Stock Buybacks and Earnings Per Share

Transcription

1 tock Buybacks and anings e hae Macelle Aak Many textbooks give the misleading impession that stock buybacks always incease eanings pe shae. They always do incease opeating pofits pe shae. Howeve, stock buybacks only incease net income pe shae unde cetain cicumstances. These cicumstances involve the elationship between the ate of inteest and the invese of the pice-eanings atio. This aticle deives the citical mathematical conditions and illustates them with a table, which shows the outcomes fo vaious cases. INTRODUCTION tock buybacks have become inceasingly common in the last few yeas, Accoding to Institutional Investo [icke, 1998], thee have been about 100 announcements pe month in the 1990 s compaed to only about two dozen a month in the 1980 s. Yet ou students ae often ill-pepaed to analyze the effect of stock buybacks on eanings pe shae. They hea in the financial news that buybacks aise eanings pe shae (and its appaent gowth ate.) Meantime, most of ou textbooks in accounting and financial management fail to give the student any insight on this matte. Many of them say nothing on this issue of stock epuchase and eanings pe shae. O, what they say leaves the student (and the typical financial analyst) with the impession that eanings pe shae will incease as a esult. Fo example, one financial management text [inches, 1990] says With fewe shaes outstanding afte a epuchase, and assuming the epuchase does not advesely affect the fim s eanings, the eanings pe shae of the emaining shaes will incease. One financial accounting text (olomon, 1989) says companies acquie thei own stock to impove eanings pe shae by educing the numbe of shaes. eveal Univesity of Coloado at Denve, Denve, CO The autho acknowledges the helpful comments and assistance of L. Ann Matin, tuat Rosenstein and Dean Taylo. intemediate accounting texts ( fo example, kousen, tice & tice [1995], Kieso & Weygandt [1998], Dyckman, Dukes & Davis [1995]) say that a copoation may epuchase stock to educe the numbe of shaes outstanding and (theeby) incease eanings pe shae. A book on contolleship (Willson, Roehl-Andeson, & Bagg [1995]) states that eanings pe shae will incease as a esult of any one of these actions: epuchase of common shaes as long as the ate of etun on equity does not decease. In fact, the geneal peception that eanings pe shae will incease is tue fo opeating pofits pe shae. But, it is not necessaily tue that buybacks aise net income pe shae, the majo measue epoted in the financial statements and the financial pess: it all depends upon the eanings- pice atio elative to the inteest ate. When the pice-eanings atio is low, and consequently its invese, the eanings pice atio, is above the afte-tax inteest ate, shae buybacks have a positive impact on net income pe shae. In contast, in an envionment whee the pice-eanings atio is high, high enough to dive the invese below the afte-tax ate of inteest, eductions in outstanding shaes though buybacks actually have a detimental effect on net income pe shae. TH MATHMATIC OF ARNING R HAR Assume that a fim has only opeating pofits and inteest evenue and expense. In that case, eanings Fall

2 pe shae() can be calculated as opeating eanings (B) plus net inteest, afte taxes, divided by the numbe of shaes: ( 1 t)( B+ C) = (1) whee is the inteest ate (decimal), C is the net inteest eaning assets, is the numbe of shaes outstanding, and t is the tax ate. Let epesent the stock pice. The cost of educing the shaes outstanding fom to is (- ) plus expenses. Fo now, let us assume that the expenses ae small and can be neglected. 1 Then, eanings pe shae afte the buyback ( ) diffe fom the initial eanings pe shae () because cash equal to (- ) is used up by the stock epuchase (and theefoe eans no futhe inteest) and the numbe of shaes ( ) is diffeent: quation (3) can then be ewitten as: ' = ( 1 t) x (6) To see the effect of the buyback on eanings pe shae, take the deivative of with espect to x, the factional buyback: d' = ( 1 t) dx ( 1 ( 1 ( 1 t) x (7) The deivative will be positive if the ight-hand side is positive, i.e. B C ' ( t) ( + = 1 ) ( ) () ( ( 1 t) ( 1 t) > 0 (8) Multiplying each tem on the ight-hand-side by (/), we can ewite the tems as: ( B C) ( ) ' = ( t) + 1 Now, eplace (1-t)(B+C)/ by (see equation(1)) and simplify the second tem, ' = ( t) ( 1 ) ' 1 Let x be the factional eduction in shaes: (3) Multiplying all tems by (1-, a positive numbe, and moving the second tem to the ight-hand side, the condition fo a positive eanings effect is: ( 1 t) x > ( 1 t) O expanding the ight-hand side ( 1 t) x > ( 1 t) ( 1 t) x (8a) Note that the -(1-t)x on the left-hand side cancels with the -(1-t)x on the ight-hand side. Thus, equation (8a) simplifies to: Then x = 1 (4) O > (1-t) / > (1-t) (8b) 1 = ( 1 (5) To summaize the esults: Jounal of Financial ducation

3 and d' > 0 if > ( 1 t) dx d( ') dx < 0 if < ( 1 t) (9a) (9b) quation (9a) indicates that a eduction in shaes outstanding bolstes eanings pe shae if the eaningspice atio exceeds the afte-tax inteest ate. Altenatively, as shown by equation(9b), shae buybacks lowe eanings pe shae if the eanings pice atio is below the afte-tax inteest ate. The Meaning of the Outcome Many people view stock buybacks as changing the numbe of shaes without changing eanings. Obviously, if thee wee no eanings eduction, and the sole effect of the buyback wee to poduce a smalle shaes denominato, stock buybacks would boost eanings pe shae. Howeve, cash eans inteest and thus a buyback educes inteest eanings. If cash is low-yielding compaed to investment in the fim as measued by the eanings of the fim elative to maket pice, then using cash to educe shaes is positive fo eanings pe shae. In contast, if cash is high yielding elative to fim eanings elative to pice, using up cash to buy back stock is negative fo. A simila agument applies if money is boowed to finance the buyback, except that, in this case, it is the afte-tax inteest ate paid elative to the eanings pice atio of the fim. ince the inteest ate on boowing exceeds the inteest ate eaned on cash, we would use a highe inteest ate fo the analysis of this case. A negative effect on is theefoe moe likely if boowing is used. XAML OF TH FFCT OF TOCK BUYBACK Table 1 illustates the effect of a 3% buyback on the eanings pe shae, unde diffeent / assumptions, shown as the top ow of the table. The pice of the stock initially was assumed to be $100 and the numbe of shaes outstanding initially was assumed to be 100,000,000. Opeating eanings in each scenaio wee computed to achieve the / of ow 1, taking account of the eanings on initial cash and assuming a tax ate of 35%. The last ow shows the esults of the analysis: the popotional change in eanings pe shae. A value of zeo indicates no change in eanings pe shae. Fo the 5% inteest ate scenaio, the zeo change occus when the / is about 30, giving an eanings pice yield of.033, which is almost equal to the afte-tax inteest ate of (1-.35).05, i.e. (.035). / s below 30 poduce a positive change in eanings pe shae since, if the / is less than 30, the eanings pice atio is highe than.035, i.e. highe than the afte-tax inteest ate eaned on cash. In contast, in the case whee the / is 35 o 40, a stock buyback poduces a negative effect on eanings pe shae.. Fo example, at a / of 40, a 3% buyback educes eanings pe shae by about 1%,. The bottom half of the table shows esults of a simila analysis using a 7% inteest ate. Note that a / of 30 now implies a negative effect on eanings fom a stock buyback in this case the eanings pice atio of.033 is below the afte-tax maket ate of inteest of (1-.35).07, i.e. (.0455). The Chat illustates the esults fo the two inteest ate scenaios. Note that up to this point we have ignoed the administative costs involved in the buyback, counting only the diect cost of the shaes puchased. In the time peiod of the buyback, total expenses would be highe and eanings would suffe moe than the above analysis indicates. On an ongoing basis, what is omitted above is only the inteest on the administative cost of the buyback. That inteest loss would be quite small. To put some numbes on the size of the omission, suppose that administative expenses wee 0.5% of the buyback. That would amount to $.015 pe shae in upfont administative expense(=.005x100x.03x100,000,000/97,000,000) in the peiod of the buyback; afte-tax, that would be about $.01 pe shae. The ongoing inteest loss in subsequent yeas would the afte-tax inteest ate applied to $.01---consideably less than $.001, figued at a single digit inteest ate. Fall

4 Table 1. tock Buybacks (3% of Outstanding) at A: Inteest Rate is 5% / B 354,615,385 48,80, ,384, ,30, ,641,06 1,5,051,8 / ,000, ,000, ,000, ,000, ,000, ,000, C 600,000, ,000, ,000, ,000, ,000, ,000,000 C' 300,000, ,000, ,000, ,000, ,000, ,000, ' '/ at Inteest ate is 7% / B 34,615, ,80, ,384,615 77,30, ,641,06 1,40,051,8 / ,000, ,000, ,000, ,000, ,000, ,000, ,000,000 97,000,000 97,000,000 97,000,000 97,000, C 600,000, ,000, ,000, ,000, ,000, ,000,000 C' 300,000, ,000, ,000, ,000, ,000, ,000, ' '/ Definitions: B=opeating income =shaes outstanding initially =shaes outstanding afte buyback C=initial cash holdings C'=cash holdings afte buyback =eanings pe shae initially '=eanings pe shae afte buyback =inteest ate =pice of the stock The tax ate is Jounal of Financial ducation

5 NDNOT 1 xpenses lowe eanings in the peiod of buyback by the afte tax value of the dolla expenses and theeafte by the inteest eanings on that expense. It is possible fo a fim to play a timing game: buying back shaes towad the end of the epoting peiod so that most of the inteest on the cash has been eaned aleady. Then that time peiod might show an eanings impovement even though the steady state effect is negative. RFRNC Dyckman, Thomas R., Roland. Dukes, & Chales J. Davis. Intemediate Accounting, 3 d ed. Iwin Kieso, Donald. and Jey J. Weygandt. Intemediate Accounting, 9th ed, John Wiley icke, Ida. xpensive Bagains Institutional Investo, Vol.3, Numbe 11, (Novembe, 1998). inches, Geoge. ssentials of Financial Management, 3 d ed., Hape & Row Willson, James D., Janice M. Roehl-Andeson, &teven M. Bagg, Contolleship, 5 th ed., John Wiley olomon, Lanny M., Richad J. Vago, and Lay M. Walthe. Financial Accounting nd ed., John Wiley 1989 kousen, K. Fed, al K. tice and James D. tice. Intemediate Accounting, 13 th ed. outh-westen College ublishing Fall