A Case Study in More Realistic Retirement Planning

Transcription

1 A Case Study i More Realistic Retiremet Plaig Harold B. Tamule, Providece College Richard B. Goldstei, Providece College ABSTRACT Fiacial plaig etails the projectio of expected cash flows compouded at a realistic rate of retur to estimate a potetial future value. Stadard formulae use oly simplistic assumptios which may lead to biases, or worse, icorrect estimates. Usig more realistic assumptios, we develop a fiacial model to correct such potetial error. To exted this aalysis further, we employ our model to develop a uderstadig of a cotroversial case of CEO retiremet beefits compesatio. While our model is limited by mathematical parameters, we show that this case of defied beefits CEO retiremet compesatio could oly be eared by a competig defied cotributio pla with uusually high cash flow iputs. INTRODUCTION Early i their college educatios, busiess majors egage i thorough study of discouted cash flow aalysis, or the time value of moey. While the various preset value formulae demostrate the stadard valuatio process, the future value equatios are also useful. I fact, some studets may erroeously see more sigificace i future value operatios, possibly due to the etertaimet value of seeig modest ivestmets become large from compoudig over log holdig periods. Noetheless, future value operatios are likely to be importat i the modelig of retiremet. The primary purpose of this paper is to show that the curret basic future value equatio that is a stadard compoet of itroductory fiace courses may mislead those plaig for retiremet, especially if the periodic cash flow experieces real growth over the ivestmet horizo. A secod purpose is to examie a cotroversial case study of retiremet savigs. A REALISTIC FINANCIAL PLANNING MODEL The stadard classroom applicatio for retiremet is typically the future value of a ordiary auity. A traditioal example of this type of ivestmet is a whole life isurace policy with cash surreder value. With regard to retiremet savigs, usually a employee s retiremet accout receives a employer s ed-of-period retiremet cotributio paymet, or the idividual deposits their ow paymet at the ed of the period (A). Studets see this operatio i the future value of a -period ordiary auity formula as the ed-of-period paymet is discretely compouded at the periodic opportuity rate-of-retur (r) as follows: (1 + r) 1 FVAORD = A* r

2 2 This will be i error uless the opportuity rate-of-retur is the real rate-of-retur ad the recurrig retiremet paymet is a costat ad real, ot omial amout. For a more realistic retiremet example, this aalysis must be modified. I the case i which the fiacial aalyst uses omial values ad omial expected ivestmet rates-of-retur, a more accurate retiremet plaig model would reflect a growig aual base salary to reflect cost-of-livig adjustmets as well as merit or real raises from a promotio, etc. As log as the employer keeps the percetage cotributio of employees salary costat, the employee (studet) will ratioally expect a growig series of cash flow beig ivested for retiremet. This would mea that ratioal ewly-hired employees would referece their projected ed-of-period paymets (A) which grow at a aual rate of g ad compoud to a retiremet accout balace as follows: FVA = A*(1 *(1 + r) + A*(1 *(1 + r) A*(1 *(1 + r) (1) With somewhat familiar algebraic maipulatio, oe ca develop a more cocise versio of a effective retiremet plaig model. First assume that r>g ad that the growth i a employee s aual salary ad thus retiremet paymet grows at a costat rate (g). The defie a costat (C): 1+ r C = 1 + g ad multiply both sides of equatio 1 with the costat to obtai: 1 r FVA * + = A*(1 *(1 + r) + A*(1 *(1 + r) A*(1 *(1 + r) (2) 1+ g The factor the A 0 from both equatios 1 ad 2. The subtract equatio 1 from equatio 2 to obtai: [(1 *(1 + r) (1 *(1 r) ] (3) 1+ r FVA * FVA = A* + 1 g + By subtractig ad the crossmultiplyig, the future value of the -period growig, but fiite auity, i.e. FVFBGA becomes: [(1 + r) (1 ] FVFBGA = A* (4) r g For example, suppose that a umber of studets have just accepted a job ad are sufficietly farsighted to cotemplate their retiremet. Furthermore assume that the yearly retiremet beefit will be 10% of their startig salary of 40,000 ad is payable ito their accout i a lump sum at the ed-of-the-year. These studets may ratioally expect their omial aual salary to grow at a 5% rate over their 40-year career, hypothetically ivest i a 50/50 allocatio betwee bods [E(ROR) =.06] ad equities [E(ROR) =.10] ad costatly rebalace to maitai the 50/50 allocatio. The the future expected value of the retiremet accout balaces ca be calculated as follows: [(1.08) (1.05) ] [ ] FVA 40 = $4,000* = $4,000* = $1,957,938 (5) Ay sophisticated studet will wat to iquire ito the error i usig the stadard future value of a auity istead of this more accurate ad realistic equatio. To aswer this, the

3 3 istructor ca require a spreadsheet assigmet that easily produces the compariso. To cotiue with the above example, Table 1 reflects the growth versus o-growth cases. By subtractig the value of the growig, but fiite retiremet auity from the stadard fixed auity, the studet ca calculate the improvemet i their omial retiremet balace as their cotributio grows. I cotrast to the stadard formula, after a forty-year career, the employee who ejoys a growig retiremet paymet will have a additioal $921,712 (+88.95%). At the extreme a employee who cotemplates a fifty-year career would pla o accumulatig more tha twice the retiremet balace tha the fixed auity ower. The error for misusig these formulae leads to substatial error. As oe ca see from Figure 1 the error due to the misused formula is a expoetial shaped fuctio. Aother exercise ito the differece betwee these formulae is the cosideratio of iflatio. The Fisher effect states that the omial iterest rate (r) equals the product of the real iterest rate, r real ad the expected rate of iflatio, E(I). If a recet college graduate ratioally, but pessimistically, expects to receive oly a omial aual raise, the the fiacial plaig for retiremet is simplified. I this case, the future value available upo retiremet is a fuctio of the stadard future value of a auity equatio. This is most easily see usig the preset value formula. The preset value of expected retiremet paymets equals: 2 A*(1 A*(1 A*(1 PVA = (6a) 2 (1 + r) (1 + r) (1 + r) As the Fisher effect states that: 1+ r = (1 + rreal ) * (1 + E( I)) ad by substitutio: 2 A*(1 A*(1 A*(1 PVA= (6b) 2 2 (1 + rreal ) *(1 + E( I)) (1 + rreal ) *(1 + E( I)) (1 + r) *(1 + E( I)) If the ew employee oly receives a omial raise to keep pace with iflatio, the g = E(I) ad after cacelig terms, equatio 6b becomes similar i form to a stadard fixed auity. After multiplyig by the compoudig factor (1+r), the stadard future value formula is produced as follows: 1 1 (1 + r ) real (1 + rreal ) 1 FV = PV *(1 + rreal ) = A * *(1 + rreal ) = A * (7) rreal rreal Usig the data of the previous example, assume that the recet college graduates expect the rate of iflatio to equal their expected omial raise of 5% over their 40-year career. I that case, oe ca easily solve for the real rate of growth of 2.86% ad a real aual retur of 4.85%. The their expected real retiremet accout balace will be approximately less tha half the omial amout as follows: FVA 40 = $4,000* $4,000* = $466,788 (8).0485 = Of course, most studets will look at this projectio as urealistically low because they do expect real icreases i their salaries. To complete a sesible example, we calculate the real

4 4 future value of retiremet savigs with 3% iflatio, 8% omial portfolio retur, ad a 5% omial growth rate of aual cotributios as follows: FVA 40 = 4,000 * $4,000* = $617,462 (8a) = Part B of Table 1 displays the real, as opposed omial error of the simulatio. Here the forty-year employee who receives compesatio that is growig at 5%, but experieces 3% aual iflatio is oly $151,589 (+32.54%) better off tha the fixed auitat. The extreme case of the fifty-year employee sees his/her additioal real retiremet balace at $1,108,285, or oly 38.87% better off. A more realistic applicatio of Equatio 4 is to calculate future value of retiremet savigs usig a cotiuous algorithm. I other words, the paymets ito the retiremet accout are made o a discrete basis, either aually or mothly, but the retur ad growth are geerated cotiuously. This reflects a global ecoomy i which fiacial markets are ope cotiuously ad assets are traded cotiuously. To modify Equatio 4, the period rate-of-retur ad the growth rate must be modified to a cotiuous form. Takig Equatio 1 ad modifyig it with k subperiods i each discrete iterval to the cotiuous process yields: 0 k* 1 1 k* 2 k* 1 A g r A g r A g Re tiremet = * 1 + * * 1 + * * 1 + * 1 + FVA k k k k k k k k (9) As the limit of k approaches ifiity, ad usig L Hôpital s Rule, Equatio 9 reduces to: *r *g ( e e ) FVA Retiremet = A (10) r g Table 2 displays the simulatio results of a cotiuous process of earig employee beefits. The realism of this approach is rooted i the firm operatig costatly, i.e. geeratig cash flows costatly that ca be allocated to the employee beefits of salary ad retiremet ad the ivestmet assets of the retiremet accout are trade i cotiuously operatig fiacial markets. The parameters of the simulatio remai costat. With a cotiually compoudig retur ad icreasig auity paymets, the retiremet accout clearly produces a higher future value. The cotiuous process results i Table 2 show that the forty-year employee should expect a additioal edig balace of $327,859 (+16.7%). The logest term employee, the fifty-year worker, is $930,859 (19.7%) better off. ANALYSIS OF CEO RETIREMENT COMPENSATION This fiacial modelig is critical i aalyzig importat evets i the fiacial markets. For example, a cotroversy erupted i 2003 subsequet to the public disclosure of the compesatio of the Chairma of the New York Stock Exchage. His pay package ot oly dwarfed that of other chief executives of ot-for-profit corporatios, but it exceeded the average of may private sector CEOs. I 2002 the NYSE Chair eared $10 millio i salary ad bous, while the CEOs of the 500 largest corporatios eared oly a average of $6.2 millio i salary, bous, ad itrisic value of exercised stock optios [Ackma 2003]. The revelatio of the NYSE Chair s compesatio produced widespread reactio i various aveues of the media. r k 0

5 5 Ufortuately, most of the reactio teded to be very emotioal ad lackig i aalytical objectivity. Moreover, the refereces to the situatio were at a miimum hyperbolic, ad at worst hysterical. Some resposes described the etire cotroversy: a firestorm [Morgeso ad Thomas 2003] ; startlig [Kelly ad Craig 2003]; pure greed [Valdmais 2003]; Members Mutiy over Chairma s Bouty [Aderso 2003]; ad, a embarrassig episode [White 2003]. Other commetators reported o their ow feeligs: shocked, outraged, privately icredulous, revulsio [Kelly, Craig, ad Duga 2003]. Yet others isolated o the NYSE Chairma himself: the ewest symbol of ruaway greed [McGeeha ad Thomas]; bluderig ad clueless [Tharp 2003]; [NYSE Chair] has succeed at makig Wall Street gasp i astoishmet at someoe else s compesatio, [Thomas 2003]; ad, a $188 Millio weddig cake with tier upo tier of bouses ad pesio ehacemets stacked so high they left olookers gapig [McGeeha 2003]. A objective aalysis would examie the relevat cash flows usig a appropriate, or reasoable opportuity rate-of-retur. While most of the media outrage occurred i 2003 as a result of the NYSE Chair accumulatig a miimum of $139.5 millio i pesio beefits ad deferred compesatio ad a maximum of $188 millio, a complete aalysis of the case study must begi earlier. The NYSE Chair bega workig for the NYSE i April 1968 as a low-level clerk oly makig $82.50 per week, i.e. $82.50*52 or $4,290 per year. By all reports, he worked very diligetly, eared may well deserved promotios, i 1988 became CEO, ad evetually i Jue 1995 rose to NYSE Chairma. At that time he egotiated a pay package that allowed him to withdraw his accumulated defied-beefit retiremet balace of $6.5 millio ad to ear 8% o this withdraw amout ad ay other subsequet accumulated savigs balaces. Thereafter his base salary of $1.4 millio was augmeted by substatial bouses which resulted i his total compesatio exceedig $10 millio i I 2003 his accumulated balace of his retiremet ad deferred compesatio of $139.5 millio became publicly kow. The large ad cotroversial amout of the NYSE Chair s est egg of retiremet ad deferred compesatio lead to his forced resigatio ad is a perfect example for our fiacial modelig. I additio, the fiacial modelig is etirely objective ad does ot impart emotios or persoal opiios to this situatio. To aalyze the reasoableess of the retiremet ad savigs package requires the simple fiite, but growig auity to model the outcome of a defied cotributio retiremet pla. First, the model calls for practical assumptios. Give that various sources report that the former NYSE Chairma started workig earig $4,290 yearly i 1968, received $2,160,000 ($1,260,000 i aual salary ad a $900,000 bous) i 1995 ad at the same time egotiated a withdrawal of $6,571,397 from his retiremet accout ad deferred compesatio savigs balace, oe must idetify a costat growth of his compesatio, a aual rate-of-retur, ad a cotributio percetage of salary. First, oe ca quickly calculate a approximate 25.65% aual rate of icrease (g) i his total compesatio usig a simple geometric model as follows: $ 2,160,000 = $4,290*(1 Sice the NYSE Chair s subsequet compesatio cotract guarateed him a aual 8% rateof-retur o certai accout balaces, a iitial calculatio must assume this opportuity rate. The last iput is the NYSE s cotributio percetage ito his retiremet ad savigs accout. This is assumed to be 12% ad projected to begi at the iceptio of his career. 1 Ufortuately, 1 A subsequet employmet cotract offered the NYSE Chair a supplemetal savigs pla i which the NYSE would match his cotributio up to 6% of his salary.

6 the NYSE Chairma had such a uusually successful career whose icreases i compesatio yield a growth rate that exceeds the assumed opportuity rate-of-retur. Sice equatio 4 caot be used directly, as a alterative we employ a excel spreadsheet i which the sum fuctio essetially replaces equatio 4. Give the three parameters of hypothetical cotributio, retur ad duratio we calculate that the NSYE Chair s simulated retiremet balace would grow to $1,443,822 after 26 years of employmet (Table 3A). Give the iputs of our simulatio, clearly the 1995 balace of $6,571,397 was uattaiable. Therefore, the fiacial aalysis requires some sesitivity aalysis to proceed further. A secod degree of complexity is to cosider a supplemetary employee savigs that augmet a primary retiremet accout. Some qualified employees of tax-exempt corporatios may take advatage of a 403(b) Pla or SRA to augmet their primary retiremet program. The beauty of our fiacial aalysis is that this additioal retiremet savigs ca modeled by simply addig a ew colum of data. Sice the amout to be saved is speculative, our aalysis takes advatage of Excel s goal seek process. I this maer we calculate the amout of periodic savigs ecessary to reach a certai goal. Table 3B shows that the NYSE Chair would have eeded to save 42.62% percet of his aual salary to supplemet his primary hypothetical defied beefit i order to reach $6,571,397. For most years this grossly exceeds the IRS maximum limit of total 403(b) cotributio. Aother optio to cosider is the realistic possibility that the employee s fuds were ivested i a equity accout over the sample iterval. While the NYSE pla offered a guarateed 8% aual rate-of-retur o certai accouts, may retiremet programs have equity accout choices. To test this possibility, we obtaied the total aual rate-of-retur o the S&P500 idex from the begiig of employmet (April 1968) to the ed of his CEO cotract (Jue 1995), i.e. the begiig of his Chairma s cotract. I this iterval the mea aual arithmetic (geometric) rate of retur is 11.74% (10.83%). Because the average equity market retur exceeded the 8% cotractual guarateed rate of retur over this 27 year period, the cumulative year ed balace of the retiremet ad savigs accout is higher ($1,884,359) tha the result of Table 3A ($1,443,822), but substatially less tha the amout that was actually withdraw. We repeat the simulatio ivolvig the persoal savigs rate ecessary to accumulate ad fid that a additioal cotributio of 27.20% of his salary is ecessary to produce a termial value of $6,571,397. A logical extesio to this simulatio is the use of small capitalizatio equity returs, sice some retiremet plas may offer their members such a ivestmet optio. This outcome which is reported i Table 4C yields little differece from Table 4A results of large capitalizatio equities. To reflect a more realistic sceario, we ivestigate the case of mothly compoudig as most busiess professioals should expect twelve paychecks per aum. To simplify matters we assume that the idividual ears oe-twelfth of the idicated yearly retur per period ad all fuds are ivested i a equity accout. First Table 5A shows the case of mothly retiremet cotributios ad compoudig. Obviously the amout of ecessary persoal savigs is reduced from the aual case, oetheless, at 19.34% of salary the required persoal savigs rate is still very high. Table 5B that reflects mothly compoudig with small firm stock returs shows a improved coditio for the executive as his required persoal savigs declies to 14.12% of his compesatio. For the cotiuous compoudig, the results which are ot show do ot differ appreciably from those of Tables 5A ad 5B. 6

7 7 CONCLUSION We ivestigate a fiacial plaig model that is more precise tha the stadard formula that is geerally used i fiace courses. We demostrate the error by usig the wrog model ca icrease substatially over log itervals. I additio we employ this fiacial plaig model to aalyze a cotroversial case study of retiremet beefits usig simulated cash flow aalysis. While our basic model requires a restrictive relatioship of its variables, use of a spreadsheet easily overcomes such a limitatio. Thus, we show that this particular retiremet beefit ca oly be eared by employig uusually liberal cash flow iputs. Our result is cogruet with Bebchuk ad Jackso (2005) who show that CEO pesio beefits costitute a large percetage of CEO career compesatio, alog with rather opaque firm disclosure of the wealth paymet. I additio, Sudaram ad Yermack (2007) likewise show the high value of CEO retiremet obligatios as part of their aalysis of the CEO pesio as a iside debt cotract. Our aalysis emphasizes the ad hoc ature of the defied beefit pesio as opposed to a defied cotributio. Possibly the CEO uses his/her job market power to extract more assets from the firm through their retiremet beefit that is above ad beyod the wealth from aual salary, bous ad equity-based icetive awards. While the firm s decisio to fud their CEO s retiremet with a defied beefit paymet may be greatly iflueced by IRS tax policy, the icompatibility betwee discouted cash flow modelig ad commo CEO retiremet paymets may force them to review such a decisio. I fact, ay orgaizatio that typically compesates their employees with a defied beefit retiremet may wish to revisit such a policy.

8 8 Table 1 Future Value Comparisos Part A: Nomial Values No-Growth, Growig, Fiite Nomial Auity Fiite Nomial Auity Period ROR FVA Growth Rate FVA Error % 4, % 4, % % 8, % 8, % % 12, % 13, % % 18, % 19, % % 23, % 25, % % 57, % 70, % % 108, % 145, % % 183, % 267, % % 292, % 461, % % 453, % 765, % % 689, % 1,235, % % 1,036, % 1,957, % % 1,546, % 3,058, % % 2,295, % 4,724, % Part B: Real Values (Assumptio of 3% Aual Iflatio) No-Growth, Fiite Real Auity Growig, Fiite Real Auity Period ROR FVA Growth Rate FVA Error % 4, % 4, % % 8, % 8, % % 12, % 12, % % 17, % 17, % % 22, % 22, % % 49, % 54, % % 85, % 96, % % 130, % 152, % % 187, % 226, % % 259, % 324, % % 350, % 451, % % 465, % 617, % % 612, % 831, % % 798, % 1,108, %

9 9 Table 1 Auity Error 3,000,000 2,500,000 2,000,000 Diferece 1,500,000 1,000, , Years

10 10 Period Table 2 Future Value Comparisos Discrete Growth ad ROR Cotiuous Growth ad ROR Growth Rate FVA FVA Error ROR ,000 4, % ,520 9, % ,612 14, % ,331 20, % ,740 27, % ,671 76, % , , % , , % , , % , , % ,235,911 1,425, % ,957,938 2,285, % ,058,059 3,614, % ,724,562 5,655, %

11 11 Table 3A NYSE Simulatio Results of 1995 Retiremet Balace Retiremet % 12.00% Guarateed ROR 8.00% B-O-Y Employmet Year E(Aual Compesatio) Retiremet Paymet Retiremet Balace , , , , , ,010 1,081 3, ,321 1,358 5, ,224 1,707 7, ,872 2,145 9, ,456 2,695 13, ,216 3,386 17, ,453 4,254 23, ,546 5,345 30, ,971 6,716 39, ,326 8,439 51, ,363 10,604 66, ,027 13,323 84, ,503 16, , ,283 21, , ,240 26, , ,727 33, , ,702 41, , ,881 52, , ,932 65, , ,723 82, , , , , ,088, , , ,368, ,181 1,145, ,719, ,290 1,443, ,160,000 N/A N/A Growth Rate 25.65%

12 12 Table 3B Fiacial Model Simulatio of 1995 Retiremet with Persoal Savigs Retiremet % 12.00% Persoal Savigs Rate 42.62% Guarateed ROR 8.00% B-O-Y Employmet Year E(Aual Compesatio) Retiremet Paymet Persoal Savigs Retiremet Balace , ,828 2, , ,432 5, , ,056 10, ,010 1,081 3,840 15, ,321 1,358 4,824 23, ,224 1,707 6,062 32, ,872 2,145 7,617 45, ,456 2,695 9,570 61, ,216 3,386 12,025 81, ,453 4,254 15, , ,546 5,345 18, , ,971 6,716 23, , ,326 8,439 29, , ,363 10,604 37, , ,027 13,323 47, , ,503 16,740 59, , ,283 21,034 74, , ,240 26,429 93, , ,727 33, ,932 1,014, ,702 41, ,179 1,285, ,881 52, ,184 1,627, ,932 65, ,937 2,057, ,723 82, ,937 2,598, , , ,326 3,279, ,088, , ,051 4,137, ,368, , ,071 5,215, ,719, , ,618 6,571, ,160,000 N/A N/A N/A Growth Rate 25.65%

13 13 Table 4A Fiacial Model Simulatio of 1995 Retiremet with Aual Equity Returs Retiremet % 12.00% Guarateed ROR 8.00% Employmet Year E(Aual Compesatio) Retiremet Paymet Large Firm Stock Market ROR Retiremet Balace , % , % 1, , % 2, ,010 1, % 3, ,321 1, % 5, ,224 1, % 6, ,872 2, % 7, ,456 2, % 12, ,216 3, % 16, ,453 4, % 19, ,546 5, % 28, ,971 6, % 38, ,326 8, % 59, ,363 10, % 62, ,027 13, % 103, ,503 16, % 128, ,283 21, % 173, ,240 26, % 259, ,727 33, % 369, ,702 41, % 388, ,881 52, % 494, ,932 65, % 657, ,723 82, % 829, , , % 1,038, ,088, , % 1,310, ,368, , % 1,503, ,719, , % 2,011, ,160,000 N/A N/A N/A

14 14 Table 4B Fiacial Model Simulatio of 1995 Retiremet with Persoal Savigs ad Aual Equity Market Returs Retiremet % 12.00% Persoal Savigs 27.20% Guarateed ROR 8.00% B-O-Y Employmet Year E(Aual Compesatio) Retiremet Paymet Persoal Savigs Large Firm Stock Market ROR Retiremet Balace , , % 1, , , % 3, , , % 7, ,010 1,081 2, % 11, ,321 1,358 3, % 16, ,224 1,707 3, % 20, ,872 2,145 4, % 25, ,456 2,695 6, % 40, ,216 3,386 7, % 53, ,453 4,254 9, % 63, ,546 5,345 12, % 92, ,971 6,716 15, % 124, ,326 8,439 19, % 193, ,363 10,604 24, % 205, ,027 13,323 30, % 337, ,503 16,740 37, % 420, ,283 21,034 47, % 568, ,240 26,429 59, % 847, ,727 33,207 75, % 1,206, ,702 41,724 94, % 1,268, ,881 52, , % 1,616, ,932 65, , % 2,147, ,723 82, , % 2,708, , , , % 3,393, ,088, , , % 4,280, ,368, , , % 4,910, ,719, , , % 6,571, ,160,000 N/A N/A N/A N/A

15 15 Table 4C Fiacial Model Simulatio of 1995 Retiremet with Persoal Savigs Ad Aual Small Firm Equity Market Returs Retiremet % 12.00% Persoal Savigs 31.56% Guarateed ROR 8.00% B-O-Y Employmet Year E(Aual Compesatio) Retiremet Paymet Persoal Savigs Small Firm ROR Retiremet Balace , , % 1, , , % 3, , , % 6, ,010 1,081 2, % 11, ,321 1,358 3, % 16, ,224 1,707 4, % 15, ,872 2,145 5, % 18, ,456 2,695 7, % 41, ,216 3,386 8, % 77, ,453 4,254 11, % 109, ,546 5,345 14, % 153, ,971 6,716 17, % 245, ,326 8,439 22, % 362, ,363 10,604 27, % 429, ,027 13,323 35, % 596, ,503 16,740 44, % 862, ,283 21,034 55, % 818, ,240 26,429 69, % 1,145, ,727 33,207 87, % 1,304, ,702 41, , % 1,274, ,881 52, , % 1,741, ,932 65, , % 2,126, ,723 82, , % 1,850, , , , % 3,158, ,088, , , % 4,511, ,368, , , % 6,023, ,719, , , % 6,571, ,160,000 N/A N/A N/A N/A

16 16 Table 5A Fiacial Model Simulatio of 1995 Retiremet with Persoal Savigs ad Mothly Compoudig of Aual Equity Returs Retiremet % 12.00% Persoal Savigs 19.34% Guarateed ROR 8.00% B-O-Y Employmet Year Retiremet Paymet Persoal Savigs Large Firm Stock Market ROR Retiremet Balace E(Aual Compesatio , % 1, , , % 3, , , % 5, ,010 1,081 1, % 8, ,321 1,358 2, % 13, ,224 1,707 2, % 15, ,872 2,145 3, % 18, ,456 2,695 4, % 34, ,216 3,386 5, % 53, ,453 4,254 6, % 78, ,546 5,345 8, % 87, ,971 6,716 10, % 112, ,326 8,439 13, % 160, ,363 10,604 17, % 248, ,027 13,323 21, % 275, ,503 16,740 26, % 389, ,283 21,034 33, % 543, ,240 26,429 42, % 658, ,727 33,207 53, % 995, ,702 41,724 67, % 1,309, ,881 52,426 84, % 1,527, ,932 65, , % 2,001, ,723 82, , % 2,949, , , , % 3,171, ,088, , , % 4,638, ,368, , , % 5,453, ,719, , , % 6,571, ,160,000 N/A N/A N/A N/A

17 17 Table 5B Fiacial Model Simulatio of 1995 Retiremet with Mothly Persoal Savigs ad Compoudig of Aual Small Firm Equity Returs Retiremet % 12.00% Persoal Savigs 14.12% Guarateed ROR 8.00% B-O-Y Employmet Year Retiremet Paymet Persoal Savigs Small Firm Stock Market ROR Retiremet Balace E(Aual Compesatio) , % 1, , % 3, , , % 4, ,010 1,081 1, % 6, ,321 1,358 1, % 10, ,224 1,707 2, % 13, ,872 2,145 2, % 13, ,456 2,695 3, % 17, ,216 3,386 3, % 44, ,453 4,254 5, % 86, ,546 5,345 6, % 120, ,971 6,716 7, % 167, ,326 8,439 9, % 280, ,363 10,604 12, % 420, ,027 13,323 15, % 487, ,503 16,740 19, % 684, ,283 21,034 24, % 1,004, ,240 26,429 31, % 938, ,727 33,207 39, % 1,313, ,702 41,724 49, % 1,443, ,881 52,426 61, % 1,381, ,932 65,872 77, % 1,861, ,723 82,767 97, % 2,183, , , , % 1,946, ,088, , , % 3,507, ,368, , , % 5,011, ,719, , , % 6,571, ,160,000 N/A N/A N/A N/A

18 18 APPENDIX 1. A alterate way to derive formula 4 is a two-level process that first looks at the preset value of a growig, but fiite auity. Some advaced ivestmets or fiacial theory texts may cover this subject, i.e. Copelad, Westo ad Shastri (2004). Keepig all previous assumptios, the basic preset value formula of a costatly growig, but fiite stream of cash flow is: A *(1 PVA = 1 (1 + r) 1 A *(1 + 2 (1 + r) 2 A *( (1 + r) (9) For the first step we calculate the preset value by first multiplyig equatio 9 by the costat (1+r)/(1+g): (1 + r) A *(1 A *(1 PVA * = A (1 (1 + r) (1 + r) 1 (10) The subtractig equatio 9 from equatio 10 yields: (1 + r) A *(1 PVA * PVA = A (1 g) + (1 + r) (11) To complete the first step we subtract ad crossmultiply to arrive at the preset value of a fiite ad growig auity equatio that will be familiar to advaced studets: A (1 PVA = * 1 (r g) (1 + r) (12) As this is the total value ow of all projected retiremet savigs, a ew employee ca calculate i a secod step the future value by simply multiplyig by the appropriate compoudig factor to reproduce equatio 4: FVA= PVA*(1 + r) A = * (r g) [(1 + r) (1 ] (13) 2. The basic formula for the costatly growig ifiite auity is the familiar: A * (1 PV = (14) r g Reflectig cotiuous discoutig ad agai usig L Hôpital s Rule, Equatio 14 remais the same. This leads to the itermediate step i the costatly growig, but fiite auity case:

19 19 (15) 1 1 * g r k g k r A FVA k k + + = As k, Equatio 16 simplifies to: ( ) g r e e A FVA g r = * * * (16)

20 20 BIBLIOGRAPHY Ackma, D., Dick Grasso ad the Compay He Keeps, Forbes.com, May 5, Aderso, J. Grasso Clipped Members Mutiy over Chairma s Bouty, The New York Post, September 2003, p. 39. Bebchuk, L. ad J. Fried, Pay Without Performace: Overview of the Issues, Joural of Applied Corporate Fiace, Fall 2005, pp Bebchuk, L. ad R. Jackso, Executive Pesios, Joural of Corporate Law, December 2005, pp Cohe, L. ad D. Solomo, NYSE Feels Heat from Iside ad Outside, The Wall Street Joural, September 16, 2003, p. C1. Copelad, T., J.F. Westo ad K. Shastri, Fiacial Theory ad Corporate Policy, Pearso Addiso Wesley, Core, J. ad W. Guay, Is U.S. CEO Compesatio Broke? Joural of Applied Corporate Fiace, Fall 2005, pp Elkid, P. ad J. Levistei, The Fall of the House of Grasso, Fortue, October 18, 2004, p Gaspario, C., K. Kelly ad S. Craig, Grasso is NYSE s $10 Millio Ma, The Wall Street Joural, May 5, 2003, p. C1. George, B. ad A. McLea, Richard Grasso ad the NYSE, Ic. (A), Harvard Busiess School Press, Kelly, K. ad S. Craig, Grasso Forgoes Extra $48 Millio, Raisig New Questios for NYSE, The Wall Street Joural, September 10, 2003, p. A1. Kelly, K. ad S. Craig, Several NYSE Directors Cosider Removig Grasso to Stem Pay Flap, The Wall Street Joural, September 15, 2003, p. A1. Kelly, S. Craig, ad I. Duga, Grasso Quits NYSE Amid Pay Furor, The Wall Street Joural, September 18, McGeeha, P. Quick: What s the Boss Makig? New York Times, September 21, 2003, p. 3.1.

21 21 McGeeha, P. ad L. Thomas, Jr., Market Chief Holds Firm i Storm Over Pay, New York Times, September 14, 2003, p Morgeso, G. ad L. Thomas, Jr., Chairma Quits Stock Exchage i Furor over Pay, New York Times, p. A1. Sudaram, R., ad D. Yermack, Pay Me Later: Iside Debt ad Its Role i Maagerial Compesatio, The Joural of Fiace, August 2007, pp Tharp, P., NYSE Dis-Grasso: Agry Spitzer Offers a Clea Team Wish List, The New York Post, March 25, 2003, p. 35. Thomas, L., A Pay Package that Fat Cats Call Excessive, New York Times, August 29, 2003, p. C1. Valdmais, T., NYSE Faces Thursday Without Richard Grasso, USA Today, September 18, White, B., NYSE Ousts Grasso as Chairma, Washigto Post, September 18, 2003, p. A1