therefore, to satisfy the firm A shareholders:

X ( [pic] (7)

We know that X = [n/(2,000,000 + n)]. Substitute this into (7):

[pic] ( [pic] (8)

Rearranging (8) we find that, to satisfy the firm A shareholders it must be that (see the Appendix at the end of this handout for rules on inequalities):

n ( 619,047 (9)

To satisfy the firm B shareholders:

Cost = portion of Gain going to the firm B shareholders

= [Value of firm A stock paid to firm B shareholders] ( [pic]

= X ([pic]) ( [pic]

= X ($275) ( $50

( $8 (10)

Therefore, using (10), to satisfy the firm B shareholders:

X ( [pic] (11)

We know that X = [n/(2,000,000 + n)]. Substitute this into (11):

[pic] ( [pic] (12)

Rearrange (12) and it follows that, to satisfy the firm B shareholders, it must be that:

n ( 534,563 (13)

Using (9) and (13), it follows that any n satisfying (14) will meet the demands of both the firm A and the firm B shareholders.

534,563 ( n ( 619,047 (14)

If firm A offers at least 534,563 shares but no more than 619,047 shares, the shareholders of both firm A and firm B will be satisfied. The final outcome will depend on the negotiating effectiveness of both sides.

APPENDIX: SOME RULES ON INEQUALITIES

[1] For any positive number P, an inequality still holds if both sides of the inequality are multiplied by P, divided by P, added to P, or reduced by P. Thus, if x < y then:

[1a] Px < Py

[1b] (x/P) < (y/P)

[1c] x + P < y + P

[1d] x ( P < y ( P.

[2] For any negative number N, an inequality is reversed if both sides of the inequality are multiplied by N or divided by N; but the inequality still holds if both sides of the inequality are added to N, or reduced by N. Thus, if x < y then:

[2a] Nx > Ny

[2b] (x/N) > (y/N)

[2c] x + N < y + N

[2d] x ( N < y ( N.

Example 1: Rules [1] and [2] are illustrated below.

[1] Let P = 10, x = 5 and y = 6. Then, since P > 0 and x < y:

[1a] Px < Py and, in the example, 50 < 60

[1b] (x/P) < (y/P) and, in the example, .5 < .6

[1c] x + P < y + P and, in the example, 15 < 16

[1d] x ( P < y ( P and, in the example, ( 5 < ( 4

[2] Let N = ( 10, x = 5 and y = 6. Since N < 0 and x < y:

[2a] Nx > Ny and, in the example, (50 > ( 60

[2b] (x/N) > (y/N) and, in the example, ( .5 > ( .6

[2c] x + N < y + N and, in the example, ( 5 < ( 4

[2d] x ( N < y ( N and, in the example, 15 < 16

Example 2: Earlier, we said that (8) implies (9), where:

[pic] ( [pic] (8)

n ( 619,047 (9)

Since (2,000,000 + n) > 0 and 275 > 0, we can apply [1a]. First, multiply both sides of (8) by 275; by [1a], this produces:

[pic] ( 65 (A.1)

Now multiply both sides of (A.1) by (2,000,000 + n), by [1a], this produces:

275n ( [pic] ( 65

which implies that:

275n ( 130,000,000 + 65n (A.2)

Now subtract 65n from both sides of (A.2); by [1d] this produces:

210n ( 130,000,000 (A.3)

which implies (9) above. So, (8) implies (9).

12/03/2004

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