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How To Value Apple's Share Buybackby Magnus Erik Hvass Pedersen, February 15, 2014 During the past year, a few celebrity investors have been pushing for Apple to increase share buybacks because the investors believe Apple's shares are undervalued. But the investors do not provide arguments as to why share buybacks would be good for the longterm shareholders; why Apple's shares are undervalued; or what will ultimately happen if the investors are wrong in their beliefs. Share buybacks are usually misunderstood. Some scholars claim that share buybacks can substitute for dividend payouts, possibly with a tax advantage. Others claim that share buybacks signal management's insider knowledge that the stock is undervalued, which should result in an increased shareprice. These notions are illfounded. Share Buyback ValuationWhen a company makes a share buyback it makes a peculiar kind of bet on behalf of its remaining shareholders, by exchanging current dividend payouts for a reduction in the number of shares, which potentially increases future dividends per share. Thus, the outcome of the bet depends on the future earnings available for dividend payout being sufficient to justify the shareprice. Furthermore, a loosing bet is far more destructive to shareholder value than a winning bet, as demonstrated below. To determine the impact of a share buyback on the value to longterm shareholders we first need to know the value without a share buyback. That is, if all excess cash and future earnings were to be paid out as dividends, what is the present value of those payouts? A share buyback would lower the amount of cash available for dividend payout and decrease the number of shares outstanding. Using these numbers we can find the value of a share buyback relative to the value without a share buyback. The formula is:
Value with Share Buyback / Value without Share Buyback
where v is the excess cash and present value of future earnings available for dividend payout, also called the 'intrinsic value' of the company. This formula for the relative value of a share buyback is given in Eq. 36 in the introductory paper on share buyback valuation. Apple's Share BuybacksThe marketcap (i.e. market value of all the company's shares) of Apple is about USD 450b at the time of this writing in early February 2014. Apple's future earnings cannot be known in advance so we will consider two different scenarios and the reader is encouraged to experiment with other assumptions. First assume the intrinsic value is actually 20% greater than the marketcap so that v = 120% x USD 450b = USD 540b. If a share buyback is made for USD 50b at the current marketcap then the relative value is calculated using the above formula:
Value with Share Buyback / Value without Share Buyback
That is, the value to longterm shareholders is increased by about 2.08% as a result of such a share buyback. Now consider the opposite scenario where the intrinsic value is instead 20% less than the marketcap so that v = 80% x USD 450b = USD 360b. If a share buyback is made for USD 50b at a marketcap of USD 450b then the formula tells us that the relative value of the share buyback is about 96.88%, that is, the value to longterm shareholders is decreased by about 3.12% as a result of such a share buyback. Note how the resulting loss of 3.12% is much greater than the gain of 2.08% from such a share buyback, depending on whether the intrinsic value v is 20% smaller or 20% greater than the marketcap. This is because of the nonlinearity of the relative value formula, which is explained in more detail and also shown graphically in the paper. When the share buyback amount is increased or the discrepancy between the intrinsic value and the marketcap is increased, the losses become disproportionally greater than the gains. PerShare NumbersApple has about 892m shares outstanding according to its most recent financial statement, which means the shareprice at a marketcap of USD 450b is MarketCap / Shares = USD 450b / 892m = USD 504. In the first scenario the intrinsic value was assumed to be 120% of the marketcap, or equivalently 120% of the shareprice. The intrinsic value pershare is then about USD 605. If a share buyback is made for USD 50b at a marketcap of USD 450b (i.e. a shareprice of USD 504), then we know from above that the relative value of the share buyback is about 102.08%. That is, the intrinsic value pershare becomes USD 605 x 102.08% = USD 617.58 as a result of the share buyback. In the second scenario the intrinsic value was assumed to be 80% of the marketcap, or equivalently 80% of the shareprice. The intrinsic value pershare is then about USD 403. If a share buyback is made for USD 50b at a marketcap of USD 450b (i.e. a shareprice of USD 504), then we know from above that the relative value of the share buyback is about 96.88%. That is, the intrinsic value pershare becomes USD 403 x 96.88% = USD 390.43 as a result of the share buyback. Cash RepatriationThe formula for valuing Apple's share buyback is actually a bit more complicated than this because Apple may fund their share buybacks from borrowing money in USA secured with their large foreign cash holdings, which will eventually have to be repatriated and taxed in USA. The formula for valuing this is given in the treatise on share buyback valuation. Further Reading

