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T R A N S A C T I O N S O F S O C I E T Y O F A C T U A R I E S1 9 8 5 V O L . 3 7

SELECT AND ULTIMATE FINANCIAL ASSUMPTIONS INPENSION PLAN VALUATIONS: AN ANALYSIS OF THE ISSUESSOCIETY OF ACTUARIES COMMI'VFEE ON PENSION PRINCIPLES AND

RELATED RESEARCH*1. ABSTRACT

Over the last several years, interest rates have risen and fallen dramaticallywithin very short time periods. Wage increases have also fluctuated consid-erably. At the same time, actuaries have received increasing numbers ofrequests for information regarding pension plans. Examples include newaccounting standards for reporting pension plan assets and liabilities in fi-nancial statements, and multiemployer withdrawal liability calculations. Thesecircumstances have focused increasing attention on financial assumptionsused to value pension plans. Greater interest in using select and ultimatefinancial assumptions for pension plan valuation purposes has resulted.The objective of this paper is to examine the advantages and disadvantagesof using select and ultimate financial assumptions and the technical issuesinvolved. The effect of such assumptions on the incidence of plan cost isstudied. The discussion of technical issues and the study of plan cost inci-dence deal mainly with the interest assumption.

Il. ADVANTAGES AND DISADVANTAGES OF SELECT AND ULTIMATEFINANCIALASSUMPTIONS

This section will examine the advantages and disadvantages of adoptingselect and ultimate financial assumptions. Technical issues as well as poten-tial problems and solutions which arise due to such assumptions are consid-ered in a later section.A. Advantages

In recent years, increased attention has been focused on pension actuarialworkproducts. The Financial Accounting Standards Board (FASB) has takena keen interest in plan cost disclosure. The Multiemployer Pension Plan

*Authors of this paper are Vincent Amoroso, Alley Bailin. Edward W. Brown, Yuan Chang,Patricia J. Conger, Robert P. Ford, Jeffrey Furnish, Michael J. Gulotta, John J. Haley. Richard L.Helms, Mark S. Hoyt, Michael Krosky, Martin Pepper, Neela Ranade, A, Frederick Rohlfs, Jr.,William E. Schroeder, T, Thomas Simester and Susan M. Smith.351

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35 2 F I N A N C I A L A S S U M P T I O N S I N P E N S I O N P L A N V A L L 1 A T I O N SA m e n d m e n t s A c t o f 1 9 80 ( M P P A A ) c a n r e q u i r e a r b it ra t o rs a n d j u d g e s t oq u a n t i f y a p l a n ' s v e s t e d l i a b i l i t y , T h e I n t e r n a l R e v e n u e S e r v i c e ( I R S ) r e -q u i r e s t h a t a p l a n ' s m i n i m u m c o n t r i b u t i o n a n d m a x i m u m d e d u c t i b l e c a l c u -l a ti o n s b e b a s e d o n t h e s a m e s e t o f r e a s o n a b l e a c t u a r i a l a s s u m p t i o n s . I ta s s e ss e s t h e r e a s o n a b l e n e s s o f a m a t ri x o f a s s u m p t i o n s o n t h e b as is o f e m e r g -i n g e x p e r i e n c e . A c c o r d i n g l y , l e v e l f i n a n c i a l a s s u m p t i o n s t h a t a r e l o w e r t h a np r e v a i l i n g e x p e r i e n c e a r e m o r e l i k e l y t o b e c h a l l e n g e d b y t h e I R S r e g a r d l e s so f e s t a b l i s h e d a c t u a r i a l p r a c t i c e . O t h e r r e g u l a t o r y a g e n c i e s s u c h a s t h e F e d -e ra l C o m m u n i c a t i o n s C o m m i s s io n a n d th e D e f e n s e C o n t r a c t A u d i t A g e n c ya r e a ls o c o n c e r n e d a b o u t th e u s e o f le v e l i n t e r e s t a s s u m p t i o n s t h a t a re l o w e rt h a n p r e v a i l i n g e x p e r i e n c e .In a v o l at il e e c o n o m i c e n v i r o n m e n t , l a y m e n a r e s o m e t i m e s s u r p r i se d b ys e e m i n g l y a n a c h r o n i s t i c , l o n g - t e r m a c t u a r ia l a s s u m p t i o n s . I n t e re s t r a t e s , s a l -a r y i n c r e a s e s a n d i n f l a t i o n h a v e t y p i c a l l y v a r i e d w i t h t h e b u s i n e s s c y c l e .U n t i l r e c e n t l y , t h e v a r i a t i o n w a s r e l a t i v e l y n a r r o w , a n d l e v e l f i n a n c i a l a s -s u m p t i o n s p r e d o m i n a t e d . In t h e c u rr e n t e n v i r o n m e n t , t h e a ct u a ry m a y c o n -s i d e r u s in g s e l e c t a n d u l t i m a t e f i n a n c i a l a s s u m p t i o n s . H i s j u s t if i c a t i o n w o u l db e th e p h e n o m e n o n o f t h e b u si n e ss c y c l e .

A d o p t i n g s e l e c t a n d u l t i m ~ t t e a s s u m p t i o n s c a n m i n i m i z e t h e n e e d t o u s ed i f f e r e n t s et s o f a s s u m p t i o n s f o r d i f f e r e n t p u r p o s e s . F A S B s ta n d a rd s a p p l yt o p l a n v a l u a t i o n . T h e i n t e r e s t r a t e u s e d f o r q u a n t i f y i n g a p e n s i o n p l a n ' sa c c r u e d b e n e f i t li a b i li t y " s h a l l r e f l e c t t h e e x p e c t e d r a te s o f r e tu r n d u r i n g t h ep e r i o d s f o r w h i c h p a y m e n t o f b e n e f i ts is d e f e r r e d a n d s h a ll b e c o n s i s t e n tw i t h r e t u r n s r e a l i s t i c a l l y a c h i e v a b l e . " A s e l e c t a n d u l t i m a t e a p p r o a c h w o u l ds a t i s f y t h e r e q u i r e m e n t s p r o m u l g a t e d b y t h e F A S B .

A n e m p l o y e r c e a s i n g t o h a v e a n o b l i g a t io n t o m a k e c o n t r ib u t i o n s to am u l t i e m p l o y e r p la n m a y b e l i a b l e fo r a n a l l o c a b l e s h a r e o f t h e p r e s e n t v a l u eo f t h e p l a n ' s u n f u n d e d v e s t e d b e n e f i t s . F a c e d w i t h th i s l ia b i li ty , th e e m p l o y e rm i g h t c h a l l e n g e t h e a c t u a r i a l a s s u m p t i o n s o n w h i c h t h e p l a n ' s d e t e r m i n a t i o ni s b a s e d . R e c e n t l y , o p p o s i n g p a r t i e s h a v e a d v o c a t e d d i s p a r a t e p o i n t s o f v i e wo n t h e s t r u c t u r e o f th e i n t e r e st r a te . S u c h d e b a t e s m i g h t b e a w ) i d e d b y u s i n ga n i n t e r e s t r a t e a s s u m p t i o n t h a t d o e s n o t a p p e a r u n r e a s o n a b l e t o a w i t h d r a w -i n g e m p l o y e r , a n a r b i t r a t o r o r a j u d g e . S e l e c t a n d u l t i m a t e r a te s o f f e r s o m ep r o m i s e h e r e .

C o m p u t a t io n s to d e t e r m i n e m i n i m u m f u n d i n g r e qu i re m e n t s an d m a x i m u md e d u c t i b l e l i m i t s m u s t b e b a s e d o n t h e s a m e a c t u a r i a l a s s u m p t i o n s . S u c ha s s u m p t i o n s a r e h e l d t o a g e n e r a l r e a s o n a b l e n e s s s t a n d a r d . H i s t o r i c a l l y , t h eI R S h a s a s s e s s e d t h e r e a s o n a b l e n e s s o f a c t u a ri a l a s s u m p t i o n s o n t h e b a s i so f g a i n s a n d l o s s e s o r c h a n g e in th e a c c r u a l r a t e fo r a g g r e g a t e m e t h o d s . T h e

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F I N A N C I A L A S S U M P T I O N S I N P E N S I O N P L A N V A L U A T I O N S 353IRS's assessment criteria have recently been published as a set of actuarialaudit guidelines. The IRS instructions contained in the guidelines confirmthat the IRS is interested in confronting assumptions that appear undulyoptimistic (from a minimum standpoint) or unduly conservative (from adeductibility standpoint). Using select and ultimate assumptions might behelpful in diffusing this potential controversy.

Perhaps the greatest advantage of using select and ultimate financial as-sumptions is the opportunity to enhance communications with plan sponsors,accountants, participants and others interested in the actuary's results. In-creasing public awareness and the volatile economic environment have re-sulted in closer scrutiny of pension plan valuation. Using select and ultimateassumptions may enhance the actuary's credibility as well as satisfy profes-sional and legal responsibilities.

Select and ultimate interest rates can provide greater consistency in valuingassets and actuarial liabilities. Typical U.S. asset valuation is based on mar-ket or some market-related method. There is no direct relationship betweenthe market's short-term outlook for interest rates and the long-term rate atwhich the actuary is discounting future benefit payments. If select and ul-timate financial assumptions are used, the initial rate can be the rate that themarket uses to discount assets. Some consistency between the two sides ofthe balance sheet is then achieved.B. Disadvantages

There are potential disadvantages in using select and ultimate financialassumptions. Traditionally, most pension plan valuations have been basedon interest rate and salary scale assumptions that are level over time. Theserates are applied prospectively and, to the extent required by the fundingmethod, retrospectively. The recent volatility of market interest rates hasdamaged the credibility of level interest assumptions and sparked the currentinterest in select and ultimate assumptions. By separating short-term andlong-term financial considerations, the select and ultimate approach mayimprove credibility and, therefore, communications with plan sponsors, ac-countants, and participants. The select and ultimate approach also may createan implication of greater accuracy than a level long-term assumption. If so,communications may be hampered if the investment manager views theselect assumptions as annual investment targets. Level financial assumptionswould be used,if there was an expected rapid return to low levels of inflationor a belief that future levels of inflation are unpredictable.

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35 4 FINANCIAL ASSUMPTION S IN PENSION PLAN VALUATIO NS

Technically, select and ultimate financial assumptions are more complexthan level assumptions. For example, investment return is said to be com-posed of an inflation rate plus a real rate of return, while salary scales includean inflation rate, longevity increases, and merit and productivity increases.The actuary must decide whether the changing inflation rate would implythat the other components of the salary and investment assumptions alsovary over time. Experience studies have suggested that turnover, disability,and death rates are also affected by changing economic conditions.

Changes in Internal Revenue Code section 415 imposed by the Tax Equityand Fiscal Responsibility Act (TEFRA) have caused financial assumptionsto reach historical levels. In projecting plan benefits under pay-related plans,the expected benefit at retirement cannot exceed the current section 415dollar limit. The dollar limit is adjusted annually to reflect changes in theconsumer price index. The increased limit can be funded as it becomeseffective. TEFRA reduced the existing maximum dollar benefit by morethan one-third. Moreover, there is a five-year (1983-198"7) moratorium onannual cost-of-living adjustments to this limit, so the ultimate effect on planfunding will be even more pronounced. Long-term financial assumptionswhich assume an orderly return to past economic experience could improvethe fluctuating funding that is otherwise possible. Lower salary increaseassumptions mean fewer projected benefits would bump into the lower dollarlimits. In Canada, the maximum dollar limit is currently defined in Infor-mation Circular 72-13R7, and future increases in the limit cannot be as-sumed. Nevertheless, inflation and pension industry lobbying may well forceadjustments to the limit. Thus, the difficulties with the approach are evenmore pronounced in Canada.Select and ultimate assumptions typically would be developed on a val-uation year basis. That is, they apply to specific time periods following aparticular valuation date. With succeeding valuations, adoption of the sameassumptions will lead to a contracting select period. The assumptions willtherefore become level rates (the ultimate rate) at the end of the select periodunless the select period is regularly lengthened. Select and ultimate assump-tions may require more frequent changes than level assumptions, The actuaryshould consider the potential effects of frequent changes in assumptions onthe funding stability of the program.

Extending this analysis to methods requiring retrospective financial as-sumptions illustrates subtle features of the role of financial assumptions inthe valuation. Consider select and ultimate assumptions in three parts--theultimate rate, the retrospective rates, and the select rates.

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FINANCIAL ASSUMPTIONS IN PENSION PLAN VALUATIONS 3 5 5T h e u l t i m a t e r a t e w i l l b e a l e v e l r a t e . T o m i n i m i z e g a i n s o r l o s s e s c a u s e d

b y t h e d i f f e r e n c e b e t w e e n c u r r e n t i n v e s t m e n t e x p e r i e n c e a n d t h e u l t i m a t er a t e , w e w o u l d c o n s c i o u s l y d e c i d e t h a t th e l o n g - t e r m s t a b i l it y o f t h e a s -s u m p t i o n s h o u l d b e o v e r r i d d e n t o t h e e x t e n t t h a t t h e s e l e c t r a t e s v a r y f r o mt h is l e v e l r a t e . I n a n e w p l a n , h o w e v e r , t h e l a c k o f as s e ts w o u l d s e e m t op r e c l u d e s u c h a d e c i s i o n . I t s e e m s m o r e a p p r o p r i a t e i n a w e l l - f u n d e d p l a n .

I t i s a p p a r e n t t h a t a c h a n g e t o s e l e c t a n d u l t i m a t e a s s u m p t i o n s f r o m l e v e lr a te s w i l l a l te r f u t u r e c o s t s . T h e e f f e c t s o f t h e s e c h a n g e s w i ll v a r y d e p e n d i n gu p o n t h e d i s t r i b u t i o n o f l i a b i l i t i e s u n d e r a n i n d i v i d u a l p l a n . T h u s , t w o p l a n sw h i c h h a v e c o m p a r a b l e c o s t p a t t e r n s u n d e r i d e n t i c a l l e v e l r a t e a s s u m p t i o n sm a y h a v e d i s s i m i l a r c o s t p a t t e r n s u n d e r i d e n t i c a l s e l e c t a n d u l t i m a t e a s -s u m p t i o n s .

T h e c o m m o n t h r e a d i n t h e s e o b s e r v a t io n s i s t h at t h e v a l u a t i o n 's f i n a n c i a la s s u m p t i o n s c a n b e v i e w e d a s d e f i n i n g l i a b i l i t i e s , w h i c h m a y b e d i f f e r e n tt h a n v i e w i n g t h e m a s t h e p r e d i c t i o n o f f u t u r e p l a n i n v e s t m e n t p e r f o r m a n c e .T h i s i s s t a n d a r d v a l u a t i o n p r a c t i c e , a s a s s e t s a r e g e n e r a l l y m e a s u r e d i n r e -l a t i o n t o c u r r e n t b o o k o r m a r k e t v a l u e s . A l t h o u g h a n i n t e r e s t a s s u m p t i o nw h i c h m a t c h e s f u t u r e in v e s t m e n t e x p e r i e n c e w i ll m i n i m i z e i n v e s t m e n t g ai n sa n d l o s s e s , o t h e r m e a s u r e s o f l ia b il it y c o u l d b e u s e d . F o r e x a m p l e , t h es p o n s o r m i g h t w i s h t o v a l u e l i a b i l i t i e s b a s e d o n t h e e x p e c t e d f u t u r e c o s t o fm o n e y . I n a n y e v e n t , t h e a c t u a r y s h o u l d b e s a t i s f i e d t h a t t h e s e l e c t a n du l t i m a t e a p p r o a c h i s a p p r o p r i a t e f o r d e f i n i n g l ia b i li ti e s b e f o r e a d o p t i n g t h ist e c h n i q u e .

III. TECHNICAL ISSUES INVOLVED IN THE USE OF SELECT AND ULTIMATEFINANCIA L ASSUMPTIONS

T h e r e a r e s e v e r a l t e c h n i c a l i s s u e s c o n c e r n i n g a c t u a r i a l v a l u a t i o n s w h i c hd o n o t a r i s e w i t h l e v e l f i n a n c i a l a s s u m p t i o n s b u t d o w i t h v a r i a b l e f i n a n c i a la s s u m p t i o n s . O t h e r t e c h n i c a l i s s u e s t h a t a r e p e r t i n e n t t o b o t h l e v e l a n d v a r -i a b l e f i n a n c ia l a s s u m p t i o n s h a v e a s o m e w h a t d i f f e r e n t e m p h a s i s w i t h t h el a t t e r .A. Nomenclature

I n t h e l i t e r a t u r e , t h e t e r m select and ultimate interest assumptions h a sb e e n i n t e r p r e t e d i n t w o d i f f e r e n t w a y s , O n e i n t e r p r e t a t i o n i s t h a t t h e s e l e c tp e r i o d , a n a l o g o u s t o t h e s e l e c t p e r i o d i n m o r t a l i t y t a b l e s , r e m a i n s c o n s t a n t .F o r e x a m p l e , i f t h e ra t e s f o r t h e f i rs t v a l u a t i o n y e a r t 9 8 3 a r e s e t a s 1 0p e r c e n t f o r t h e f ir s t t e n y e a r s a n d 5 p e r c e n t t h e r e a f t e r , t h e r a te s f o r 1 9 8 4w o u l d a l s o b e 1 0 p e r c e n t f o r t h e f i r s t t e n y e a r s , a n d 5 p e r c e n t t h e r e a f t e r .

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356 FINANCIAL ASSUMPTIONS IN PENSION PLAN VALUATIONST h e s e c o n d i n t e r p r e t a t i o n i s t h a t t h e i n t e r e s t r a t e i s v a r i a b l e f o r a c e r t a i n

c a l e n d a r p e r i o d c a l l e d t h e s e l e c t p e r i o d , a f t e r w h i c h t h e i n t e r e s t r a te a tt a i n si ts u l t i m a t e l e v e l . I f t h e r a t e s f o r th e f i r st v a l u a t i o n y e a r 1 9 8 3 a r e e s t a b l i s h e da s 1 0 p e r c e n t f o r th e f i r s t t e n y e a r s , a n d 5 p e r c e n t t h e r e a f t e r , t h e r at e s f o r1 9 8 4 w o u l d b e 1 0 p e r c e n t f o r t h e f i r s t n i n e y e a r s , a n d 5 p e r c e n t t h e r e a f t e r .I n o t h e r w o r d s , t h e i n t e r es t r a te s a r e c a l e n d a r s p e c i f i c .

T h e f i r s t i n t e r p r e t a t i o n r u n s c o u n t e r t o t h e U . S . r e a s o n a b l e f u n d i n g r e g -u l a t i o n s , b u t c o u l d b e u s e d w i t h C a n a d i a n p e n s i o n p l a n s .

C o n s i d e r t h e p r e s e n t v a l u e o f b e n e f i t s , P V B , a t t h e b e g i n n i n g o f y e a r 1:

P V B i = 1 + i ~1 !B~ +1 + i j ( 1 + i l ) ( 1 + i 2 )

By + . . .

w h e r e B k = b e n e f i t s p r o j e c t e d t o b e p a i d at t h e e n d o f y e a r k .i.,. = . 1 0 f o r 1 _ < s ~ 1 0

.05 for s > 10 .T h e e q u a t i o n f o r th e e x p e c t e d p r e s e n t v a l u e o f b e n e f i t s a t t h e en d o f y e a r

1 is :E x p e c t e d P V B 2 := P V B I (1 + i l ) - B ] .U n d e r t h e r e a s o n a b l e f u n d i n g r e g u l a t i o n s , t h e a c t u a l P V B 2 m u s t e q u a l

e x p e c t e d P V B 2 i f e x p e r i e n c e e x a c t l y m a t c h e s a s s u m p t i o n s .A s s u m i n g t h at t he p r o j e c t e d b e n e f i ts B 2 , B 3 . . . . r e m a i n t h e s a m e a t t h e

e n d o f y e a r 1 a s a t t h e b e g i n n i n g , a c t u a l P V B 2 u n d e r t h e f i r s t a p p r o a c h ,w h e r e i n t e r e s t ra t e s f o r th e 1 9 8 4 v a l u a t i o n a r e 1 0 p e r c e n t f o r th e f ir s t t e ny e a r s a n d 5 p e r c e n t t h e r e a f t e r , c a n b e w r i t t e n a s :

1 !P V B 2 - B 2 + B ~ + . . .1 + i I ( I + i t ) ( l + i 2 )

A c t u a l P V B 2 u n d e r t he s e c o n d a p p r o a c h , w h e r e i n t e r e s t r a te s fo r t h e 1 9 8 4v a l u a t i o n a r e 1 0 p e r c e n t f o r t h e f i r s t n i n e y e a r s a n d f i v e p e r c e n t t h e r e a f t e r ,c a n b e w r i t t e n a s

1 1P V B 2 - - - B 2 + B 3 + . . .I + i 2 ( 1 + i 2 ) ( ! + i 3 )

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FINANCIAL ASSUMPTIONS IN PENSION PLAN VALUATIONS 357

W i th t h e s e c o n d a p p r o a c h , PVB2 = E x p e c t e d PVB 2, m e e t i n g t h e r e q u i r e -m e n t s o f t h e r e a s o n a b l e f u n d i n g r e g u l a t i o n s . T h i s is n o t t he c a s e w i th t h ef i r s t a p p r o a c h .

T h e s p e c i fi c a p p r o a c h w i l l h a v e i m p l i c a ti o n s f o r t h e d e t e r m i n a t i o n o fa c t u a r i a l g a i n s o r l o s s e s . I n t h e r e s t o f t h i s p a p e r , r e f e r e n c e s t o s e l e c t a n du l t i m a t e i n t e r e s t r a t e s w i l l m e a n c a l e n d a r s p e c i f i c v a r i a b l e i n t e r e s t r a t e s ,u n l e ss s p e c i f ie d o t h e r w i s e .B. Choosing Select and Ultimate Interest Rates

D e t e r m i n i n g s p e c i f i c v a l u e s f o r t h e s e l e c t a n d u l t im a t e i n t e re s t a s s u m p t i o ni s a m o r e c o m p l e x p r o c e s s t h a n c h o o s i n g a l e v e l i n t e r e s t a s s u m p t i o n . V a l u e smus t be as s igned t o t he i n i t i a l r a t e , t he u l t ima t e r a t e , t he s e l ec t pe r i od andt h e i n t e r i m r a t e s .

I n a n e c o n o m i c c l im a t e w h e r e p r e v a i l i n g r at es a r e m u c h h i g h e r th a n t h o s ee x p e c t e d o v e r t h e l o n g t e r m , t h e i n i t i a l r a t e c o u l d b e a f u n c t i o n o f a r e c -o g n i z e d i n d e x . A r e c e n t a v e r a g e o f th e p r i m e a s c o m p i l e d b y t h e F e d e r a lR e s e r v e o r o f M o o d y ' s l o n g - te r m c o r p o r a te b o n d y i el d s fo r h i g h q u a l it yi s sues can s e rve as t he i n i t i a l r a t e . Then t he i n i t i a l r a t e a s sumpt ion has t hea u t h o r i t y o f t h e i n d e x u s e d . T h e b u r d e n o f p r o o f w o u l d s h if t t o a n y o n em a k i n g t h e a l l e g a t i o n t h a t t h e a s s u m p t i o n d o e s n o t r e f l e c t p r e v a i l i n g r a t e s .A n a l t e r n a t e a p p r o a c h t o d e t e r m i n i n g t h e i n i t i a l i n t e r e s t r a t e w o u l d b e t ob a s e i t u p o n r e c e n t p l a n e x p e r i e n c e a n d t h e e x p e c t e d s h o r t - t e r m r a t e o fr e t u r n .

T h e c o n s i d e r a t i o n s a p p l i c a b l e t o c h o o s i n g t h e u l t i m a t e i n t e r e s t r a t e a r e t h es a m e a s i n d e t e r m i n i n g a l e v e l i n t e r e s t a s s u m p t i o n . T h e u l t i m a t e r a t e c a n b ev i e w e d a s th e s u m o f t h r e e c o m p o n e n t s : t he " r i s k l e s s " r e tu r n , th e r is kp r e m i u m f o r p o t e n t i a l l o s s o f p r i n c i p a l , a n d t h e in f l a t io n r is k p r e m i u m . T h es u m o f f i r s t t w o s o m e t i m e s i s c a l l e d t h e r e a l r a t e o f r e t u r n . H i s t o r i c a l l y ,s u c h a r a t e h a s o s c i l l a t e d w i t h i n t h e r a n g e o f 2 p e r c e n t t o 4 p e r c e n t f o rq u a l i ty i n s tr u m e n t s . A l t h o u g h r e c e n t r e al r a te s h a v e b e e n w e l l in e x c e s s o ff i v e p e r c e n t , it i s i m p o r t a n t t o n o t e th e c y c l i c a l n a t u r e o f f in a n c i a l m a r k e t s( i l l u s t r a t e d b y h i s t o r i c a l s t u d i e s r e l a t i v e t o a p e n s i o n p l a n t i m e f r a m e ) . I nt h e f i n a l a n a l y s i s , it is th e a c t u a r y ' s j u d g m e n t r e g a r d i n g f u t u r e l e v e l s o fi n f l a t i o n a n d r e a l r e t u r n s t h a t w i l l d e t e r m i n e t h e l e v e l o f t h e u l t i m a t e r a t e .

T h e M a c a u l a y d u r a t io n o f th e f u n d ' s b o n d i n v e st m e n t s m a y p r o v i d e ab a s i s f o r d e t e r m i n i n g t h e s e l e c t p e r i o d . A t c u r r e n t i n t e r e s t r a t e s , t h i s d u r a t i o nf o r a lo n g - t e r m b o n d is a b o u t o n e - t h i r d o f t h e t e r m o f t h e b o n d . A b o n dp o r t f o l i o w h i c h i n v e s t s m a i n l y i n i n v e s t m e n t s t h i r ty to f o r t y - f i v e y e a r s l o n gw o u l d h a v e a d u r a t i o n o f t e n to f i ft e e n y e a rs . A n i n v e s t m e n t s t r a te g y , e v e n

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358 FIN A N CI A L SSUMPTIONS IN PENSION PLAN VALUATIONSi f m o r e a g g r e s s i v e t h an a n i m m u n i z a t i o n s t r a te g y , c a n b e a s s u m e d t o y i e ldr e t u r n s a t l e a s t a s g o o d a s t h o s e e a r n e d o n a n i m m u n i z e d p o r t f o l i o . O n t h i sb a s i s , a n a c t u a r y w i t h a p e n s i o n f u n d i n v e s t e d s u b s t a n t i a l l y i n l o n g - t e r mf i x e d i n c o m e s e c u r it ie s c o u l d c h o o s e a s e l e c t p e r i o d o f t e n t o f i f te e n y e a r s .

T h e d i f f e r e n c e b e t w e e n t h e i n it ia l r a te a n d t h e u l t im a t e r a t e w i ll a l s o h a v ea b e a r i n g o n t h e l e n g t h o f t h e s e l e c t p e r i o d . I n t h e o r y , t h e b i g g e r t h e d if -f e r e n c e b e t w e e n t h e i n i t i a l r a t e a n d t h e u l t i m a t e r a t e , t h e l o n g e r t h e p e r i o d .

T h e a c t u a r y w h o h a s d e c i d e d u p o n t h e s e l e c t p e r i o d , t h e i n i t i a l r a t e , a n dt h e u l t i m a t e r a t e , m u s t n o w d e v e l o p i n t e r i m r a t e s . O n e c o n s i d e r a t i o n i s h o wq u i c k l y a n d s m o o t h l y t h e t r a n s i t i o n b e t w e e n t h e i n i t i a l r a t e a n d t h e u l t i m a t er a t e is t o b e m a d e . A s l o w t r a n s i t io n i s p o s s i b l e b y i n t r o d u c i n g s m a l l c h a n g e sin t h e b e g i n n i n g o f th e s e l e c t p e r i o d w i th s u c h r a t e s a p p l y i n g f o r r e l a t i v e l yl o n g e r t i m e i n t e r v a ls . C o n v e r s e l y , t h e e a r l y s e l e c t r a t e s c a n a p p l y f o r r e la -t i v e l y s h o r t p e r i o d s w i t h r e l a t i v e l y l a r g e r d i f f e r e n c e s i n s u c c e s s i v e i n t e r v e n -i n g r a t e s. O f c o u r s e , t h e f a s t e r th e t r a n s i t io n b e t w e e n t h e i n it ia l r a t e a n d t h eu l t im a t e r a t e , t h e g r e a t e r th e e f f e c t t h e u l t im a t e r a te w i l l h a v e o n t h e r e s u lt a n tl i a b i l i t y d e t e r m i n a t i o n . T h e a c t u a r y m a y d e c i d e u p o n a u n i f o r m t r a n s i t i o n .A f t e r d e t e r m i n i n g s p e c i f i c r a t e s f o r t h e f i r s t f e w y e a r s o f t h e s e l e c t p e r i o d ,h e o r s h e m a y c h o o s e r a t e s f o r t h e r e m a i n i n g p o r t i o n o f t h e s e l e c t p e r i o d i na n a r i t h m e t i c o r g e o m e t r i c p r o g r e s s i o n , m e r g i n g i n t o t h e u l t i m a t e r a t e .

T h e a s s e t v a l u a t i o n m e t h o d h a s a b e a r i n g o n t h e c h o i c e o f t h e s e l e c t r a te s .O f t e n t h e a s s et v a l u a t io n m e t h o d h a s s u b st an t ia l s m o o t h i n g p r o p e r ti e s . T h ei n t e r e s t a s s u m p t i o n i s, o f c o u r s e , t h e e x p e c t e d a c tu a r i a l r a t h e r th a n t h e m a r -k e t r a t e o f r e t u r n . T h e s m o o t h i n g t e c h n i q u e t o b e u s e d f o r d e v e l o p i n g t h ea c t u a r i a l v a l u e o f a ss e t s c a n b e a p p l i e d t o th e e x p e c t e d m a r k e t r a t e s o f r e t u rnt o d e v e l o p t h e s e l e c t i n t e r e s t a s s u m p t i o n s .

W h e n s e l e c t a n d u l t i m a t e i n t e r e s t a s s u m p t i o n s a r e u s e d f o r t h e v a l u a t i o n ,t h e s a la r y s c a l e a s s u m p t i o n n e e d s t o b e e x a m i n e d f o r c o m p a t i b i li t y w i th t h ei n t e r e s t a s s u m p t i o n s . I t i s c o m m o n t o u s e t h e s a m e i n f l a t i o n c o m p o n e n t i nt h e i n t e r e s t a n d t h e s a l a r y s c a l e a s s u m p t i o n s . I t m a y b e n e c e s s a r y t o r e v i s et h e s a l a r y s c a l e a s s u m p t i o n t h a t w a s u s e d w i t h a l e v e l i n t e r e s t a s s u m p t i o n .C. Valuation Procedures

A c t u a r i a l v a l u a t i o n s u s u a l l y a r r i v e a t a p r e s e n t v a l u e o f b e n e f i t s b y o n eo f tw o m e a n s . T h e t r a d it io n a l m e t h o d is t o us e c o m m u t a t i o n f u n c t i o n s , w h i c ha r e a p p l i e d t o p r o j e c t e d b e n e f i t s t o d e t e r m i n e t h e p r e s e n t v a l u e . W i t h t h ea d v e n t o f h i g h - s p e e d c o m p u t e r s , it h a s b e c o m e p o s s ib l e t o a d o p t a p r o c e d u r es i m i l a r t o a c a s h - f l o w p r o j e c t i o n . I n t h is c a s e , t h e a n t i c i p a t e d b e n e f i t o u t g oi n e a c h y e a r i s d e t e r m i n e d , a n d t h e s e a m o u n t s a r e t h e n d i s c o u n t e d w i t h

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FINANCIA L ASSUMPTI ONS IN PENSION PLAN VALUATIONS 3 5 9i n te r e s t. T h i s l a t te r a p p r o a c h l e n d s i t s e l f m o r e e a s i l y t o v a r i a b le i n t e r e s t r a t e s.F o r i n s t a n c e , l e t u s s u p p o s e t h a t th e v a l u a t i o n d e t e r m i n e s a p r o j e c t e d b e n e f i tp a y o u t o f B i , B2 . . . . . B ,, f o r t h e n e x t n y e a r s . T h e n , t h e c a s h - f l o w m e t h o dp r o d u c e s a P V B o f

NZ lk = I (1 + i ) k B k "T h e o n l y a l te r a ti o n t h a t n e e d s to b e m a d e t o th i s f o r m u l a t o a c c o m m o d a t e

v a r i a b l e i n te r e s t a s s u m p t i o n s is to r e p l a c e e a c h o f t h e c o e f f i c i e n t s ,i k k 1with 1II

1 + i ' s = 1 ( 1 +is)S i n c e e a c h o f t h e B k ' s h a s t o b e i s o l a t e d a n d a s e p a r a t e i n t e r e s t d i s c o u n t

f a c t o r a p p l i e d , g e n e r a l l y t h e r e w i l l b e n o d i f f i c u l t y r e f l e c t i n g t h e s e l e c t a n du l t i m a t e i n t e r e s t d i s c o u n t f a c t o r .

W i th r e g a r d t o t h e c o m m u t a t i o n f u n c t i o n a p p r o a c h t o a c tu a r ia l v a l u a t i o n s ,t h e r e a p p e a r s t o b e s o m e a d d e d c o m p l e x i t y w h e n a s e l e c t a n d u l t i m a t e i n -t e r e s t a s s u m p t i o n i s e m p l o y e d . T h i s i s b e c a u s e t h e r e i s a n e w c o m m u t a t i o nf u n c t i o n f o r e a c h a t t a i n e d a g e . T h i s i s n o t n e c e s s a r i l y a s e r io u s d r a w b a c k .I t i s p o s s i b l e t o s o r t a l l o f t h e v a l u a t i o n d a t a b y a t t a i n e d a g e a n d c a l c u l a t ec o m m u t a t i o n f u n c t i o n s b a s e d u p o n a t t a in e d a g e . F o r a v a l u a ti o n w i th e m -p l o y e e s r a n g i n g f r o m 1 7 t o 6 5 , t h is m e a n s t h e c a l c u l a ti o n o f f o r t y - n i n ec o m m u t a t i o n ta b l e s ra t h e r t h a n o n e . H o w e v e r , w i th th e s p e e d o f t o d a y ' sc o m p u t e r s , t h e a d d e d c o s t f o r t h is t y p e o f v a l u a t i o n i s g e n e r a l l y n o t s i g n i f -i c a n t . I n a d d i t i o n , t h e c o m p u t e r c o s t s a r e s u c h a s m a l l p o r t io n o f th e t o t a lt h a t e v e n a f a i r ly l a r g e i n c r e a s e i n t h e c o m p u t e r c o s t is s ti ll a m i n o r i n c r e a s ei n t h e c o s t o f t h e v a l u a t i o n . T h u s , i t a p p e a r s f e a s i b l e t o i n t r o d u c e s e l e c t a n du l t i m a t e f i n a n c i a l a s s u m p t i o n s w i t h e i t h e r o f th e t w o v a l u a t i o n p r o c e d u r e s .D . Am o r t iza t i o n o f U n f u n d e d Ac t u a r i a l L i a b il it ie s

T h e r e a r e a n u m b e r o f a p p r o a c h e s w h i c h c o u l d b e t a k e n i n a m o r t i z i n gu n f u n d e d a c t u a r i a l l ia b i l it ie s , b o t h f o r m i n i m u m f u n d i n g s t a n d a r d p u r p o s e sa s w e l l a s f o r a c t u a l fu n d i n g p u r p o s e s . T h r e e s u c h a p p r o a c h e s a r e :1 . L e v e l a n n u a l i n s t a l l m e n t s d e t e r m i n e d u s i n g t h e s e l e c t a n d u l t i m a t e in t e r -

e s t r a t e s . T h e a m o r t i z a t i o n s c h e d u l e w o u l d a l s o u s e t h e y e a r - b y - y e a rin t e res t r a t e s .

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36 0 FINA NCIAL ASSUMPTIONS 1N PENSION PLAN VALUA TIONS

2 . L e v e l a n n u a l i n s ta l l m e n t s d e t e r m i n e d u s i n g t h e s e l e c t a n d u l t i m a t e i n t e r-e s t r a t e s . H o w e v e r , th e a m o r t i z a t i o n s c h e d u l e w o u l d u s e a n a v e r a g e i n -t e r e s t r a t e d e r i v e d f r o m t h e r e l a t i o n s h i p o f t h e l e v e l i n s t a l lm e n t s a n d t h eU n f u n d e d A c t u a r i a l L i a b i l i t y ( U A L ) .

3 . A n n u a l i n s t a l l m e n t s w h i c h w o u l d r e m a i n l e v e l fo r t he d u r a t i o n o f a p a r -t i c u l a r i n t e r e s t r a t e a s s u m p t i o n . W h e n a n e w s e l e c t i n t e r e s t r a t e ( o r t h eu l t i m a t e r a t e ) b e c o m e s e f f e c t i v e , a n e w l e v e l a m o u n t w o u l d b e d e t e r -m i n e d u s i n g t h e r e m a i n i n g u n a m o r t i z e d U A L , t h e n u m b e r o f y e a r s re -m a i n i n g , a n d t h e n e w i n te r e s t r a t e .

I n t h e e x h i b i t s w h i c h f o l l o w , a m o r t i z a t i o n s c h e d u l e s o f 1 0 , 1 5 , a n d 3 0y e a r d u r a t i o n s a r e s h o w n f o r t h e t h r e e a p p r o a c h e s n o t e d . E x h i b i t s 1 , 2 , a n d3 h a v e a s s u m e d i n t e r e s t r a t e s o f 1 0 p e r c e n t f o r t e n y e a r s a n d 5 p e r c e n tt h e r e a f t e r , w h i l e e x h i b i t s 4 , 5 , a n d 6 h a v e a s s u m e d a n i n t e r e s t r a t e o f 1 0p e r c e n t f o r t h e f i r s t y e a r , g r a d i n g d o w n b y 1 /2 p e r c e n t p e r y e a r t o 5 p e r c e n tf o r y e a r s e l e v e n a n d l a t e r .

I t s h o u l d b e n o t e d t h a t i n t h e f i r s t a p p r o a c h , t h e U A L i n c r e a s e s d u r i n gt h e f i r s t t e n y e a r s , s i n c e i n t e r e s t r e q u i r e m e n t s a r e n o t b e i n g m e t . A p p r o a c h2 c o r r e c t s t h i s p r o b l e m b u t i n t r o d u c e s a n o t h e r . A c c o r d i n g t o R e g u l a t i o nS e c t i o n 1 . 4 1 2 ( c ) ( 3 ) - 1 o n r e a s o n a b l e f u n d i n g m e t h o d s , t h e p r e s e n t v a l u e o ff u t u r e b e n e f i t s m u s t e q u a l t h e p r e s e n t v a l u e o f f u t u r e n o r m a l c o s t s , p l u su n a m o r t i z e d p o r t i o n s o f a m o r t i z a b l e b a s e s , p l u s a s s e ts , l e s s c r e d i t b a l a n c e .S i n c e a p p r o a c h 2 r e d u c e s t h e u n a m o r t i z e d b a s e s a t a d i f f e r e n t i n t e r e s t r a t et h a n i s u s e d f o r t h e o t h e r p i e c e s , t h e e q u a t i o n w i l l n o l o n g e r b a l a n c e . A p -p r o a c h 3 s o l v e s t h e p r o b l e m s i n t h e s e f i r s t t w o a p p r o a c h e s , b u t d o e s n o t u s el e v e l i n s t a l lm e n t s . T h i s i s a p r o b l e m b e c a u s e s e c t i o n 4 1 2 ( b ) o f t h e I n te r n a lR e v e n u e C o d e r e q u i r e s t h a t " a m o u n t s n e c e s s a r y t o a m o r t i z e i n e q u a l a n n u a li n s t a l l m e n t s " b e u s e d in f u n d i n g s t a n d a r d a c c o u n t c a l c u l a t i o n s . T h i s s u g -g e s t s t h a t t h e f i r s t a p p r o a c h w o u l d b e t h e o n l y a l l o w a b l e m e t h o d f o r m i n i -m u m f u n d i n g s t a n d a rd p u r p o s e s . S i m i l a r l y , u n d e r t h e v a ri o u s p r o v in c i a lr e g u la t io n s i n C a n a d a , " s p e c i a l p a y m e n t s c o n s is ti n g o f e q u a l a n n u a l a m o u n t s "w o u l d b e t h e acceptable a p p r o a c h .

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$100.0O097,20294.12490,73987,01482.91878,41273.45568,00262.00555,40745,37934.85023.79512,1870100,000

am 1oak + v]loq~ ay 5~Maximum FundingUALYear Jan. I

1 $ I O 0 , O ~ X )2 93,7253 86.8234 79,23 I5 70.8806 61,6937 51.5888 40,4729 28,245I0 14,795I1 0100.000tliO" lOq

Payment+$ 12,798

12.7980$191,970

Payment~$ 16,275

16,2750

$162,750

361

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EXHIBIT 2~;SE OF SELECT AND ULTIMATEINTEREST RATES OF 10 PERCENT FOR TEN YEARS ANt)5 PERCENT TllEREAFTER FOR MINIMUM FUNDINGFIFTEEN YEAR FUNDINGAND MAXIMUM FUNDING

Approach 2 - -Level Annual Payment: Amortization Schedule UsingAverage Effective Interest RateMinimum Funding*UAL

Year Jan. II $ 1 0 0 , 0 0 02 99,1643 98,2594 97,2795 96,2176 95,0687 93,8238 92,4749 91,01410 89,434I1 87,72012 85,86813 83,85714 81,68215 79,32616 76,77517 74,01218 71,02019 67,78020 64,27121 ~,47122 56,355

23 51,89824 47,07125 41,84426 36,18327 30,05228 23,41229 16.22230 8,43531 0* i = 8.2972 pe~ em

Payment$ 9.133

15 Year Funding+UALYear Jan. I1 $ 1 0 0 , 0 0 0

2 96,7343 93.1564 89,2385 84,9466 8(I.2457 75,0968 69,4569 63,27810 56,512I I 49.10012 40,98213 32.09114 22,35215 I 1,68416 0#i = 9.5319

9.1330273.990

YearMaximum Funding

UALJan. II $ 1 0 0 . 0 0 02 93.7253 86,8234 79,2315 70,8806 61.6937 51,5888 40,4729 28,245

IO 14.795II 0

Payment+$ 12.798

12.7980$191.970

Payment$ 16,275I

6.2750$162.75(I

362

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E X H I B I T 3USE OF SELECT AND ULTIMATE

INTEREST RATES OF 10 PERCENT FOR TEN YEARS AND5 PERCENT THEREAFrER FOR MINIMUM FUNDING,FIFTEEN YEA R FUNDING AND M AXIMUM FUNDING

A p p r o a c h 3 - -L e v e l A n n u a l P a y m e n t f o r D u r a t io n o f I n t e re s t R a t e ;A m o r t i z a ti o n S c h e d u l e U s i n g S e l e c t R a t e s i n E f fe c t b y Y e a rM i n i m u m F u n d in gU A LY e a r J a n . 1

1 $ 1 0 0 , 0 0 02 9 9 , 3 9 23 9 8 , 7 2 34 9 7 , 9 8 85 9 7 , 1 7 96 9 6 . 2 8 97 9 5 , 3 0 98 9 4 . 2 3 39 9 3 , 0 4 81 0 9 1 , 7 4 5I1 90 ,3111 2 8 7 , 5 8 01 3 8 4 . 7 1 214 81 ,7011 5 7 8 . 5 3 91 6 7 5 , 2 1 91 7 7 1 , 7 3 318 68,O731 9 6 4 , 2 3 02 0 6 0 , 1 9 52 1 5 5 , 9 5 82 2 5 1 , 5 0 92 3 4 6 , 8 3 82 4 4 1 , 9 3 32 5 3 6 , 7 8 32 6 3 1 , 3 7 52 7 2 5 , 6 9 72 8 1 7 , 7 3 52 9 1 3 . 4 7 53 0 6 , 9 0 231 0

1 0 0 , 0 0 0

9 0 , 3 1 1ay615~

P a y m e n t$ 1 0 . 6 0 8 "

1 0 , 6 0 87 , 2 4 7 * *

7 . 2 4 70 *$ -~0 -

1 5 Y e a r F u n d i n gU A LY ear J an . 11 $ 1 0 0 , 0 0 02 9 6 , 8 5 33 9 3 , 3 9 14 8 9 , 5 8 25 8 5 , 3 9 36 8 0 , 7 8 57 7 5 , 7 1 68 7 0 , 1 4 09 6 4 , 0 0 71 0 5 7 , 2 6 01 1 4 9 , 8 3 91 2 4 0 , 8 2 0

1 3 3 1 , 3 4 91 4 2 1 , 4 0 515 10 ,96416 01 0 0 , 0 0 0f p = - -a i 3 - 1 l o ~

4 9 , 8 3 9,p=M a x i m u m F u n d in gU A LY e a r J a n . 1

I $ 1 0 0 , 0 0 02 9 3 , 7 2 53 8 6 , 8 2 34 7 9 . 2 3 15 7 0 , 8 8 06 6 1 , 6 9 37 5 1 , 5 8 88 4 0 , 4 7 29 2 8 , 2 4 5I 0 14 ,79511 0

P a y m e n t$ 1 3 , 1 4 7 t

1 3 . 1 4 711,512.~

I 1 . 5 1 2$ 1 8 9 . 0 3 0

P a y m e n t$ 1 6 , 2 7 5

1 6 , 2 7 50$ 1 6 2 , ~ O

363

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YearI234567

89I0I11213141516171819202122232425262728293O31

EXHIBIT 4USE OF SELECT RATES or: 10 PERCEN'IGRADING [)OWN ARITIIMETICALLYTO 5 PERCENTOVER TEN YEARS FOR MINIMUM FUNDING.FIFTEEN YEAR FUNDINGANt) MAXIMUM FUNDINGApproach I -- Level Annual PaymenlAmortization Schedule UsingSelect Rates in Effect by Year

Minimum FundingUALJan. I$ 100,0(~)101,962103,611104,898105,777106,201106,129105,520104,341102.564100,16797,138

93,95790.61787,11083,42879,56275,5O271,24066,76462,06557.13051,94946,5(1940,79634.79928,50121,88814,9457,6540

Payment Year$ 8,038 12

3456789I0II1213141516

Ycar

15 Year FundingUALJan. I$ 100,0(~)98.34996,04(I

93.03289.28984.78079,48773.4(X)66,51958.85950,44541.31531,73021.665[ 1,0960

Maximum FundingUALJan. II $ 1 0 0 . 0 0 02 94,6823 88,3594 80,9948,038 5 72,5616 63,048$ 241.140 7 52,4598 40,8139 28,148

IO 14,51911 0

Payment$ I ,651

1 ,651$ 174,765

Payment$ 15,318I5.318

153,180

364

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EXHIBIT 5USE OF SELECT RATES OF 10 PERCENTGRADING DOWN ARITHMETICALI.YTO 5 PERCENT OVERTEN YEARS FOR MINIMUM FUNDING.FIF~I"EEN YF.AR FUNDINGAND MAXIMUM FUNDINGApproach 2 - - Level Annual PaymentAmortization Schedule Using Average Efl~cclive Interest Rate

Minimum Funding*UALYear Jan. 11 $ 100,0(~2 98.9363 97.7984 96,5815 95.2796 93,8867 92,3968 90,8039 89,09710 87,27311 85,32212 83,235

13 81,00214 78,61315 76,O5916 73.32517 70,40118 67,27419 63,92820 60.34821 56,51922 52,42323 48,04224 43,35425 38,34126 32.97727 27,23828 21,10129 14,53530 7,51031 0

Payment$ 8,038

8 , 0 3 8$ 241 ,]T6

*i ~ 6.9741 percent equivalent interest

15 Year FundingfUALYear Jan. I PaymcntI $ 1 0 0 , 0 0 0 $ 1 1 . 6 5 12 96.3043 92,3144 88.0(175 83.3576 78,3377 72.9188 67,0689 60.75810 53.935I 1 46,57412 38.628

13 30.05014 20.79015 10.793 I 1.65116 0 $ 174.7657.9552 percent equivalent interes,~

Maximum Funding~UALYear Jan. I Payment1 $ 100,000 $ 15,3182 93,2953 86,0134 78,1035 69,5146 60.1837 50,0498 39,0439 27,08710 14.103 15.318II 0 $ 153.180

$i = 8.6312 percent equivalent interest

365

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YearI

2345678910II1213

141516171819202122232425262728293031

EXHIBIT 6USE OF SELECT RATES OF lO PERCENTGRADING DOWN ARITHMETICALLYTO 5 PERCENT OVERTEN YEARS FOR MINIMUM FUNDING.FIFTEEN YEAR FUNDINGAND MAXIMUM FUNDING

Approach 3 - - Level Annual Payment for Duration o f Interest RateAmortization Schedule Using Select Rates in Effect by YearMinimum FundingUALJan. I

$ 100,00099.39298.66Xl97.78696.75495.54494,13992,52190,67488,58486,23983,63180,89378.01874,99971.82968.50065,00561,33557.48253.43649.18844,72740,04335,12529,96124,53918.84612.8686,59(I(I

15 Year FundingUALPayment Year Jan. I$ 10.608 I $ 100,0t~

10,174 2 96,8539.753 3 93,2639,344 4 89,2(~8.950 5 84,6378,571 6 79,5528.208 7 73.9287,861 8 67,7567.530 9 61.0327,217 10 53.7616.920 II 45.95612 37,63913 28.90614 19,73615 10,10816 0

6.920$ 22~.616

YearMaximum FundingUAL

Jan. I

Payment$ 13,147

12.79112,45712.14511,85611.59011,34711.12810,9331(I.7621(I,615

1(I,615$ 171,231

PaymentI $ I00 ,(~ ) $ 16.2742 93.726 15,9533 86,677 15.6604 78,818 15,3995 70,119 15.1686 60.561 14,9687 50.135 14,8018 38.843 14,6669 26.702 14,564lO 13,740 14.995

11 0 0$ 152.448

366

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FINANCIAL ASSUM PTIONS IN PENSION PLA N VALUATIONS 36 7E. Determination of Option Factorsl

A n o t h e r t e c h n i c a l i s s u e w h i c h n e e d s t o b e a d d r e s s e d i s t h e d e t e r m i n a t i o no f o p t i o n f a c t o r s u s i n g s e l e c t a n d u l t i m a t e i n t e r e s t r a t es . I n t h is d i s c u s s i o n ,it i s a s s u m e d t h a t th e p e n s i o n p l a n m a k e s a l l o w a n c e f o r o p t i o n a l f o r m s o fr e t i r e m e n t b e n e f i t b a s e d o n a c t u a r i a l e q u i v a l e n c e t o t h e n o r m a l f o r m .

I n th e c a s e w h e r e t h e s e l e c t a n d u l t im a t e r a t e s a r e 1 0 p e r c e n t f o r t e n y e a r sa n d 5 p e r c e n t t h e r e a f t e r , w h a t r a t e s s h o u l d b e u s e d t o d e t e r m i n e o p t i o nf a c t o r s in t he s e c o n d y e a r ? S h o u l d 1 0 p e r c e n t f o r n in e y e a r s a n d 5 p e r c e n tt h e r e a f t e r b e u s e d , o r s h o u l d t h e t e n y e a r s e le c t p e r io d b e r e ta i n e d ? I t w o u l ds e e m t h a t i f a c t u a r i a l a s s u m p t i o n s a r e n o t c h a n g e d , t h e n it is a p p r o p r i a t e t ou s e a s h o r t e r s e l e c t p e r i o d a s t i m e e l a p s e s f o r p u r p o s e s o f d e t e r m i n i n g o p t i o nf a c t o r s .

T h e f o l l o w i n g t a b le s h o w s t h e lu m p - s u m v a l u e o f $ 1 p e r m o n t h p a y a b l ef r o m a g e 6 5 b a s e d o n t h e 1 9 7 1 G A M t a b l e . T h e u l t i m a t e i n t e r e s t r a t e i s 5p e r c e n t a n d t h e s e l e c t p e r i o d i s g r a d u a l l y r e d u c e d f r o m t e n y e a r s t o z e r oy e a r s .

S e l e c t P e r i o d L u m p - S u m ($ 1 p e r m o n t h )10 91 .619 9 2 . 7 5

8 9 4 . 1 27 9 5 . 7 66 9 7 . 7 25 1 0 0 . 0 44 102 .793 106 .012 1 0 9 . 7 91 1 1 4 . 2 00 119 .23

T h e l u m p - s u m v a l u e i n c r e a s e s s t e a d i ly , r a i s in g t h e q u e s t io n o f e q u i t y i np l a n p a r t i c i p a n t s ' o p t i o n a l b e n e f i t s . T h i s q u e s t i o n i s b r o u g h t i n t o s h a r p e rf o c u s w h e n c o n s i d e r i n g t w o e m p l o y e e s w h o s e r e t i r e m e n t s a t a g e 6 5 a r e o n em o n t h a p a r t w i th o n e e m p l o y e e r e t ir i n g b e f o r e a n d t h e o t h e r re t ir i n g a f t e rt h e v a l u a t i o n d a t e .

~Sev e r a l q u es t io n s a r i se r eg a r d in g th e ap p r o p r i a t e ap p l i ca t io n o f ex i s t i n g r eg u la t io n s to o p t io nf ac to r s ca lcu la t ed u s in g se l ec t an d u l t ima te in t e r es t r a te s . To c l a r i fy su ch i s su es , t h e Pen s io n C o m-mi t t ee su b mi t t ed a l e t t e r t o t h e I n t e r n a l R ev en u e Se r v ice r eq u es t in g g u id an ce . Th e l e t t e r an d th eI R S r e sp o n se a r e p u b l i sh ed in th e ap p en d ix .

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368 F I N A N C I A L A S S U M P T I O N S I N P E N S I O N P L A N V A L U A T I O N SFor options other than lump-sum, the difference between select and ulti-

mate rates and level rates may not be material enough to warrant the extracomplexity. For example, compare the following factors at age 65 using the1971 GAM Table.

Life only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .L ife guaranteed f ive years . . . . . . . . . . . . . . . . . . . . . . . . . .L ife guaranteed ten years . . . . . . . . . . . . . . . . . . . . . . . . . . .Joint and 100 percent survivor(spouse three years younger) . . . . . . . . . . . . . . . . . . . . . .Joint and 50 percent survivor(spouse three years younger) . . . . . . . . . . . . . . . . . . . . . .

Factor For Converting From Life OnlySelect and Ultimate

1.0000.9777.92077566.8614

Ultimate Only1.0000.9760.9121

.7216

.8383

Other important considerations are provisions of the Internal RevenueCode. Code Section 41 l(d)(6) requires that the accrued benefit of a partic-ipant shall not be decreased by an amendment of the plan. Revenue Rulings79-90 and 81-12 give specific advice on the effect of changes in actuarialassumptions on accrued benefits.Revenue Ruling 79-90 states that a defined benefit plan must specify theactuarial assumptions used to compute the amounts of optional benefits whichare "actuarially equivalent" in order for the benefits to be definitely deter-minable. If the actuarial assumptions stated in the plan for determination ofoptional benefits are later modified by a plan amendment, the accrued ben-efits resulting from the use of the new option factors must satisfy the anti-cutback and grandfathering rules. Revenue Ruling 81-12 describes two methodsof stating the assumptions for determination of optional benefits: adoptionof a fixed standard which requires a plan amendment to change the optionfactors, and adoption of a variable standard which permits the underlyingassumptions for the option factors to float with some outside source, suchas the prime rate.

Thus, select and ultimate assumptions could be stated in one of the fol-lowing forms:Fixed Standards1. 10 percent for the next ten years, and 5 percent thereafter.2. 10 percent for years 1983 to 1992 and 5 percent thereafter.

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FINANCIAL ASSUMPTIONS IN PENSION PLA N VALUATIONS 36 9Variable Standards3 . P r i m e r a te i n e f f e c t o n J a n u a r y 1 o f t h e c a le n d a r y e a r o f r e t i r e m e n t f o r

t h e n e x t t e n y e a r s a n d 5 0 p e r c e n t o f s u c h p r i m e r a t e t h e r e a f t e r .4 . P r i m e r a te i n e f f e c t o n J a n u a r y i o f t he c a l e n d a r y e a r o f r e ti r e m e n t u n ti l

1 9 9 2 a n d 5 0 p e r c e n t o f s u c h p r i m e r a te t h e r e a f te r .I f a f i x e d s t a n d a r d is u s e d , a s e t o f o p t i o n f a c t o r s i s p r o d u c e d w h i c h w i l l

n o t c h a n g e w i t h o u t a p l a n a m e n d m e n t . T h i s a p p r o a c h p r o v i d e s a se t o f o p t io nf a c t o r s w h i c h w i l l r e m a i n c o n s t a n t ( o r a t l e a st p r e d i c t a b l e ) f r o m y e a r t o y e a r ,e l i m i n a t i n g t h e n e e d f o r f r e q u e n t r e c a l c u l a t i o n o f t h e o p t i o n f a c t o r s a n dp e r m i t t i n g c o n s i s t e n t e s t i m a t e s o f f u t u r e b e n e f i t s f o r p l a n p a r t i c i p a n t s .F i x e d s t a n d a r d s , h o w e v e r , w i l l n e e d t o b e r e v i e w e d f r e q u e n t l y i n o r d e rt o f o l l o w c h a n g i n g e c o n o m i c c o n d i ti o n s . W h e n a c h a n g e i s m a d e , s i g n if i c a n td i f f e r e n c e s m a y o c c u r a n d t h e a p p l ic a t i o n o f t h e R e v e n u e R u l i n g 8 1 - 1 2 r u l e sm a y r e s u l t i n t h e g r a n d f a t h e ri n g o f m a n y a c c r u e d b e n e f i ts . I f fr e q u e n t c h a n g e sa r e n o t a n t i c i p a t e d , i t w o u l d s e e m t h a t a s i m p l e i n t e r e s t a s s u m p t i o n w o u l db e m o r e a p p r o p r i a t e t h a n a f i x e d s e l e c t a n d u l t i m a t e s t a n d a r d .

A v a r i a b l e s e l e c t a n d u l t i m a t e s t a n d a r d c a n b e d e s i g n e d t o f o l l o w a r e l i a b l em a r k e t i n d e x . O n c e a s u i t a b l e i n d e x i s f o u n d , t h e o p t i o n f a c t o r s w i l l a u t o -m a t i c a l l y r e f l e c t c u r r e n t m a r k e t c o n d i t i o n s . T h i s i s a p a r t i c u l a r ly i m p o r t a n tc o n s i d e r a t i o n w h e n t h e p l a n p r o v i d e s f o r a l u m p - s u m o p t i o n , a n d t h e p l a ns p o n s o r w a n t s t o r e f l e c t c u r r e n t i n t e r e s t r a t e s i n t h e c a l c u l a t i o n . A v a r i a b l es t a n d a r d h a s t h e a d d e d a d v a n t a g e t h a t w h e n t h e a u t o m a t i c c h a n g e s o c c u r ,t h e r e i s n o n e e d t o a p p l y t h e R e v e n u e R u l i n g 8 1 - 1 2 r u l e s . E v e n t h o u g h t h ev a r i a b l e m e t h o d c a n r e s u l t in o p t i o n f a c t o r s t h a t d e c r e a s e , t h e c u t b a c k r u l e so r g r a n d f a t h e r i n g a r e n o t t r i g g e r e d u n l e s s a p l a n a m e n d m e n t t h a t c h a n g e st h e o u t s i d e s o u r c e r e s u l t s in a d e c r e a s e i n c u r r e n t l y a p p l ic a b l e o p t i o n f a c t o r s .

T h e m a i n d i s a d v a n t a g e s o f v a r ia b l e s t a n d ar d s a r e t h e f re q u e n t r e c a l c u la -t io n o f o p t i o n f a c t o r s a n d t h e u n p r e d i c t a b i l i t y o f b e n e f i t s . W i th t h e a v a i l a -b i l i t y o f s o p h i s t i c a t e d c o m p u t e r p r o g r a m s , t h e f r e q u e n t r e c a l c u l a t i o n s a r en o t o f a s m u c h c o n c e r n a s t h e y w e r e p r e v i o u s l y . H o w e v e r , i f th e n e c e s s a r yp r o g r a m s a r e n o t r e a d i l y a v a i l a b l e , t h e y w o u l d s t il l b e a m a j o r c o n s i d e r a t i o n .T h e u n p r e d i c t a b i l i t y o f f u t u r e b e n e f i t s i s a m o r e d i f f i c u l t p r o b l e m t o o v e r -c o m e . C o m m u n i c a t i o n w i t h p la n p a r t i c ip a n t s w i ll b e n e e d e d t o e x p l a i n t h att h e v a l u e o f t h e i r o p t i o n a l b e n e f i t s ( p a r t i c u l a r l y lu m p s u m s ) w i ll d e p e n d o nt h e v a l u e o f th e c h o s e n i n d e x a t t h e t im e o f r e ti r e m e n t . T h i s p r o b l e m c a nb e l e s s e n e d s o m e w h a t b y p r o v i d i n g t h a t t h e i n d e x w i l l n o t c h a n g e m o r ef r e q u e n t l y th a n o n c e a y e a r . T h u s , o n c e t h e v a l u e s ar e s et f o r a g iv e n y e a r ,a c c u r a t e p r o j e c t i o n s c a n b e m a d e f o r t h a t y e a r .

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37 0 FINANCIAL ASSUMPTIONS IN PENSION PLAN VALUATION S

F. Effect ~f the Use ~" Select and Ultimate Assumptions on Selection ~"Funding MethodsA s s u m p t i o n s a b o u t p r io r p e r i o d s h a v e n o b e a r in g o n c u r r e n t r e su l ts u n d e r

the majo r i t y o f ac tua r ia l cos t me thods . Un der t he acc rued benef i t cos t me thod ,f o r e x a m p l e , t h e c a l c u l a t i o n s a r e b a s e d o n a c c r u e d b e n e f i t s w h i c h a r e in -d e p e n d e n t o f th e a c t u a r ia l a s s u m p t i o n s . T h i s i n d e p e n d e n c e is a l so a c h a r -a c t e r i s t i c o f t h e a g g r e g a t e m e t h o d , t h e p r o j e c t e d u n i t c r e d i t s e r v i c e p r o r a t am e t h o d a n d t h e a t t a i n e d a g e n o r m a l m e t h o d .

T h i s i n d e p e n d e n c e i s n o t c h a r a c t e r i s t i c o f a l l c o s t m e t h o d s . U n d e r t h ee n t r y a g e n o r m a l c o s t m e t h o d , t h e p a r t i ti o n o f p l an c o s t s b e t w e e n p r i o r a n df u t u r e p e r i o d s i s a f u n c t i o n o f a s s u m p t i o n s a b o u t p r i o r e x p e r i e n c e . T h en o r m a l c o s t i s d e t e r m i n e d a s a l e v e l p e r c e n t a g e o f p a y o r a l e v e l d o l l a ra m o u n t o v e r b o t h p a s t a n d f u t u r e p e r i o d s t h a t w i ll a c c u m u l a t e t o th e n e e d e ds u m a t r e t i r e m e n t . T h i s r e q u i r e s a n i n t e r e s t r a t e a s s u m p t i o n ( a n d a s a l a r yi n c r e a s e a s s u m p t i o n f o r p a y - r e l a t e d f u n d i n g ) a p p l i c a b l e t o p r i o r p e r i o d s a sw e l l a s f u t u r e p e r i o d s .

W h a t r a t e s a n d a s s u m p t i o n s a r e a p p r o p r i a t e f o r p a s t p e r i o d s ? A l t e r n a t i v e si n c l u d e ( a ) u l t i m a t e r a t es o n l y ; ( b ) t h e s e l e c t r at e s a s to e x p e r i e n c e a n t i c i p a t e df r o m p r i o r v a l u a ti o n s ; o r ( c ) s o m e o t h e r i n d e p e n d e n t s e t o f a s su m p t i o n s .W h i l e ( a ) o r ( c ) m i g h t b e e a s y t o a p p l y , t h e y w o u l d i n t r o d u c e a s y s t e m a t i ca c t u a r i a l g a i n o r l o s s f r o m o n e v a l u a t i o n t o t h e n e x t . F o r p l a n s s u b j e c t t ot h e m i n i m u m f u n d i n g s t a n d a r d s o f E R I S A , t hi s c o u l d r e s u l t i n a te c h n i c a lv i o l a t io n o f r e a s o n a b l e f u n d i n g r e g u l a ti o n s . O n t h e o t h e r h a n d , t h e e f f e c t o ft h i s sys t emat i c ga in o r l o s s i s t o sh i f t cos t s be tween acc rued ac tua r i a l l i a -b i l i t i e s a n d f u t u r e n o r m a l c o s t s r a t h e r t h a n t o i n c r e a s e o r d e c r e a s e t o t a le x p e c t e d p l a n c o s t s . I t m i g h t h a v e o n l y a n i m m a t e r ia l e f f e c t o n t h e c u r r e n tl e v e l o f p l a n c o n t r i b u t i o n r e q u i r e m e n t s o r o n t h e i n c i d e n c e o f p l a n c o s t sf r o m y e a r t o y e a r . U s e o f th e u l ti m a t e r a te f o r p a s t p e r io d s w o u l d c o m ec l o s e r to t h e c o m m o n l y u s e d a p p r o a c h . I f t h e a ss u m p t i o n f o r sa l ar y i n c r e a sew e r e 1 0 p e r c e n t f o r t h e n e x t f iv e y e a r s a n d 5 p e r c e n t t h e r e a f t e r , t h e 5 p e r c e n tu l t i m a t e r a t e c o u l d b e a p p l i e d t o p r i o r p e r i o d s . T h e a s s u m p t i o n w o u l d t h e nb e e x p l a i n e d a s b e i n g a l o n g - t e r m , a l l - p e r i o d r a te o f 5 p e r c e n t , w i th a na d j u s t m e n t f o r th e n e x t f i v e y e a r s o f a n a d d i t i o n a l 5 p e r c e n t t o r e f l e c t s h o r t-t e r m e x p e c t a t i o n s . I t i s p o s s i b l e t h a t a s s e l e c t a n d u l t i m a t e a s s u m p t i o n s g a i ng r e a t e r r e c o g n i t i o n , o t h e r p r a c t i c a l a p p r o a c h e s w i l l b e d e e m e d a c c e p t a b l eb y t h e r e g u l a t o r y a u t h o r i t i e s .G. Numerical Illustrations

ASSUMPTIONST h e f o l l o w i n g t a b l e s i l l u s t r a t e t h e e f f e c t o f e x p e r i e n c e o n c o n t r i b u t i o n

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FINAN CIAL ASSUMPTIONS IN PENSION PLAN VALUATI ONS 371

p a t te r n s u n d e r d i f f e r e n t b e n e f i t f o r m u l a s a n d t w o d i f fe r e n t c o s t m e t h o d sw h e n e i t h e r l e v e l o r s e l e c t a n d u l t i m a t e i n t e r e s t a s s u m p t i o n s a r e c h o s e n t ov a l u e t h e p la n . F o u r d i f f e r e n t b e n e f i t f o r m u l a s w e r e s t u d i e d u n d e r f o u r d i f -f e r e n t c o m b i n a t i o n s o f v a l u a ti o n a s s u m p t i o n s a n d e x p e r i e n c e r a te s . C o n t r i-b u t i o n r a t e s a s a p e r c e n t o f p a y r o l l w e r e p r o d u c e d u n d e r b o t h t h e e n t r y a g en o r m a l a n d a g g r e g a t e c o s t m e t h o d s . T h e b e n e f i t f o r m u l a s s t u d i e d w e r e a sf o l l o w s :

F o r m u l a l 1 p e r c e n t o f fi n a l f i v e y e a r a v e r a g e p a y t im e s y e a r s o f s e r v ic e( T a b l e s ! a n d 2 ) .

F o r m u l a 2 I p e r c e n t o f c a r e e r a v e r a g e p a y ti m e s y e a r s o f s er v i ce ( T a b l e s3 a n d 4 ) .F o r m u l a 3 $ 1 0 p e r m o n t h p e r y e a r o f s e r v i c e (T a b l e s 5 a nd 6 ).F o r m u l a 4 1 p e r c e n t o f f in a l f iv e y e a r a v e r a g e p a y m i n u s 1 p e r c e n t o f

p r i m a r y S o c i al S e c u r i t y t im e s y e a r s o f se r v i c e ( T a b le s 7 a n d8) .

T o s i m p l i f y c a l c u l a t i o n s , t h e p l a n p o p u l a t i o n w a s c h o s e n t o h a v e n o r e t i r e dl iv e s . T h i s i s n o t e x p e c t e d to m a t e r i a l l y a f f e c t t h e c o n c l u s i o n s . T h e a v e r a g ea c t iv e a g e w a s 3 8 a n d t he a v e r a g e a m o u n t o f p a s t s e rv i c e w a s tw e l v e y e a r s .T h e a v e r a g e s a l a r y w a s $ 2 4 , 8 7 3 . T h e i n it ia l le v e l o f a s s e ts w a s a s s u m e d t oe q u a l 2 5 p e r c e n t o f t h e p r e s e n t v a l u e o f f u t u r e b e n e f i ts . E a c h t a b l e d i s p l a y sc o n t r i b u t io n r e q u i r e m e n t s f o r th e n e x t te n y e a r s . T w o d i f f e r e n t a s s u m p t i o nse t s were u sed i n t he ana l ys i s :

S e t 1 1 0 p e r c e n t i n t e r e s t th e f i r st y e a r , d e c r e a s i n g 1 p e r c e n t p e r y e a r toa n u l t i m a t e r a t e o f 6 p e r c e n t .

S e t 2 8 p e r c e n t i n t e r e s t in e v e r y y e a r .T h e a s s u m e d r a t e o f s a la r y i n c re a s e w a s 1 p e r c e n t l e ss t ha n th e a s s u m e di n t e r e s t r a t e in e v e r y i n s t a n c e . U n d e r th e e n t r y a g e n o r m a l m e t h o d , t h e i n it ia l

u n f u n d e d a c c r u e d l ia b i li ty w a s f u n d e d o v e r a p e r i o d o f t w e n t y - f i v e y e a r s .T h e i n it ia l p a y r o l l f o r a c ti v e e m p l o y e e s w a s $ 2 4 , 8 7 2 , 7 6 9 . S e c t io n 4 1 5 l im i t sw e r e i g n o r e d f o r p u r p o s e s o f t h e s e i l l u st r a ti o n s .

OBSERVATIONSC e r t a i n o b s e r v a t i o n s t h a t m a y b e m a d e f r o m t h e t a b l e s a r e i n d e p e n d e n t

o f t h e m e t h o d o l o g y u s e d f o r t h e v a l u a t io n a s s u m p t i o n s b u t a r e c h a r a c te r i s ti co f th e c o s t m e t h o d , b e n e f i t f o r m u l a , o r l e v e l o f a s s u m p t i o n s c h o s e n .

C o n t r i b u t i o n r a t e s u n d e r t h e e n t r y a g e n o r m a l c o s t m e t h o d i n c l u d e a m -o r t iz a t i o n o f th e u n f u n d e d a c c r u e d l ia b il it y . W h e n a s s u m p t i o n s e x a c t l y m a t c he x p e r i e n c e , c o s t s a r e l e v e l u n d e r t h e a g g r e g a t e c o s t m e t h o d w h i l e t h e y d e -c r e a s e m o n o t o n i c a l l y u n d e r t h e e n t r y a g e n o r m a l m e t h o d . A c c r u a l r a t e s a r eh i g h e r u n d e r S e t I a s s u m p t i o n s t h a n S e t 2 , s i n c e S e t 1 r e p r e s e n t s a lo w e r

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37 2 FINANCIAL ASSUMPTIONS IN PENS|O N PLAN VALUATIONSl e v e l o f i n t e r e s t r a t e s . T h e t a b l e s s h o w t h a t c o s t s w i l l b e l o w e r a n d d e c r e a s ef a s t e r f o r b e n e f i t f o r m u l a s w h i c h a r e l e s s r e s p o n s i v e t o i n f l a t i o n ( s u c h a sf o r m u l a s 2 a n d 3 ) .

T h e t a bl es m a y b e u s e d t o e x a m i n e w h e t h e r t h e e f f e c t o f v a r i a ti o n o fe x p e r i e n c e f r o m a s s u m p t i o n s i s d i f f e r e n t w h e n s e l e c t a n d u l t i m a t e i n t e r e s ta s s u m p t i o n s r a t h e r t h a n l e v e l i n t e r e s t a s s u m p t i o n s a r e u s e d . S u c h a n e x -a m i n a t i o n i s m a d e i n t h e f o l l o w i n g t a b u l a t i o n :

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b l e s 1 t h r o u g h 8 o r t h e l as t ta b u l a t i o n r e g a r d i n g w h i c h b e n e f i t f o r m u l a i ssub j ec t to the g rea t es t va r i ab i l i t y . F o r ex am ple , in t hese i ll u s t r a t ions t he f l a t-d o l l a r f o r m u l a s h o w s t he g r e a t e s t v o la t il it y o v e r th e y e a r s w h e n e x p e r i e n c ed o e s n o t m a t c h a s s u m p t i o n s . T h e r e a s o n i s t h a t o n l y t h e c h a n g e i n i n t e r e s tr a t e s ( a c t u a l v e r s u s e x p e r i e n c e d ) a f f e c t s t h e r e s u l t s . F o r t h e o t h e r f o r m u l a s ,t h e r e su l ts r e f l e c t th e a s s u m e d 1 p e r c e n t s p r e a d b e t w e e n e x p e r i e n c e s a la r yr a t e s a n d e x p e r i e n c e i n te r e s t ra t e s w h i c h d a m p e n s t h e v a r i a b i l it y o f t h e i n-t e r e s t r a t e s a n d m a k e s t h e f o r m u l a s a p p e a r l e s s v o l a t i l e .

R o w ( 5) o f th e t a b u l a ti o n s h o w s t h a t u n d e r th e e n t r y ag e n o r m a l m e t h o dt h e e f f e c t o f v a r i a t io n o f e x p e r i e n c e f r o m a s s u m e d r a te s o n t h e a c c r u a l r a t ea f t e r t e n y e a r s i s i n d e p e n d e n t o f w h e t h e r s e l e c t a n d u l ti m a t e o r l e v e l v a l -u a t io n a s s u m p t i o n s w e r e u s ed . W h e n e x p e r i e n c e d i f fe r s f r o m th e a s s u m p -t i o n s , t h e e f f e c t o n t h e p a t t e r n o f a c c r u a l r a t e s i s a f u n c t i o n o f t h e d i f f e r e n c eb e t w e e n t h e v a l u a t i o n i n t e r e s t r a t e s a n d e x p e r i e n c e i n t e r e s t r a t e s r a t h e r t h a nt h e m e t h o d o l o g y ( i . e . , s e l e c t a n d u l t i m a t e v e r s u s l e v e l i n t e r e s t r a t e s ) . C a l -c u l a t i o n s u n d e r t h e a g g r e g a t e c o s t m e t h o d b e a r o u t t h e s a m e c o n c l u s i o n .

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B e n e f it f o r m u l a - I p e r c e n t o f f i n al f i v e - y e a r a v e r a g e p a y t i m e s y e a r s o f s e rv i c e.V a l u a t i o n a s s u m p t i o n s - C o n s t a n t i n t er e s t ra t e a n d s a l a r y s c a le .N o T E . - - E x p e r i e n c e s a l a r y r a t e a s s u m e d t o b e 1 p e r c e n t l o w e r t h a n th e e x p e r ie n c e i n t er e s t ra t e.

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B e n e f i t f o r m u l a - I p e r c e n t o f c a r e e r a v e r a g e p a y t im e s y e a r s o f s e r v ic e .V a l u a t i o n a s s u m p t i o n s - C o n s t a n t i n t er e st r a te a n d s a l a r y s ca l e .N o T E . - - E x p e r i e n c e s a l a r y r a t e a s s u m e d t o b e I p e r c en t l o w e r t h a n th e e x p e ri e n c e i n t er e s t r a te .

T A B L E 4I L I . U S T R A T I O N O F E F F E C T O F A S S U M P T I O N S A N D E X P E R I E N C E

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B e n e f i t f o r m u l a - I p e r c e n t o f c a r e e r a v e r a g e p a y t im e s y e a r s o f s e r vi c e .V a l u a t i o n a s s u m p t i o n s - S e l e c t a n d u l t i m a t e i n t e re s t r a te a n d s a l a r y s c a le u n i f o r m l y d e c r e a s i n g t ot h e u l t i m a t e r a t e .N o T E , - - E x p e r i e n c e s a l a r y r at e a s s u m e d t o b e 1 p e r c e n t l o w e r t h a n th e e x p e r i e n c e i n t e re s t r a te .

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U n f u n d e d A c c r u e d L i a b il i ty = $ 2 , 8 8 6 , 4 1 2

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B e n e f it f o r m u l a - S 1 0 p e r m o n t h t i m e s y e a r s o f s e r v i c e .V a l u a t i o n a s s u m p t i o n s - C o n s t a n t i n t e r e s t r a t e a n d s a l a r y s c a l e .N o T E . - - E x p e r i e n c e s a l a r y r a t e a s s u m e d t o b e I p e r c e n t l o w e r t h a n th e e x p e r i e n c e i n te r e s t r a te .

T A B L E 6I L L U S T R A T I O N O F E F FE C T O F A S S U M P T I O N S A N D E X P E R I E N C E

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C o n t r i b u t i o n C o n m b u t i o nRa te Ra te

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U n f u n d e d A c c r u e d L i a b i li t y = $ 3 , 6 6 2 , 9 0 2

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E xpe r ie nc eInterest

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-EAN -AG., : i2 . 1 9 . 7 52 . 1 9 . 8 02 . 1 6 . 8 22 . 1 2 . 8 22 . 0 4 . 7 91 . 9 5 . 7 31 . 8 5 . 6 71 .74 . 6 01 .64 .531 .53 .46

B e n e f i t f o r m u l a - S 1 0 p e r m o n t h t i m e s y e a r s o f s e r v ic e .V a l u a t i o n a s s u m p t i o n s - S e l e c t a n d u l t i m a t e i n t e r e s t r a t e a n d s a l a r y s c a l e u n i f o r m l y d e c r e a s i n g t ot h e u l t i m a t e r a t e .N O T E . - - E x p e r i e n c e s a l a r y ra t e a s s u m e d t o b e 1 p e r c e n t l o w e r t h a n t he e x p e r i e n c e i n t e r e s t r a t e .

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B e n e f i t f o r m u l a - I p e r c e n t o f f in a l f i v e - y e a r a v e r a g e p a y l e ss I p e r c e n t o f S o c i a l S e c u r i t y t im e sy e a r s o f s e r v i c e,V a l u a t i o n a s s u m p t i o n s - C o n s t a n t i n t e r e s t r a t e a n d s a l a r y s c a l e .N O T E . - - I n c o m p u t i n g t h e S o c ia l S e c u r i t y o ff s e t, t h e s a l a ry s c a le , S o c i al S e c u r it y w a g e b a s e , a n dC P I w e r e a s s u m e d t o b e l o w e r t h a n t h e i n t er e s t r a t e b y I p e r c e n t , 2 p e r c e n t , a n d 3 p e r c e n t r e s p e c t i v e l y .

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B e n e f i t f o r m u l a - I p e r c e n t o f fi n a l f i v e - y e a r a v e r a g e p a y l e ss I p e r c e n t o f S o c i a l S e c u r i t y t i m e sy e a r s o f s e r v i c e .V a l u a t i o n a s s u m p t i o n s - S e l e c t a n d u l t i m a t e i n te r e st r a t e a n d s a l a r y s c a le u n i f o r m l y d e c r e a s i n g t ot h e u l t i m a t e r a t e .N O T E . - - I n c o m p u t i n g t h e S o c ia l S e c u r i t y o f f s e t, t h e s a l a r y s ca l e , S o ci a l S e cu r i ty w a g e b a s e , a n dC P I w e r e a s s u m e d t o b e l o w e r th a n t h e i n te r e s t r a t e b y I p e r c e n t , 2 p e r c e n t , a n d 3 p e r c e n t r e s p e c t i v e l y .

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FINANCIAL ASSUMPTIONS IN PENSION PLAN VALUATIONS

APPENDIXLetter to the IRS

37 7

D e a r M r . C o h e n :T h e S o c i e t y o f A c t u a r i e s C o m m i t t e e o n P e n s i o n s i s c u r r e n t l y p r e p a r i n g

f o r p u b l i c a ti o n a p a p e r o u t l i n i n g o u r r e s e a rc h o n p h i l o s o p h i c a l a n d t e c h n i c a lc o n s i d e r a t i o n s i n v o l v e d i n u s i n g s e l e c t a n d u l t i m a t e f i n a n c i a l a s s u m p t i o n s .W h e n s e l e c t i n t e r e s t a s s u m p t i o n s a r e a p p l i e d o n a c a l e n d a r - s p e c i f i c b a s i s( i . e . , 10 pe rce n t in 1984 , 9 pe rcen t in 1985 , and 8 pe rcen t the rea f t e r ) , thea c t u a r i a l e q u i v a l e n c e f a c t o r s c r e a t e d b y t h e s e a s s u m p t i o n s w i l l v a r y o v e rt i m e . W e a r e u n a b l e t o d e t e r m i n e t h e a p p r o p r i a t e a p p l i c a ti o n o f e x is t in gr e g u l a t i o n s t o t h e s e f a c t o r s a n d r e q u e s t y o u r g u i d a n c e o n t h e q u e s t i o n s d e -s c r i b e d b e l o w .

A s R e v e n u e R u l i n g 8 1 - 1 2 i n d i c a t e s, a l l o f t he f a c t o r s a f f e c t i n g t h e c o m -p u t a t i o n o f a p a r t i c i p a n t ' s a c c r u e d b e n e f i t , i n c l u d i n g a c t u a r i a l f a c t o r s u s e df o r d e t e r m i n i n g o p t i o n a l b e n e f i t s , a r e t a k e n i n t o a c c o u n t w h e n c o n s i d e r i n gt h e r e q u i r e m e n t s o f C o d e s e c t io n 4 1 l ( d ) ( 6 ) t h a t a c c r u e d b e n e f i t s c a n n o t b ed e c r e a s e d . T h e f i r s t q u e s t i o n t h e n , i s :

1. H o w i s th e t e r m a c c r u e d b e n e f i t d e f i n e d ? I s it t h e d e f i n i ti o n a t r e g u -la t ion sect ion 1 .411 (a) -7(a) ( l ) ( i i )?

T h e r e g u l a t o r y d e f i n i t i o n c it e d in 1 s t a te s , " T h e a c c r u e d b e n e f i t i n c l u d e sa n y o p t i o n a l s e t t l e m e n t a t n o r m a l r e t i r e m e n t . " I t i s n o t u n c o m m o n f o r d e -f i n e d b e n e f i t p l a n s t o o f f e r p a r t i c i p a n t s a v a r i e t y o f a c t u a r i a l l y e q u i v a l e n to p t i o n a l s e t t l e m e n t f o r m s a t r e ti r e m e n t ; E R I S A r e q u ir e s t h e j o i n t a n d s u r-v i v o r o p t i o n . O t h e r c o m m o n o p t i o n s i n c l u d e lu m p s u m s , p e r i o d c e r t a i n a n dl if e t h e r ea f t er , e a r l y c o m m e n c e m e n t p r o v i si o n s , a n d s o o n . T w o q u e s t i o n sa r i s e in th i s connec t ion .

2 . Do the r equ i r em en ts o f 41 l (d ) (6 ) a nd 81 -12 a pp ly to a ll op t iona l s e t -t l e m e n t f o r m s a n d h o w is o p ti o n a l s e tt l em e n t f o r m d e f i n e d ?

3 . C a n a p l a n s p o n s o r e l i m i n a t e a n o p t i o n a l s e tt l e m e n t f o r m w i t h re s p e c tt o b e n e f i t s a c c r u e d t o d a t e o r f o r f u t u r e a c c ru a l s o n l y ? P u t a n o t h e rw ay , i s the e l ig ib i l i ty to e l ec t an op t ion a l ben ef i t fo rm i t s e l f pa r t o fthe acc rue d ben ef i t , a nd , the re fo re , sub jec t to 41 I (d ) (6 )?

M a n y p l a n s o f f e r b e n e f i t s t h a t a r e n o t s u b j e c t t o t h e v e s t i n g a n d a c c r u a lr e q u i r e m e n t s ; a v a r i e t y o f s u b s i d i z e d e a r l y r e t i r e m e n t b e n e f i t s i n c l u d i n g e a r l yo u t p r o v i s io n s a n d s o - c a l l e d a n c i l l a r y b e n e f i t s , f o r e x a m p l e . T h e d e f i n i t i o nc i t e d in 1 p r o v i d e s , " a c c r u e d b e n e f i t s d o n o t i n c l u d e ( e i th e r ) a n c i l la r y b e n -

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e f i t s . . . ( o r ) a s u b s i d i z e d e a r l y r e t i r e m e n t b e n e f i t . ' " P l a n s t h a t o f f e r s u c hb e n e f i t s d o n o t h a v e t o e x t e n d t h e m t o p a r t i c i p a n t s w h o t e r m i n a t e e m p l o y -m e n t , w i t h a v e s t e d i n t e r e s t , p r i o r t o t h e p l a n ' s n o r m a l r e t ir e m e n t a g e . W ea s s u m e t h a t t h e r a t i o n a l e f o r t h is c o n c l u s i o n is th a t th e s e b e n e f i t s a r e n o tp a r t o f a p a r t i c i p a n t ' s a c c r u e d b e n e f i t a n d , t h e r e f o r e , d o n o t h a v e t o v e s t .A p p l y i n g t h i s r a t i o n a l e o n e s t e p f u r t h e r ,

4 . I f a p l a n p r o v i d e s b e n e f i t s t ha t a r e n o t p a r t o f a p a r t ic i p a n t ' s a c c r u e db e n e f i t , c a n s u c h b e n e f i t s b e e l i m i n a t e d b y p l a n a m e n d m e n t , f o r p a r -t i c i p a n t s n o t i n p a y s t a t u s , w i t h o u t v i o l a t i n g 4 1 1 ( d ) ( 6 ) , r e c o g n i