Pension benefits effects on capital market equilibrium, firm value, and financing decisions

J BUSN RES 1992 25 1-25

1

Pension Benefits Effects on Capital Market Equilibrium, Firm Value, and Financing Decisions Yueh H. Chen Nahonal Sun Yat-sen Uncversrty

Winston T. Lin State Vntversrty

of New York at Buffalo

The lmphcatlons of the impact of pension benefits for capital market equlhbrmm, Investment, induced retirement, and the firm’s value and financing decisions are analyzed A static utility-maxlmlzatlon model 1s proposed The model implies a new return-risk equation that exphcltly incorporates the effect of penslon compensatlons and 1s compared with the standard equation The new model more adequately describes the return-risk relatlonshlp of a capital asset than the tradltlonal model and implies that the program of pension benefits has a significant influence on the movement of stock prices The model further implies that the firm’s value 1s affected by a change m pension benefits and Increases as its leverage Increases, and that while the Modlgham-Miller first proposltlon 1s not affected by the leverage of the pension fundmgs, it 1sno longer valid m the presence of corporate income taxes A special form of the Modlgham-Miller second proposltlon 1s also denved from the model

Introduction The theory of capital market eqmhbnum, as represented by the capital asset pricing model (CAPM) developed by Sharpe (1964), Lmtner (1965), and Mossm (1966) (SLM), lmphes that the expected return on a capital asset 1s equal to the risk-free rate of interest plus a risk premium The risk premium 1s defined either as the product of the market pnce of risk and the systematic risk of the capital asset or as the product of the risk premmm of the capital market (1 e , the difference between

Address correspondence to Wmston T Lm School of Management State Unwenlty New York at Buffalo, Jacobs Management Center, Buffalo, NY 14260 The authors are grateful to the anonymous referees of this Journal Andrew H Chen W&am Hamlen, and Frank Jen for then helpful suggestmns and comments on earher drafts of this paper Any errors that reman are solely the responslbdlty of the authors

Journal of Busmess Research 25, 1-25 (1992) 8 1992 Elsewer Science Pubhshmg Co , Inc 655 Avenue of the Americas,, New York, NY 10010

0148-2%3/92/$5

00

2

J BUSN RES 1992 25 l-25

Y H Chen and W T Lln

the expected return on the market portfoho and the risk-free rate) and the beta coefficient, where the beta coefficient is defined as the ratio of the systematic risk of the capital asset to the systematic risk of the market portfolio The extant research conducted on this subject has paid much attention to the nature, structure, and estimation of the beta coefficient Emplncally, the pricing equation has been treated as a linear regression model by a number of authors such as Black et al (1972) and Levy (1978) to test the validity of the SLM model Theoretically, Black (1972), Breeden (1979), Chen and Boness (1975), Mayers (1972, 1974), Lm (1990), Lm and Jen (1980), and Merton (1973), among others, have attempted to extend the standard CAPM by developmg a new pricing equation that differs from the SLM model simply m the measure of the beta coefficient The empirical study by Fama and Schwert (1977) concludes that the Mayers’ extended model under condltlons of wage uncertainty and full employment 1s not dlstmgulshable flom the original SLM equation The mtertemporal model of Merton (1973) and Its extension by Breeden (1979) are theoretically sound but are not easily subject to direct empirical tests There are CAPMs with nonlinear functional forms, e g , Jensen (1969), Lm and Chen (1990), and Lm et al (1992) Nevertheless, virtually all of these studies fall to investigate how the structure of the market price of risk of a security affects its return, and all of them fad to examme the effects of pension benefits on capital market equlhbrmm, firm value, and the firm’s financing decisions Lm’s (1990) recent work has tried to address the former issue In his model, ,ob search, the duration of unemployment, and unemployment compensations, are mcorporated mto the measurement of the market price of risk Then their impacts on the pricing of capital assets are examined The model 1s developed by employmg two fundamental theoretical concepts concerning the probablhty dlstrlbutlon of random wages and the condltlonal expected wage The wage income for the employee (investor) is treated as a weighted average of the condltronal expected wage and unemployment benefits The weight used serves as an indicator of the probabdlty of employment and 1s treated as a decision variable m the model Lm has theoretically and emplrlcally shown that the market pnce of risk, which considers the probablhty and duration of unemployment and unemployment compensations, has substantial influence on the pricing of capital assets However, m an imperfect Job market, income IS not Just generated from two sources rental labor service and the temporary benefits of unemployment, as Lm put It From the vlewpomt of the firm, pension payments are significant cost factors to corporate budgeting and should affect the firm’s employment and investment policies From the vlewpomt of the employee, pension benefits are important future income sources when retired The pension benefits are the deferred income, considered as part of wage income, and should play a vital role in the asset valuation process With the passage of the Employee Retirement Income Security Act (ERISA) (see Appendix A), the firm 1s obligated to honor its pension hablhty as a senior debt for which the firm must put aslde money each year mto its pension fund Pension promise IS often substantially greater than the long-term debt shown on the balance sheet, which influences the firm’s capital budgeting and structure, the value of the firm, and the prices of shares Sharpe (1976) argues that the firm can

Effects of Pension Compensation

J BUSN RES 1992 25 l-25

3

take advantage of an improper premium charged for pension fund insurance and then increases its market value by increasing pension hablhtles, or decreasing pension assets, or increasing the risk m the fund The significant negattve estimate of the coefficient of the unfunded vested pension m the Oldfield (1977) study, which examined the firms with homogeneous betas by a cross-sectional regresslon, IS explained as an adverse effect on the share prices and understates the true penston obhgatlons Tepper (1981) Indicates that pension funding and investment pohcy should be treated as interrelated financial dectslons He states that the firm does not pursue optimal financial pohcles for fully funded pension plans to obtain the maximum benefits He discusses the capital structure of corporate pension pohcy and mvestment of penslon funds He argues that, under a more general framework of imperfect capital markets mvolvmg bankruptcy costs of the firm and the differential personal tax rate of the shareholders, tax advantages exist only if the pension funds are totally invested m bonds, regardless of the sources of pension funding Feldstem and Sehgman (1981) have discussed the impacts of pension hablhtles (including pension expenses, unfunded vested pension benefits, and unfunded past service) on firm value, firm financial structure, and share prices In testing the aggregated effect of penslon hablhtles, they use a regression model to pool data for nearly 200 firms The negative estimate of the coefficient of the unfunded vested benefits 1s interpreted as the adverse effects on the market value of the firm and share prices Their model, however, lacks theoretical foundation This research will focus on pension benefits that determine the vested benefit obhgatlon The promise of pension benefits may alter both the employee’s and employer’s investment and employment declslons The employee works for next X years and then retires for Y years How do the income from labor wages and pension benefits affect the employment and investment decisions over his/her lifetime? The amount of pension benefits paid 1s not necessarily equal to the amount of pension costs funded The behavior of the two sides of a corn differs One side concerns the employee and affects the firm, whereas the other side interests the firm Their effects on capital market eqmhbnum differ accordmgly All of the existing studies concentrate on the side of pension fundmg and its impacts on share prices and aggregate savings (e g , Feldstem and Sehgman 1981, Oldfield 1977), on investment pohcles of the firm (e g , Tepper 1981), and on firm value, (e g , Feldstem and Sehgman 1981, Oldfield 1977, Sharpe 1976) This study, unlike Blcksler and Chen (1985)) who are concerned with optimal corporate pension strategies, takes the standpoint of the employee’s pension benefits and considers their impacts on capital market equlhbnum, firm value, and financing declslons Thus, the pnmary objective of this research is to analyze the effects of penslon benefits on capital market equlhbnum, firm value, and the financing decisions of the firm, as well as to provide necessary emplncal tests A utlhty-maxlmlzatlon model 1s developed, tested emplncally, and compared with the standard SLM model The model mvolves the probability of receiving pension benefits as a declslon vanable m the employee’s utlhty-maxlmlzmg process The eqmhbrmm capital market model lmphes a new return-risk relatlonshlp for a capital asset that exphcltly incorporates pension compensations The importance of the market price of nsk m the determination of capital asset prices IS analyzed

J BUSN RES 1992 25 I-25

Y H Chen and W T Lm

The lmphcations for asset valuation and firm value are discussed The relatlonshlp between the firm’s financmg decisions and the equlhbrmm capital market model, m conJunction with the Modlgham-Miller (1958, 1963) (MM) proposltlons, 1s also examined Empmcal tests are performed to determine the validity of the new pricing equation m comparison with the traditional SLM equation More specifically, two fundamental hypotheses are tested based on the model developed, namely Hl

H2

The probability of recelvmg pension benefits affects capital market equlhbrmm, suggestmg that the new CAPM provides a more adequate descrlptlon of the return-nsk relatIonshIp of a capital asset Fmn value IS affected by changes m penslon benefits through their effects on capital markets

The remainder of this article 1s divided into four sections The model 1sdeveloped m the next section and the analytical results and their lmphcatlons are given m the third section Then, empmcal tests are described Finally, the paper concludes with a summary

Development

of the Model

The model will be developed Assumptions

under the followmg assumptions

on Pension Systems for all Fwms

Noncontnbutory pension plans are prevailing, that IS, the funds are contributed by the employers alone The calculated penslon benefits to each employee differ, depending on the service duration and average earnings At least one year service and 25 years old are required for partlclpatmg the plans, a compulsory retirement 1s set at the age of 65 Employees can claim 100% fully vested rights after 10 years of granted cumulative service, and the spell of dlscontmuous rental labor service will not be counted Assumpttons

on Employees

(Investors)

In maxlmlzmg his/her utdlty on the net final wealth, the employee pursues the optimal investment and employment pohcles Because of imperfect labor markets, the employee may not have a hfetlme employment contract, that is, the employee 1s facing the posslblhty of bemg temporardy laid off durmg his/her hfetlme working period, but chooses to ignore the temporary benefits of unemployment We assume that wages and penslon benefits are the sources of income for the employee, and further assume that hourly wage rates are random, denoted by I@,, for employee I working for firm J The vested penslon rights are fully Insured, that is, the income from pension benefits IS secured after retirement or plan termmatlons Homogeneous expectation with respect to the returns on marketable assets for all investors 1s assumed Dejinltzons

of the Symbols

Used

We define the followmg symbols to be used for the model

J BUSN RES 1992 25 t-25

Effects of Penslon Compensation t works for firm J, where

h,, = labor hours that employee

, n, and J =

I = 1,

, J m the economy

1, WC,,=

5

the

expected

W?,)

hourly = w:,, where

wage

income

wp, =

the expected

w*, =

total weighted Income sonal income tax

k,j =

the proportlon

of risky secunties

such that 2

k,, = K, IS the market

pension

for

E 1s the mathematical benefits

I

for employee

conslstmg

CK, = K is the aggregate

employee I from firm J, 1 e , expectation operator

of wages and pension

invested

market

in firm

value of firm

J

benefits

after per-

held by employee

J’S

equity

I,

and cck,, 1 I

=

value of all secuntles

I

yo, =

the mltlal

wealth

of employee

I of which c

k,, IS invested

m risky assets

and B, m rlskless bonds to achieve the ma:lmum of the termmal wealth, such that Y”, = c k,, + B, and r” = c Y”, 1s the aggregate mittal I I endowment m the economy r

=

the risk-free

rate

return on risky security J with E(R,) = R, and the covarlance the returns on securltles 1 and 1’ 1s equal to Cov(&, I?, ) = a,,

I?, = the random between

p

= the random Cov(R,,

F,

return on = u,m

R”)

= the random

terminal

the

wealth

market

portfolio

for employee

with

E(Z?-)

= R” and

I

The Utdlty-Maxlmlzatlon Model The model employees

1s developed under the above assumptions on pension The income of employee z 1sderived from current wages,

the sum of the products of the hourly wage rate and the number of worked hours, on the vested pension rights and pension benefits, wpl, which 1s dependent Let S, be the probablhty of receiving pension benefits for employee I, which 1s an increasing function of cumulative service years, where 0 I S, I 1 When s, = 1, under the assumption of vestmg rights, employee 1 currently enjoys ha/her retlrement holidays or IS out of Job permanently and receives Income from penslon last Job contract, since benefits m the amount of wp,, which depends on ha/her the employee can switch the money value of pension nghts to a new employer When S, = 0, the employee 2s income 1s comprised of working wages amounting to xh,,w’,, When 0 I S, < 1, employeel 1s cumulating his/her vesting nghts The total welghted

income

can be wrttten

as

6

J BUSN RES 1992 25 l-25

Y H Chen and W T Lln

w*, = (1 - s,) Ch,,w’,,+ s,wp,, 0

5 s, 5

1

(1)

Under the assumptions introduced above, the mltlal wealth, Y’,, will exhaustively be invested m risky securltles and m rlskless bonds k,, m security 1 at the random rate of return R, and B, m bonds with the rate of return r Then, we can define the random net terminal wealth m the period as conslstmg of the return from investment and the total weighted Income from employment p, = B,(l + r) + zk,,

(1 + R,) + w*,

(2)

We assume that employee I behaves as an expected utility maxlmlzer of the final wealth, I e , MUX [ U,( p,)] with respect to these decision variables h,,, k,,, and S, For slmphclty and convenience without loss of generality, the utility function 1s assumed to be quadratic, 1 e , U,( p,) = ?, - b,q2,, where 6, 1s the coefficient of nsk aversion Then, the optlmlzatlon problem can be defined as maxlmlzmg the expected utlhty function, E [U,( F,)] = E( pl:) -

b,E(y’,),

for all l,~,

(3)

with respect to the decision variables Partial differentiation leads to the followmg first order condltlons (see Appendix B for detailed derivations) [l - 2b,E( y,)] (R, - r) - 26, xk,,a,,

[ 1 - 2b,E(q,)] [

Analytical

J,

(1 - s,)w’,, = 0, for all I, J,

1 - 2b,E(q,)]

Results

= 0, for all I,

( -

~h,,wC,

(4)

(5)

+ wp,) = 0, for all I

(6)

and Impllcatlons

The above condltlons can be used to explam the investor’s optimal strategies of investment and employment and the firm’s financing decisions The Valuation

Equation

and the Market Pme

of Risk

Dlvldmg both sides of Condltlon (4) by 2b,, summing over I, and mcorporatmg with the expected value of Equation (2), we get a new pricing equation given by R, = r + R*8*,,

where R* = 1 / (c

(7) (1 / 26,) - [K(R”’ - r) + p

pnce of risk, with W* = c

(1 + I) + W*]) 1s the market

w*,, and 0*, = Ku,,,, IS the systematic risk of security

J That is, the expected rate of return of asset J is equal to the rlskless rate of interest plus a risk premium which 1s the product of the market price of risk (R*) and the systematic risk of asset J (e*,) A similar equation for the market portfolio can be obtained as R” = r + R*8*,,

(8)

J BUSN RES 1992 25 l-25

Effects of Pension Compensation

7

That is, the expected market rate of return where 8*, = KCov(l?“, I?-) = Ku,, (R”) 1s the sum of the rlskless rate of interest and a nsk premium, which 1s the product of the market pnce of risk and the systematic risk of the market portfolio (e*nz) Usmg Equations (7) and (8), the new pricing equation can be rewritten as a linear function of the so-called beta coefficient, denoted by p*,, R, = r + (R”

- r)p*,,

(7’)

where p*, = R*9*,/( R” - r) IS the beta coefficient of asset J Implied by the model The beta coefficient 1s the ratio of R*,8*, to (R” - r), 1 e , the ratio of the product of the market price of risk and the systematic risk of the capital asset to the difference between the market rate of return and the interest rate The Probabdrty of Recervmg Pension Benefits The probablhty of receiving pension benefits 1s an unknown decision variable equlhbnum value can be found from Condltlon (5) By (5), we have S *,

=

1I2

WC,,

Its

(5’)

In eqmhbnum, the reciprocal of the total expected hourly wage income received by investor I 1s his/her probablhty of receiving penslon benefits The higher the expected hourly rate, the smaller the probability ~111be This makes sense because when investor 11s expected to earn a high pay, he/she is unlikely to retire to receive pension benefits The Investor’s Wage Income and Pension Benefits Condltlon (6) implies that

c hp’,,

=

wp,,

meamng that, m equlhbrmm, the investor’s wage income must be the same as pension benefits In other words, the retirement income 1sexpected to be equivalent to the wage income at equlhbrlum The Market Prrce of Risk and Vanatlons m Work Hours, Risky Investments, Perwon Benefits, and the Probabdlty of Recewmg Pensron Benejits We also can observe some interesting results by differentiating the market price of nsk m Equation (7) with respect to h,,, k,,, s,, and wp, In other words, how the market pnce of nsk 1s affected by the variations m the declslon variables and expected pension benefits can be analyzed as follows First, we find that aR*/ah,, = (R*)‘(l

- s,)w’,, 2 0, as 0 5 S, I 1

(9)

8

J BUSN RES 19Y2 2.5 l-2.5

Y H Chen and W T Lm

The market pnce of nsk responds posltlvely to a rise m work hours as 0 5 s, < 1, equality takes place as S, = 1, implymg that when investor I 1s no longer m the work force (because of retirement), changes m work hours have nothing to do with the market pnce of nsk Thus, increased (decreased) work hours increase (decrease) the market pnce of risk The interpretation of this result IS that the increase (decrease) m wage income, as a result of increased (decreased) work hours, may lead the investor to Increase (decrease) risky investments and, consequently, raises (lowers) the market price of risk, even without the pension, as s, = 0 This result is further confirmed and Justified by dR* I

ad, = (R*)* s, 2 0, as 0 25 s, 5 1

(10)

The result of Equation (10) implies that the market price of risk responds posltlvely to an increase m pension benefits when the probabdlty of receiving pension benefits IS positive The interpretation is the same as that given to Equation (9) When s, = 0, shifts m retirement income have no impact on the market price of risk since investor I has no chance to receive penslon benefits Secondly, It 1s shown that aR*lds,

= - (R*)*(~h,,w’,, I

- wp,) $2 0, as xh,,w’,, !

$2 wp,

(11)

The effect of a change m the probablhty of receiving pension benefits on the market pnce of nsk is indeterminate For example, a rise m the probablhty of receiving pension benefits has a positive impact on the market price of risk, provided that the expected pension benefits are larger than the expected wage income In equlhbnum, a shift m the probablhty of recelvm pension benefits 1s totally powerless to influence the market price of risk due to 2 h,,w’,, = wp, as implied by Condltlon I (6) or (6’) Fmally, it IS found that dR*ldk,,

= (R*)‘(l

+ R,) > 0

(12)

Increasing risky investments pushes the market price of risk up as 1 + R, IS positive The mterpretatloms that the more the risky investments are undertaken, the more the capital 1s needed as long as the expected rate of return IS posltlve This actlvlty will mtenslfy the capital market and, consequently, force the market price of risk to nse The Effect of Vanatlons

WI Decmon

Vanables

on Firm Value

Define V, = K, + B,, where B, IS the firm’s debt-financmg

such that c B, = CB,

Then the expected rate of return of asset J (R,) has the conventional in terms of firm value R, = (V, - V-,,)lV

- I,,

form expressed (13)

where V, = IIT(v,) with ‘cr, being the random value of firm J at time t and VP,, IS the firm value m the previous period Using Equations (7) and (13), we get the firm value function expressed m terms of the market pnce of risk and the systematic nsk

J BUSN RES 1992 25 l-25

Effects of Penslon Compensation

V, = [l + (r + R*e*,)]V_,,

9

(14)

Then we can show how a change m one of the decision vanables affects firm value First, we consider firm value and the probablhty of receiving pension benefits For this, it 1s observed that

aV,lds, = V_,,(R*)28*,(wP,

- c h,,w’,,) S 0, as 9: $ 0 and I

wp, -

c I

h,,wC,,5 0

(15)

According to Equation (15), the effect of a change m the probability of receiving pension benefits on the future value of the firm 1s ambiguous However, d the pension 1s larger (smaller) than the current wage income, accompamed by a positive (negative) systematic risk, then a nse m the probablhty of receiving expected pension benefits will increase (decrease) firm value That an increase (decrease) m the chance of receiving expected pension benefits will lead to an increase (decrease) m firm value 1s due mainly to the firm’s financially sound (weak) pension plans The good (bad) prospect leads to a positive (negative) impact on the value of the firm This analytical result supports Hypothesis 2, namely, firm value 1s affected by changes m pension benefits through their effects on capital markets Secondly, we consider firm value and portfolio selection It IS shown that av,/ak,,=

V_,,(R*)%*, (1 + R,) iZ 0, as e*, ZZ0

(16)

According to Equation (16), the impact of risky investment declslons by investor I on the value of firm J IS also ambiguous, depending on the sign of the systematic nsk (0*,), given a positive value of the expected rate of return, 1 e , (1 + R,) > 0 In practice, we observe that risky investments m the firm may not actually reflect the true value of the firm This explains why the firm value cannot be determined simply on the basis of the investor’s portfolio selection, Its interrelation with the capital market should be taken mto conslderatlon Finally, we consider firm value and work hours It can be shown that

aV,lah,, = V_,,(R*)2e*, (1 -

s,)w’,,

225

0, as e*, Zz 0

(17)

That is, firm value 1s increased (decreased) as the number of work hours increases (decreases), provided that the firm’s return 1sposltlvely (negatively) correlated with the market’s return The result given by Equation (17) 1s further confirmed by the following av,lad,

= v_,,(R*)2e*;, S 0, as e*,s 0

(18)

The future value of the firm 1s increased by a nse m pension benefits as the firm’s systematic nsk 1s positive A nse m pension benefits 1s the result of an increase m wage income under our assumptions The result of Equation (17), like Equation (15), confirms Hypothesis 2, suggesting that pension benefits, the market price of nsk, and the systematic nsk of the firm affect the firm’s value

The Firm’s Fmancmg Declslons To discuss the financing declslons of the firm, we begin with some additional notations defined as follows

10

J BUN RES 1992 25 l-25

Y H Chen and W T Lm

penslon assets of firm

J,

random net operating income of firm

J,

random net return from penslon assets, 6, + p, = total random net income, portion of current pension expense that IS debt-financed, portion of current sources,

pension expense that 1s financed from internal

PBX, + PBZ, = total current pension expense as the firm’s senior obligation, K, + PX, = current market value of the firm.

(2, - rPBX,)IK, = (6, + p, - rPBX,)IK, = the random rate of return on equity, where rPBX, IS the largest payment on borrowed pension funds, and p,/A, = the random rate of return on pension assets In the sequel, a variable with a tilde (-) placed above the variable 1s a e g , E(d,) = G,, E(Z?,) = R’,, etc Furthermore, the subscript J will be omitted hereafter for slmphclty All variables with a superscript u denote the variables of unlevered or borrowed-free pension expenses, that is, the pension expenses that are fully funded by internal sources R” = .8?lK = J?lV since PBX = 0 and K = V (We exclude the debts for non-pension purposes ) First, we consider the case of pension fundmgs with no corporate income taxes Equation (7) can alternatively be expressed as R, = r + h*Cov(&,

where X* = K/[~(%BJ 1

I?“‘), - xE(J!,)] I

(7”) 1s the equity market risk of the cost of capital

to all firms Usmg Equation (7”) and the definition of the random rate of return m terms of the ratio of income to equity, we have the expected value of the random operatmg income for levered pension expenses given by G = (K + PBX - A)r + A [Cov(l?,

I?)

- hCov(l?“,

Ep)],

(19)

where X = h*K, h = AIK = the pension-equity ratio, and K + PBX - A = the net residual market value of the firm Slmllarly, the expected value of the random operatmg income on unlevered pension expenses can be expressed as G” = (K - A)r + A [Cov(Z?“, Z?‘) - hCov(d”, If C? = &, Equations v=v”

rip)]

(20)

(19) and (20) imply that (21)

J BUSN RES 1992 2s 1-25

Effects of Pension Compensation

11

Equation (21), obtained after followmg the same procedure as Chen and Boness (1975), lmphes that the level of penslon debt funding 1s irrelevant to firm value Therefore, the pension fundmg level will not change the MM’s (1958) first proposltton, which states that the firm’s value is independent of its capital structure m the absence of corporate income taxes If d # G”, the firm’s value will at least be affected by an increase (decrease) of interest payments on the borrowed penslon funds, rPBX The expected rate of return on levered equity can be expressed as R’=r+X*6

em(TU m c1

(22)

where cr, IS the standard deviation of the return on equity, urn 1s the standard deviation of the market return, and S,, 1s the correlation between the return on equity and the return on the market portfolio, such that COV(@, Rm) = &.,,,ueu, Slmllarly, the cost of borrowed pension funds can be stated as Rb = r + A*&,pbum

(23)

According to Haugen and Pappas (1971, 1972), the covarlance between the return on the eqmty of levered funds and the return on the market portfolio can be expressed as &,,ueum = [(K + PBX)IK]S”,,u”,u,

+ [l - (K + PBX)IK]Gb,ubu,,

(24)

where (K + PBX)IK is the ratio of investment to equity and where [l - (K + PBX)IK] 1s the ratio of borrowed pension funds to equity Incorporatmg Equations (23) and (24) mto (22), we have R’ = r + h*{(K

+ PBX)IK]8’,,cr”,a,

+ [ 1 - (K + =

R” + ,I(,,,

= R” + h’(R’”

PBX)/K]8,,U,U,}

- Rb) - r), as Rb = r,

(25)

where h’ = PBXIK Equation (25) 1s the special form of the MM’s (1958) second proposltton implied by the present valuation model It states that the rate of return on eqmty 1s linear with respect to leverage and has a slope equal to the difference between the expected unlevered rate of return on equity, R’“, and the cost of borrowed funds, r Rearranging Equation (25), the special form of the MM’s proposltlon II can be expressed m terms of the financial leverage on the risk premium of the firm’s equity R’ = r + X*Cov(ReU, 22”) + h’{[r

+ A*Cov(RPU, am)] - [r + A*Cov(Z?“,l?“)]}

= r + A*Cov(l?‘,

Em) + h’A*[Cov(R’“,

The second term on the right-hand-side

R”)

- Cov(kb,l?“)]

(26)

of Equation (26) 1s the busmess risk premium of the firm’s equity, and the third (last) term 1s the financial risk premium of the difference between unlevered eqmty and borrowed pension funds Thus, the equlhbnum expected rate of return on a levered firm’s equity can be decom-

12

J BUSN RES 1992 25 l-25

Y H Chen and W T Lm

posed mto three components a risk-free rate, a premium for its busmess risk, and a premium for the difference between Its financial risk on equity and debt Secondly, we consider the case of pension fundmgs with corporate Income taxes The rate of return on equity m the presence of corporate Income taxes and taxexempt on returns of pension assets IS defined as I?” = [(G - rPBX)(l

- u) + PI/K,

(27) where u 1s the tax rate Rearranging Equatron (27) by taking the expectation on both sides and mcorporatmg Equation (7”), we have the expected value of the net operating income after taxes for a levered firm G(l -

- u) = [K + (1 - u)PBX - A]r + X[Cov(I?-, hCov(R~,

I?“)

z?)]}

(28)

Slmllarly, the expected value of the net operating levered firm IS given by

income after taxes for an un-

GU(l - u) = (K - A)r + A [Cov(&‘“, I?‘) - hC~v(l?~, I?“)] We now observe that If C? = C?, then Equations

(29)

(28) and (29) imply that

V = V” + uPBX

(30)

Thus, the MM’s results m the presence of corporate income taxes can be derived from the valuation equation The result lmphes that the firm value Increases as Its leverage Increases since the tax subsidy IS given based on the Interest payments of Its debt capital But the mcentlve tax-exempt on returns from pension assets IS not present m the result, nor does it produce any posltlve effect on firm value This can be further proved by expressing Equation (28) m an after-tax form as G(l - u) = [K + (1 - u)PBX

- A]r + h*Cov(d,

Z?“)

(28’)

The tax-exempt

incentive on the return of the pension asset IS neutral to the value of the firm The result may be explained partly by the fact that the firm may Invest Its capital (Internal or external) on other opportumtles other than penslon plans m order to make a compensative return Just as pension plans may have, and partly by the fact that the firm need not pass on any of the earmngs from penslon assets to Its former employees The result also explains why the firm does not use taxexempt advantages to fully fund the pension programs and why the underfunded pension plans are currently existing The effect of tax shield on firm value 1s solely a matter of the tax deductlblhty of Interest payments In contrast, Tepper (1981) stresses that the capital structure of pension fundmgs IS not a matter related to the firm value The MM’s proposItion I 1s no longer valid m the presence of corporate income taxes If G # C.?, the firm value 1s Increased (or decreased) at least by an amount of after-tax interest payments, (1 - u)rPBX In the presence of corporate mcome taxes, the expected value of the firm, according to Equation (30), 1s given by V = [G(l

- u) + PI/R”” + uPBX,

(31)

since G = CP Furthermore, d we define the after-tax net operating income as C?” = (1 - u)G + urPBX + 1”, then Equation (31) becomes

J BUSN RES 1992 25 1-25

Effects of Pension Compensation C/V

= R“” - vH(R”

- r),

(32)

where H = PBXIV = the target debt-value ratio Equation (32) lmphes that m the presence of corporate income taxes, the cost of capital on the tax-adjusted basis can be lowered with leverage, as noted by Equation (11 c) of MM (1963) That is, the effect of leverage on the expected after-tax capltahzatlon rate, C/V, 1s solely a matter of tax saving on interest payments The pension return under the tax conslderatlon plays no role m the determination of capital or financial structure By substractmg the pension debt, PBX, from both sides of Equation (31) and defining c as the sum of the random net profit after taxes (II”) and interest payments (R = rPBX), we obtain the after-tax equity capltahzatlon rate (see Appendix B) II”/K = R”” + (1 - v)h’ (R” - r),

(33)

where h’ = PBX/K = the pension debt-equity ratio and E(W) = II” Equation (33) implies that the after-tax yield on equity capital increases as the firm’s leverage increases The results re-state the MM’s (1963) Equation (12 c) the cost of equity capital 1s dependent on the firm’s leverage m the capital mix The government subsidy on debt capital has a major influence on the reduction of the cost of equity capital Once again, the pension return plays no role m the determmatlon of the capltahzatlon rate, which 1s slgmficantly affected by the presence of corporate income taxes The firm value will not benefit from the tax-exempt on the return of pension assets, but from the tax-saving on borrowed fundmgs The result supports the findings of Sharpe (1976) that the value of the firm can be increased by increasing pension hablhtles, decreasing pension assets, or mcreasmg the risk m the fund The result also suggests that the firm should take tax advantages on interest payments rather than on pension returns, the firm should use debt-financing rather than self-financing The lmphcatlon contrasts with Tepper’s (1981) argument Emplncal

Tests and Findings

Empmcal tests are performed to determine whether the new capital asset pricing equation mcorporatmg wage and pension compensations improves on the descnptlon of the return-risk relationship m eqmhbrmm The Data The monthly returns of 175 randomly selected stocks and the returns of the market portfoho from CRSP tape were transformed mto annual rates The choice of the sample and the transformation are m cooperation with the data avallablhty of the other vanables included m the equation The time period covers 1965 through 1984, yielding 20 annual observations The rlskless interest rate was represented by the three-month Treasury bill rate, collected from the Economic Indicators published by the U S Department of Commerce The sum of the market value of stocks and bonds listed on the NYSE was taken as the total mltlal wealth as reported m the Statlstlcal Abstract, again published by the U S Department of Commerce The sum of the wage and salary

14

J BUSN RES 1992 25 l-25

Y H Chen and W T LIII

disbursements and the propnetors’ income portlon, collected from the Survey of Current Busmess published by the U S Department of Commerce, was taken as the total wage income The number of seasonally adjusted clvlhan labor force employed was collected from the Labor Statlstlcs of the U S Department of Labor The data of penston contnbutlons, generated from both the Statlstlcal Abstract and Survey of Current Business, were used as a proxy of penslon benefits All these values were deflated by the consumer price mdex

The Tests To compare the vahdlty and adequacy of the new return-nsk equation (7’) with the SLM model, the emplrlcal tests are conducted as follows To slmphfy the empirical work, the risk-aversion coefficient (6,) of the quadratlc utlhty function IS assumed to be the same for all investors The number of persons m the seasonally adjusted employed labor force IS used as the actual number of investors m the economy To find the sensltlvlty of the new beta (p*,) m response to the variation of s,, we assume that s, = s for all I and consider 11 different values of s, namely, 1 0, 0 9, 0 8, 0 7, 0 6, 0 5, 0 4, 0 3, 0 2, 0 1, and 0 0 The estimates of betas based on the SLM model, which IS treated as a tlmeserves regression (Black et al 1972, Levy 1978), are obtained by the ordmary leastsquares method and are denoted by 6, The variance of the residuals from the fitted regresslon IS calculated and denoted by s,’ X, IS used to denote the devlatlon of the average return (Z?,) from the average risk-free rate (!), that IS, X, = t?, - f The average return of the market portfoho IS represented by Z?’ The /th stock’s vanance V,’ IS also computed, for all 1 The 11 estimates of the new beta based on (7’) are calculated and denoted by ^*4, where s = 1 0, 0 9, ,Ol,OO P To test the vahdlty of the SLM model compared with the new model and to determme whether S*, or V’, contributes to the determmatlon of stock prices, we form-these hnear ;egresslon*equatlons (X,, p,), (X,, SF), (X,, V,‘), (X,, p,, St),

(X,, P,, Vj2), (X,, P*,), (X,, P*,,, s,‘) and (X,, P*v,, V,% I = 1, 2, , 175, where s = 1 0, 0 9, 0 1, 0 0 In all these regressions, X, serves as the regressand These equations ire cross-sectional regressions estimated using the data over J The estlmatlon results are reported m Tables 1, 2, and 3 Empmcal

Fmdmgs

First, m Table 1, (X,, a) represents the second step of the 2-step process for testing the vahdlty of the SLM model (see Black et al 1972) The intercept of the regression 1s significant at the 10% level with a magnitude of 0 013007 Its slope 1s slgmficant at the 1% level and 1s positive equal to 0 038298, which overestlmates the actual premmm, Rm - r = 0 02446913, by more than 56% This Implies that the result from the SLM model IS skeptlcal for the financial deaslon-making When pension benefits and the probabdlty of receiving pension benefits are mcorporated into the market price of risk m the new model, we find that m the regresslon (X,, p*,), the intercept 1s indifferent from that of the SLM model, whereas the slope IS slgmficant at the 1% level and, when s = 0 5, It 1s remarkably close to R” - ? On average, it was 0 024695, which 1s close enough to the actual

J BUSN RES 1992 25 l-25

Effects of Pension Compensation Table 1. Regression

so

15

Results of Betas

Constant

Betab

b2

Rk

Wsi) 0 013007

0 038298

(1 510524)

(4 082745)d

0 001667

0 0888

0 001667

0 2889

0 001667

0 2889

0 001667

0 2889

0 001667

0 2889

0 001667

0 2889

0 001667

0 2885

0 001667

0 2883

0 001667

0 2884

0 001667

0 2884

0 001667

0 2884

0 001667

0 2882

(x,sk,) 10

09 08 07 06 05 04 03 02 01 00

0 013007

0 033311

(1 510495)

(4 082741)

0 013007

0 031587

(1 510497)

(4 082748)

0 013007

0 029864

(1 510487)

(4 082748)

0 013007

0 028141

(1 510479)

(4 082766)

0 013007

0 026418

(1 510485)

(4 082760)

0 013007

0 024695

(1 510473)

(4 082755)

0 013007

0 022972

(1 510494)

(4 082755)

0 013007

0 021249

(1 510503)

(4 082754)

0 013007

0 019526

(1 510489)

(4 082747)

0 013007

0 017803

(1 510534)

(4 082723)

0 013008

0 016080

(1 510533)

(4 082710)

*s IS the probablhty of recewmg pensmn benefits bBeta IS the estimate of the coefficvznts of i, and p’, ‘R* IS the coefficient of determmatmn dThe numbers m parentheses are r-values

premium (0 0246913) by a neghglble difference of 0 0000037, suggesting that the new model outperforms the SLM model Therefore, based on the empirical evldence, we may conclude that the new model, which considers penslon benefits and the probability of recelvmg pension benefits, provides a more adequate explanation for the return-nsk relatlonshlp of a risky asset This confirms Hypothesis 1 From the new model, we further observe that the coefficient of b*s, decreases as the probablhty of recelvmg pension benefits decreases at an increasing rate rangmg from 5 5% to 11 07% per 10% change m s For example, from Table 1, when s = 1 0, the estimate of the coefficient of p*, 1s 0 033311 When s = 0 0, the estimate has noticeably been reduced to 0 01608, which 1s less than 48% of 0 033311 The nsk premium per unit of risk seems to be highly sensltrve to changes m the probablhty of recelvmg pension benefits In this regard, the firm can find a proper estimate of the beta coefficient based on the crltena of its pension obhgatlons and fundmgs This finding 1s m contrast with Lm’s (1990) findmg that the risk premium per unit of risk 1s not considerably affected by changes m the probablhty of unemployment This difference may be attnbutable to the dlffermg characterlstlcs of the pension and unemployment compensations The former 1sfunded by the employer’s

16

J BUSN

RES 1992 25 1-25

Y H Chen and W T Lm

Table 2. RegressIon

Results of Betas and S,’

Constant

s

0 030104 (4764352)

Beta

(X,47 -

b-2

R2

0 312776 (2873578)

0001745

00461

s,

c4si.m

10

09 08 07 06 05 04 03 02 01 00

-0 000762 (-0 078072)

0 037145 (4035260)

0 294038 (2816769)

0001602

0 1295

-0 000762 (-0 078070) -0000762 (-0 078084) -0 000762 (-0078081) -0 000762 (-0 078092) -0 ooO762 (-0 078070) -0 000762 (-0 078098) -0 000762 (-0 078074) -0 000761 (-0 078052) -0 000762 (-0 078080) -0 000761 (-0 078035) -0 000761 (-0 078017)

(x,>P'$J 0 032307 (4035260) 0 030636 (4035282) 0 028965 (4035278) 0 027294 (4035295) 0 025623 (4035277) 0023952 (4035295) 0 022280 (4035285) 0 020609 (4035258) 0 018938 (4035283) 0017266 (4035233) 0015595 (4035217)

0 294038 (2816770) 0 294038 (2816772) 0 294038 (2816772) 0 294038 (2816769) 0 294038 (2816772) 0 294038 (2816772) 0294038 (2816769) 0 294037 (2816760) 0 294038 (2816768) 0294038 (2816763) 0 294037 (2816753)

0001602

0 2895

0001602

0 2895

0001602

0 2895

0 001602

0 2895

0001602

0 2895

0001602

0 2895

0 001602

0 2886

0 001602

0 2889

0 001602

0 2886

0001602

0 2890

0001602

0 2885

Footnotes

as In Table 1

and/or employee’s contrlbutlons for the retu-ees and 1s managed by the fiduciaries The latter IS funded by the employer’s money for the layoffs and IS handled by the government agencies The emplrlcal finding, however, may suggest that the factor of pension compensations IS more mfluentlal than that of unemployment benefits m the capital asset pncmg process The emplrlcal results also confirm the analytical results of Equation (11) That IS, the empirical finding explains why the firm must put aside some of its capital, either from Internal or external sources, to meet its pension obhgatlons, when the probablhty of receiving pension benefits IS high This activity hence creates the uncertainty of the capital market and raises the market price of risk, and finally forces the cost of capital to rise Second, m Table 2, the estimate of the coefficient of S,’ from the regression (X,, S,‘) 1s 0 312776, which IS highly slgmficant and IS consistent with the results of Miller and Scholes (1972) and Levy (1978), but coqtradlcts the result of Lm (1990) Third, adding S,’ to the regresslons (X,,p,) and (X,,b*,) as an addItiona explanatory variable leads to positive and significant estimates of the coefficients of both the beta coefficient and S,’ The averaged coefficient of p,, 0 037145, still overestimates the actual nsk premium The averaged estimate of the coefficients The estimate of of ri*, 1s 0 023952, slightly lower than the actual risk premium

J BUSN RES

Effects of Pension Compensation

1992 25 1-25

17

Table 3. Regression Results of Betas and V,’ s

Constant

.2 CT

R2

0 406586 (4 716310)

0 001619

0 1151

0 301158 (2 929547)

0 001596

0 1326

0 (2 0 (2 0 (2 0 (2 0 (2 0 (2 0 (2 0 (2 0 (2 0 (2 0 (2

0 001596

0 2926

0 001596

0 2926

0 001596

0 2926

0 001596

0 2926

0 001596

0 2926

0 001596

0 2925

0 001596

0 2924

0 001596

0 2898

0 001596

0 2897

0 001596

0 2995

0 001596

0 2994

Beta

0 015076 (2 094700)

S.

wvP*,xY 0 005561 (0 631795) 10 09 08 07 06 05 04 03 02 01 00

0 (0 0 (0 0 (0 0 (0 0 (0 0 (0 0 (0 0 (0 0 (0 0 (0 0 (0

005560 631758) 005560 631732) 005560 631752) 005560 631747) 005560 631745) 005560 631725) 005560 631762) 005560 631744) 005560 631753) 005561 631788) 005560 631768)

0 020416 (1 852097) (x,,lj*,.v,‘) 0 017758 (1 852127) 0 016839 (1 852161) 0 015921 (1 852139) 0 015002 (1 852160) 0 014084 (1 852157) 0 013165 (1 852165) 0 012246 (1 852141) 0 011328 (1 852154) 0 010409 (I 852143) 0 Cm490 (1 852116) 0 008572 (1 852108)

301158 929553) 301158 929553) 301158 929550) 301157 929550) 301157 929553) 301157 929550) 301158 929552) 301157 929535) 301157 929542) 301159 929569) 301160 929571)

Footnotes as m Table 1

the coefficient of fi*s, again responds sensitively to, and varies with, changes m the probablhty of receiving pension benefits This further supports the notion that the pension benefit 1s a more important income source than the unemployment compensation Introducing S,’ does gam some accuracy of estlmatlon over the simple regr$sslon (X,,b*s,) The estimated coefficients of S,’ and R2 m both regressions (X,&i,, St) and (X,, fi*s,, S,‘) are different The intercept IS mslgmficant and does not differ m sign and magnitude for both cases The estimated coefficients of S,’ support the findings of both Miller and Scholes (1972) and Levy (1978) but contradict the finding of Lm (1990) that the coefficient of S,’ 1s mslgmficant and negative and, therefore, S,’ 1s not a relevant factor to the behavior of stock prices Finally, S,’ 1s replaced by V,’ Table 3 presents the results of the simple regression (X,,Vj2) and the multiple regressions (X,,p,,VF) and (X,,b*,,V,“) The estimated coefficient of V,’ IS slgmficant and positive for all three regressions When V,” IS added as an additional explanatory vanable, the estimated coefficient (0 020416) of p, underestimates_ the actual nsk premium The averaged estimate (0 013165) of the coefficient of p*, is also lower than the actual risk premium by 50 8% when V,’ appears m the equation

18

J BUSN RES 1992 25 1-25

Y H Chen and W T Lm

The traditional Durbm-Watson statlstlcs suggest the absence of serial correlation m most cases except for 5 securities with observed Durbm-Watson values smaller than 1 15, which were not significant at the 1% level

Conclusions This research has been devoted to the mvestlgatlon of the Impacts of pension benefits on capital market eqmhbrmm, firm value, and the financing declslons of the firm A utility-maxlmlzation model was developed The model suggests a new capital asset pricing equation that was tested emplrlcally to show that it appears to more adequately describe the behavior of stock prices and the return-risk relationship of a capital asset than the standard model Emplrlcally, we found that the higher the probability of receiving penslon benefits, the higher the risk premium will be That IS, the program of pension benefits significantly influences the movement of stock prices The prices of stocks behave m response to the situation of the firm’s pension benefits and obligations The value of the firm 1s increased (decreased) by a rise m pension benefits If the firm’s systematic risk 1s positive (negative) This result essentially supports the hypothesis that firm value is affected by the change m pension benefits through their impacts on the capital market The leverage of the pension fundmgs does not change MM’s first proposltlon, which states that the market value of the firm and its cost of capital are independent of Its capital structure m an economy without corporate income taxes However, the MM’s first proposltlon IS no longer valid m the presence of corporate income taxes A special form of the MM’s second proposition was derived from the new model, which states that the rate of return on equity 1s linear with respect to leverage and has a slope equal to the difference between the expected unlevered rate of return on equity and the cost of borrowed pension fundmgs Based on the special form, the equlhbrmm expected rate of return on a levered equity can be decomposed mto a risk-free rate, a premium for the firm’s busmess risk, and a premium for Its financial risk associated with equity and debt The government subsidy of interest payments on debt capital IS a maJor factor to influence the after-tax yield on eqmty capital The new model also lmphes that the firm’s value increases as its leverage increases since the tax subsidy IS given to interest payments of its debt capital But taxexempt on the return of pension assets does not produce any effect on the firm’s value That IS, the model implies that the tax-exempt incentive for pension programs IS neutral to the value of the firm The result may be explained by the fact that the firm may invest its capital (internal or external) on opportunities other than pension assets to make a compensative return Just like pension plans may have The result also explains why the firm does not use tax-exempt advantages to fully fund the pension programs and why some of the pension plans are currently underfunded The impact of tax shield on firm value IS solely a matter of the tax deductlbdlty of interest payments As a possible extension to this study for future research, social security benefits may be included m the development of the model As mentioned earlier, social security and pension benefits differ m their nature, funding, and payment Then impacts on capital market equlhbrmm may differ accordmgly

J BUSN RES 1992 25 1-25

Effects of Pension Compensation

19

In a second extension, the optimal control approach may be applied to investigate the effects of pension benefits on the optimal investment and financing decisions of the firm An optimal control model incorporating adjustment costs (e g , Lm 1981, Lm and Tan 1990) is of special interest m this area It 1s useful to compare the optimal control solution of corporate pension strategies with the optlmal corporate pension strategies proposed m Blcksler and Chen 1985, Black 1980, Harrison and Sharpe 1983, Sharpe 1976, and Tepper 1981 A third extension concerns the methodological problem The new proposed model may be reconstructed as an error-components model and then 1s estimated by the error-components and seemingly unrelated regressions method as m the energy study by Lm et al (1987) To do this, the error term of the model 1s decomposed mto three components the temporal, the cross-sectional, and the remainder factor The error-components and seemingly unrelated regressions method, however, 1s much more complicated than the ordinary least-squares method Furthermore, the new model may be recast as a variable mean response random coefficients model and then 1s estimated by a four-step generalized leastsquares procedure as m Lm et al (1992)

Appendix

A The Private Penslon Systems

Pension systems (cf Mcglll and Grubbs 1979, Munnell 1982, Pension Facts 1981, Private and Public Plans 1975, Treynor et al 1976, True 1976, Schulz 1976) are now firmly established m the United States economic and social structure The plans were intended as the sources of mcome mamtenance for the aged m the years they are not working The pension plans have become mcreasmgly important for employees of all ages and have provided meaningful benefits and vital financial well-being to their future Both the public and the private plans have tremendous impacts on the hves of retired persons and have become a major source of aggregate capital accumulation m the United States economy over the past decades According to Pension Facts 1981, pp 6-9, about 50 mllhon participants were covered by major pension retirement programs and the sum of total assets and reserves exceeded $712 bdhon m 1980 Pension annuities are addltlonal sources of income for the retirees A maximum of pension funding obhgatlons allowed by the IRS 1s tax-deductible and the returns on the pension assets are tax-exempt Both are incentives for the employer to take full advantages of tax shield, to make its great efforts to support the systems, and to stabilize the private work force The employer (the pension sponsor) has a great flexible choice m provldmg the contnbutlons and m managing penslon funds for the purpose of meeting future benefits payments due The costs of the plans are a large portlon of today’s corporate budget (according to Munnell 1982, p 152, the private employer contrlbutlons for employee benefits were about 12 4% of private sector wages and salaries m 1980), and the plans should help the employer attract and retam a competltlve labor force MaJor Charactermcs

Governed

by ERISA of 1974

The approaches of the private penslon differ widely m several major charactenstlcs, such as type and admmlstratlon, benefit determmatlon, partmpatmg, vesting and portablhty requirements, fundmgs, and fiduciary responslblhtles These character-

20

J BUSN RI23 1992 25 1-25

Y H Chen and W T Lln

Istics are regulated by the passage of the ERISA of 1974 ERISA, which was developed essentially from legal and actuanal prospectives, alters the capital structure of every firm that has unfunded vested penslon hablhty and affects the capital allocation m the U S economy

Type and Admmutratton Type and admmlstratlon can be identified by angle-employer and multi-employer plans Most single-employer plans are managed by the employer alone, whereas multi-employer plans are almost operated by a group of representatives from labor and management The pnvate plans also can be dlstmgulshed between contributory and noncontnbutory plans The former requires employees and employers to make payments to a pension fund, whereas the latter 1s funded entirely by the employer Most covered employees participate m noncontnbutory plans m the United States This IS partly because the employer contrlbutlons to pensions are tax-free, but not for employees, and partly because the employer does not have to earmark assets or put aside money for each employee at the time hls/heL rights are vested In addition, the employer needs not pass on any of the earnings from penslon assets to the former employees

Ben&t Determrnatlon There are two malor ways of calculating benefits defined benefits plans and defined contnbutlon plans The calculation of the former 1s dependent on the plans’ specified terms such as fixed amount or benefit rate for each employee, length of service, earnings, combined service duration and earnings, and social security mtegratlon Many compames adJust penslon calculation to reflect their social security contributions That IS, pension benefits are computed by deducting all or part of an employee’s social secunty benefit from the amount computed by the company pension plan formula, or benefits are calculated by the maximum earnings used to calculate social secunty benefits at the time the company plans are designed Because social security replaces a large portion of lower-paid workers’ wages, mtegratlon has an impact on lower-pald employees Defined contrlbutlon plans are either money purchase plans or deferred profit-sharing plans For more detalled explanations of both types, see Schulz 1976, pp 116-117 The provlslons of ERISA make defined contnbutlon pension plans more attractive than defined benefits plans.

Parhclpatmg Requwements The employee

(the penslon member), who has contracted rental labor service to the firm m return of wage compensations, must meet the condltlons of partlclpatmg the plans, such as one year service, at least 25 years old, and havmg been hlred for more than 5 years before reachmg retirement

Portabrlity and Vestrng Requwements Portablhty of penslon nghts allows the employee to transfer the money value of these nghts and credits into another plan regardless of his/her voluntary or mvol-

Effects of Penslon Compensation

J BUSN RES 1992 25 l-25

21

untary quit to help the employee

keep a track of vested benefits The ERISA leglslatlon created the Indlvldual Retirement Account (IRA) to encourage employees who are not currently covered by any plans to set aslde penslon funds on their own The 1981 Economic Recovery Tax Act allows both covered and uncovered employees to contribute as much as 100% of compensation to an IRA (up to an amount of $2,000 a year) and deduct the contribution from taxable IRA income The tax reform of 1986 has changed the IRA The vestmg nghts of penslon benefits are not contingent on the employee’s contmumg to work for the employer The ERISA’s vesting and portablhty nghts provide an equal and fair treatment to all participants and restnct “service-broken” rules that hmlt vestmg avallablhty to many employees before ERISA Each plan should choose one of the followmg vesting methods accordmg to ERISA 1) 10 years of service granted An employee may claim 100% full vested nghts after 10 years of service, 2) graded vesting an employee has 25% vested right after 5 years of service, then Increasing by 5% each year for the next 5 years and by 10% thereafter so that there 1s 100% vesting, and 3) rule of 45 an employee 1s entltled for 50% of accrued benefits when his/her age and 5 years of service add up to 45, increasing by 10% each year thereafter until 100% 1s reached, additionally, an employee under the rule of 45 must be 50% vested after 10 years of service and 100% vested after 15 years of service regardless of his/her age

Fundmg Requirements The funding requirements

must be based on all vested and nonvested hablhtles The new funding rules under ERISA requu-e that the employer with a defined benefit plan must pay annual normal cost of the plan, amortize past service costs accruing over no more than 40 years for the plans in existence on January 1, 1974, and no more than 30 years for new plans, and amortize experience gains and losses over no more than 15 years Defined contrlbutlon plans must be funded accordmg to the firm’s designed benefit method The funding provlslons of ERISA require the employer to accumulate adequate funds for benefit payments due, to fund prior service costs, and to consistently amortize expenence gains and losses Those employers who fall to meet the mmlmum funding standards are subject to a 5% excise tax penalty on the accumulated deficiency and a 100% excise tax if the deficiency 1s not corrected m time, say, 90 days

Flduclary Responslbhty To protect pension assets from abuse, fiduciary standards, which apply to a person who has some power over the penslon plan, are mtroduced m ERISA ERISA requires “fiduciary responablhty” for pension plan trustees, for investment managers, and for other persons who may exert some control over the plans The provlslons state that fiduclanes must manage penslon assets with the skill and dlhgence of a prudent person based on the sole interest of the partlclpants and beneficlanes A fiduciary IS personally liable to the plans for clvll penaltles resultmg from vlolatlons of h&her fiduciary responslblhty

22

J

BUSN RES 1992 25 l-25

Y H Chen and W T Lm

Plan Termnatlon

Insurance

To protect partmpants’ vested benefits against plan termmatlons, both fiduciary responslblhtles and fundmg standards are mandated, and ERISA has established the Pension Benefit Guaranty Corporation (PBGC) PBGC 1s a quasi-government Insurance agency It issues pension benefits up to a maximum amount per month when the plans are m default and has the authority to assess 30% of the net worth of the corporation for funding deficiency m the contmgency of a plan termmatlon Plan termmatlons have dumped big deficits on PBGC, which owes about $3 3 b&on m long-term benefits to pensloners, but has only $835 mdhon m Its own value Wlthout a substantial Increase m the Insurance premium, PBGC can’t guarantee the defaulted benefit payments (see Radey 1984, p 82)

Appendix

B Mathematical

Derivations

Shown here are the details leading to the key equations dlsplaycd m the text The equation numbers correspond to those mdlcated m the text Since E( FZ,) = V( I’) + [ E( ?,:)I2 then dE[U,(F,)]l&,,

= &!z(F,)ldk,, - b,a[E(F,)]lak,, = &F(Y,)ldk,, - b,aV(Y,)lak,, = (R, - r) - 2b, c = [1 -

2b,E(p,)]

k,,u,, -

(R, -

r) -

- 26,E(F,)aE(F,)/ak,, 2b,E(p,) 26, c

(Z?, -

r)

k,, a,,

= 0, for all 1, J aE[U,(?,)]lah,,

(4) - b,aV(Y,)Iah,, - 26, aE(%:)ldh,,

= dE(~,)lah,,

= [l - 2b,E(F,)]

dE(%‘,)lah,

= [ 1 - 2b,E(p,)]

(1 - s,)w’,, = 0, for all 1, J

b,dV(f’,)/dh,, (5)

= [1 - 2b,E(Y,)] dE(~,)lds,

&?[U,(f,)]/as,

= [ 1 - 2b,E(?,)] E(G‘) = KE(R’) = K[r

-

+ rPBX

-

+ A*Cov(l?‘,l?)]

(- 2

h,,w’,, + wp,) = 0, for all I

E(P) - A[r

+ ACOV(Z?~,Z?‘)] + rPBX

= (K + PBX

- A)r

+ A*[KCov(f?“,~)

= (K + PBX

- A)r

+ A[Cov(l?“,i?)

where A = A*K and h = AIK

(6)

- ACov(l?“Jip)] -

~COV(~?~,~~)],

(19)

J BUSN RES 1992 25 l-25

Effects of Pension Compensation

E(G) (l-u)

= [K + (1 - u)PBX - A]r -

where

the second

+ A[C~Y(~~,!?~)

hcov(Rqm)],

(28)

term on the right-hand-side

X* K[ Cov(R”,Z?“)

-

-

1s equal

ACOV(&I?~)]

(1 - u)lK + pIK,km]

rPBX)

(1 - u) + PJ?“]

rPBX)

-

-

= h*{Cov[(G

- rPBX)

(1 - u), a”‘] + Cov(i),/?‘)

= A*{Cov[(G

-

(1 - u)$?‘]

rPBX)

ACOU(~/A,Z?~)}

- Cov(pJ?)}

= h*{Cov[(G’

= A*{Cov[~(l

to

(AIK)Cov@?‘,I?)]

= X*[KCov@“,fim) = h*{KCov[(G

23

-

COV(~,!?~)}

- u),fim]

= A*(1 - u)Cov(~J?“‘] Thus, we get (28’) Finally, to get (33), we note that (?” = (1 - u)G + rPBX+P where

By subtractng PBX from both sides of Equation

R = rPBX

K = E{I;? = E{[(I?

-

= IIU + R

(31), we get

PBX + R)

-

urPBX

-

P]

+ E(p)}IE(Wm)

+ uPBX

-

PBX,

where E(i?‘“)

= E(p)IK

+ urPBXIK

-

urPBXIK

-

(PBXIK)

(I - u)E(Rm)

Then W/K

= E(p)IK

= E(a”“)

= E(I?‘“)

-

rh’(1

-

= E(Rm)

+ [E(I?‘“)

-

rh’ + urh’

u) + h’(l -

-

r] h’ (1 -

= R“” + (1 - u) h’ (Rm -

r)

+

h’(1 - u)E(I?‘“)

u)E(Z?‘“)

u)

(33)

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J BUSN RES 1992 25 l-2.5

Effects of Penslon Compensation

25

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Councd of Life Insurance

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Under Condltlons 36 (1981) Reality

1-13

of Pension

Institute for Public