UNIVERSITY OF TORONTO
Joseph L. Rotman School of Management
RSM333
PROBLEM SET #2
SOLUTIONS
1. (a) Before the acquisition
V
A
= $10
°
25
m
= $250
m
and
V
B
= $8
°
5
m
= $40
m
.
Consider the three possible values of the synergies:
i) In this case the combined °rm AB [the former A] is worth
$250
m
±
$50
m
(
cash
out
) + $50
m
(
value of assets purchased + value of synergy
) = $250
m
. AB still has 25
million shares, and so the share price is
$250
m=
25
m
= $10
, so is unchanged. There
is no net change/bene°t for the shareholders of A. The shareholders of B gained $10
million (premium
±
V
B
= $50
m
±
$40
m
), so all the bene°t due to the synergies accrued
to the shareholders of B.
ii) In this case the combined °rm AB is worth
$250
m
±
$50
m
+$45
m
= $245
m
. AB still
has 25 million shares, and so the share price is
$245
m=
25
m
= $9
:
80
. The shareholders
of A have experienced a loss of
$
:
20
°
25
m
= $5
m
. Again, the shareholders of B gained
$10 million, but only $5 million of synergies was created, so the shareholders of A took
a $5 million hit.
iii) In this case, the combined °rm is worth $255 million.
AB still has 25 million
shares, and so the price/share is
$255
m=
25
m
= $10
:
20
, and so the shareholders of
A have gained
$
:
20
°
25
m
= $5
m
of wealth, as a result of the transaction.
The
shareholders of B gained $10 million.
(b) Consider the three possible values of the synergies:
i) AB has 30 million shares outstanding, and the combined °rm is worth
$250
m
+
$40
m
+ $10
m
= $300
m
. The shares should trade at
$300
m=
30
m
= $10
. Hence there
is no bene°t to the shareholders of A, but the shareholders of B end up with shares of
AB worth $10 ±they started with shares of B worth $8, so they bene°ted to the tune
of $10 million as before.
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 Spring '11
 SabrinaButti
 Shareholders

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