We start of with making the calculations for the premium that Vodafone is going to pay for Mannesmann. We know that Mannesmann will own 47.2% of the equity of the newly combined company. This is 47.2% from € 275 375 million, which is €129 997 million. Vodafone is offering 53.7 shares of the value of December 17, so € 4,957, for every share of Mannesmann. Mannesmann has 517,9 million shares, so Vodafone would pay 517,9 million * 53,7 * € 4,957 = € 137 860.3 million. This would be a premium of € 137 860.3 million - €129 997 million = €7 863 million. This premium we are going to compare with some possible different estimates for the synergy that will follow from the acquisition.
(1a) We know that Vodafone and Mannesmann have respectively 31105 million and 517.9 shares outstanding in the period of 21st of October and 17th of December.
Based on the stock price from October 21, Vodafone at £ 2,70 / 0.645 = € 4,186 and Mannesmann at € 145,35 , the value of the firms would be € 4,186 * 31105 million = € 130205,53 million for Vodafone and € 145,35 * 517,9 million = € 75276,765 million for Mannesmann. Combined this would give a value of € 205483,74 million.
If we perform the same calculations for the stock price of December 17 (Vodafone: £ 3,11 / 0,6274 = € 4,957 Mannesmann: € 234), we find a value of € 154186,404 for Vodafone and € 121188,6 for Mannesmann, combined for a value of € 275 375 million.
Now we have the value of the combined firms before the market ever considered a take over, and a combined value after the bid was made public. The difference of those two values divided by the probability that the market gives for a successful acquisition will be the market’s estimate of the synergies resulting from the deal. In this case this will be (€ 275 375 million - € 205 483,74 million ) / 0,6 = 116 486.17 million.
So if you compare the premium with the market’s estimate of the synergies, this would be a great deal for the shareholders. We take the