Harmelink, Philip J.

Posey, Imogene A.

English

eGrove (Univ. of Mississippi)

Woman C.P.A. Volume 38 Issue 1 Article 3 1-1976 New Approach to Calculating Earnings Per Share Philip J. Harmelink Imogene A. Posey Follow this and additional works at: https://egrove.olemiss.edu/wcpa  Part of the Accounting Commons, and the Women's Studies Commons Recommended Citation Harmelink, Philip J. and Posey, Imogene A. (1976) "New Approach to Calculating Earnings Per Share," Woman C.P.A.: Vol. 38 : Iss. 1 , Article 3. Available at: https://egrove.olemiss.edu/wcpa/vol38/iss1/3 This Article is brought to you for free and open access by the Archival Digital Accounting Collection at eGrove. It has been accepted for inclusion in Woman C.P.A. by an authorized editor of eGrove. For more information, please contact egrove@olemiss.edu. A New Approach to Calculating Earnings Per ShareDr. Philip J. Harmelink is Assistant Professor of Accounting at The University of Tennessee-Knoxville. He has a Ph.D. from the University of Iowa. His teaching and research interests are financial accounting and taxes. He is the author of several articles published in accounting and business journals including the Journal of Accounting Research.Imogene A. Posey, CPA, is Associate Professor of Accounting at the University of Tennessee-Knoxville. She has an M.S. from the University of Tennessee and holds a CPA Certificate from the state of Tennessee. Professor Posey is a member of various professional organizations, including AWSCPA, and currently serves as President of the Knoxville Chapter of the Tennessee Society of CPAs and as a Vice-President of the Knoxville Chapter of the NAA.Dr. Philip J. Harmelink Imogene A. Posey, CPA Knoxville, TennesseeThe authors describe a worksheet they devised to aid in the calculation of earn­ings per share.Since the issuance of APB Opinion 15 in 1969 one of the more difficult accounting topics to understand has been Earnings Per Share (EPS). The Opinion and other informational and interpretive sources in­variably present examples in “segments” and therefore readers seldom get to see a comprehensive illustration. Further, no efficient method for calculating EPS is ever presented.The intent of this article is to illustrate a different, more efficient approach to solv­ing comprehensive EPS problems — an approach that should be of assistance to practitioners in staff training or profes­sional development programs. The cases or examples in this article, which include numerous essential points, also cover many of the types of problems and ques­tions actually arising as a result of the ambiguities of the Opinion. The approach would also be useful as a basis for com­puterization of EPS calculations — some­thing that is done in practice, especially by companies with complex capital struc­tures.Although this article covers or reviews many of the more important points of APB Opinion 15 essential for coverage at vary­ing levels for different purposes, instruc­tors or discussion leaders will want, of course, to supplement this article with the reading of the Opinion and probably some additional interpretive material.FormatThe format used in the illustrations is a worksheet approach. This approach is convenient both for original calculations and for illustration of different alternatives and assumptions. The step-wise method used is necessary in order to determine whether a particular common stock equiv­alent or security is “dilutive,” i.e., de­creases EPS.The worksheet is divided vertically into four sections: use of the assumed proceeds from assumed exercise of stock options and warrants; adjustment of earnings (Ei); adjustment of the number of shares (Si); and consecutive EPSi figures necessary to determine dilutiveness of individual items.The basic data used in the illustrations are given in Table 1. Three cases (Table 2) are illustrated in this article. Note that Cases 2 and 3 have changes in order to cover additional points and refinements.The IllustrationsThe description of Case 1 is more detailed than that of the remaining two cases because the latter descriptions include only an account of the changes that were made in order to illustrate very specific points.Case 1 A good opening point is to explain that pre-Opinion 15 EPS would be — labeled EPS1 in this article and equal to $1.83 in this case [$880,000 (E1) divided by the weighted average number of shares outstanding of 480,000 (S1)]. This is done to determine whether there is 3% or greater dilution in subsequent EPSi calcu­lations.The next step in discussion of the prob­lem would be the term “common stock 8 / The Woman CPAequivalent” (CSE); which is "a security which is not in form a common stock but which usually contains provisions to ena­ble its holder to become a common stock­holder and which, because of its terms and the circumstances under which it was issued, is in substance equivalent to a common stock” (APB Opinion 15, para­graph 25). Included for consideration as possible CSE's are stock options and war­rants, convertible debt, and convertible preferred stock.Stock options and warrants are always CSE's except that it should be explained that if the exercise price is greater than the market price, options and warrants should not be assumed to be exercised because such an assumption would be antidilutive.1 In Case 1, the market price ($27) is above the exercise price ($23) which makes the assumed exercise dilu­tive. Actually, where there is a low net income (Case 3) or a net loss, assumed exercise of stock options and warrants can be antidilutive even where average price is greater than exercise price.In Case 1, the assumed exercise of the options gives rise to a new earnings (E2) through interest savings on assumed re­tirement of the long-term nonconvertible debt and the convertible debt.2 S2 is the result of adding to S1 the number of shares issued from the assumed exercise of the stock warrants less the number of treasury shares acquired. E2/S2 gives us our EPS2 which is less than EPS1, making the stock warrants dilutive. The difference between primary and fully diluted EPS2 relative to stock options or warrants is due to the assumption of a higher year-end market price of common stock as compared to the average market price (APB Opinion 15, paragraph 42). In addition, for fully di­luted EPS, where we assume retirement of convertible debt ($1,200,000), a smaller amount is left to be converted ($800,000).In determining whether the convertible securities are CSE's, we must apply the 66 2/3% rule. If the yield rate of interest at time of issuance is less than 66 2/3% of the prime rate of interest at time of issuance, then the security is a CSE (APB Opinion 15, paragraph 33). The convertible debt is not a CSE for primary EPS because 4% is not less than 66 2/3% of 5%. It is assumed that the 4% convertibles were issued at par which makes the nominal rate of interest equal to the yield rate of interest. Because the convertible debt is not a CSE and therefore not assumed converted for pri­mary EPS, we have no adjustment to E for any interest savings or any adjustment to S. However, for fully diluted EPS, any convertible security is treated as if it were converted if it is dilutive. Therefore, thereDATA FOR THE THREE CASESLong-term nonconvertible debt (7½%) $ 400,0004% convertible debt (issued at 100 on 1/1/70 when prime rate ofinterest was 5%; each $1,000 bond can be converted into 20common shares) $2,000,0006% convertible preferred (20,000 shares, $100 par, issued on 1/1/71 at$120 when prime rate of interest was 6%. Each share isconvertible into 5 common shares) $2,000,000Common stock, shares outstanding at 1/1/75 420,000Common stock, shares issued on 4/2/75 80,000The company had 200,000 warrants outstanding. Each warrant could be exercised for one share of common stock at a price of $23.Average market price of common stock for 1975 $27Market price of common stock at 12/31/75 $30After-tax net income for 1975 $1,000,000Income tax rate 40%Interest on government securities 8%Required:Case 1. Compute primary and fully diluted EPS from the above information for 1975.Case 2. Repeat (1) assuming that the 4% convertible debt is 6% and the prime rate of interest is 7%.Case 3. Repeat (1) assuming a net income of $200,000.would be an adjustment in E to arrive at E3 and an adjustment to S to arrive at S3 and a new EPS3 which is lower than EPS2 mak­ing the convertible debt dilutive for fully diluted EPS.The preferred stock is not a CSE because $6 divided by $120 is 5% which is not less than 66 2/3% of 6%. The effect of this for primary EPS is that dividends were de­ducted to arrive at E1, whereas for fully diluted EPS, because all convertibles are treated as if they were converted, the dividends (savings) have to be added back to arrive at E4. Also, for fully diluted EPS, there is an effect on S. If the preferred stock were a CSE, preferred stock would, of course, be given the same treatment in primary EPS as described for fully diluted EPS. In Case 1, the convertible preferred stock is dilutive for fully diluted EPS because EPS4 is less than EPS3.Each item considered in Case 1 is dilu­tive. It is helpful to mention the ”3% rule” whereby both primary and fully diluted EPS must be at least 3% less than pre­Opinion 15 EPS in order to be reported unless more dilution is anticipated in a subsequent period (APB Opinion 15, foot­note 2). In other words, in Case 1, primary and fully diluted EPS would have to be less than $1.77 in order to be reported.Case 2. In Case 2, we changed the 4% convertible debt to 6% convertible debt and the prime rate of interest at the time of issuance to 7%, which means that the convertible debt is still not a CSE. But the convertible debt is now antidilutive in the fully diluted EPS calculation to arrive at E3; i.e., EPS3 is greater than EPS2. Therefore, the additions to convert from E2 and S2 to E3 and S3 must be excluded in arriving at E4 and S4. The assumed preferred stock conversion for fully diluted EPS is still dilutive since EPS4 is less than EPS2.Case 3. The third case has the same assumptions as Case 1 except for a lower reported net income of $200,000. Here even the assumed exercise of stock war­rants is antidilutive since EPS2 is greater than EPS1. Therefore, the adjustments to E2 and S2 must be eliminated in testing whether the convertible debt and conver­tible preferred stock are dilutive for fully diluted EPS. (The latter two securities areJanuary 1976 / 9SOLUTIONS TO EPS PROBLEMSCase 1 Case 2 Case 3Primary Fully Diluted Primary Fully Diluted Primary Fully DilutedAssumed proceeds (200,000 x $23 each) $4,600,000 $4,600,000 $4,600,000 $4,600,000 $4,600,000 $4,600,000Application of proceeds:Acquisition of treasury stock (1) $2,700,000 $3,000,000 $2,700,000 $3,000,000 $2,700,000 $3,000,000Retirement of 7½% L-T nonconvertibles 400,000 400,000 400,000 400,000 400,000 400,000Retirement of convertible debt(remainder of proceeds) 1,500,000 1,200,000 1,500,000 1,200,000 1,500,000 1,200,000$4,600,000 $4,600,000 $4,600,000 $4,600,000 $4,600,000 $4,600,000Adjustment of net income:Reported net income $1,000,000 $1,000,000 $1,000,000 $1,000,000 $ 200,000 $ 200,000Preferred stock dividends (120,000) (120,000) (120,000) (120,000) (120,000) (120,000)E1 $ 880,000 $ 880,000 $ 880,000 $ 880,000 $ 80,000 $ 80,000Interest on L-T nonconvertibles[$400,000 x 7½% x (1 - 40%)] 18,000 18,000 18,000 18,000 18,000 18,000*Interest on convertible debt retired (2) 36,000 28,800 54,000 43,200 36,000 28,800*E2 $ 934,000 $ 926,800 $ 952,000 $ 941,200 $ 134,000 $ 126,800*Interest on convertible debt converted[remaining convertible debt x in-terest rate x (1 - 40%)] 19,200 28,800* 48,000* (7)E3 $ 946,000 $ 970,000* $ 128,000*Preferred Dividend Savings 120,000 120,000 120,000E4 $1,066,000 $1,061,200 $ 200,000Adjustment of shares:Weighted average no. of shares, S1 (3) 480,000 480,000 480,000 480,000 480,000 480,000Exercise of warrants (200,000-100,000) (4) 100,000 100,000 100,000 100,000 100,000 100,000*S2 580,000 580,000 580,000 580,000 580,000 580,000*Convertible debt (conversion) (5) 16,000 16,000* 40,000* (7)S3 596,000 596,000* 520,000*Convertible preferred stock (6) 100,000 100,000 100,000S4 696,000 680,000 580,000EPS1 (E1/S1) 1.83 1.83 1.83 1.83 .17 .17EPS2 (E2/S2) 1.61 1.60 1.64 1.62 .23** .23**EPS3 (E3/S3) 1.59 1.63** .25**EPS4 (E4/S4) 1.53 1.56 .34*** This item is excluded from succeeding E and S calculations, since the CSE or security under consideration was antidilutive.** This figure would not be reported since it is antidilutive.(1) Primary EPS: (500,000 shares x 20% limitation) x $27; Fully diluted EPS: (500,000 shares x 20% limitation) x $30.(2) Amount of convertible debt retired x interest rate x (1 - tax rate).(3) 420,000 + (9/12 x 80,000).(4) 200,000 shares from the exercise of warrants minus (500,000 shares x 20% limitation).(5) [($2,000,000 minus convertible debt retired)/$l,000] x 20 shares.(6) (20,000 shares x 5).(7) Since previous adjustments are antidilutive, it must be assumed that there is no retirement of convertible debt. Therefore, the full amount of debt is used in this adjustment.10 / The Woman CPAnot CSE's for primary EPS.) In consider­ing the effect of the convertible debt on E3 and S3 (with elimination of the adjust­ments to arrive at E2 and S2), one adds the convertible debt adjustments directly to Ei and S1 instead of to E2 and S2 in order to arrive at E3 and S3. EPS3 is larger than EPS1 and therefore the convertible debt is also antidilutive. In calculating E4 and S4 to consider whether the convertible pre­ferred stock is dilutive, the adjustments will be added to E1 and S1 (because ad­justments to arrive at E2, E3, S2, and S3 are eliminated). EPS4 is greater than EPS1, indicating antidilutiveness of the conver­tible preferred stock also. Thus, the as­sumed exercise of the stock warrants, the convertible debt, and the convertible pre­ferred stock (the latter two considered only for fully diluted EPS) are all antidilu­tive and EPS1 would be the reported figure. The solution to Case 3 shows that the step-by-step procedure in our work­sheet format is an effective and desirable approach.Other factors might cause antidilutive­ness. Even with a higher income (say $1,000,000 as in Case 1), a higher interest rate on the convertible debt or a lower conversion rate for either bonds or pre­ferred stock could cause antidilutiveness.Concluding CommentsIn addition to the unique worksheet for­mat which facilitates both original compu­tations and illustrations, the cases illus­trate many specific points with just one set of data. The cases include pre-Opinion 15 EPS calculations; stock warrants with end­ing market price of stock greater than the average price for treasury stock acquisi­tion purposes and the accompanying 20% rule; convertible debt and convertible pre­ferred stock; calculation of a yield rate of interest different from the nominal rate of interest; an income tax rate other than 50% to more clearly illustrate the net-of-tax savings; and the weighted average calcu­lation of the number of shares for the denominator. Many of these individual points arise in practice although they are seldom given attention in examples in informational and interpretive sources.For additional illustrations, instructors or discussion leaders could increase the number of cases by including other things — all within the same format. For exam­ple, one could have two issues of conver­tible debt and all convertible debt could be assumed to be CSE's or convertible pre­ferred stock could be assumed to be a CSE. These changes can be made with only minor changes in the data. One could illustrate that most items are antidilutive when a net loss is shown. Introducing the issuance of a convertible debt during the current year, or an even more challenging actual conversion of a convertible security during the current year would provide ample opportunity for expanding the problem to the degree desired by the instructor.The format would facilitate com­puterization of EPS calculations and thus would have the advantage of providing an opportunity for the instructor to explain to practitioners that some large companies do computerize their EPS calculations — that computerization may, in fact, be the most feasible way of calculating EPS for companies with complex capital struc­tures.Another advantage of the illustrations in this article is that the problem(s) can be adapted to fit the needs of different types or levels of practitioners. For example, if an instructor is working with practitioners who are concerned with EPS calculations for purposes of general understanding only, he or she would cover only the basics of this problem (probably only Case 1). If the instructor is working with those in­volved with EPS calculations for corpora­tions with complex capital structures, he or she could include all of the material covered in this article or introduce other variations which may be important into the format described in this article.The authors wish to express their appreciation to Dr. Bradley J. Schwieger, The University of Tennessee-Knoxville, for his helpful comments and suggestions.Notes1There are some other requirements as well, such as: issuance must be exercisable within five years (APB Opinion 15, paragraph 57) and market price must have exceeded the exercise price for “substantially all of three consecutive months ending with the last month of the period to which earnings per share data relate" (APB Opinion 15, paragraph 36).Paragraph 38(b) of APB Opinion 15 regarding the order of the assumed use of the proceeds from the assumed exercise of the options or warrants is confusing. It appears that the order after assumed retirement of 20% of outstanding shares is retirement of short-term borrowings and long-term borrowings. These long-term borrowings include any long-term debt to the extent that the debt may be retired. "Debt is eligible to be retired when it either may be "called" or is trading and could be purchased in the market" (Unofficial Accounting Interpreta­tions of APB Opinion No. 15, paragraph 77). Since any long-term debt can be retired, this does include convertible debt, both CSE's and other potentially dilutive securities; therefore, in general, it should be assumed that all conver­tible debt is retired before proceeds are invested in government securities, and this is the as­sumption in the present article.At Robert Half, our counselors are accountants, bankers and systems managers.We figure it takes one to know one.Whether you’re seeking employment or employees in any of these specialized areas, you can be sure the person you speak with at Robert Half understands the field from your side. Call any Robert Half office, we speak your language.ROBERT HALFPERSONNEL AGENCIESSpecialists in Finance, Banking, Accounting and EDP.Albuquerque / Allentown / Atlanta / Baltimore Boston / Buffalo / Charlotte / Chicago / Cincinnati Cleveland / Columbus / Dallas / Denver / Detroit Hartford / Houston / Indianapolis / Kansas City Lancaster / Long Island / Los Angeles / LouisvilleMemphis / Miami / Milwaukee / Minneapolis Newark / New York / Oakland / Omaha / Orange, Cal.Philadelphia / Phoenix / Pittsburgh / Portland Providence / San Diego / San Francisco / San Jose Scranton / Seattle / St. Louis / StamfordTampa / Washington / WilmingtonLondon, England / Toronto, Canada / Vancouver, B.C.January 1976 / 11

New Approach to Calculating Earnings Per Share

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New Approach to Calculating Earnings Per Share

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