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Defined benefit vs. defined contribution retirement plans for faculty: an exploration of the cost of a portable retirement.
Abstract:
This study is designed to illustrate the differences between a defined benefit and a defined contribution plan for university faculty. It is a case study of the University System of Georgia and examines the actual cost of a faculty member selecting a "portable retirement system."

Subject:
Baby boom generation (Compensation and benefits)
Baby boom generation (Economic aspects)
Defined contribution plans (Economic aspects)
Personal finance (Baby boom generation market)
Personal finance (Economic aspects)
Workers (Compensation and benefits)
Retirement
Authors:
White, John B.
Miles, Morgan P.
White, Roger
Pub Date:
01/01/2011
Publication:
Name: Academy of Accounting and Financial Studies Journal Publisher: The DreamCatchers Group, LLC Audience: Academic Format: Magazine/Journal Subject: Business Copyright: COPYRIGHT 2011 The DreamCatchers Group, LLC ISSN: 1096-3685
Issue:
Date: Jan, 2011 Source Volume: 15 Source Issue: 1
Topic:
Event Code: 280 Personnel administration; 240 Marketing procedures Advertising Code: 80 Targets & Markets
Product:
Product Code: 8829000 Consumer Assets & Liabilities; 9915800 Personal Financial Mgmt; 9108912 Retirements (Honors) NAICS Code: 81411 Private Households; 92119 Other General Government Support
Organization:
Government Agency: Georgia. Teachers Retirement System of Georgia
Geographic:
Geographic Scope: United States Geographic Code: 1USA United States
Accession Number:
256603222
Full Text:
"In 2005 Alaska hastily reviewed its pension plan and found that the costs increased dramatically. This is part of the reason the legislature held hearings this year to move back to the pension system. And in West Virginia and Nebraska, lawmakers moved back to the pension system after a failed experiment with a system of individual defined-contribution accounts." Anonymous 2009: A 18.

INTRODUCTION

Providing for an adequate retirement is a topic of considerable interest today (Ezra 2007). As baby boomers approach retirement, more and more information can be found on how to make your "nest egg" last. Suggestions include everything from scaling back retirement lifestyles to postponing retirement to not actually retiring but continuing to work in some capacity. These compromises with retirement all stem from their retirement plan being insufficiently funded to support their original goal or retirement at a certain age. This failure is not surprising, given the vagaries of market returns and their own mortality. Recent high-profile bankruptcies have also played havoc with retirement plans.

Academics are not immune to these retirement uncertainties. What should make retirement planning easier for a faculty member at public colleges, state-sponsored defined benefit retirement systems, adds its own elements of risk. State retirement systems sometimes have vesting periods that exceed the tenure decision timeline. For example, in the University of Georgia System, vesting

occurs after ten years service, but the normal tenure decision is in year seven. This creates the chance that you may have to leave the system before you vest, which often entails losing the state's contribution to your retirement fund. Even if the tenure decision is positive and you are able to vest, the state defined benefit plan may act as an impediment to furthering your career through mobility. Most defined benefit plans reward service longevity by making the benefit formula a function of years of service and some average salary figure (such averaging the highest two consecutive years). For most employees, these "high two" salaries are the last two years worked. Should you take a new position after your twelfth year, you have locked up an annuity at retirement based on your average salary for years eleven and twelve. As faculty salaries tend to rise (from merit and/or annual cost of living raises), there is a great deal of difference in the average of the salary in year 11 and 12 as compared to years 24 and 25 or 29 and 30. If your intention is to work thirty years and retire, you have only 18 years to build up a sufficient private retirement to supplement what is already vested.

Because of these risks from the state retirement plans, private retirement plans evolved to serve the academic community. TIAA-CREF is the first of many plans that offer instant vesting and portability to the faculty member. Because of these two advantages, faculty members at state institutions often do not consider the cost of these benefits when weighed against the retirement payout of a defined program.

This study looks at one particular state, Georgia, and compares the contributions and payout of its state retirement plan, the Teachers Retirement System of Georgia (TRSGA), with the optional retirement plan (ORP) available to faculty in the state university system. The cost of one plan over the other will be expressed as the present value of the difference in the payout (assuming a reasonable reinvestment rate). The cost will also be expressed as the difference in return required in the optional plan to produce a payout equivalent to the TRSGA plan.

LITERATURE REVIEW

There have been numerous studies of retirement systems, examining the various investment options and payout decisions faced by the participants. Even TIAA-CREF, which was established in 1918, is the result of Andrew Carnegie's observation that academics changed jobs frequently and needed a retirement fund that would be portable. In the last ninety years, other private retirement plans have evolved and compete with (and complement) a variety of state retirement plans. However, the variability in contribution rates, vesting periods, assumed rates of return and payout options makes the comparison of these plans difficult.

Lahey, Michelson, Chieffe, and Bajtelsmit (2008) recently conducted a descriptive comparative analysis of the largest public university in each state. Several studies have compared a defined benefit retirement program with the retirement income that a similar investment into a defined contribution plan would produce. A study by Johnston, Hatem and Forbes (2001) makes such a comparison. Their study also demonstrates how certain defined benefit features, such as survivor benefits or cost of living adjustments, can be incorporated into a defined contribution plan through the purchase of a lifetime annuity or setting the retirement payout as a growing annuity. The study estimated that the two plans were equal after thirty years if the defined contribution plan earned a rate of return of between 7% and 8%. (The required return varies depending on the assumed salary growth rate. For instance, a 1.5% rate of salary growth yields a 7.16% required return, while a 2.5% growth rate requires 7.88%.) Craig and Toolson (2008) include a number of different scenarios in comparing defined benefit and defined contribution programs. They point out that the defined benefit payout varies between 1.5% per year of service up to 2.5% per year. This suggests that a thirty-year career would translate into a retirement benefit that could vary from 45% of the final salary to 75%. The other critical variable is the level of the participant's retirement contribution, and whether the employer makes a contribution as well. Finally, since defined benefit programs favor those who remain at an institution for long periods, the choice between the two programs often depends on long-term plans and expectations of tenure. Given the number of variables involved, they do come to a general conclusion that a defined benefit plan is better if you intend to remain at the institution, the more generous the credit per year of service, and the lower the total contribution to the participant's retirement fund. Conversely, if you expect to move frequently, the service credit is only 1.5% per year, and/or the total retirement contribution is generous, then the defined contribution plan is optimal.

This study differs from earlier studies in several significant ways. First, it explicitly examines the value that results from some of the characteristics specific to the Georgia Teachers Retirement System. For instance, Georgia allows for the purchase of service credit for military service and public education performed in another state. Indeed, it is possible to purchase up to three years of service credit not earned. This service credit is referred to as "air time," since it comes out of "thin air." Finally, Georgia also credits unused sick leave as service credit (Member's Guide).

The focus on a single state, Georgia, makes this study much less general than previous studies. However, other state retirement systems have benefits and features (crediting sick leave, purchase credit, etc.) similar to those in Georgia's TRSGA. The lack of generality in this study provides the framework to evaluate an individual's position in another defined benefit plan encompassing many different methods to accumulate retirement credit. This study also demonstrates how the specific features should be included and valued in the analysis comparing defined benefit and defined contribution programs.

Finally, this study expands the literature by focusing on a single state and its two competing systems. The conclusions of any general comparison of a defined benefit program and a defined contribution program are driven by the assumptions made regarding the two programs. This study makes no assumptions with regard to contributions or payout. The actual rates are used in the analysis. Using these actual rates allows someone to evaluate the price of portability.

COMPARISON OF THE TWO RETIREMENT SYSTEMS

Prior to 1990, the Teachers Retirement System of Georgia (TRSGA) was the only retirement system open to faculty members in the Georgia state university system. Members contributed 6% of their salary to TRSGA. (The member's contribution was decreased to 5% in 1994 without any change in benefits. The system required ten (10) years to vest. The basic benefits formula was:

Monthly payment = 2% x number of years of service x average monthly salary of highest 24 consecutive months.

Benefits can be paid after 30 years of service (regardless of age) or at age 60, with at least 10 years of service (required to vest). Thus, someone who retired with 30 years service and an average monthly income of $5000 per month (averaged from their highest 24 months) would be eligible for $3000 per month, regardless of age (Member's Guide). (Monthly benefit = 2% x 30

years x $5000 = $3000.)

In 1990, the University System of Georgia introduced an optional retirement plan which allowed faculty members to contribute 6% of their salary into a private retirement system (such as TIAA-CREF, VALIC, etc.) instead of TRSGA. Currently, both TRSGA and ORP participants contribute 5% of their salary to retirement. The state originally contributed 4% of salary into the ORP participant's retirement fund. The state's contribution has increased and has been 8.14% for the past several years. Thus, a member of the ORP has 13.14% (5% + 8.14%) of their salary going into their retirement fund.

Faculty members at the time were required to make an irrevocable decision as to which retirement system they wanted to participate in. Obviously, those close to retirement age or 30 years of service remained in TRSGA. Those faculty members that were not yet vested and expected to leave the state system opted for ORP. For those in between the two extremes and/or uncertain of their future plans, the decision was not as easy. Indeed, new hires today must make this irrevocable decision during their new faculty indoctrination. They have even less certainty regarding their long-term prospects in the Georgia system. Most public higher education systems require a similar, irrevocable decision by the participant at the beginning of their employment. Florida is the exception to the rule. A defined contribution plan was introduced in 2002 and state employees were given the option of the new system or the traditional defined benefit plan. However, those who opted out of the defined benefit plan were given the right to convert back to the defined benefit at any point prior to retirement (Milevsky and Promislow; 2004).

A direct comparison between these two systems is more difficult because it is not simply a case of comparing cash flows. As stated before, vesting periods and portability differ greatly. TRSGA also allows the "purchase of creditable service" for years served in another state university system. Prior military service years may also be purchased. Another distinction, with significant financial impact, is that earned sick leave was allowed to count as service time in TRSGA due to

an amendment in state regulations in 1994. Finally, TRSGA participants close to retirement may purchase what is known as "air time," which is service credit for periods not actually worked. The participant effectively funds the year of retirement income that would be received a year earlier than if you actually worked the year. The tax code permits the transfer of pre-tax funds from a 403b account to purchase an "air year. "This is especially beneficial for someone who wants to accelerate their retirement but has no out-of-state service years to be purchased.

SCENARIO COMPARISONS

In each of the following scenarios, several assumptions remain constant. The employee's contribution is 5%, and the state contribution to ORP remains at 8.14%. The initial salary is $40,000 per year and raises are 2.5% annually. In addition, TRSGA continues to give a 3% cost of living adjustment to TRSGA retirees.

Internal Rate of Return (IRR) for TRSGA Participant

For the TRSGA member, their initial salary of $40,000 grows to $79,860 in year 29 and $81,856 in year 30. The average salary for their high two year period is $80,858. Their initial annual retirement income is 60% of $80,858, or $48,515, and this amount is expected to grow at 3% per year. They have contributed 5% of their salary each year. Retirement contributions and retirement income amounts are shown in

Table 1. Retirement income is guaranteed for as long as the retiree lives. If you die in the first two years after retirement, you have not withdrawn all of your contribution. The undisbursed balance plus interest is passed to your estate. However, if you survive for 5 years, the internal rate of return on your funds (5% of your salary) invested in retirement is 6.07%. At 10 years, the IRR is 8.96%. Survive 20 years into retirement, and your IRR is 10.75%, and a 30-year retirement yields an 11.29% return on the TRSGA member's investment. (Internal rate of return analysis is featured in many finance textbooks. For instance, see Brealey, Myers and Marcus, 2009, Brigham and Daves, 2007, or Ross, Westerfield and Jaffe, 2008.)

An ORP participant will make an initial deposit of $5256 ($40,000 x (5% + 8.14%)) into their retirement account. This deposit will increase by 2.5% annually with the pay increases. The deposit stream for thirty years is shown in Table 1. For the ORP participant to withdraw an equal annual amount to the TRSGA member in retirement, the required return on the ORP investment depends on the years in retirement. Since the ORP participant's account receives 13.14% of the faculty member's salary, the required returns for an equivalent payout is less than the IRR of TRSGA for equivalent retirement periods. Table 1 shows that the ORP account needs to earn only 0.54% to fund a 5-year retirement. The 10-year retirement must earn 4.41%, while 6.92% is required to fund a 20-year retirement. The ORP account must earn 7.71% to match TRSGA's 30-year retirement payout. Thus, the required rates of return to make ORP produce an equivalent retirement payout to TRSGA are quite reasonable to expect. It should be noted that while the ORP required return of 7.71% is only 2.71 percentage points higher than the assumed 5% risk-free rate, it does represent a return 54% above the risk-free rate of 5%.

The significant internal rates of return reflect only the defined benefit participant's contribution to the retirement system. The state is also making a contribution, but that amount does not belong to the participant should they leave they system. If you assume that the state's contribution to an employee's retirement is 8.14%, regardless of the retirement system, then the defined benefit participant earns what the ORP participant earns. However, several key differences between the systems remain. First, the ORP participant has a portable retirement, but it is possible to outlive the retirement fund if returns are too low and/or the annual payout is too high. The TRSGA participant has a retirement portfolio that is free of investment risk and will continue to pay as long as the retiree lives, but the retirement lacks portability.

Maintaining Equivalent Risk

Another, and perhaps better, way to compare the two retirement systems is to keep the risk and return equivalent. Since the TRSGA is backed by the State of Georgia, then a nearly risk-free rate of interest would be the appropriate discount rate to present value the future TRSGA retirement benefits. For the TRSGA member, the initial salary of $40,000 grows to $79,860 in year 29 and $81,856 in year 30. The average salary for their high two year period is $80,858. Their first retirement check is 60% of $80,858, or $48,515. Assuming a 30-year retirement and a 5% discount rate, the present value of this growing annuity ($48,515 the first year and growing at 3% annually) is $1,063,393 at the time of retirement. (See Ross, Westerfield and Jaffee (2008) for a discussion of present value and future value of growing annuities.)

If the ORP member invests in similar, risk-free portfolio earning 5%, they will accumulate $497,922 in 30 years. This is less than half of the amount needed to fund a 30-year retirement payout equivalent to TRSGA. To accumulate $1,063,393 in 30 years, the ORP participant's initial deposit must be $11,225.28, over twice as much as the $5256 that is currently deposited into their account. Thus, to achieve the same future value at an equivalent risk-free return requires an ORP participant's contribution to be an additional $5969.28 ($11,225.28-$5256), or an additional 14.9% of the initial $40,000 salary. The ORP participant's total contribution would be $7969.28 ($2000+$5256), which is 19.9% of their salary.

If the TRSGA member works 30 years and draw retirement for 20 years, the present value of the TRSGA retirement annuity is only $774,516, since the retirement checks stop after 20 years. (You died!) For the ORP retirement fund in a risk-free (5%) portfolio to reach that level in 30 years requires an initial investment of $8704.87. Subtracting the normal contribution of $5256, an additional $3448.87, or an additional 8.6% of your salary, is required to produce a retirement equivalent to TRSGA. The total contribution into the retirement fund is 21.74% of the salary, with 13.6% (5% + 8. 6%) coming from the ORP participant. As expected, a shorter retirement requires a smaller contribution. Table 2 displays the ORP contribution required to match the TRSGA payout if risk-free investments are used.

Double Dipping

One aspect of the TRSGA retirement system is that the member is eligible to draw a retirement benefit of 60% of your salary after 30 years of creditable service. For some, the prospect of retiring before the Social Security minimum age of 62, or even before you can use an IRA without penalty (59%), or even younger, is especially appealing. But many faculty members enjoy the academic life and would prefer to continue teaching even after they are eligible to receive retirement benefits. If you are eligible in TRSGA to receive 60% for NOT working, then continuing to work beyond 30 years implies you are actually earning only the 40% differential between your salary and the retirement benefit you could receive. ORP imposes no such penalty for continuing to work, since your ORP retirement account continues to grow as you continue to work and make contributions.

However, once you are eligible to receive benefits, if you retire and accept a comparable position at any position outside of the University System of Georgia, then you would see your income increase by 60% (the amount of the retirement payment). While the salary from the new position is not retirement income, per se, it does represent additional cash flow made possible by the retirement from TRSGA. Assume you accrue thirty years of service in TRSGA and opt to take your retirement but continue to work in a new position for an additional ten years. Further assume that your new position maintains your former salary and the 2.5% salary growth. Finally, assume you continue to save 5% of your salary, with a match from your new employer of 8.14% (to match the Georgia ORP). You save ALL of your retirement income received during those final ten years of employment to supplement your ultimate retirement, which will begin in ten years. (This maintains equal incomes for the ORP participant and the TRSGA member at the new job.) Finally, assume these savings will be invested at the risk-free rate of 5%.

Saving 5% of your growing income for the ten years of the "second career" (the first deposit is $11,024.81, 13.14% of $83,902.70), and the deposits earning 5%, will yield an additional $153,822.60 in a retirement fund at the end of the ten year period. (This is the future value of an annuity growing at 2.5% earning 5% for ten years when the initial payment is $11,024.81.) The deferred (unspent and saved) retirement annuity, with a first payment of $47,332, will yield $674,430 at the end of the ten years. (Again, this is the future value of an annuity growing at 3% earning 5% for ten years when the initial payment is $47,332.) The sum of these two amounts, $828,252, would produce a 20-year growing annuity (growing at 3%) with an initial payment of $51,879.94 to supplement the TRSGA retirement payment. Thus, the retirement payment in year 41 (the first year of complete retirement) rises from $63,610 from TRSGA to $115,490 from both sources. Your earned salary in year 40 was $104,783, so your initial retirement check is 110% of your final earned salary. (This additional retirement payment will cease after 20 years, as the $828,252 fund will be exhausted.) Although the additional payment will end at some point in the future, the TRSGA retirement benefit will pay as long as the member lives.

The ORP participant, working the additional 10 years, continues to have their retirement account grow with contributions of 13.14% of their salary. Assuming their retirement fund earns 7.5% during their 40-year, they will accumulate $1,614,556 in the account. If they continue to earn 7.5% and have an initial payout $115,490 that grows at 3% per year, then the retirement fund would pay out a retirement annuity for 23 years (see Table 4). If the ORP account is in a risk-free investment earning 5%, then the fund accumulates only $915,579 and will pay out an amount equivalent to TRSGA for only eight years. In order for the ORP participant to have a retirement similar to a TRSGA participant that "double dips," the ORP account needs to average a 7.25% annual return over the 60 year period (40 work years and 20 years retired). After 20 years, the TRSGA participant's supplemental 403.b account is exhausted, but the basic TRSGA benefit continues. The ORP participant, on the other hand, has exhausted their retirement fund and has outlived their savings.

ADDITIONAL CONDSIDERATIONS

For faculty who select the TRSGA option and remain healthy and are not forced to consume sick leave are allowed to count this year towards years of service. This allows a faculty member in TRSGA to enjoy full retirement with 29 years of service and not be required to work the full 30 years. Retiring after 29 years of active service and one year of sick leave credit means the member's "high 24 month period" will be years 28 and 29, or an annual income of $77,912 and $78,859.80, respectively. The average salary is $78,885.90, which implies an annual retirement income of $47,331.54 (60% of $78,885.90). Retiring a year early gives you an additional year of retirement. The present value of the growing retirement annuity for 31 years discounted at the 5% risk-free rate is $1,062,791.

Recall the present value of the growing retirement annuity for 30 years, after having worked for 30 years was $1,063,393 at the time of retirement. It appears that applying sick leave towards retirement reduces the value of the retirement annuity by $602 ($1,063,393--$1,062,791). However, working 30 years makes the retirement begin a year later. The present value of the 30-year retirement in year 29 is $1,012,755. Thus, the value of a year of sick leave applied towards retirement in this scenario is $50,036. This sick leave value increases as you add the value of an additional year of leisure in retirement or an additional year of salary in another job as you "double dip." In the example above, a year's sick leave credit means you could work 11 years in a new job while drawing retirement from your previous job and still retire completely at the same age.

HEDGING YOUR "BET"

The biggest question new faculty members have regarding the selection of retirement plans is the uncertainty concerning future employment in the system. The retirement system selection must be made now, but a tenure decision is years away. Is there a way to hedge some of this risk away? One way to reduce the retirement risk would be to opt into the TRSGA system, but save an additional amount (in a 403-b, for instance) if you are denied tenure in the future. This is not an insignificant amount, as was shown in Scenario 1. You are saving an additional 16% of your salary. However, this additional saving is required only until your tenure decision is known (or becomes apparent). If the decision is positive, you will have a tidy sum in your 403-b awaiting you in retirement, even if you stop contributing once tenured. If the tenure decision is negative, you withdraw your TRSGA retirement contributions and move them into your 403-b.

This situation ignores those faculty members that may leave the system after being tenured and vested. However, the assumption has to be that if you voluntarily leave one job for another, then the new situation must be better than the current one. People generally do not move unless the new salary and benefits package represents an improvement. How a move effects your retirement plan is part of this package, so if tenured vested faculty are observed to move, then the assumption must be that their financial situation has improved.

RELEVANCE & LIMITATIONS

From one perspective, this study is may seem limited in scope to the case of public universities in one state, Georgia and therefore the findings may not be directly applicable in other contexts. However, this study contributes to the literature by illustrating how different retirement systems might be financially compared. Obviously, any Georgia public university faculty member that participates in TRSGA would find this study helpful if they were to contemplate taking another job outside of the system, as well as anyone evaluating an offer from a Georgia public university. This study gives them a benchmark as to the value of their derived benefit retirement.

There has also been some discussion in the 2009 Georgia legislative session about permitting faculty members in the optional retirement system to move into TRSGA. (The bills, House Bill 740 and Senate Bill 257, both died in committee this year and cannot be considered again in the 20092010 biennium session.) This study provides a compelling argument for those tenured faculty members who would be immediately vested (ten or more years of service) in TRSGA if allowed to convert the state system.

From a broader perspective, the study provides a framework to compare any defined benefit plan with the competing defined contribution plan. Critical variables to consider include the payout formula and years to vest in the defined benefit plan and the employer's contribution to the defined contribution plan. Private university and non-Georgia system faculty could make good use of this study if they were considering a new position that includes a defined benefit plan. This study shows the value of the retirement portion of their compensation package, which should be considered when evaluating a job offer.

Finally, benefit managers would benefit from understanding the concepts presented in this analysis. Too often, new faculty members select their retirement program with only the most cursory explanation of each. Implicit in a recommendation of one plan over another is an assumption about market returns on investment, probability of remaining at the institution long enough to vest and/or earn retirement benefits, and even assumptions about life expectancy, to name a few. For the faculty member to make an informed decision about retirement, they must understand the implications of any assumptions being made.

CONCLUSION

Careers and retirement options are both economically significant and risky decisions. In this case of one state, Georgia, the defined benefit TRSGA plan is economically superior to the optional retirement plan for the faculty member that remains in the University of Georgia system until retirement. The potential to apply sick leave towards retirement service only enhances the superiority of the TRSGA plan. Finally, while the financial benefit of maintaining the university system health insurance was not explicitly evaluated, it is an additional (and considerable) benefit of TRSGA.

However, for some faculty the portable nature of the ORP plan has an option value that may is worthwhile. What this study develops is a framework to estimate a value of the portability option. Different people will continue to come to different conclusions when evaluating which retirement plan to select, even if their cash flow estimates are the same. The different conclusions result from different expectations on their future employment, as well as their tolerance for risk. Both plans will remain popular with their proponents, suggesting they are satisfied with their choice. The key is that the decision be an informed one, since it is irrevocable in many situations.

REFERENCES

Anonymous (2009), Dumping defined-benefit plans has a cost, too. The Wall Street Journal, June 1, A18.

Brealey, R. A., S. C. Myers, & A. J. Marcus (2009). Fundamentals of corporate finance (Sixth Edition). Boston: McGraw Hill Irwin.

Brigham, E. F. & P. R. Daves (2007). Intermediate financial management (Ninth Edition). Mason, OH: Thomson/SouthWestern.

Craig, C. K. & R. B. Toolson (2008). Retirement plan options for public university faculty--The high cost of a wrong choice. Journal of Deferred Compensation, 13(3), 36-65.

Ezra, D. (2007). Defined-benefit and defined-contribution plans of the future. Financial Analysts Journal, 63(1), 26- 29.

Johnston, K., S. Forbes, & J. Hatem (2001). Choosing between defined benefit and defined contribution plans. Journal of Financial Planning, 14(8, August), 86-92.

Lahey, K., S. Michelson, N. Chieffe, & V. Bajtelsmit (2008). Retirement plans for college faculty at public institutions. Financial Services Review, 17, 323-341.

Member's guide (2009). Teachers Retirement System of Georgia, Retrieved August 20, 2009, from http://www.trsga.com/publications.aspx.

Milevsky, M. A. & S. D. Promislow (2004). Florida's pension election: From DB to DC and back. Journal of Risk and Insurance, 71(3, September), 381-404.

Ross, S. A., R. W. Westerfield, & J. Jaffe (2008), Corporate Finance (Eighth Edition). Boston: McGraw Hill Irwin.

John B. White, United States Coast Guard Academy

Morgan P. Miles, Georgia Southern University

Roger White, University of Pittsburgh
Table 1: Internal Rate of Return on TRSGA and Defined Contribution
Retirements

  Year         Defined           Defined            Years
 Worked        Benefit        Contribution         Retired
               Deposit           Deposit

1              $2,000            $5,256              1st
2              $2,050             $5387              2nd
3              $2,101            $5,522              3rd
4              $2,154            $5,660              4th
5              $2,208            $5,802              5th
6              $2,263            $5,947              6th
7              $2,319            $6,095              7th
8              $2,377            $6,248              8th
9              $2,437            $6,404              9th
10             $2,498            $6,564             10th
11             $2,560            $6,728             11th
12             $2,624            $6,896             12th
13             $2,690            $7,069             13th
14             $2,757            $7,245             14th
15             $2,826            $7,427             15th
16             $2,897            $7,612             16th
17             $2,969            $7,803             17th
18             $3,043            $7,998             18th
19             $3,119            $8,198             19th
20             $3,197            $8,403             20th
21             $3,277            $8,613             21st
22             $3,359            $8,828             22nd
23             $3,443            $9,049             23rd
24             $3,529            $9,275             24th
25             $3,617            $9,507             25th
26             $3,708            $9,744             26th
27             $3,801            $9,988             27th
28             $3,896            $10,238            28th
29             $3,993            $10,494            29th
30             $4,093            $10,756            30th

  Year       Retirement          Defined           Defined
 Worked        Payout          Benefit IRR      Contribution
                                                     IRR

1           $ (47,331.54)         < 0%              < 0%
2           $ (48,751.49)         0.63%             < 0%
3           $ (50,214.03)         3.27%             < 0%
4           $ (51,720.45)         4.91%             < 0%
5           $ (53,272.07)         6.07%             0.54%
6           $ (54,870.23)         6.93%             1.69%
7           $ (56,516.33)         7.61%             2.59%
8           $ (58,211.82)         8.15%             3.31%
9           $ (59,958.18)         8.59%             3.91%
10          $ (61,756.92)         8.96%             4.41%
11          $ (63,609.63)         9.28%             4.83%
12          $ (65,517.92)         9.54%             5.20%
13          $ (67,483.46)         9.77%             5.51%
14          $ (69,507.96)         9.97%             5.79%
15          $ (71,593.20)        10.15%             6.04%
16          $ (73,741.00)        10.30%             6.25%
17          $ (75,953.23)        10.43%             6.45%
18          $ (78,231.82)        10.55%             6.62%
19          $ (80,578.78)        10.66%             6.78%
20          $ (82,996.14)        10.75%             6.92%
21          $ (85,486.03)        10.83%             7.05%
22          $ (88,050.61)        10.91%             7.16%
23          $ (90,692.13)        10.97%             7.27%
24          $ (93,412.89)        11.03%             7.36%
25          $ (96,215.28)        11.09%             7.45%
26          $ (99,101.73)        11.13%             7.53%
27         $ (102,074.79)        11.18%             7.61%
28         $ (105,137.03)        11.22%             7.67%
29         $ (108,291.14)        11.25%             7.74%
30         $ (111,539.87)        11.29%             7.79%

Table 2: Required Deposits to Defined Contribution Plan if Investing
in Risk-Free Assets

Retired     Present        Initial       Additional     Additional
 for N      Value of      Amt Saved       $ Amount       $ as a %
 years     retirement      Required                     of income

5           $222,388        $2,499        $(2,757)        -6.9%
10          $424,380        $4,770         $(486)         -1.2%
15          $607,871        $6,832         $1,576          3.9%
20          $774,516        $8,705         $3,449          8.6%
25          $925,913       $10,406         $5,150         12.9%
30         $1,063,393      $11,225         $5,969         14.9%

Table 3: Double Dipping

Work 30 years, retire from TRSGA and work another 10 years.
Contribute 5% + 8.14% to a 403.b these 10 years, earning a
risk-free rate of 5%.

                             Retirement       TRSGA benefit
  YR      Earned income        savings           (saved)

31         $83,902.70        $11,024.81        $47,332.00
32         $86,000.27        $11,300.44        $48,751.96
33         $88,150.27        $11,582.95        $50,214.52
34         $90,354.03        $11,872.52        $51,720.95
35         $92,612.88        $12,169.33        $53,272.58
36         $94,928.20        $12,473.57        $54,870.76
37         $97,301.41        $12,785.41        $56,516.88
38         $99,733.94        $13,105.04        $58,212.39
39        $102,227.29        $13,432.67        $59,958.76
40        $104,782.98        $13,768.48        $61,757.52

             Earned                               TRSGA
           Income = $0                           benefit
            (Retired)

41              0                              $63,610.25
42              0                              $65,518.56
43              0                              $67,484.11
44              0                              $69,508.64
45              0                              $71,593.90
46              0                              $73,741.71
47              0                              $75,953.97
48              0                              $78,232.58
49              0                              $80,579.56
50              0                              $82,996.95
51              0                              $85,486.86
52              0                              $88,051.46
53              0                              $90,693.01
54              0                              $93,413.80
55              0                              $96,216.21
56              0                              $99,102.70
57              0                             $102,075.78
58              0                             $105,138.05
59              0                             $108,292.19
60              0                             $111,540.96

           Total Saved
  YR       (earns 5%)

31
32         $121,327.05
33         $189,190.87
34         $262,243.89
35         $340,798.00
36         $425,182.22
37         $515,743.62
38         $612,848.23
39         $716,882.07
40         $828,252.18

             403. b             Total
             payout          retirement
                               income

41         $51,879.94        $115,490.19
42         $53,436.34        $118,954.90
43         $55,039.43        $122,523.54
44         $56,690.61        $126,199.25
45         $58,391.33        $129,985.23
46         $60,143.07        $133,884.78
47         $61,947.36        $137,901.33
48         $63,805.78        $142,038.37
49         $65,719.96        $146,299.52
50         $67,691.55        $150,688.50
51         $69,722.30        $155,209.16
52         $71,813.97        $159,865.43
53         $73,968.39        $164,661.40
54         $76,187.44        $169,601.24
55         $78,473.06        $174,689.27
56         $80,827.26        $179,929.95
57         $83,252.07        $185,327.85
58         $85,749.64        $190,887.69
59         $88,322.13        $196,614.32
60         $90,971.79        $202,512.75

Table 4: Years to exhaust ORP fund matching TRSGA payout at various
rates of return

$1,614,556 Balance at retirement

YR         Nest egg           Annual          End-of-year
           i = 7.5%           Payout            Balance

41        $1,735,648         $115,490         $1,620,158
42        $1,741,669         $118,955         $1,622,714
43        $1,744,418         $122,524         $1,621,894
44        $1,743,537         $126,199         $1,617,337
45        $1,738,638         $129,985         $1,608,652
46        $1,729,301         $133,885         $1,595,417
47        $1,715,073         $137,901         $1,577,171
48        $1,695,459         $142,038         $1,553,421
49        $1,669,927         $146,300         $1,523,628
50        $1,637,900         $150,689         $1,487,212
51        $1,598,752         $155,209         $1,443,543
52        $1,551,809         $159,865         $1,391,944
53        $1,496,339         $164,661         $1,331,678
54        $1,431,554         $169,601         $1,261,953
55        $1,356,599         $174,689         $1,181,910
56        $1,270,553         $179,930         $1,090,623
57        $1,172,420         $185,328           $987,092
58        $1,061,124         $190,888           $870,236
59          $935,504         $196,614           $738,889
60          $794,306         $202,513           $591,793
61          $636,178         $208,588           $427,590
62          $459,659         $214,846           $244,813
63          $263,174         $221,291            $41,883
64           $45,024         $227,930         $(182,905)

$915,579 Balance at retirement

Y          Nest egg           Annual          End-of-year
R           i = 5%            Payout            Balance

41          $961,358         $115,490           $845,868
42          $888,161         $118,955           $769,206
43          $807,667         $122,524           $685,143
44          $719,400         $126,199           $593,201
45          $622,861         $129,985           $492,876
46          $517,520         $133,885           $383,635
47          $402,816         $137,901           $264,915
48          $278,161         $142,038           $136,123
49          $142,929         $146,300           $(3,371)

$1,521,979 Balance at retirement

Y          Nest egg           Annual          End-of-year
R          i = 7.25%          Payout            Balance

41        $1,632,322         $115,419         $1,516,903
42        $1,626,879         $118,882         $1,507,997
43        $1,617,327         $122,448         $1,494,879
44        $1,603,257         $126,122         $1,477,136
45        $1,584,228         $129,905         $1,454,323
46        $1,559,761         $133,802         $1,425,959
47        $1,529,341         $137,817         $1,391,524
48        $1,492,409         $141,951         $1,350,458
49        $1,448,367         $146,210         $1,302,157
50        $1,396,563         $150,596         $1,245,968
51        $1,336,300         $155,114         $1,181,187
52        $1,266,823         $159,767         $1,107,055
53        $1,187,317         $164,560         $1,022,757
54        $1,096,907         $169,497           $927,410
55          $994,647         $174,582           $820,065
56          $879,520         $179,819           $699,700
57          $750,429         $185,214           $565,215
58          $606,193         $190,770           $415,422
59          $445,541         $196,493           $249,047
60          $267,103         $202,388            $64,715
61           $69,439         $208,460         $(139,021)
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