Review of Boston College DROP Study for Philadelphia City Council - February 22, 2011 Thomas Lowman, FSA, EA Bolton Partners, Inc. 575 S. Charles ...

Review of Boston College DROP Study for
       Philadelphia City Council

                 February 22, 2011

             Thomas Lowman, FSA, EA
                Bolton Partners, Inc.
           575 S. Charles Street, Suite 500
                Baltimore, MD 21201

            John Rust, Ph.D. Economics
             Department of Economics
              University of Maryland
Review of Boston College DROP Study
Philadelphia City Council

                                                   Table of Contents

Executive Summary ................................................................................................................... 1 - 4

Section 1: Definition of Cost .................................................................................................... 5 - 7

Section 2: Adjustments to the Model ........................................................................................ 8 - 9

Section 3: Impact on Funding ............................................................................................... 10 - 12

Section 4: Choice of Discount Rate ...................................................................................... 13 - 15

Section 5: “Peak” Retirement Age and the DROP ratio ....................................................... 16 - 20

Section 6: The BC Study Retirement Model ........................................................................ 21 - 29

Section 7: Data Analysis ....................................................................................................... 30 - 31

Appendix 1: Adjusting BC’s Cost for Employees’ Extra Service ................................................32

Appendix 2: General DROP Concepts ................................................................................. 33 - 35

Appendix 3: DROP Ratio Illustrations ................................................................................. 36 - 43

                                                                                                                Bolton Partners, Inc.
Review of Boston College DROP Study
Philadelphia City Council

                                   Executive Summary

Bolton Partners has been asked by the City Council to review the study done by Boston College
(BC) of the Deferred Retirement Option Program (DROP) provision of the City of Philadelphia
Municipal Retirement System (the Plan). We have been assisted in this project by economist
John Rust.
The BC study determined that the DROP provision has led to an increase in employees’ period
of employment beyond their normal retirement ages (i.e. the existence of the DROP causes
employees to delay their retirement) and has increased the employer cost. We agree that
employees are working longer and that the DROP provision has increased the cost of the Plan.
We believe that BC’s estimate of 15 months as the average delay in the retirement age by
Municipal (non-uniformed) employees due to the DROP is reasonable. Most of the DROP’s
increase in cost is for this group.
We found two issues that we discussed with BC that, if corrected for, would lower BC’s cost
estimate. The first was that the plan provides a free post retirement survivor benefit. The
“Survivor Benefit” adjustment will lower the cost of DROP and is discussed in section 2.
There is also a cost reduction not reflected in BC’s analysis because of the pension benefit that
would have been earned by new employees replacing the current employees, if these current
employees had not worked longer. If corrected for this would also lower BC’s cost estimate.
The “Replacement Cost” adjustment is discussed in section 1. It should be understood that the
pension replacement cost adjustment is just part of the total economic replacement cost (e.g. it
does not consider payroll cost).
BC previously estimated the cumulative additional cost due to the DROP as $258 million over
the 11 years effective period of the DROP provision. BC has agreed that their model should be
revised to reflect the changes for the Survivor Benefit and the Replacement Cost, which we
expect will reduce the estimated cost of the DROP from $258 million to approximately $150
million (which BC has agreed is a reasonable estimate).
We believe that the BC estimate that uniformed employees work an average of 2 to 11 months
longer due to DROP significantly underestimates the delay in retirement by these employees.
There is a significant increase in the retirement ages for uniformed employees (which may be
due more to the change in plan retirement age and employees being hired at later ages than the
addition of the DROP). However, we think the change due to DROP is more likely to be in the
range of 12 to 36 months. This difference may be partially due to problems in the data. Possible
corrections in this area get us to a final cost in the range of $100 million. See section 7 for more
Our other key findings are
   1. We believe that there is more than one definition of “cost” and to understand the BC
      study you must understand these definitions. One key point is to understand that BC did
      not measure the cost in terms of the impact on the past and current City contributions to
      the Plan. There are two separate aspects to this observation:

                                                 1                              Bolton Partners, Inc.
Review of Boston College DROP Study
Philadelphia City Council

                                 Executive Summary

          a. For the last several years there has been a significant debate within the actuarial
             community over whether to view pension cost in economic terms or the more
             common “expected” cost terms. The expected cost concept is the current basis for
             the funding determinations for the Plan. The economic concepts were the basis
             for the BC study of the cost of the DROP. The BC method is valid but requires
             understanding that the methods used are not related to those currently used for
             funding the Plan. Application of this economic value approach would make
             Philadelphia one of the first jurisdictions in the US to apply such principles to a
             decision making process for public pension plans. However, applying this
             economic value approach to the analysis of the cost of the DROP reduces the
             “cost” of the DROP over the cost that would be determined using the expected
             cost approach, even though the economic value approach results in substantially
             higher measurements of liabilities for pensions in general. This occurs because a
             DROP basically allows a participant to trade off some of their pension annuity for
             a lump sum, and the economic value approach substantially increases the value of
             this pension. The implications of using the economic value are discussed more in
             Section 4. It should also be understood that the BC DROP study and prior
             actuarial DROP studies focused solely on pension cost (even if not all about
             funding) and not any other payroll or personnel cost. In this sense the BC cost is
             not intended to represent the full economic impact.
          b. Second is the practical effect on the current City contribution of removing the
             DROP provision prospectively. We believe that, if done properly, the immediate
             impact would be a decrease in the City’s contributions to the Plan. However, see
             section 3 for more information.
   2. Looking at the increase in total “cost” of even $100 million, may make the cost increase
      seem larger than when viewed in terms of proportions. $100 million or $258 million is
      indeed a large “cost” increase. However, pensions (and Social Security) are expensive.
      We believe that it is also important to put this on an individual level. Table 8A from the
      BC study did this, to some extent (e.g. a mean value for a police officer was $24,300
      using the BC base case assumptions). We think it is also important to know as a
      percentage, how much this increases the value of the benefit. For many employees
      DROP increases the value of the benefit by about 3% to 5%. The increase is greater for
      Municipal than uniformed employees and in some cases there is no increase.
      In electing DROP an employee is effectively trading the pension benefit that they would
      have earned during the DROP period for a lump sum. There are two key reasons for the
      resulting higher relative cost for Municipal employees. First, the value of the pension
      benefit given up (but not the DROP lump sum) declines with age and Municipal plan
      members retire at later ages. Second, the benefit accrual rate declines after 20 years of

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Philadelphia City Council

                                          Executive Summary

         service1 (from 2.5% to 2%) for Municipal members which means their pension benefit is
         increasing much more slowly, so they are giving up less in increased pension benefits for
         the DROP lump sum (this is also an issue in the 1987 Plan for Police and Fire). The
         variation in cost per person is also much higher for the Municipal group as is reflected in
         the BC median (that is ½ above and ½ below) cost of $16,000 as compared to an average
         (or mean) cost of $29,700. Below are some illustrations from Appendix 3. In this
         illustration there is no cost for a police officer because they elected DROP prior to what
         BC called the “peak” retirement age2.

    Employee                   Value of benefit at          Value with            Increase          Percentage
    Group                      Normal Retirement,           DROP                  (decrease)        increase in
                               Without DROP                                       in value          value
    Group D (Police)                          $485,426              $475,208           (10,218)             (2.1%)

    Group J (Municipal)                       $494,291              $519,134             24,843               5.0%

     3. To the extent that employees find “utility” in receiving part of their benefits as a lump
        sum even if there were no cost to the City, finding a way to eliminate the additional cost
        without eliminating the DROP could be considered. Giving “choice” to “buy or sell”
        annuities always comes with some anti-selection risk (cost). We also understand that
        these groups of employees are not covered by Social Security. Because the plan does not
        provide automatic post-retirement cost-of-living-adjustments (COLA), members should
        be encouraged to consider rolling over lump sums received as part of the DROP to be
        used later in their retirement.
Since we assume that not all the readers of this report are intimately aware of the actuarial and
economic issues raised by DROP provisions, we also address the following issues in more detail
elsewhere in our report:
         1. The importance of the discount rate selection in determining the cost of DROP. (see
            question 1 in section 4)
         2. Approaches for choosing among possible discount rates. (see question 2 in section 4)
         3. The difference between BC’s measurement of DROP cost and the impact on past and
            current City contributions to the Plan, or why is BC's estimated $258 million DROP
            cost (or even a recalculated DROP cost that takes into account the corrections we
            propose) not what the City has contributed to pay for the DROP? (see section 3)

  The reduction is the accrual rate in the 1987 Plan is after 10 year s of service and not 20 years as in the 1967 Plan.
  It should be noted that this savings for a police officer would become a cost if a higher discount rate were used
(e.g. the 2.1% reduction becomes a 6.2% increase if the discount rate were changed from 5% to 8%).
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Review of Boston College DROP Study
Philadelphia City Council

                                  Executive Summary

Bolton Partners is an actuarial consulting firm, specializing in employee benefit programs. This
report is not intended to provide any advice regarding the City’s legal authority in changing the
DROP provision.
If you have any questions, please call me at 443-573-3909.

Submitted by Bolton Partners, Inc.

Thomas Lowman, FSA, EA, MAAA

                                               4                              Bolton Partners, Inc.
Review of Boston College DROP Study
Philadelphia City Council

                                 Section 1: Definition of Cost

As noted in the Executive Summary, there are different definitions of cost. These can be thought
of as relating to:
        1. Funding/Employer Contribution
        2. Extra value to employee
        3. Extra liability of employer
        4. Replacement Cost (part of total economic cost)
Funding/Employer Contribution
Both Bolton Partners and BC agree that this was not the focus of the BC study. As a result, the
BC result may not be what some decision makers are looking for. The main points regarding
funding are:
        1. Neither the BC cost of $258 million nor the Cheiron cost range of -$62 million to
           +$203 million represent past City contribution increases nor do they tie into the
           actuarial funding method calculation.
        2. The result of removing the DROP prospectively should decrease the current cost of
           (contribution to) the plan if the retirement rate assumption is changed. Currently the
           retirement rates are tied to when someone enters DROP. If there were no DROP the
           retirement rates would be tied to when someone stops working. Since the time in
           DROP is longer than the amount of time the DROP is causing members to work
           longer, the net effect is to lower the retirement rates and the City has more time to
           fund their benefits.
Some of the issues discussed below (e.g. replacement cost) and when “normal cost” ends for an
individual (see section 3) are also factors to consider when looking at a funding model.
That leaves us with two other definitions of cost to focus on: the extra value to the employee and
the extra liability to the employer. We are not covering all replacement cost issues.
Extra Value to Employee
With some modifications, we believe that the BC methodology produces something which does
approximate the extra value to the employee3. The choice of the risk free discount rate to
measure the extra value to the employee is often cited4 as an approximate rate to measure the
market consistent value of a public pension benefit. However, there are also arguments that the

  In a true economic model the value to the employee would tie in the concept of “willingness to pay”. If this were
factored in the “discount” rate would vary by person and depend on other factors.
  See presentations by Jeremy Gold and David Wilcox at the 2009 Society of Actuaries’ Public Pension Finance
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Philadelphia City Council

                                 Section 1: Definition of Cost

discount rate should be slightly higher to reflect liquidity restrictions (i.e. a person cannot sell or
assign his pension benefit). Also, in the current environment, reflecting the funded status of the
City’s pension fund, there might also be some default risk which would suggest using a higher
interest rate reflecting this risk. Finally, commercial annuity purchase rates are often higher than
the risk free rate. We would encourage BC to consider these factors. However, we are willing to
accept the risk free rate as a possible choice to measure the value of the extra benefit to
employees. We would also note that while the focus of the BC study was on the cost using risk
free interest (discount) rates, they did show results using other higher rates.
The choice of the discount rate is probably the most important assumption in the analysis of the
DROP cost. For that reason Section 4 is devoted to explaining the issues with the choice of
discount rate. However, the interest rate used is part of the “Definition of Cost”.
Additional Cost to Employer of DROP
The title of the BC paper is: “The Impact of a DROP Program on the Age of Retirement and the
Employer Pension Cost”. BC is trying to determine the cost to the employer and not the value to
the employee. The “law of one price” suggests that the two are generally equal. If the employee
is given a benefit of $1, it must cost the employer $15. However, to the extent that the DROP
results in employees working longer, there is an exchange transaction (pay in exchange for work)
which must also be considered. Analysis of the exchange transaction is both simple and
complicated. First the simple example in the following illustration:
        Assume an employer defined a Normal Retirement Age for its employees of age 60.
        Assume that until age 60 the employer makes a contribution of 10% of pay to a defined
        contribution plan and 0% after age 60. As a result, most employees choose not to work
        after age 60. Now assume the 10% pension contribution is continued until age 61 and
        employees now work an additional year. Under the original methodology expressed in
        the quote from page 8 of the BC report, the change in the plan "cost" to the college is
        10%6 of pay for employees who work past age 60.
This can be viewed as an increase in cost. However, if this is viewed as an additional cost to the
employer, we need to point out the following:

                This does not consider the pension as part of an exchange transaction where the
                 employee works and earns an additional pension each year.

 Either in direct funding or in the cost of assumed risk.
  The actual (original) BC methodology was to determine the cost (for this simple illustration) based on the
difference between the account balance with the extra 10% contribution less the account balance without the extra
10%. For illustration purposes, have focused on simply on the 10% contribution.
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Review of Boston College DROP Study
Philadelphia City Council

                            Section 1: Definition of Cost

              This ignores that fact that without the plan change the employer would have
               replaced the staff and hired an employee for whom the employer would have paid
               the additional 10% in the illustration (which we will refer to as Replacement

              The Replacement Cost concept for a pension plan is more complex than the
               simple example above. Replacement Cost is also much higher using the risk free
               discount rate in the BC “economic model” rather than the 8.25% (or recently
               adopted 8.15%) discount rate used in the “funding model”.

              The law of one price is not a perfect model in the labor market. There are many
               frictions and imperfections and individuals have different subjective expectations
               and preferences that lead different people to value future cash flow and benefit
               streams differently.
Bolton Partners and BC agreed that the initial BC cost estimate needs to be adjusted downward
to remove the “cost” for the extra service worked. We will call this the “Replacement Cost”
adjustment. Why and how this should be done is a more complex discussion. The discussion
of our ideas on “how” to adjust for the Replacement Cost is in Appendix 1. The “why” is not as
difficult to address.
Why reduce the cost for extra service worked? We think most will accept on face value that the
employer must pay the employee for the work that they do. We are sure to hear from some that
in these difficult financial times the employer may need to downsize. However, if that were
always the case the employer should eliminate the DROP to encourage employees to retire
earlier. There are also many non-pension cost factors that could be considered. These non-
pension factors are both difficult to determine in a complete fashion and beyond the scope of the
studies undertaken by us and BC. That being said, everyone on our team who was involved in
this study commented on this limitation. Thus, we expect that the City should expect the same
question from other stakeholders.

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Review of Boston College DROP Study
Philadelphia City Council

             Section 2: Adjustments to the model not related to
                            the definition of cost

Survivor Benefit adjustment: Change to reflect value of payment Option 4:
The cost of DROP depends in part on the difference between the lump sum payments and the
value of the reduced annuity benefit. The value of the annuity is a present value concept. The
greater the value of the reduced annuity, the lower the net cost of DROP. In some cases the
normal form of annuity is paid in the form of a life annuity (with some guarantees covering
employee contributions). However, for members of the 1967 Plan the normal form is a more
valuable unreduced 50% Joint and Survivor benefit. Effective 7/1/2006 this was extended to
cover firefighters in the 1987 Plan and on 7/1/2008 it was extended to cover police officers in the
1987 plan.
The original BC cost estimates did not reflect the value of the Option 4 benefit. Bolton Partners
and BC agree that this is an oversight that should be corrected and will lower the cost of the
DROP. We note that most of the cost of DROP is for Municipal members in the 1967 Plans and
that in the future Municipal members in the 1987 Plan will not have receive an unreduced 50%
Joint and Survivor benefit; thus, the DROP cost increase will be greater for the municipal
members in the 1987 plan.
Change in Mortality Table:
BC used Social Security generational mortality tables. Generally pension plans do not use Social
Security tables because Social Security tables include mortality experience for those people
unhealthy enough that they cannot work. The best pension actuarial practice is often to use the
RP2000 mortality table, projected by scale AA. This gives a generational table, has separate
male and female tables, has a blue collar version and is based on mortality experience for people
covered by pension plans.
The Pension Board’s valuation actuary recommended a new mortality table for the 2010
valuation. However, this table does not include any future mortality improvement. BC did raise
issues about occupation specific tables. Given this information, using the RP2000 Blue collar
table with future mortality improvement using scale AA would be an appropriate assumption for
this model.
Gain sharing considerations:
We understand that the plan provides for "gain sharing". The PAF notional account holds
"excess assets" to provide additional benefits to retirees. We understand that these funds have
generally been paid to retirees as lump sums and the lump sums were paid in uniform amounts to
all retirees (i.e. they did not vary in proportion to annuity amount or years of service)

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Review of Boston College DROP Study
Philadelphia City Council

             Section 2: Adjustments to the model not related to
                            the definition of cost

Our understanding is that those in DROP (between their DROP entry and exit ages) are not
allocated a portion of the excess earnings. This might be looked at as a disadvantage of electing
DROP verses simply retiring. However, since this is just a question of who gets the excess funds
and not how much in total is allocated, this is not an issue for the City in terms of direct plan cost
for the DROP.
Estimate of extra time worked:
Estimating the extra time employees worked due to DROP is just that: an estimate. We can
easily see that employees are retiring at older ages now than they were before there was a DROP.
Some of this is due to DROP and some is not. Things that are not due to DROP include:

      The change (delay) in retirement eligibility ages for those hired after 1988: The five year
       change in retirement eligibility age certainly will have some impact even if not a full five

      The change in the average age at hire: Based on a review of the data, our approximation
       is that every one year increase in the average age at hire may add three months to the
       average retirement age.
There are other factors that have an impact on employee retirement age, including the economy
and pay and working conditions. To improve on the confidence of the BC model we would like
to see a more complete reconciliation of the increase in the average retirement age from all
sources. Given the complexity and material difference in methods used by Cheiron and BC, we
use the word “reconciliation” only in the most general sense. The following table compares the
BC results to an earlier Cheiron study and shows that there were significant differences between
these two studies.

             Employee Group            Cheiron: Extra service BC extra service
                                       worked (2007 study)    worked (2010 study)
             Police                                       1.2           0.183 (2/12)
             Fire                                         3.3           0.95 (11/12)
             Municipal                                    2.4           1.27 (15/12)

                                                  9                               Bolton Partners, Inc.
Review of Boston College DROP Study
Philadelphia City Council

    Section 3: Impact on Funding and should the Cost cover more than
               just the employees electing DROP in the past?

General Comment:
As noted earlier, the BC measurements were not tied to current funding rules. Under a funding
“cost” approach, cost is determined by taking into account “each member’s projected future
benefit”7, reflecting future entry into the DROP by members. However none of the prior DROP
studies (Mercer 2003, Cheiron 2007, nor BC 2010) measured any cost beyond those members
already in DROP.
The cost of most pension changes is usually measured in terms of the impact on all participants
and factoring in future expectations. For example, consider if the Fire plan changed the Option 4
free 50% Joint and Survivor benefit to a free 100% Joint and Survivor benefit for anyone who
works at least 25 years. The actuary would determine a higher current cost that would reflect
this increase even for those who have yet to reach 25 years. This would be based on an
expectation that some newer employees would retire after attaining 25 years. Accounting rules
also work this way.
The BC methodology did not determine a cost based on the value to all employees with a
probability of becoming eligible to retire and joining DROP. The BC concept reflects only cost
for employees who were currently eligible for the DROP. This approach is inappropriate for
determining pension plan funding, as it does not advance fund for benefits employees are likely
to earn in the future, only reflecting the cost when the employee actually earns the benefit. For
example, using this approach would lead to ignoring the effect of future salary increases on
service already earned. However, the BC approach is one possible way to look at the additional
“cost” of the DROP. To the extent that the employer has the right to eliminate the DROP for
future members, this would lessen the problems with the BC methodology. However, other
methods are still better suited to analyzing the cost of the DROP, particularly for purposes of
determining the annual contributions to the plan.
We did note that the prior actuarial studies also were limited to employees who already elected
DROP. Commenting on this is largely beyond the scope of the study even if it would need to be
considered in terms of total future economic cost to the City. However, we believe that the
funding of the plan should reflect the cost of DROP and should include each member’s projected
future benefit including DROP to the extent it is material (assuming the DROP is continued).
This is true even if the benefit can be removed in the future.
How would one measure the impact of DROP on Funding:
There are two parts to this discussion. The first is an amount that is easy for the plan actuary to
calculate if he can make an assumption about the impact of the removal of DROP (for those not

    Quote from page 29 of 2009 Actuarial report
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Review of Boston College DROP Study
Philadelphia City Council

Section 3: Impact on Funding and should the Cost cover more than
           just the employees electing DROP in the past?

yet in DROP) on when people retire. The second part would be difficult for anyone to calculate
and is the cost for those who already elected DROP.
       1. Cost for members not yet in DROP:
          Under the actuarial funding method used by Cheiron, the retirement rates have been
          based on when employees are expected to enter DROP (or retire for those who never
          enter DROP). This is one method to prefund the cost of DROP and increases the City
          contribution. If the DROP were eliminated, we expect that the Actuary would
          normally change the retirement rates to no longer reflect a DROP entry date and to
          reflect the fact that without a DROP provision, members might not work as long (but
          will work longer than just to the DROP entry date). For the Municipal employees this
          would likely mean a lowering of the retirement rates to reflect an increase in years of
          funding of 2 to 3 years. Assuming that members work longer means that the City's
          cost would decline. Therefore, the current City's contribution should decline if the
          DROP is eliminated (although there are likely to be other more significant reasons
          that the year over year contribution will increase, in particular investment losses).
          The plan actuary may want to be cautious about lowering the cost by changing the
          retirement rates (should the DROP be eliminated) knowing that the actuary has
          already recommended lowering the interest assumption and there is a material
          difference between the actuarial value of assets and market value. That being said the
          general actuarial approach is for each assumption to be individually reasonable.
       2. Cost for members who already elected DROP (including those in the last few months)
          This cost is one that would not be avoided by eliminating the DROP. However, the
          cost is one that will be built into the City's existing contribution. It would be
          measured using methods similar to what Cheiron did in their 2007 DROP study. To
          do it exactly would require making assumptions about when members would have
          retired had there been no DROP, adjusting for the lack of employee contributions
          during the DROP period and factoring in replacement cost. While an estimate could
          be made, being exact would be difficult.
Other DROP funding methods:
There are at least two different ways to handle DROP for funding purposes. The plan actuary
has a funding method that prefunds for DROP by assuming that the DROP entry date is the date
of retirement for retirement rate purposes. This is a common method and one the Trustees often
understand more easily that the other method. This method reflects the additional cost of the

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 Section 3: Impact on Funding and should the Cost cover more than
            just the employees electing DROP in the past?

DROP through gains and losses amortized after the employees’ working lifetime. While we do
not recommend this method, we do not object to the use of this method.
The other method is to base the retirement rates on the exit date from DROP. This would require
the anticipation of DROP benefit amounts (often greater that the regular benefit amounts) and
continues normal cost until the DROP exit date. This has the advantage of making the
contribution rate sensitive to variations in designs such as the DROP interest credit rate, as well
as reflecting the cost of the DROP benefits during the employees’ working lifetime.

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                            Section 4: Choice of Discount rate

The prior section ended with a discussion of funding. This leads into a discussion of the discount
rate: 8.25% used by the plan actuary for funding vs. the risk free rate used by BC. For the last
several years there has been a significant debate within the actuarial community8 over whether to
view pension cost in economic terms or the more common “expected” value terms. We can
accept the BC rate given their definition of cost. However, it presents both minor and major
issues. But first we shall answer two basic questions that some might ask which are:
    1. Why does the discount rate matter?
        The pension promises made by the City are paid over the lifetime of the retirees. One
        could simply project out the payments to the date of (actual or expected) death and add
        them up. This would be like in your mortgage disclosure where they tell you the sum of
        your mortgage payments over the next thirty years. This might be interesting to know but
        it does not reflect the smaller value which is the amount of the mortgage or the pension
        equivalent which is the current value (present value) of the future annuity payments. The
        amount of the mortgage equals the future mortgage payments discounted back at the loan
        interest rate. The present value of the pension is the month annuity payments discounted
        back with interest and mortality. Mortgages have no mortality discount since the
        payments are due even if the home owner dies. Pension payments stop on death and so
        their value needs to consider life expectancy. Mortgages come with a built in permanent
        interest (discount) rate. The same is not true with pensions (it is neither built in nor
        permanent). For pensions you need to assume a discount rate. BC used a "risk free"
        interest rate tied to US Government securities. This was less than the expected but risky
        return assumption used by the plan actuary of 8.25%. The higher the interest rate the less
        "principal" you need to support an annuity payment. Fixed pensions are worth more in a
        low interest rate environment and the cost of buying an annuity from an insurance
        company increases when interest rates are low. This is why the plan's actuary raises the
        City's cost whenever the interest assumption is reduced.
        In the case of the cost of DROP the normal effect of higher City cost using a lower
        discount rate is reversed. When someone takes a DROP benefit they are trading a lump
        sum for an annuity. For the most part the value of the lump sum is not dependent on the
        discount rate since it already is in the form of a present value (i.e. lump sum). The DROP
        cost is the value of this lump sum offset by the present value of the reduction in the
        annuity. The present value of the reduced annuity is larger at a lower discount rate but
        because this is an offset to the cost of DROP, the lower discount rate creates a lower cost
        to DROP.

  There was a Society of Actuaries symposium on this topic and the topic of risk in 2009. Information can be found
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                           Section 4: Choice of Discount rate

    2. Why are there two different Interest Rates?
        The short answer is that one rate is used for funding (i.e. 8.25%) and the second rate is
        tied to floating market interest rates on US Treasuries. For this discussion let's assume
        the current market rate is between 4% and 5%. The market rate does a fairly good job of
        measuring the value of the pension annuity to a member and has been referred to as the
        market value of the liability or the economic value of the liability. Not surprisingly,
        when you hire an economist, they focused on the economic value.
        Public employers almost always take risk when funding their pension plans. The major
        risk is that they invest in equities because of the higher expected returns. The higher (and
        riskier) rates of return are then used to determine the discount rate used for funding.
        Ideally the employer (or trustees) would set an acceptable level of investment risk and
        determine a discount rate to match that risk (and not the other way around). In 2009, the
        plan actuary assumed an 8.25% discount rate for funding purposes (we understand this
        was recently lowered to 8.15%). The lower the rate assumed the higher the current
        contribution. When you hire an actuary they will usually focus on the funding assumption
        (as was done in the two prior DROP studies by actuaries).
        The difference in liabilities between the two rates is a moment-in-time measurement of
        some of the risk the employer is taking. To go beyond this discussion probably takes us
        too far into the existing debate. We would suggest that the right discount rate to use
        depends on the purpose.
One of the “minor” (but still significant) issues is the view of the 4.5% interest crediting rate on
the DROP account. Since the valuation interest rate was over 8%9, the actuaries viewed the
4.5% rate as conservative and 4.5% was “intentionally included to offset the potential cost of the
program”10. However, since the 4.5% rate was generally higher than the risk free discount rate,
the BC study viewed this as a cost and not a savings. The key line from page 8 of the BC study
which covers this and a key point in section 1 of our report is: “If employees simply extend their
careers, then the program will be cost-neutral if the interest rate paid during the period of deferral
equals the risk-free interest rate.” Thus the 4.5% rate was not cost neutral under the BC analysis.

  We understand that at the time the DROP feature was added, the valuation assumption was 9% and the 4.5% rate
was selected as half the valuation rate.
   See page 8 of Cheiron 2007 study
                                                      14                                 Bolton Partners, Inc.
Review of Boston College DROP Study
Philadelphia City Council

                            Section 4: Choice of Discount rate

The methodology used by BC raises several more important questions:
     1. Would the City use this same risk free interest rate methodology for all future benefit
     2. Does the City understand that the use of a risk free interest rate has less impact on DROP
        cost than it is likely to have for other changes? Using a lower discount rate actually
        reduced BC’s estimated DROP cost since it increased the value of the reduction for the
        increase in annuity forgone due to the DROP election.
     3. Assuming that the City is not going to fund using a risk free discount rate (a safe
        assumption given the material (2 to 3 times) contribution increase that would result), does
        the City understand that unions are unlikely to accept a higher cost associated with
        benefit changes than the City is actually funding11? For example, if the City offered the
        union either $x in wage increases or the same $x dollars in pension benefits you might
        think that the union might view this as a balanced choice. However, if the $x dollars in
        pension benefits was based on a low interest rate and the City funded a much smaller
        amount based on a higher interest rate, the union might want to credit (in their
        negotiations with the City) a smaller value to the pension improvement than $x or see the
        City contribute $x.
     4. Does the City understand that in the near term that the measurement of the value of most
        benefit cuts (other than the elimination of the DROP) based on risk free interest rates
        produces a higher cost savings than the actual reduction in the liabilities used to
        determine annual contributions to the plan?
The market related cost produced by BC might be an important tool in understanding the value
of these promises but there are other relevant values and considerations. The impact on funding
is one of them.
The point of this section 4 is to make the City think about what it needs and might ask for in the
future related to other pension changes. The Economic model might “inform” the City even if it
does not tie into immediate funding changes. Will this confuse the user of this information or is
the user sure that it will be understood and used in an appropriate fashion?
Finally, we do not object to the use of a risk free rate in the economic value. However, over the
last several months, experience is starting to show that there may be more risk to pension plan
members that one might have assumed previously. This should be monitored and revisited, not
so much for this study by BC but for studies by others.

   Perhaps for the same reason that the federal government requires contractors to actually contribute amounts to
their pension plans before this cost may be allocated to a year and assigned to government contracts (Cost
Accounting Standard 412.50(d)(1)).
                                                      15                                    Bolton Partners, Inc.
Review of Boston College DROP Study
Philadelphia City Council

           Section 5: The significance of "peak" retirement age
                  and the related concept of DROP ratio

The next section discusses the BC model. However, we first introduce two ideas that will help in
the understanding of the BC model. In this section we combine the BC idea of age at Peak Value
and our related concept of DROP ratio. Sections 5 and 6 should be read together as part of the
same discussion of the BC model.
Definition of age of Peak Value
BC focused on the age when an employees pension value is maximized, assuming that
employees will tend to retire at that age to maximize the economic value of their pension. The
cost and concept of the DROP feature is very much related to the "peak" retirement age.
Generally the election of a DROP allows a member to retire (exit from DROP) without a decline
in the value of their pension since their DROP entry date. The following observations should be
   1. By value we mean the concept of a present value. This is different than simply looking at
      the amount of the monthly pension benefit. Monthly pension amounts will continue to
      grow for each year an employee works, even beyond the age of peak value. The net
      decline in value (even while the annuity amount grows) is largely due to increase in age,
      which decreases the remaining life expectancy, reducing the value of a pension.
   2. Peak retirement age is calculated separately for each member, based on their date of hire,
      current age and salary history.
   3. Peak age is almost never achieved before normal retirement age. In the Philadelphia plan
      a member eligible for early retirement who works an extra year will not only accrue an
      extra year’s worth of pension but will avoid a 6% reduction in the annuity, due to the
      reduction for payment prior to the normal retirement date. For this reason there is no
      peak value before normal retirement age in the plan.
   4. Once a member works beyond their normal retirement age (NRA) the increase in age
      often reduces the value by more than the value of the extra annuity benefit that is being
      earned. However, the next three points need to be understood to understand this
      generalization. Note BC’s peak age for uniformed members was often around 54 which is
      well beyond normal retirement age.
   5. As was established in earlier actuarial studies, peak age will not be at NRA for members
      with few years of service at NRA. Because the annual increase in service is a relatively
      large percent of their total service, their benefits grow too fast to be at their peak

                                              16                             Bolton Partners, Inc.
Review of Boston College DROP Study
Philadelphia City Council

                Section 5: The significance of "peak" retirement age
                       and the related concept of DROP ratio

           retirement age. This is more often the case for Municipal employees than for uniformed
           employees because there is a greater likelihood that Municipal employees will be hired in
           their 40's, 50's and 60's than there is for uniformed employees.
       6. Since peak value is a present value concept, the selection of discount rate is important.
          For a career uniformed employee their peak retirement age might be 54 using risk free
          market rates. However, using the actuarial funding assumption of 8.25%, the peak age
          might easily be the NRA.
       7. Employee contributions should be factored into peak wealth. If the value of the benefit at
          one year past NRA (NRA+1) is greater than at NRA or any age after NRA+1 you might
          consider NRA+1 the age of peak wealth. However, if the difference in value between
          NRA+1 and NRA is less than the required employee contribution for that year, a more
          reasonable conclusion is that the peak value is higher at NRA.
       8. Peak retirement age is a function of age and benefit accrual rates. The municipal plan
          accrual rate (unlike the uniform plan accrual rates) declines from 2.5% to 2.0% after 20
          years12. This is one reason why the graph in the BC study showed a peak age at 55
          (NRA) for Municipal employees. The later the NRA, the more likely that NRA will be
          the peak age. Both of these reasons account for the flat value curve (between ages 51 and
          57) for uniformed employees13 in figure 1B of the BC study.
DROP Ratios as a tool to understanding cost
The DROP ratio is the ratio of the value of a benefit with a DROP to the benefit without the
DROP assuming that the member would have retired at the same age without the DROP as when
they would have exited DROP. While the member data shows that the two ages are more than a
year apart in the Philadelphia plan, the DROP ratios are handy for illustration of the dynamics of
DROP cost.
Illustration #1 show the DROP ratios for the Municipal plans for a member entering DROP at
age 55 and leaving at age 59. The ratio at age 59 is 105.0% or 103.1% (as explained below).
This means that the DROP benefit is more valuable (by 5% or 3.1%) than the non DROP benefit.

     The reduction is the accrual rate in the 1987 Plan is after 10 year s of service and not 20 years as in the 1967 Plan.
     We will refer to police and fire employees jointly as uniformed or uniformed employees.
                                                              17                                     Bolton Partners, Inc.
Review of Boston College DROP Study
Philadelphia City Council

           Section 5: The significance of "peak" retirement age
                  and the related concept of DROP ratio

Next we need to understand the sensitivity of these ratios to the following:
   1. Change in form of annuity payment
   2. Change in discount rate
   3. Change in retirement age
   4. Change in interest crediting rate on DROP account
After understanding these situations we will also look at (1) differences between the Municipal
and uniformed groups, (2) treatment of employee contributions and (3) differences between
DROP exit age and retirement age had there not been a DROP.
Change in form of annuity: Illustration #1 shows two DROP ratios: 105.0% and 103.1%. The
first is when the form of annuity payment is a single life annuity. This is the normal (unreduced)
form of payment for the Municipal employees in the 1987 Plan. However, it is not the normal
form of payment for the 1967 Plan or for uniformed employees. The second ratio is less and
reflects the unreduced "Option 4" 50% survivor option. The important factor in the cost of the
DROP is the exchange between receiving a lump sum and a smaller annuity in lieu of the larger
annuity that would have been received if there was no DROP. The annuity offset is more
valuable when Option 4 is available.
Change in discount rate: Illustration #2 is the same except the discount rate is now different. In
Illustration #1 we used a 5% discount rate and in Illustration #2 we used an 8% discount rate.
The ratio for the single life annuity benefit increases materially, from 105.0% to 113.1%. BC did
similar comparisons with similar results.
Change in Retirement Age: Illustration #3 is the same as Illustration #1 except we assume the
employee entered DROP at age 60 and exited at age 64. The ratio for the single life annuity
benefit increases materially, from 105.0% to 110.6%. BC results reflect the same dynamic
which accounts in part for the wide variation in DROP cost between different Municipal group
members (since Municipal employees are more likely to retire at older ages).
Change in interest crediting rate on DROP account: Illustration #4 reflects a change from
Illustration #1 to reduce the DROP interest crediting rate from 4.5% to 0%. The ratio for the
single life annuity benefit decreases from 105.0% to 102.7%. This change in the DROP ratio is
smaller than those mentioned earlier, showing the relatively small effect on the value of DROP
due to the interest rate credited on the DROP balance. We agree with BC that the interest
crediting rate is not the main driver of DROP cost or savings.

                                                18                             Bolton Partners, Inc.
Review of Boston College DROP Study
Philadelphia City Council

           Section 5: The significance of "peak" retirement age
                  and the related concept of DROP ratio

Uniformed members: We have created illustrations 1A, 2A, 3A and 4A to parallel the prior
four calculations. However, because of their younger retirement ages we have changed the
DROP participation ages of 55-59 and 60-64 to 50-54 and 54-58. We selected 54 as a key age
because BC identified this as a common peak age for this group. A comparison of 1A, 3A and
4A suggest that there might be no material cost for uniformed employees if the interest crediting
rate were lowered from 4.5% to 0%. The same cannot be said for municipal employees or when
viewed using higher discount rates. It should be kept in mind that these illustrations do not
model behavioral effects. Lowering the interest rate from 4.5% to 0% could have negative
behavioral effects that can impact the cost of DROP.
Using the “economic” interest rate, these ratios confirm the BC conclusion of a peak retirement
age around 54 for uniformed employees. A ratio of 100.0% at the DROP exit age is similar to
the flat portion of the BC Figure 1A and a ratio above 100.0% indicates an age beyond peak.
Using an 8% discount rate, the peak age for uniformed employees is close to their Normal
Retirement Age.
Treatment of employee contributions: There are two issues about the treatment of employee
contributions. First is how to treat employee contributions when determining the peak value of
the non DROP benefit. The second is how employee contributions are factored into the cost of
DROP. The peak value issue can involve a debate about employee perception.
The treatment of employee contributions when determining the cost of DROP is an important
factor in both the BC cost analysis and the DROP ratios. The DROP ratio of 105.0 in Illustration
#1 is the ratio of A/B where:
A = Value of DROP benefit at age 59 ($519,134), which consists of the following:
       Present Value at age 59 of an annuity of $30,000/yr = $378,600, plus
       DROP Lump Sum of $131,474 at age 59, plus
       Present Value of employee contributions not contributed between age 55 and 59: $9,055
B = Value of Non DROP benefit at age 59 ($494,291) made up of the following:
       Present Value at age 59 of an annuity of $39,167 = $494,291
An acceptable alternative treatment of employee contributions would be to exclude the value
from "A" as well as from "B". Either method for reflecting the employee contributions results in
the same value of the increase in cost of the DROP. When determining the present value, the
interest discount rate for employee contributions should match the basis used to measure the
value of the annuities.

                                               19                             Bolton Partners, Inc.
Review of Boston College DROP Study
Philadelphia City Council

           Section 5: The significance of "peak" retirement age
                  and the related concept of DROP ratio

Handling differences between DROP exit age and retirement age had there not been a
DROP: The DROP ratio does not directly handle this difference. However, we agree with BC
that the delay in retirement is a key factor which must be reflected in the calculation of the cost
of DROP. The cost of DROP now becomes A - B where:
A = Value of DROP benefit consists of:
       Present Value of the reduced DROP annuity, plus
       Present Value of DROP Lump Sum, plus
       Present Value of employee contribution not contributed between DROP entry date and
       date they would have retired without a DROP
B = Value of Non DROP benefit consists of:
       Present Value of non DROP annuity including payments from non DROP retirement date
       to DROP exit age, minus
       Present Value of replacement cost from non DROP retirement date to DROP exit age.
This approach is similar to the A and B used in the DROP ratio above, but now reflect (1) more
than two ages (the DROP entry and exit plus the difference between DROP exit and exit without
DROP) and (2) a replacement cost. Both the A and B present values must be adjusted to the
same age. BC uses the non-DROP retirement age which we think is a logical choice. The
alternative of using the DROP retirement age has the advantage that there is no need to discount
DROP lump sum since discounting makes the value of a common lump sum amount depend on
the discount rate.

                                                20                              Bolton Partners, Inc.
Review of Boston College DROP Study
Philadelphia City Council

        Section 6: Comments on the BC Study Retirement Model

General Thoughts:
The economic model underlying the BC study can be described simply as “maximization of the
expected present value of pension benefits”. That is, a worker chooses a retirement date that
results in the highest expected present value of pension benefits, where the term “expected” is
used because the lifespan of the employee is uncertain, and hence the duration over which he/she
will collect retirement benefits is uncertain. The expected present value calculation therefore
forecasts the present value of the stream of pension benefits over different potential lifespans and
takes a weighted average, where the “weights” are the probabilities of surviving to different ages
(conditional on the employee having survived up to a given age, e.g. 50 or 55). Figures 1A and
1B in the BC study plot the expected present value of pension benefits as a function of the age of
retirement for a man born in 1950 who starts work at age 30, with the benefits discounted to age
50. The figures show a “pension wealth” of zero for retirement ages prior to 40 since there is a
10 year “vesting period” — i.e. the worker is not entitled to any pension benefits if the worker
leaves prior to accumulating at least 10 years of service. After this initial 10 year vesting period,
the present value of pension benefits rises rapidly until age 55 (in figure 1A) and between age 51
to 56 (in figure 1B) depending on the specific type of pension plan considered. After this “age of
peak pension wealth” the present value declines. This is because while further one year delays in
retirement age increase the monthly pension benefit by 2.0% (for the additional year of service),
the rates of mortality at each passing year imply that further delays in retirement decrease the
present value of benefits that are paid out. Thus, if an individual was solely interested in
maximizing the expected present value of their future stream of pension benefits, they could look
at figures 1A and 1B in the BC study to determine the optimal age to retire (either age 55 in
figure 1A or between ages 51 to 56 in figure 1B, depending on the type of pension plan they are
In the BC paper, the DROP generally does not affect the age at which the Present Value of
pension benefits peak, so this model would seem to predict that the DROP has no effect on
retirement ages. The BC model is more flexible and treats the age at which the Present Value of
pension benefits is maximized as just one of the considerations. Nevertheless, this is the main
avenue by which their model is used to make the counterfactual calculations of how retirements
would change in the absence of the DROP, and thus the model’s prediction of the effects of
DROP. Thus, if DROP does not affect the age at which the Present Value of pension reaches its
peak, then it is hard to see how this model will predict a significant effect of DROP on retirement
However, retirement decisions are clearly more complex and involve many other considerations
that the simplest maximization of the expected present value of pension benefits. For one thing,
this calculation ignores other sources of income such as wage income that comes from delaying
retirement age, and also the additional Social Security benefits an employee may get (from non-
City employment) in addition to their pension from the city of Philadelphia. For employees in
physically demanding jobs such as policemen and firemen, their health will also play a key factor
in their decision to retire (or apply for disability benefits, if they have a sufficiently serious
health problem). Other factors, such as other postretirement employment opportunities, levels of

                                                 21                              Bolton Partners, Inc.
Review of Boston College DROP Study
Philadelphia City Council

        Section 6: Comments on the BC Study Retirement Model

wealth and retirement savings (including windfalls such as lottery winnings or inheritances) and
family considerations (a spouse who is ill and needs special care) can also affect retirement
Economists recognize that these additional complex factors can play an important role in
retirement decisions, and thus the model of “maximization of the present value of pension
benefits” is generally recognized as too simplistic and unlikely to provide good predictions of
actual retirement decisions. For these reasons the pension maximization model has been
modified in important ways to try to capture these other factors while still taking into account the
important role played by pensions in an individual’s choice of age of retirement.
One way this been done in previous work, and adopted by the BC study, is to use an econometric
model of retirement that includes pension accrual as one of the “explanatory variables” that
predict age of retirement. Pension accrual is defined as the change in the expected present value
of pension benefits from delaying retirement by an additional year. The hypothesis is that when
the value of pension accrual is very high, there are high incentives for the employee to delay
retirement by another year. Conversely when the value of pension accrual is very low or even
negative, then there are very low or even negative incentives to delay retirement, and this implies
that the individual has a higher likelihood of retiring.
Since the pension accrual variable seems to capture many of the pension based economic
incentives influencing retirement decisions, a common approach to modeling retirement
decisions in the economic literature has been to include the pension accrual measure as a
covariate or “explanatory variable” in a probit model of the decision to retire. A probit model
predicts the conditional probability that a person will retire at any given age, conditional on not
having retired already and conditional on the value of their pension accrual at that age and other
variables that affect retirement decisions. The probit model does not try to predict whether an
individual employee will retire or not, but rather predicts the probability that an individual will
retire at that age (just as the pension actuary uses a set of retirement probabilities to determine
the funding contribution). This approach recognizes that there are a host of factors that affect
whether a given individual will retire or not, some of which we can “observe” (such as the
person’s age, salary and pension accrual) and other factors that we cannot observe (such as the
person’s health, and family situation or other postretirement employment opportunities, etc).
Thus, while we recognize that we cannot predict with any degree of certainty whether a specific
individual will retire at a specific age or not, we may be able to at least accurately predict the
probability the individual will retire at this age. If we can accurately predict these probabilities,
and show how these retirement probabilities shift in response to a change in pension policy such
as DROP, then even though we cannot accurately predict the retirement age of any specific
individual, we may be able to forecast the average retirement age (and the distribution of

                                                 22                              Bolton Partners, Inc.
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