The settlement of pension plans: turning the need into opportunity?

OLYMPIO Neil

Towers Perrin

71 High Holborn London WC1V 6TP

United Kingdom

Tel.: +44 (0) 207-170-3294 Fax: +44 (0) 207-170-2222

neil.olympio@towersperrin.com

Abstract In this paper, we will study how the risk is modified when a company gets rid of a pension plan and will also suggest a model to leave the cost of capital of a firm virtually unaffected by a buy-out. The empirical findings in this paper tend to show that the use of the CAPM model or the use of the WACC to calculate the cost of capital does not have the same impact when it comes to neutralizing the effect of a settlement in terms of risk. With further developments, this shows that the buy-out could be an opportunity to pilot the cost of capital. Keywords: Cost of Capital, pensions, settlement, Capital Asset Pricing Model (CAPM), Weighted Average Cost of Capital (WACC), leverage, market capitalization.

Introduction

Pension costs have been increasing for many years and this has of course increased the probability of insolvency for the firms sponsoring a pension plan. This evolution raised serious concerns not only for the governments who provide benefits at retirement, but also for private pensions. More and more firms may be tempted to settle their pension plans given the performances of the financial markets and the increasing deficits of pension plans. In this paper, we will see that getting rid of pension plans has an impact on the overall risk of the firms as seen by a potential investor (cost of capital). Depending on the strategy, some companies will decide to get rid of their pension plans whereas others will keep the plans in order not to impact the overall risk level. We will therefore assess the change in risk when getting rid of the pension plan. Then, we will focus on the impact of externalizing and assess the settlement needed to maintain the initial cost of capital. The level of risk will be estimated with the cost of capital given by the Capital Asset Pricing Model (CAPM), or with the weighted average cost of Capital (WACC). The formulas will need to be adapted for the case of pension plans. The model will be implemented with a sample of multinational firms sponsoring pension plans.

2

Contents

1 ASSESSING THE RISK WHEN BUYING OUT........................................................................4

1.1 NOTATIONS ...................................................................................................................................4 1.2 IMPACTS OF BUY-OUT ..................................................................................................................4 1.2.1 IMPACT ON THE OPERATING ASSETS ...........................................................................................4 1.2.2 IMPACT ON EQUITY AND DEBT...................................................................................................5 1.3 CALCULATION OF THE COST OF CAPITAL AFTER BUY-OUT.......................................................6 1.3.1 WACC ........................................................................................................................................6 1.3.1.1 Treating the pension surplus as negative debt .........................................................................6 1.3.1.2 Finding the cost of the pension surplus ...................................................................................7 1.3.2 CAPM.........................................................................................................................................8

2 MAINTAINING INITIAL RISK ..................................................................................................9

2.1 MAINTAINING BETA OF OPERATING ASSETS ..............................................................................9 2.2 MAINTAINING THE WACC........................................................................................................10

3 RESULTS......................................................................................................................................14

3.1 INITIAL RISK ...............................................................................................................................14 3.2 INCREASE OF DEBT ONLY ..........................................................................................................14 3.3 MAINTAINING THE COST OF CAPITAL – COMPARISON OF METHODS.....................................15

CONCLUSION ...................................................................................................................................23

BIBLIOGRAPHY...............................................................................................................................24

APPENDIX..........................................................................................................................................25

3

1 Assessing the risk when buying out

1.1 Notations Let us consider a company with n pension plans P1, P2 ...Pn Define: OA as the value of operating-assets, E as the value of Equity, D as the value of Debt, OAβ , Eβ and Dβ as the

corresponding betas; as the levered beta and as the unlevered beta, r as the market return and as the risk-free rate.

Lβ Uβ m fr

For i=1 to n, PA(i) as the value of pension assets for Plan Pi, PL(i) as the value of pension liabilities for Plan Pi, S(i)=PA(i)-PL(i) as the pension surplus for Plan Pi. We then have:

PA = ∑=

n

i

iPA1

)( as the total pension assets for the company,

PL = ∑=

n

iiPL

1)( as the total pension liabilities for the firm,

S = ∑=

n

iiS

1)( as the total surplus for the firm.

We will assume as it is the case for many firms, that S<0, that is the firm’s total pension plans are in deficit rather than in surplus. If the firm decides to get rid of the plan Pk. We will then have:

S’ = - S(k) as the new total surplus for the firm, assumed to be a deficit ∑=

n

i

iS1

)(

1.2 Impacts of buy-out

1.2.1 Impact on the operating assets

We have assumed that S<0, namely the pension liabilities are greater than the pension assets. The pension plan we want to get rid of also has a deficit, therefore our new deficit will be lower than the previous one when we had all pension plans. Case1: the value of operating assets decreases A lower value of the firm can be assimilated to a decrease in Equity or a decrease in Debt. In both cases, this would actually cost money. Since the pension plan is sold to an insurer, this is an outflow and not an inflow. A firm can raise more money by issuing more debt, but we have just seen that here, the level of Debt (or Equity) would be lowered. Therefore, after the buy-out, the value of the operating assets can not decrease. Case2: the value of operating assets increases This is really unlikely that a company buys out and has more money after the buyout than there was previously. This could actually be assimilated to a free lunch. There would therefore be an arbitrage opportunity. We will then consider that an increase of the value of the operating assets of the firm is not possible. It is therefore important in modeling the situation, that the level of operating assets remain the same.

4

1.2.2 Impact on Equity and Debt

Impact on Equity We do not know if the level of Equity will decrease or increase, we will simply define the new Equity as E’=E+y Impact on Debt As for the Equity, we will consider that the new Debt is given by: D’=D+x The situation is summarized in the following diagram: Before buy-out:

Asset Liability E

OA D

PA PL

(Diagram 1-1)

Alternatively,

Asset Liability E

D OA

S

(Diagram 1-2)

After the buy-out, the situation is as follows:

Asset Liability E + y

D + x OA

S’

(Diagram 1-3)

With y being the amount of increase in Equity, and x being the amount of increase in Debt. Those amounts can be either negative (decrease) or positive (increase). To maintain the level of operating assets, we have:

OA = Previous allocation= E + D – S = E + y + D + x - S’ = new allocation = OA This implies a constraint for x and y:

SSyx −=+ ' (2) Given our hypothesis on the surpluses, we have that S’ - S > 0 (since S is a deficit, S and S’ are negative amounts). This already shows that x and y can not both be negative. In addition, in economic terms, x and y being negative would mean a free-lunch. To sum up, x and y can be both positive which would mean an increase of both the level of Debt and the level of Equity; or the parameters can have opposite signs, which would mean that an increase in one of the two parameters would be used to decrease the level of the other parameter.

5

1.3 Calculation of the cost of capital after buy-out

1.3.1 WACC

Initially, the balance sheet is as follows:

Asset Liability E

OA D

(Diagram 1-4)

We can assess the cost of capital by different methods, and here we have chosen to use the weighted average cost of capital. In the initial situation, if we ignore the taxes, the weighted average cost of capital gives:

DE kOADk

OAEWACC += (3)

where:

Ek is the cost of Equity

Dk is the cost of debt When the firm sponsors a pension plan, the balance sheet is as follows:

Asset Liability E

OA D

PA PL

(Diagram 1-5)

Alternatively,

Asset Liability E

D OA

-S

(Diagram 1-6)

In that case, we have to adapt the formula, to take into account the pension plan when calculating the cost of capital. Two main possibilities are:

Treating the pension surplus as negative debt Finding the cost of the pension surplus

1.3.1.1 Treating the pension surplus as negative debt If we treat the pension surplus as negative debt, the new weighted average cost of capital is:

DE kOAS

OADk

OAEWACC

−+= (4)

However, the main drawback of this option is that the risk of the pension plan is assimilated to the risk of the debt. In some cases, it may be true, but it is also likely to be different. From the beginning, we have treated the pension liabilities as having the same risk as debt. Therefore, if the deficit, or negative surplus, is very important, we have:

6

PAPL >> In that case, we could assume that the cost of the pension plan is likely to be very close to the cost of debt. This is a case where this model could be validated.

1.3.1.2 Finding the cost of the pension surplus The other approach we could use is to find the cost of the pension surplus and derive the new weighted average cost of capital. Let kS denote the cost of the pension surplus, the new weighted average cost of capital is given by:

SDE kOASk

OADk

OAEWACC −+= (5)

Let us now derive the cost of the pension surplus. To calculate the cost of the pension surplus, we will again use the weighted average cost of capital. We have:

PLPAS −= Therefore, using the cost of capital we obtain:

PLPAS kS

PLkS

PAk −=

Where kPA is the cost of the pension assets and kPL is the cost of the pension liabilities. Since we have assumed so far that the pension liabilities are similar to debt, we have:

DPL kk = (6) Now let us derive the cost of the pension assets. If we consider there are L asset classes (l =1 to L) in the pension plan. C is the amount of class l in the pension plan.

l

We can once again use the weighted average cost of capital to assess the cost of the pension assets. We could then define this cost as:

l

L

l

lPA k

PACk ∑

=

=1

where kl is the cost of asset class l. This leads to:

Dl

L

llS k

SPLkC

PASPAk ×−××= ∑

=1

1

And this gives

l

L

llDE kC

SOASk

SPL

OAS

OADk

OAEWACC ∑

=

××−

×++=

1

1

Eventually

∑=

−

++=

L

ll

lDE k

OAC

kOAPL

OADk

OAEWACC

1 (7)

7

In practice, we have assumed that the different asset classes would generally behave either like bonds or like equity. This would therefore simplify the previous equation. Assuming the pension assets allocation can be summarized as bonds and equities. Let e denote the level of Equity in the pension assets and d the level of debt in the pension assets. Let ke and kd denote the corresponding cost of equity and debt. We can rewrite the cost of the pension assets as follows:

dePA kPAdk

PAek +=

This leads to

DdeS kS

PLkSdk

Sek −+=

And eventually

deDE kSdk

Sek

OAPL

OADk

OAEWACC ++

++= (8)

We assumed that the Equity in the pension assets has the same characteristics of the Equity of the firm (see appendix), and the same can be assumed concerning the debt of the plan assets. With these assumptions, we can derive the following formula for the weighted average cost of capital, which is the formula we will use with the different firms we will study later in this paper:

DE kOA

dPLDkOA

eEWACC −++−= (9)

1.3.2 Capital Asset Pricing Model (CAPM)

Using the CAPM, the cost of capital is given by:

( )fmOAf rrrCC −+= β (10) Using the same methodology as in JIN, MERTON and BODIE [2005], the original beta of operating assets is:

−−+= PLPADEOA OA

PLOAPA

OAD

OAE βββββ (11)

Beta of firm’s Equity From Modigliani & Miller [1958], we know that modifying the capital structure will imply a change in the beta of Equity. The change in beta of Equity following a modification of the capital’s structure could be assessed as follows; where is the levered beta and the unlevered beta. Using the standard Hamada formula: Lβ Uβ

+=

EDUL 1ββ (12)

However, this formula can not be used directly because this would not take into account the pension plans.

8

We suggest using the new beta levered as follows:

−+==

ESDU

EL 1βββ (13) (see appendix)

Thus in the case of the buy-out:

+

−++==yE

SxDUE

L '1βββ (14)

Alternatively,

yESxD

LU

+−++

='1

ββ (15)

This will assimilate the pension deficit (only negative surplus is considered in this paper) as having the same risk characteristics as Debt. In terms of leverage, the pension surplus is considered as negative Debt. The new operating-asset risk is then given by:

[ ]'''''

' '')()(1PLPADEOA PLPAxDyE

OAβββββ +−+++= (16)

If we consider the two possible errors as defined in JIN, MERTON and BODIE [2005], the new operating-asset risk would be given by: Error case 1:

''^^

EDOA xDyEyE

xDyExD βββ

+++++

++++= (17)

Error case 2:

''^ '

DEOA OASxD

OAyE βββ −+++= (18)

We understand that getting rid of a pension plan will have an impact on many parameters and in particular on the operating-asset risk. The firm could accept this change in its beta of operating assets but could also choose to maintain the level of risk exposure of its operating assets. This decision belongs to the firm’s strategy.

2 Maintaining initial risk

2.1 Maintaining beta of operating assets Maintaining the cost of capital given by the CAPM is equivalent to maintaining the operating-asset risk, namely the beta of the operating assets. We will evaluate the needed x and y that would meet the initial constraint of maintaining the level of operating assets, and another constraint which is to maintain the operating-asset risk. We consider that the beta given by equation (2) is equal to the one given by equation (16), and solve this for x and y.

9

We obtain the following:

)'('' ''''

SDEPLPADxy UOA

PLPADU

OA

DOAU

−+−−

+−+

−+−

=ββ

βββββ

βββ (19)

Proof: see appendix We then have a linear relation: y = ax + b Any point on that line would satisfy the constraint of maintaining the beta of operating assets. The next step is now to take into account the initial constraint given by equation (2), namely

x + y = S’ – S Taking into account equations (2) and (19), we find that only one point will meet both requirements to maintain the level of operating assets and to maintain the beta of the operating assets. That is for:

1'

+−−=

abSSx (20)

with UOA

DOAU

aββ

βββ−

+−=

'

(21)

and )'('' '''

SDEPLPADU

OA

PLPAD −+−−

+−=

βββββb (22)

and y will be given by the linear relation Proof: see appendix. But even if there are solutions for x and y, it does not mean that such an operation can be done for all companies. As a matter of fact, assuming we find y negative in such way that E + y < 0, this will be a non-sense for the company to have a negative Equity after getting rid of one of its pension plan. Therefore, depending on the initial parameters for a given firm, we should be cautious when applying this model.

2.2 Maintaining the WACC We can also choose to maintain the cost of capital given by the WACC method. Initially the balance sheet is as follows:

Asset Liability E

D OA

-S

(Diagram 2-1)

with, given by equation (9):

DE kOA

dPLDkOA

eEWACC −++−=

After buy-out we have

10

Asset Liability E+y

D+x OA

-S’

Diagram 2-2

and

DE kOA

dPLxDkOA

eyEWACC''

''

' −+++−+= (23)

Where e’ denotes the new level of Equity in the pension assets and d’ the level of debt in the pension assets, after getting rid of a plan. In this case, we need to have

'WACCWACC = (24)

The cost of Debt is unchanged and the cost of Equity becomes:

'Ek = )('

fmEf rrr −×+ β

= ( )

+

−++××−+yE

SxDrrr Ufmf

'1β

= ( )yE

SxDyErrrf fmU

+−+++×−×+ 'β

= ( )yE

OArrrf fmU

+×−×+ β (25)

Then, by (24) we have:

( ) ( ) ( ) WACCOAkdPLxDeyEyE

OArrr DfmU

f .''' =×−−++−+×

+

×−×+ β

Rearranging (cf. appendix), we obtain:

0... 54322

1 =++++ ααααα xyxyy (26) with

1α = fr

2α = ( )( )WACCrrOAdPLDkeEr fmU

Df −−+−++− ..)''.()'2.( β

3α = Dk

4α = DkE.

5α = ( ) ( )( ) ( )( )OArrrEedPLDkWACCOAOArrrEE fmU

fDfmU

f ...'''.... −+−−++−−+ ββ Assuming x is fixed, we have to solve

( ) ( ) 054322

1 =++++ ααααα xyxy (27) We obtain

11

( ) ( 5412

32 4 ααααα +−+=∆ xx ) (28) Provided we have 0>∆

1y = ( )

1

32

2.

ααα ∆−+− x

2y = ( )

1

32

2.

ααα ∆++− x

To picture the situation, let’s assume

154321 ===== ααααα

Solving the equation leads to:

Maintaining WACC

-400

-300

-200

-100

0

100

200

300

400

-120 -100 -80 -60 -40 -20 0

y1y2

(Chart 2-1)

12

When assessing the settlement, any point on the curve will maintain the WACC at its initial level. In addition, when maintaining the level of operating assets, we have found earlier that

SSxy −=+ '

Adding this constraint, we will find that not all points are satisfactory. Example:

Maintaining WACC

-400

-300

-200

-100

0

100

200

300

400

-120 -100 -80 -60 -40 -20 0

y1y2y

(Chart 2-2)

Depending on the parameters, one or two points only will be satisfactory solutions when assessing the settlement. To obtain the targeted points, we can also directly derive the initial equation (26) by substituting x using equation (2).

Rearranging we obtain:

0322

1 =++ ααα yy (29) with

1α = Df kr −

2α = ( ) ( )( ) ( ) fDfmDf reSSPLdDkWACCrrUOAkrE '.'''.2 −−++−+−−×+− β

3α = ( )( ) ( )[ ] ( )fmU

DffmU

f rrOAeSSPLdDkreWACCrrOArEE −−−++−+−−−×+ .'.''''.. ββ Proof: Appendix Provided we have the following solutions: 0>∆

y = 1

312

22

24

ααααα −±−

x = ySS −−' We will tend to choose the smaller solution for y considering the firm would rather have a small increase of Equity than an important increase where the consequences on the stocks (price, dividends etc.) can not easily be assessed.

13

3 Results

We will consider a sample of firms sponsoring pension plans. Using the model that has been developed previously, we will assess the risk-level of the pension plans, and will assess the impact on the overall risk level of those firms when they get rid of their pension plans. We will then compare the results obtained with the CAPM and WACC models when assessing the new allocation of Debt and Equity needed to maintain the initial risk, as calculated with each method.

The majorities of firms studied are multinational and have pension plans in foreign countries. The assets classes of those pension plans are in foreign currency. It is therefore important to have a standard measure of the risk for the whole sample; it means that all risk levels expressed in terms of betas will be brought back to the British market. In other terms, it is necessary to obtain the correlation of all asset classes (foreign and U.K) with the U.K. Equity. This step involves DFA (Dynamic Financial analysis) models to simulate the possible scenarios for the evolution of bonds, equities, inflation etc.

We used Towers Perrin CAP:Link © to obtain the correlation matrix from which we derived the different betas needed.

3.1 Initial risk For all firms, we obtain the following initial beta of operating assets and corresponding cost of capital (CC) given by the CAPM, and weighted average cost of capital (WACC):

Firm WACC OAβ CC Number of plans 1 5.44% 0.14 5.41% 1 2 7.36 0.73 7.19 1 3 7.31 0.50 6.49 2 4 6.49 0.45 6.36 2 5 8.38 1.09 8.26 1 6 9.59 1.27 8.80 3 7 5.88 0.23 5.70 1 8 7.62 0.81 7.44 2 9 8.24 0.93 7.79 3

(Table 3-1)

3.2 Increase of Debt only If only the Debt level is modified for the buy-out, the evolution of the risk is as follows and does not allow the initial level of risk to be maintained:

Firm Plan settled WACC CC 1 1 5.44% 5.46% 2 1 7.43 7.32

1 7.87 7.25 3 2 7.33 6.51 1 6.50 6.37 4 2 6.49 6.36

5 1 8.40 8.30 1 9.64 8.83 2 9.63 8.85 6 3 9.59 8.81

7 1 5.91 5.86 1 7.65 7.50 8 2 7.64 7.49 1 8.33 7.91 2 8.27 7.82 9 3 8.24 7.79

(Table 3-2)

For each firm, plans have been ordered in descending order according to the size of their assets and liabilities.

14

3.3 Maintaining the cost of Capital – Comparison of methods Both the level of debt and equity will be modified as follows to maintain the cost of capital, calculated either with CAPM or with WACC. Firm 1

Firm 1

-120

-100

-80

-60

-40

-20

0

20

40

Equity Debt

Chan

ge (%

)

CCWACC

If we use the cost of capital given by the CAPM model, in order to maintain the cost of capital, we will end up with a negative level of Debt, which is not likely to happen. The solution provided by the WACC is an increase of both Debt and Equity (probably borrow more debt to finance the equity). Firm 2

Firm 2

-350-300-250-200-150-100-50

050

100

Equity Debt

Chan

ge (%

)

CCWACC

In that case again, using the cost of capital provided by the CAPM model would lead to a negative amount of debt after buy-out.

15

Firm 3

Firm 3 - Plan 1

-1400-1200-1000-800-600-400-200

0200400600800

Equity Debt

Chan

ge (%

)

CCWACC

The pension liabilities of the plan 1 for firm 3 amount to 105% of the firm’s market capitalization. With the cost of capital given by the CAPM the decrease of debt to maintain the cost of capital is very high.

Firm 3 - Plan 2

-20

-10

0

10

20

30

40

Equity Debt

Chan

ge (%

)

CCWACC

For plan 2, the increases needed are in opposite direction for CAPM and WACC. The increase of Debt is this time much more important with the cost of capital given by the WACC.

16

Firm 4

Firm 4 - Plan 1

-40

-30

-20

-10

0

10

20

Equity Debt

Chan

ge (%

)

Series1Series2

Firm 4 - Plan 2

-4

-3

-2

-1

0

1

2

Equity Debt

Chan

ge (%

)

CCWACC

For both plans, the increases needed are in opposite direction for CAPM and WACC. The increase of Debt is this time much more important with the cost of capital given by the WACC.

17

Firm 5

Firm 5

-140

-120

-100

-80

-60

-40

-20

0

20

Equity DebtCh

ange

(%)

CCWACC

For this firm, getting rid of her pension plan and maintaining the cost of capital does not seem possible using the CAPM model. Firm 6

Firm 6 - Plan 1

-35-30-25-20-15-10-505

101520

Equity Debt

Chan

ge (%

)

CCWACC

18

Firm 6 - Plan 2

-50

-40

-30

-20

-10

0

10

20

30

Equity Debt

Chan

ge (%

)

CCWACC

Firm 6 - Plan 3

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Equity Debt

Chan

ge (%

)

CCWACC

For plan 3, the CAPM suggests that the increase of Debt and Equity are in opposite directions whereas the WACC increases both Debt and Equity.

19

Firm 7

Firm 7

-150

-100

-50

0

50

100

Equity Debt

Chan

ge (%

)

CCWACC

For this firm, getting rid of her pension plan and maintaining the cost of capital does not seem possible using the CAPM model. Firm 8

Firm 8 - Plan 1

-250

-200

-150

-100

-50

0

50

Equity Debt

Chan

ge (%

)

CCWACC

20

Firm 8 - Plan 2

-120

-100

-80

-60

-40

-20

0

20

Equity DebtCh

ange

(%)

CCWACC

Whether it is for plan 1 or plan 2, the firm 8 would not be able to maintain her cost of capital after buy-out with the CAPM. Firm 9

Firm 9 - Plan 1

-200

-150

-100

-50

0

50

100

Equity Debt

Chan

ge (%

)

CCWACC

This is the only plan in our sample that has a positive surplus. Some assumptions may not be valid in this case. Using the cost of capital given by the CAPM would imply a negative debt after buy-out. The difference between total pension assets and total pension liabilities for this firm is still a deficit (plans 2 and 3 are in deficit).

21

Firm 9 - Plan 2

-50

-40

-30

-20

-10

0

10

20

Equity Debt

Cha

nge

(%)

CCWACC

Firm 9 - Plan 3

-2

0

2

4

6

8

10

12

Equity Debt

Cha

nge

(%)

CCWACC

For plan 3, the change needed to maintain the cost of capital with WACC is, this time, greater than the one needed using CAPM. The CAPM suggest an increase of Equity to finance a decrease of Debt whereas the WACC suggests increasing the Debt and decreasing the Equity. Let us recall that, for each firm, the pension plans are classified in descending order according to the size of their pension assets and liabilities.

22

Conclusion

In this paper, we suggested the use of the cost of capital as a measure of the overall risk of the firm. The costs of capital calculated with the CAPM or with the WACC are not significantly different and we would suggest the use of the average of results given by each method. We considered the possibility for the firm to buy the pension plan out, in response for instance to a non favorable environment or a too high levy paid to the P.P.F in the U.K. or the P.B.G.C in the United States.

We have seen that this buy-out possibility has not only a financial or monetary cost but also a cost in terms of the overall risk of the firm; namely the behavior of the firm in response to the financial markets’ ups and downs. Then the model suggested an allocation of the Equity and Debt levels that would maintain the initial risk of the firm and therefore leave the firm virtually unaffected by a buy-out.

We found that, although the initial risks assessed with the CAPM or WACC are similar, the choice of a method is very important when assessing the settlement. As a matter of fact, the cost of the settlement is the same in monetary units; however the impact on the overall risk of the firm varies according to the method chosen. Regardless of the method, the cost of capital increases when the firms get rid of their pension plans, for the sample of firm studied. In addition, maintaining the initial risk seems a lot easier when using the WACC; the use of the CAPM gives in several cases no solution for that constraint. However, if a firm decides to settle one of her minor plans, it is more interesting to use the CAPM which gives a smaller modification of the capital structure than the WACC.

The use of the cost of capital as a risk indicator is one possibility amongst others. In order to set a risk-based levy, one of these possibilities may be to assess the probability of insolvency of the firm. In addition, with further developments the model could be used to assess an optimal asset allocation.

One of the main findings of the paper is the use of pension plans as a financial tool to pilot the overall risk of the firm as perceived by potential investors. As a matter of fact, it is possible to assess the new level of Debt and equity needed to reach a pre-determined cost of capital. Therefore, this enables the firm to attract or retain a chosen type of investors

23

Bibliography ANDERSON A., (1992) Pension Mathematics for Actuaries, Second Edition, ACTEX ASNESS C., (2000) Stock versus Bonds: Explaining the Equity Risk Premium – Association for Investment Management and Research BOWERS D., Franks S., (2005) Global Fund Manager Survey – Merrill Lynch CAPIELLO L., ENGLE R., SHEPPARD K., (2003) Asymmetric Dynamics in the Correlation of Global Equity and Bond Returns – European Central Bank FUNG W, HSIEH D, (1998) Empirical Characteristics of Dynamic Trading Strategies: The Case of Hedge Funds GERKE W., PELLENS B. (2003) Pension provisions, pension funds and the rating of companies – a critical analysis JIN L, MERTON R, BODIE Z (2005) Do a Firm’s Equity Returns reflect the risk of its pension plan? Journal of Financial Economics MODIGLIANI, MILLER, (1958) The Cost of Capital, Corporation Finance, and the Theory of Investment, American Economic Review 48 McGILL, BROWN, HALEY, SCHIEBER, (1996) Fundamentals of Private Pensions, Seventh Edition, Penn NESBITT S., (2004) Asset Allocation Return and Risk Assumptions – Wilshire O’BRIEN P., (2004) The Case for Bonds – Morgan Stanley Investment Management PRICEWATERHOUSECOOPERS LLP, (2005) Paying off Pension fund Deficits: Impact on company behaviour, share prices and macro economy, Report QUITTARD-PINON F., (2003) Marché des Capitaux et Théorie Financière, 3eme Edition Economica QUITTARD-PINON F., (2002) Mathématiques financières, Editions EMS SHARPE W., (1992) Asset Allocation: Management Style and Performance Measurement SMITH A., (1999) Market-Led Valuations – Presentation Bacon and Woodrow SHUETRIM G., (1998) Systematic risk Characteristics of Corporate Equity – Reserve Bank of Australia TOWERS PERRIN, (2005) PPF Becomes An Equity Investor – Monitor United Kingdom TOWERS PERRIN, (2005) PPF Announces Details of Risk-Based Levy – Monitor United Kingdom TOWERS PERRIN, (2003) Pensions and Corporate Financial Performance

24

Appendix Equations (13) to (15) In order to simplify our calculations, we will assimilate the pension surplus to either debt or equity. As we are considering only plans that have a deficit, the greater the deficit, the more it seems reasonable to assimilate the pension surplus to negative debt. We have indeed PL >> PA. This may not be valid for the only plan that has a surplus in our sample (plan 1 for firm 9). In addition, while performing the calculations, we noticed that for our sample of firms, the beta of surplus was either close to the beta of debt, or we have seen that the impact of the debt-related part in the surplus (d-PL) is greater than the equity-related part (e). Eventually Pricewaterhouse Coopers LLP [2005] show in their report that the firms’ equity beta can be written as follows when deficits are treated the same as debt, assuming pension plans are fully accounted for:

EPE

EP

ED dUL +

++×= 1ββ (see Pricewaterhouse Coopers LLP Report [2005] for derivation)

where Pd and PE represent the pension deficit and the pension equity assets respectively. Thus using our notations we have:

Ee

ESDUL +

−+×= 1ββ

Given the average ratio of pension equity assets over firm’s equity in the sample of firms studied, we have chosen not to allow for the second term of the equation. As a conclusion, we have used the following formula:

−+==

ESDU

EL 1βββ rather than

−+==

SEDU

EL 1βββ

It seemed indeed more reasonable, given the latest research available and the sample of firms studied, to assimilate the pension surplus to debt rather than equity. Proof of the linear relation relationship – Equations (19) to (22): We want to maintain the initial beta of operating assets and will find x and y such that it is the case:

'''' '')()()'( PLPADEOA PLPAxDyESxDyE βββββ +−+++=−+++

Given that

+

−++=yE

SxDUE

'1' ββ

we then have

''' '')()'()'( PLPADU

OA PLPAxDSxDyESxDyE βββββ +−++−+++=−+++

( ) '''' '')'()( PLPADDOAUU

OA PLPADSDExy ββββββββ +−+−+++−=−⇔ Eventually:

)'('' ''''

SDEPLPADxy UOA

PLPADU

OA

DOAU

−+−−

+−+

−+−

=ββ

βββββ

βββ

25

Maintaining WACC - equations (26) and (29) 1/Initially ( ) ( ) WACCOAkdPLxDkeyE DE ×=−+++−+ .''.' ' The new cost of equity is given by:

'Ek = )('

fmEf rrr −×+ β

= ( )

+

−++××−+yE

SxDrrr Ufmf

'1β

= ( )yE

SxDyErrrf fmU

+−+++×−×+ 'β

= ( )yE

OArrrf fmU

+×−×+ β

We then have

( ) ( ) ( WACCOAkdPLxDeyEyE

OArrr DfmU

f .)''' =×−−++−+×

+

×−×+ β )

( )[ ] ( )

( )[ ]

( )

( )[ ]

0

..'.

.''..

....

''....

=

−×++−

×−−+++

−×+++×−

−+++−×++×

fmU

ff

D

fmU

ff

DfmU

ff

rrryrEe

WACCOAydPLxDky

rrryrEyWACCOAE

dPLxDkErrryrEE

β

β

β

⇔

( ) ( )[ ]

( ) ( )[ ]

( )[ ]

0

..'..''..

.......

.'.''..2

2 =

−×+−

−−++

−×+×++++

−×+−−++×−×

OArrrEekWACCOAdPLDkE

OArrrEEkDExkdxyry

OArrrfedPLDkWACCOArEy

fmU

fD

D

fmU

ff

fmU

Df

β

β

β

26

⇔

( ) ( ) ( )( )[ ]

( ) ( ) ( )[ ]

( )[ ]

0

..'

''........

''.'2..2

=

−×+−

−++−−×+×+++

−−××+−++−×+

OArrrEe

dPLDkWACCOAOArrrEEkExkxy

WACCrrOAdPLDkeEryry

fmU

f

DfmU

fDD

fmU

Dff

β

β

β

Eventually we obtain

0... 54322

1 =++++ ααααα xyxyy with

1α = fr

2α = ( )( )WACCrrOAdPLDkeEr fmU

Df −−+−++− ..)''.()'2.( β

3α = Dk

4α = DkE.

5α = ( ) ( )( ) ( )( )OArrrEedPLDkWACCOAOArrrEE fmU

fDfmU

f ...'''.... −+−−++−−+ ββ 2/substituting x using , we have SSsy −=+ '

0.. 322

1 =++ ααα yy with

1α = Df kr −

2α = ( ) ( )( ) ( ) fDfmU

Df reSSPLdDkWACCrrOAkrE '.'''..2. −−++−+−−×+− β

3α = ( )( ) ( )[ ] ( )( )ffmU

DfmU

f rrrOAeSSPLdDkWACCrrOArEE +−−−++−+−−+× ..'.'''.... ββ 3/assuming we get rid of all pension plans, ( ) ( )( ) ( )( ) ( ) WACCOAkySDrrySDrrryE Dfm

Ufm

Uf .... −−−+−−−+−+×+ ββ = 0

⇔ ( )( ) ( ) ( ) ( )[ ]WACCOAkrrSDkryrrrE DfmU

DffmU

f ... −+−×−+−×+−+× ββ = 0

⇔ ( ) ( )( ) ( ) ( )[ ] WACCOAkrrSDrrrEkry DfmU

fmU

fDf ... −+−×−+−+×+−× ββ = 0

Eventually we have only one solution for y

( ) ( )[ ] ( )[ ]Df

fmU

fDfmU

krrrrEkrrDSWACCOA

y−

−+×−+−×−+×=

.. ββ

Can we assume that the equity in the PA has the same characteristics as the firm’s equity? (9) For most plans, the asset allocation would tend to be prudent rather than aggressive. In that case, if we assume that the equity in the pension assets has the same characteristics as the equity of the firm, we must distinguish between different cases:

27

- The firm’s equity has a beta lower than 1 In that case, the overall beta of the pension assets will be lower than 1 and it does not seem unreasonable to make this assumption. - The firm’s equity has a beta greater than 1 Depending on the proportion of debt in the pension assets, we can still have a beta lower than 1 for the pension assets. Let us see an example below:

Proportion of equity in the pension assets 20% Proportion of debt in the pension assets 80% Beta of equity 1.3 Beta of debt 0.175 Beta of pension assets 0.4

There are a few examples of firms in the U.K. that have a 100% equity allocation in their pension assets and a beta around 1. We can still restrict the model to be used only for firms whose beta of pension assets is not greater than 1. In that case, for our assumption to remain valid, we may need to add the following condition:

PAβ < 1

De PAd

PAe ββ +

< 1

DE de ββ .. + < PA from our main assumption

e < E

DdPAβ

β.−

For firms that already have a beta above 1, this is the threshold above which our assumption will lead to a beta greater than 1 for the pension assets. In the paper, there are four firms that have a beta above 1. For one of these firms, the above requirement is met, leading to a beta of pension assets below 1. For the three remaining firms, the above requirement is not met and this leads to betas between 1.01 and 1.03. This is not necessarily an anomaly but needs to be dealt with on an individual basis. As a matter of fact, there are examples of firms in the U.K. that have a 100% equity allocation in their pension assets and for which the beta is around 1. To sum up, this is one of the assumptions that may need to be dealt with carefully when applying the model for a firm that would have a beta above 1. We would suggest testing first that the level of equity does not exceed the threshold defined above. If it were to exceed that threshold, this would not mean that the assumption would not be valid, but we then have to make sure that it is relevant for that particular firm. Classification of the firms studied We have chosen to classify the firms studied according to 2 parameters. The first parameter is the beta of the firm’s Equity, and the second parameter is the market capitalization of the firm. - Beta of firm’s Equity The different betas are classified as follows:

Beta Classification 8.0<β Low

2.18.0 <≤ β Average β≤2.1 High (Table A-1)

28

29

- Market capitalization The different market capitalizations have been ordered as follows:

Market Capitalization in £bn Classification <10 Low

10-24 Medium 24+ High

(Table A-2) The above classifications have been chosen arbitrarily for the purpose of this paper. The different firms are ordered as given below:

Beta Low Average High

Low 1 2 3 Medium 4 5 6 Market

capitalization High 7 8 9 (Table A-3)

Firms’ profiles We will describe below the profiles of the sample of firm chosen to illustrate the different categories. For confidentiality, the firms have been assigned a number from 1 to 9.

Firm Importance of PA (relative to market

capitalization) Eβ L

(Debt/Equity) Plan Importance of plan (relative to firm’s

total PA) (%) PA/PL

1 8.01% 0.16 0.15 1 100 0.60 2 10.62% 0.86 0.13 1 100 0.90

1 96 0.80 3 104.75% 1.20 0.41 2 4 0.41 1 93 0.77 4 3.70% 0.56 0.26 2 7 0.47

5 2.65% 1.18 0.07 1 100 0.67 1 57 0.99 2 38 0.77 6 10.51% 1.86 0.46 3 5 0.63

7 14.17% 0.36 0.44 1 100 0.71 1 70 0.82 8 11.57% 0.95 0.12 2 30 0.79 1 70 1.09 2 23 0.92 9 14.39% 1.28 0.33 3 7 0.27

(Table A-4)

Note on the assumptions: A risk-free rate of 5% and a market risk premium of 3% have been used. Given the duration and characteristics of the pension obligations, we have assumed that pension obligations behave like bonds.