Estimating Preferred Shares with Regard to the Possibilities of Gaining the Voting Right by their Holders

Transcription

1 Journal o Fnance and Investment Analyss, vol. 3, no.1, 2014, ISSN: (prnt verson, (onlne Scenpress Ltd, 2014 Estmatng Preerred Shares wth Regard to the Possbltes o Ganng the otng Rght by ther Holders Yury. Kozyr 1 Abstract Ths artcle vews the technques to estmate preerred shares, the holders o whch have acqured the votng rght or the shareholder s meetng by nonpayment o dvdends on these shares. The author o ths paper attempts to show regard to the opton actor, whch relects the possbltes to gan the votng rght by preerred shareholders, drectly n specal calculaton models. In addton, the artcle proposes the crteron o decson makng by majorty (controllng shareholders on the reasonablty o ether the payment or nonpayment o dvdends to mnorty shareholders. JEL classcaton numbers: D 460, G 120, G 320 Keywords: alue o preerred votng shares, otng opton or shareholder s meetng; share o control, alue o control. 1 Introducton Not many research works are devoted to the peculartes o the method or estmatng the value o preerred shares, as dstnct rom common stock. The author o ths paper has ound ew publcatons on ths topc ([1],[2],[3],[4]. And there are even ewer studes devoted to descrbng the technques or preerred share estmaton, whch regard the exstng and potentally possble stuatons, n whch preerred shares ether are or may become votng. Among the aorementoned studes, t s necessary to partcularly emphasze paper [3], whch, accordng to the author s vew, was the rst n lterature to comment on the exstence o the votng opton or the holders o preerred shares at a general meetng and on both the value o ths opton and value o dvdend payments beng subject to consderaton whle estmatng the value o preerred shares. In ths context, Gomzn notes: the holders o common stock have somewhat smlar to the opton.e., not to pay dvdends n case the value o the votng rght at the next meetng 1 Department o Theoretcal Economy and Mathematc Research, Central Economcs and Mathematcs Insttute o Russan Academy o Scences, Moscow, Russa. Artcle Ino: Receved : December 21, Revsed : January 19, Publshed onlne : March 1, 2014

2 14 Yury. Kozyr o the shareholders s lower than that o the pad dvdends on preerred shares o the A type. Further hereon, the author o ths paper attempts to show regard to the opton actor (the actor o the possblty to gan the votng rght drectly n some specal calculaton models. 2 Peculartes o Estmatng the alue o Preerred Stock To start wth, let s try to answer the queston what are the components o the share value? Ths value comprses o the expected economc benets rom the prospects o recevng dvdends; o busness management; and o the potental possbltes o a protable stock brokng n the uture as ther market value beng ncreased. Moreover, the pecularty o preerred shares s that ther holders eature the absence o the votng rght most o the tme. Nevertheless, n some cases ( nonpayment o dvdends to the holders o preerred shares takes place the holders o these shares gan the votng rght or a general meetng. Correspondngly, the holders o preerred votng shares lose dvdends but gan the votng rght nstead. Thus, whle the necessty to estmate preerred shares, whch may become votng, occurs, t can be realzed as: 1v = 1 P(dvs (t opton 1 (t (1 1 k (1 p dv k b C p 1k = v( 0 (2 k 0.5 k = 1 (1 r = 1 N (1 r (1 r r 1v alue per one preerred votng share; 1 alue per one preerred nonvotng share, on whch dvdends are pad; P(dvs (t Present value o dvdends on preerred shares or the t-perod, wthn whch the absence o dvdend payment s supposed; opton 1 (t alue o the opton precondtoned by the presence o the votng rght on preerred shares durng the t-perod; dv Expected value o dvdend payments on preerred shares durng the perod; r - Rsk-ree dscount rate at the moment o estmaton; r r Dscount rate relectng the rsks o changes n the market value o preerred shares; b Share o control draned by preerred shares n the stuatons, when they become votng, 0 < b 0.25; C alue o control, whch s expressed n the absolute value (RUR, over the operaton o the company-emtter o estmated shares 2 durng the -perod; p Possblty o preerred shares to become votng durng the -perod; N Aggregate amount o emtted preerred shares; 2 The value o control may be estmated by both the drect and ndrect technques. The latter one estmates the value o control as the value o the company s equty captal, whch s calculated through the control-nvolved estmaton technques, mnus the estmaton technques, whch calculate the value o the whole equty captal on the mnorty level.

3 Shares wth Regard to the Possbltes o Ganng the otng Rght by ther Holders 15 k Perod o tme, durng whch (nclusvely the holder o the estmated preerred shares s gong (ntends to contnue stayng ts holder, and upon the expry o whch he plans to sell t at the rate 1k 3 ; v(0 alue o holdng preerred shares n the perod nearest to a next meetng: In the event that at the tme o estmaton (t 0 preerred shares are actually votng, and tll the nearest meetng o shareholders, the t m -tme s let: v b C = (3-1 N (1 r ( ( tm t0 r s the dscount rate appled or the lows o ncomes on common stock; - In the event that n the current perod the decson was made on payng dvdends on preerred shares n the amount o dv 0, and t p o days s let tll the payment: v dv = (3-2 0 ( 0 ( tp t0 (1 r - In the event that n the current perod the decson was made on payng dvdends on preerred shares, and ths payment has already been made: v ( 0 = 0 (3-3 The thrd summand n equaton (2 obvously represents the value o the optons embedded n preerred shares or ther holders,.e., ths s the parameter opton 1 (t n (1. Thus, the value o the embedded opton or preerred shares n every -perod can be calculated as: - Whle estmatng n real costs (as per share: b C p = opton1 (4 N - Whle estmatng n uture costs as o the current date o calculaton (as per share: b C p (5 opton1 = k 0.5 N (1 r - Whle estmatng n real costs (on the bass o the aggregate amount o shares: = b C (6 opton p 3 Paper [5], p.558, Secton 18.5 o Estmaton regardng the nal date o holdng, proves that the estmaton o both the value per share through the dscountng o dvdends on t tll a certan moment o tme and the expected sellng rate s equvalent to the estmaton o the value per share by dscountng all uture dvdends.

4 16 Yury. Kozyr - Whle estmatng n uture costs as o the current date o calculaton (on the bass o the aggregate amount o shares: b C p (7 opton = k 0.5 (1 r all the components correspond to the prevously accepted parameters. The essence o equatons (4-(7 s assocated wth the understandng that they estmate the value or the possbltes o transerrng the powers o control over the company (b C to the holders o preerred votng shares n the -perod n the event that the possblty or preerred shares to become votng n the -perod equates to p. Equatons (1-(2 can obvously be reormatted or estmatng the value o the total number o preerred shares. For ths purpose, t s necessary to use the cumulatve sum o the dvdends expected or the payment on preerred shares, and not to dvde the thrd summand by N n equaton (2: (1 p dv b C p = v( 0 (8 k k 1k k 0.5 k = 1 (1 r = 1 (1 r (1 r dv s the expected value o summed dvdend payments on preerred shares n the perod. Let s try to use equaton (8 or the estmaton. For example, let s assume that t s necessary to estmate preerred (actually votng shares, whch wll stay the same, as expected, or one more year; and ater ths perod they are expected to return nto ther votng status two more tmes wthn the 3 rd and 4 th orecast years and durng the 6 th orecast year. Then the value o these shares can be calculated as: 1 = b b4 C4 p 3.5 (1 r (1 1 C 1 dv (1 r 4 (1 dv6 p6 (1 r b3 C3 p 2.5 (1 r dv4 p4 (1 r m 7 dv = (1 r (1 dv (1 r 5 dv3 p3 (1 r b6 C6 p 5.5 (1 r 6 (9 b Share o control draned by preerred shares n the perod, when that they become votng, 0 < b 0.25; C alue o control n the perod gven n absolute values (RUR; p Probablty o preerred shares to become votng wthn the correspondng perod; dv Expected value o summed dvdend payments on preerred shares n the perod (moreover, or the 2 nd and 5 th perods, and startng wth the 7 th perod and urther, the act o dvdend payments sn t called nto queston; nevertheless, the change n these payments may possbly occur;

5 Shares wth Regard to the Possbltes o Ganng the otng Rght by ther Holders 17 r Dscount rate relectng rsks o recevng yelds on preerred shares; All the other parameters correspond to the prevously accepted. Besdes equatons (4-(7, the value o embedded optons can be calculated through the ndrect technque, on the bass o comparng the value per one common share and that per one preerred share (whch becomes possble only n the case o the developed market o these shares: = P ( dv (10 opton1 1os opton1 summed value o embedded optons per preerred share; 1os cost per common share; P(dv present value o expected dvdends as per preerred share; Δ derence between the value per common share and that per preerred share. It s necessary to pont out that accordng to [4], the average dscount on Russan emtters preerred shares amounted to 50-60%. The later observatons by the author o ths paper showed that the dscount averaged rom 30 to 40% (n rare cases, t was completely absent. 3 Addtonal Thoughts In addton to the aorementoned equatons, let s gve as set o extra ormulas, whch can be useul or estmatng the share value: os = Nos 1 os C (1 b p (11 C opton1os = (1 b p N (12 os os cost o a 100% stake o common stock (wth regard to control n the perod; N os aggregate amount o emtted common shares n the perod; 1os cost per common share n the perod n the mnorty stake; C value o control over the company n the -perod; opton1os value o the opton (as per holder o one common share provdng control over the company s actvty n the perod. Equaton (12 shows that the value o opton, whch s predetermned by the possbltes or the holders o common shares to manage the company s actvty, s the maxmum n the cases o dvdend payments on preerred shares ( p = 0, when preerred shares lacks the votng rght, and t s the mnmum n the cases o dvdend nonpayment on them ( p = 1. The structure o the aorementoned equatons clearly demonstrates that the soluton o some problems, as t oten happens, nevtably nvokes the occurrence o new ones;.e., accountng or the status o preerred votng shares stpulates the necessty to estmate the

6 18 Yury. Kozyr addtonal parameters o the calculaton models, the value o whch can be consderably ound only wth a hgh degree o subjectvty. Nevertheless, the aorementoned dsadvantage doesn t aect the justablty o the most theoretcal calculaton model/scheme. In concluson, t s reasonable to repeat the quotaton gven herenabove rom [3]: the holders o common stock have somewhat smlar to the opton.e., not to pay dvdends n case the value o the votng rght at the next meetng o the shareholders s lower than that o the pad dvdends on preerred shares < >. The author o ths paper beleves that ths dea can be expressed n other words: the holders o the controllng stakes o common stock have an opton not to pay dvdends n case the decrease n the value o the power o control (as a result o waterng the votng shares whle the votng rght s ganed by the holders o preerred shares s lower than the value o pad dvdends on preerred shares 4 ; and vce versa. The mathematc context, ths condton can be expressed as: - To pay dvdends a(b - b CS C > (Dv dv CS; - Not to pay dvdends a(b - b CS C < (Dv dv CS (13 a Share o control possessed by controllng share holders, who make a decson on dvdend payment/nonpayment on preerred shares; b CS Share (rom the whole authorzed captal o the preerred stock, whch s owned by controllng share holders; a(b - b CS C Decrease n the value o control or controllng shareholders n the event o makng the decson on dvdend nonpayment and the transer o the share o control amountng to b to the holders o preerred stock 5 ; Dv Aggregate sze o the dvdend masses on preerred stock; dv CS Sze o the dvdend masses on the preerred shares possessed by controllng shareholders (n case such a stuaton s present. Let s dscuss the example o applyng the condtons o (13. Let s suppose that the ollowng normaton s known: - The value o the company s equty captal calculated wth the cash low dscountng technque amounts to 120 mllon RUR; - The value o the company s equty captal calculated wth the adjusted net asset technque amounts to 110 mllon RUR; - The value o the company s equty captal calculated by the ndustry multpler technque amounts to 90 mllon RUR; 4 Here, the dvdends to the holders o the controllng stake (n case controllng shareholders possess a certan number o preerred shares are to be excluded rom the estmaton o the dvdend masses on preerred stock. 5 In case controllng shareholders possess a certan number o preerred shares, the parameter b must be decreased and must regard only the transer o the share o control to holders-outsders n relaton to controllng shareholders.

7 Shares wth Regard to the Possbltes o Ganng the otng Rght by ther Holders 19 - The controllng shareholder possessng a 55% stake o all the common shares consders that due to the equty captal structure and hs power n the Board o Drectors, he has 70% control over the company s actvty; - Besdes o the common stock, the company has emtted preerred shares, the number o whch amounts to 25% o the authorzed captal; - The controllng shareholder possesses 20% o all the preerred shares o the company (whch amounts to 5% o the total authorzed captal; - Accordng to the results o the current perod, the company has earned the benet o 10 mllon RUR. The controllng shareholder must make a decson on ether the payment or nonpayment o dvdends on common stock. On the bass o the ntal data, let s nd the value o ull control over the company (the parameter C. The value o a 100% stake calculated on the bass o the technques wth regard to the value o control approxmates ( /2 = 115 mllon RUR. The value o the equty captal calculated on the bass o the technque regardless o the power o control amounts to 90 mllon RUR accordng to the condtons o the task. So the value o ull control s calculated as: C = = 25 mllon RUR. Let s nd how the value o control wll decrease or the controllng shareholder n the event o the decson on the nonpayment o dvdends on the preerred stock. In accordance wth the let-sde expresson o (13: a(b - b CS C = 0.7 ( = 3.5 mllon RUR. And the controllng shareholder wll save on dvdend nonpayment the sum calculated wth the let-sde expresson o (13: 10% o the net prot (.e., = 1 mllon RUR and mnus the dvdends on the preerred shares held by hm (.e., = 0.2 mllon RUR; so the total value equates to = 0.8 mllon RUR. As t s obvous rom the calculated data that the estmated value o the decrease n the value o the powers o control at the shareholder s meetng (3.5 bllon RUR exceeds the savngs n dvdend payments on preerred stock to outsde shareholders (0.8 mllon RUR, t would be more protable or the controllng shareholder to make a decson on dvdend payment to the holders o preerred stock. 4 Concluson In ths artcle, the author proposes the technque or calculatng the value o preerred shares wth regard to the value o the embedded opton provdng the votng rght n the absence o dvdend payments, and addtonally proposes the crteron o makng a decson by majorty (controllng shareholders on the reasonablty o ether the payment or nonpayment o dvdends to mnorty shareholders. The man dsadvantage o the proposed method s a hgh subjectvty when estmatng two parameters o the calculaton models the probablty or preerred stock to become votng durng the correspondng - perod (the parameter p, and the perod, wthn whch the absence o dvdend payment s expected (the parameter t. But t s necessary to realze that the process o estmatng the value o anythng and estmatng the share value n partcular s mpossble wthout the elements o subjectvty. In ths context, the ormulas proposed n ths paper mustn t be taken as a dogma but as only a vector o movement toward the reasonablty o estmatng the values o preerred stocks.

8 20 Yury. Kozyr Fnshng the paper, the author hopes that the provsons gven heren wll help ts readers to gan a resh approach to the ssues o preerred stock prcng and wll possbly nspre some o them or urther studes n the determned drecton. Reerences [1].Shepelev, Preerred Stock and Some Peculartes o ther Estmaton, Appraser.ru, (2000. [2] O. Sngerev and O. Kalnovch, The Мalue o ote: on the Approach to Estmatng the Market alue o the Shares o Russan Stock Companes, Appraser.ru, (2002. [3] L. Gomzn, Some Peculartes o Calculatng the Market alue o Preerred Stock wth the Income Approach, Securtes Market Journal, 4(235. [4]. Gettsman and M. Shpgel, Relatve alues o Preerred and Common Stocks o Russan Companes, Yale School o Management, [5] W. Sharpe, J. Aleksander and G. Baley, Investments, M. zd. Inra-M, 1997, p.1024.