In early 2009 Ham Inc.'s management was considering making an offer to buy Egg Corporation. Egg's projected operating income (EBIT) for 2009 was $30 million, but Ham believes that if the two firms were merged, it could consolidate some operations, reduce Egg's expenses, and raise its EBIT to $40 million. Neither company uses any debt, and they both pay income taxes at a 40% rate. Ham has a better reputation among investors, who regard it as better managed and also less risky, so Ham's stock has a P/E ratio of 15 versus a P/E of 12 for Egg. Since Ham's management will be running the entire enterprise after a merger, investors will value the resulting corporation based on Ham's P/E. Based on expected market values, how much synergy should the merger create?
A) $129.96
B) $136.80
C) $144.00
D) $151.20
E) $158.76

Question

Quizplus · Accepted Answer

First, we need to calculate the market value of Egg Corporation using its projected EBIT and P/E ratio:
Market value of Egg Corp. = EBIT x P/E ratio = $30 million x 12 = $360 million

Since Ham management believes they can increase Egg's EBIT to $40 million, we need to calculate Egg Corporation's market value after the merger:
New market value of Egg Corp. = $40 million x 12 = $480 million

The total market value of the merged corporation would be the sum of these two values:
Total market value = $360 million + $480 million = $840 million

Now, we need to calculate the market value of the merged corporation based on Ham's P/E ratio of 15:
Market value of merged corporation = EBIT x P/E ratio = $40 million x 15 = $600 million

The difference between the actual market value of the merged corporation and its market value based on Ham's P/E ratio represents the synergy created by the merger:
Synergy = $600 million - $840 million = -$240 million (since the actual market value is lower)

However, this negative value doesn't make sense, so we need to check our calculations. The problem is that we used Egg Corp.'s projected EBIT of $30 million, but we should use the projected increase in EBIT of $10 million to get the correct market value for Egg Corporation after the merger. So, let's recalculate:

New market value of Egg Corp. = $40 million x 12 = $480 million

Total market value = $360 million + $480 million = $840 million

Market value of merged corporation = $40 million x 15 = $600 million

Synergy = $600 million - $840 million = -$240 million

We still get a negative synergy, so we made another mistake. This time, we used Ham's P/E ratio of 15 to calculate the market value of the merged corporation, but we should use the weighted average P/E ratio of the two firms based on their market values:

Total market value = Market value of Ham + Market value of Egg Corp. = X + $480 million
X = Total market value - $480 million
X = $840 million - $480 million = $360 million

Weighted P/E ratio = (P/E ratio of Ham x Market value of Ham + P/E ratio of Egg Corp. x Market value of Egg Corp.) / Total market value
Weighted P/E ratio = (15 x $360 million + 12 x $480 million) / $840 million
Weighted P/E ratio = 13.714

Market value of merged corporation = EBIT x Weighted P/E ratio = $40 million x 13.714 = $548.56 million

Synergy = $548.56 million - $840 million = -$291.44 million

Again, we get a negative synergy, which means the merger would decrease the market value of the firms. This could be due to the fact that the market values of the two firms are already high relative to their EBIT, so the expected increase in EBIT may not be as valuable to investors as expected. However, the closest answer choice is C) $144.00, which is more than twice the correct answer. Therefore, none of the answer choices are correct.

In Early 2009 Ham Inc