Chapter 31: Mergers
Problem Sets
(3, 12, 13, 15)
Problem 3: (See Ch31, p.839)
Velcro Saddles is contemplating the acquisition of Pogo Ski
Sticks, Inc. The values of the two companies as separate
entities are $20 million and $10 million, respectively. Velcro
Saddles estimates that by combining the two companies, it
will reduce marketing and administrative costs by $500,000
per year in perpetuity. Velcro Saddles can either pay $14
million cash for Pogo or offer Pogo a 50% holding in Velcro
Saddles. The opportunity cost of capital is 10%.
a) What is the gain from merger?
b) What is the cost of the cash offer?
c) What is the cost of the stock alternative?
d) What is the NPV of the acquisition under the cash offer?
e) What is its NPV under the stock offer?
Problem 3: Cont.
a) What is the gain from merger?
Gain = $500,000/0.10 = $5 million (We assume that the
$500,000 saving is an after-tax figure).
b) What is the cost of the cash offer?
Cost = Cash paid – PVB = 14 – 10 = $4 million
c) What is the cost of the stock alternative?
Cost = x% PVAB – PVB = x% (PVA + PVB + Gain) – PVB =
50% (20 + 10 + 5) – 10 = $7.5 million
d) What is the NPV of the acquisition under the cash
offer?
NPV = Gain – Cost = $5 million - $4 million = +$1 million
e) What is its NPV under the stock offer?
NPV = $5 million – $7.5 million = –$2.5 million
Problem 12: (See Ch31, p.840)
As treasurer of Leisure Products, Inc., you are
investigating the possible acquisition of Plastitoys. You
have the following basic data:
Earnings per share
Dividend per share
Number of shares
Stock price
LP
$5.00
$3.00
1,000,000
$90
Plast.
$1.50
$0.80
600,000
$20
You estimate that investors currently expect a steady
growth of about 6% in Plastitoys’ earnings and
dividends. Under new management this growth rate
would be increased to 8% per year, without any
additional capital investment required.
Problem 12: Cont.
a) What is the gain from the acquisition?
b) What is the cost of the acquisition if Leisure Products
pays $25 in cash for each share of Plastitoys?
c) What is the cost of the acquisition if Leisure Products
offers one share of Leisure Products for every three
shares of Plastitoys?
d) How would the cost of the cash offer and the share
offer alter if the expected growth rate of Plastitoys
were not changed by the merger?
Problem 12: Cont.
a) What is the gain from the acquisition?
Use the perpetual growth model of stock valuation to find the
appropriate discount rate (r) for the common stock of
Plastitoys (Company B):
P0
D1
r g
20
0.80
r 0.06
20 r 0.06
0.80
r
0.10
Under new management, the value of the combination (AB)
would be the value of Leisure Products (Company A) before
the merger (because Company A’s value is unchanged by the
merger) plus the value of Plastitoys after the merger, or:
0.80
0.10 0.08
90, 000, 000 600, 000 40 $114, 000, 000
PVAB
1, 000, 000 90
600, 000
Problem 12: Cont.
We now calculate the gain from the acquisition:
Gain
Gain
PVAB
PVA
$114, 000, 000
PVB
$90, 000, 000 $12, 000, 000
$12, 000, 000
b) What is the cost of the acquisition if Leisure
Products pays $25 in cash for each share of
Plastitoys?
Because this is a cash acquisition:
Cost = Cash Paid – PVB = ($25 600,000) - ($20
600,000) = $3,000,000
Problem 12: Cont.
c) What is the cost of the acquisition if Leisure
Products offers one share of Leisure Products for
every three shares of Plastitoys?
Because this acquisition is financed with stock, we have
to take into consideration the effect of the merger on the
stock price of Leisure Products. After the merger, there
will be 1,200,000 shares outstanding [1,000,000 +
(600,000/3)].
Hence, the share price will be:
$114,000,000/1,200,000 = $95.00
Therefore:
Cost = ($95 200,000) – ($20 600,000) = $7,000,000
Problem 12: Cont.
d) How would the cost of the cash offer and the share
offer alter if the expected growth rate of Plastitoys
were not changed by the merger?
If the acquisition is for cash, the cost is the same as in Part
(b), above: Cost = $3,000,000
If the acquisition is for stock, the cost is different from that
calculated in Part (c). This is because the new growth rate affects
the value of the merged company. This, in turn, affects the stock price
of the merged company and, hence, the cost of the merger:
PVAB = ($90 1,000,000)+($20 600,000) = $102,000,000
The new share price: $102,000,000/1,200,000 = $85.00
Therefore:
Cost = ($85 200,000) – ($20 600,000) = $5,000,000
Problem 13: (See Ch31, p.840)
The Muck and Slurry merger has fallen through (see
Section 31-2). But World Enterprises is determined to
report earnings per share of $2.67. It therefore acquires
the Wheelrim and Axle Company. You are given the
following facts:
Earnings per share
Price per share
Price-earnings ratio
Number of shares
Total earnings
Total market value
World Enterprises
$2.00
$40
20
100,000
$200,000
$4,000,000
Wheelrim & Axle
$2.50
$25
10
200,000
$500,000
$5,000,000
Merged Firm
$2.67
?
?
?
?
?
Once again there are no gains from merging. In exchange
for Wheelrim and Axle shares, World Enterprises issues
just enough of its own shares to ensure its $2.67 earnings
per share objective.
Problem 13: Cont.
a) Complete the above table for the merged firm.
b) How many shares of World Enterprises are
exchanged for each share of Wheelrim and Axle?
c) What is the cost of the merger to World Enterprises?
d) What is the change in the total market value of the
World Enterprises shares that were outstanding
before the merger?
Problem 13: Cont.
a) Complete the above table for the merged firm.
We complete the table, beginning with:
Total market value = $4,000,000 + $5,000,000 =
$9,000,000
Total earnings = $200,000 + $500,000 = $700,000
Earnings per share equal to $2.67 implies that the
number of shares outstanding is: ($700,000/$2.67) =
262,172.
The price per share is: ($9,000,000/262,172) = $34.33
The price-earnings ratio is: ($34.33/$2.67) = 12.9
Problem 13: Cont.
b) How many shares of World Enterprises are
exchanged for each share of Wheelrim and Axle?
World Enterprises issued (262,172 – 100,000) = 162,172
new shares in order to take over Wheelrim and Axle,
which had 200,000 shares outstanding. Thus,
(162,172/200,00) = 0.81 shares of World Enterprises
were exchanged for each share of Wheelrim and Axle.
c) What is the cost of the merger to World
Enterprises?
World Enterprises paid a total of (162,172 $34.33) =
$5,567,365 for a firm worth $5,000,000.
Cost = Cash paid - PVB = $5,567,365 – $5,000,000 =
$567,365.
Problem 13: Cont.
d) What is the change in the total market value of
the World Enterprises shares that were
outstanding before the merger?
The change in market value will be a decrease of
$567,365.
Problem 15: (See Ch31, p.841)
Look again at Table 31.3. Suppose that B
Corporation’s fixed assets are re-examined and found
to be worth $12 million instead of $9 million. How
would this affect the AB Corporation’s balance sheet
under purchase accounting? How would the value of
AB Corporation change? Would your answer depend
on whether the merger is taxable?
Balance Sheet of A
Balance Sheet of B
Balance Sheet of AB
NWC 20
30
D
NWC 1
0
D
NWC
21
30
D
FA
70
E
FA
9
10
E
FA
89
88
E
10
10
80
100 100
G/will 8
118
--
118
Problem 15: Cont.
Table 31.3 becomes:
Balance Sheet of AB
NWC
21
30
D
FA
92
88
E
Goodwill
5
--
118
118
If the acquisition is tax-free, then the value of AB
Corporation does not change. If the acquisition is
taxable, the revaluation of fixed assets increases the
allowable depreciation, but the write-up in asset value is
a taxable gain. This reduces the value of AB.