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How To Value Facebook's Acquisition of WhatsAppby Magnus Erik Hvass Pedersen, March 14, 2014 Facebook recently announced its acquisition of WhatsApp for USD 4b in cash and 230m shares and Restricted Stock Units (RSUs). (Press release) The acquisition was discussed extensively in the media but the discussions were vague and inconclusive because of the lack of proper valuation formulas. This article outlines the necessary valuation formulas which are detailed in the treatise. Two Valuation EffectsThe acquisition of WhatsApp has two effects on the value to the longterm shareholders of Facebook. First, the issuance of 230m shares causes dilution to the existing 2.55b shares of Facebook because the future earnings and dividends become divisible by 2.78b shares instead of 2.55b. Second, the shareholders of Facebook now get to share the future earnings and dividends of WhatsApp. Therefore, the value of the WhatsApp acquisition to the longterm shareholders of Facebook is affected by any mispricing of both the Facebook and WhatsApp shares. Unknown FutureBecause the future earnings are unknown we cannot know with certainty whether the shares of Facebook and WhatsApp are mispriced. But we can still use the valuation formulas to consider different scenarios and make inferences about the required return from the acquisition. The reader is encouraged to try the calculations with different assumptions. Relative ValueThe relative value of the WhatsApp acquisition measures the effect of the acquisition on the value to longterm shareholders of Facebook. The formula is derived in the treatise. For simplicity we will only consider the part of the acquisition consisting of 230m Facebook shares and RSUs. The cash payment of USD 4b is ignored here. On February 19, 2014, the day the acquisition was announced, Facebook's shareprice was about USD 68.50, so the market price of the 230m shares was about USD 15.8b. This is the share issuance amount which is denoted Issuance in the formulas below and which equals the acquisition price of WhatsApp. The present value of future earnings for WhatsApp is denoted Return. The excess cash and present value of future earnings for Facebook is denoted v. The market capitalization of Facebook is denoted MarketCap. When the shares of Facebook are overpriced and WhatsApp is underpriced then they both contribute to an increase in the value to longterm shareholders of Facebook. For example, if the intrinsic value of Facebook without the acquisition is v=USD 50b which is much less than the marketcap of about USD 175b, and if the present value of WhatsApp's future earnings is Return=USD 20b which is somewhat higher than the acquisition price of USD 15.8b, then the relative value of the acquisition is:
Value with Acquisition / Value without Acquisition
That is, the acquisition would increase the value to longterm shareholders of Facebook by about 28% under these assumptions. Conversely, when the shares of Facebook are underpriced and WhatsApp is overpriced then they both contribute to a decrease in the value to longterm shareholders of Facebook. For example, if Facebook's intrinsic value is v=USD 250b and WhatsApp's intrinsic value is Return=USD 5b, then the relative value of the acquisition is:
Value with Acquisition / Value without Acquisition
That is, the acquisition would decrease the value to longterm shareholders of Facebook by about 6.4% under these assumptions. The relative value can be plotted for different intrinsic values of Facebook and WhatsApp, as shown below. EquilibriumEquilibrium is where the value to longterm shareholders of Facebook is unaffected by the acquisition of WhatsApp. It is useful to write the equilibrium as an inequality so it is easy to see when shareholder value increases. The equilibrium can be expressed in different ways depending on what we want to infer. For example, if we want to know the required return from the WhatsApp acquisition then the following formula can be used with the known variables for the acquisition price (which equals the share issuance amount) and the marketcap of Facebook:
Value With Acquisition > Value Without Acquisition
That is, if the acquisition of WhatsApp is to increase value to longterm shareholders of Facebook, then the present value of the future earnings from WhatsApp must be greater than 0.09 times the intrinsic value of Facebook. For example, if the intrinsic value of Facebook is USD 50b, then the return on the WhatsApp acquisition must be greater than USD 50b * 0.09 = USD 4.5b. This is much less than WhatsApp's acquisition price of USD 15.8b because the payment was in the form of Facebook shares which were greatly overpriced with a marketcap of USD 175b and an intrinsic value of only USD 50b. If instead the intrinsic value of Facebook is actually USD 250b, then the return on the WhatsApp acquisition must be greater than USD 250b * 0.09 = USD 22.5b. This is higher than WhatsApp's acquisition price because the acquisition was paid with Facebook shares which were underpriced. Further ReadingFor more details see the full case study in the treatise. It is also explained in this video. 
