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Pension policy and the value of corporate-level investment.

We examine how pension policy affects the value of corporate-level investment to the firm and its various claimants using Monte Carlo simulation. Shareholders lose the greatest amount of project value to the pension plan when it is undiversified across asset classes. Improved funding levels mandated by the provisions of the Pension Protection Act of 2006 generally reduce those wealth transfers. Thus, mitigation of the overhang effect joins the reduction of financial distress costs as a motivation for homing both stocks and bonds in the pension fund.

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Corporate pension policy describes decisions that determine the funded status of the pension plan (the ratio of plan assets to plan liabilities) and the allocation of the pension fund among different asset classes. When financing constraints exist, corporate pension policy will be relevant to shareholder wealth if it influences the amount of internal finance available for capital expenditures. Pension policy also has the potential to determine the extent to which gains from corporate-level investment are shared with the bondholders and the pension fund.

This article employs Monte Carlo simulation to explore the extent to which the investment policy and funded status of a defined benefit pension plan affects the value of corporate-level investment to the firm, its senior claimants, and the shareholders. We also investigate whether changes in the speed of funding mandated by the Pension Protection Act of 2006 have an incremental effect on investment efficiency. To the best of our knowledge, the results presented here are new, and provide an additional motivation for balanced asset allocations in defined benefit plans. The insight they provide cannot be obtained from a large sample empirical study due to the endogenous relationship between pension policy and the financial strength of the plan sponsor.

The simulation results indicate that shareholder project values are indeed sensitive to the selection of corporate pension policy. Shareholder gains from investing are influenced by the asset allocation of the pension assets, the funded status of the plan, and the degree of financial leverage employed by the plan sponsor. That happens because the pension fund is both a profit center (generating volatile investment earnings) and a senior claimant (requiring a fluctuating contribution stream that is senior to debt service).

Our work is closely related in spirit to Parrino and Weisbach (1999), who employ simulation to study the impact of bondholder wealth transfers on the incremental shareholder wealth created by the acceptance of a project. The model here introduces the funding level and asset allocation of the pension fund as added influences on the shareholder value of corporate-level investment. That modification leads to another form of overhang; one that occurs because the pension fund benefits from incremental project income.

All other things equal, a higher level of funding reduces the shortfall that can be transferred to the Pension Benefit Guaranty Corporation (PBGC) in the event of a distressed plan termination. Therefore, for a given level of underfunding, some of the gain from incremental capital expenditures accrues to the pension fund in the form of additional contributions, making those investment opportunities less attractive to the bondholders and the stockholders. The investment policy of the pension fund matters here, too. A streak of poor investment performance can increase the unfunded portion of the liability making the overhang problem more severe.

Parrino and Weisbach (1999) report that low risk projects augment the wealth of the bondholders and high risk projects reduce it. Our analysis begins with an examination of a levered firm that sponsors a defined benefit pension plan that is: 1) initially fully funded and 2) holds only bonds. The results indicate that the pension fund experiences the same coinsurance effect as the bondholders. The plan gains in the form of greater contributions when the firm accepts low risk projects, and those gains decline as the level of project risk increases.

If the plan is severely underfunded, the overhang problem worsens. Corporate-level investment produces even greater gains for the pension fund. As the financial leverage of the plan sponsor increases, both the bondholders and the pension fund receive a greater share of the value of a new project. The same effect occurs when, holding the debt level of the plan sponsor constant, the projected benefit obligation is larger.

The asset allocation of the pension fund also affects the stream of payments it receives from the plan sponsor. Corporate-level investment is most beneficial to the pension plan when the pension fund is undiversified across asset classes as the cash flow stream from the project offsets the more frequent downside performance generated by an unbalanced asset allocation. A 40/60 stock/bond mix minimizes the extent to which the pension fund gains from capital expenditures, regardless as to how risky the project is. In contrast, the bondholders generally lose as the equity exposure of the pension fund increases. That is because the added stock market risk impairs the coinsurance benefit of the project to the fixed claimants.

The influence of equity exposure on the value of the project to the shareholders is determined by a combination of the incremental effect on the value of the project to the firm, the bondholders, and the pension fund. Our simulation results indicate that balanced asset allocations lead to the highest shareholder net present values (NPVs) by a small margin. That outcome occurs because a mix of stocks and bonds in the pension fund produces the greatest shareholder gain to corporate-level investment after accounting for the impact of wealth transfers, tax shields, distress costs, and pension fund investment returns. We conclude that overhang from the pension fund affects the value of corporate-level investment to the shareholders of a defined benefit pension plan and that the magnitude of the effect is shaped, in part, by the investment risk of the pension fund.

The Pension Protection Act of 2006 implemented a series of changes in the minimum funding requirements for defined benefit plan sponsors. We also examine the incremental effect of those changes on the value of corporate-level investment. The impact varies with the funded status of the plan and the investment policy of the pension fund. Our results indicate that the share of project value expropriated by the pension fund is reduced under the new law. That change occurs because the improved level of funding mandated by the Act makes the income from the project less critical to the ability of the plan sponsor to meet future required pension contributions.

This study contributes to the literature on corporate pension policy in three distinct ways. We demonstrate that pension policy is relevant to firm valuation due to its impact on the incremental value of corporate-level investment. Much of the traditional view of corporate pension policy has focused on how the investment risk of the pension fund should be employed in order to exploit the value of underpriced PBGC insurance or create a tax arbitrage. Here we demonstrate that the incentive of shareholders to invest is also shaped by the extent to which pension liabilities are funded and by the investment mix of assets in the pension fund. An important implication of our findings is that pension policy can affect the extent to which the value of the project is shared with the pension fund at the expense of the shareholders. Specifically, the wealth transfer is minimized when the pension fund holds a balanced asset allocation.

This study also complements other work regarding the impact of corporate pension policy demonstrating that pension liabilities influence leverage decisions (Shivdasani and Stefanescu, 2009) and increasing the cost of capital (Jin, Merton, and Bodie, 2006; Campbell, Dhaliwal, and Schwartz, 2012).

Finally, the analysis here indicates that the new funding rules imposed by the Pension Protection Act of 2006 appear to reduce overhang from the pension fund. Campbell et al. (2010) report that pension plan sponsors experienced an average abnormal stock price decline of 4.2% during the time the Act was first approved in the legislative process. Those abnormal returns are concentrated among the subset of firms with larger unfunded liabilities and higher capital expenditure requirements. Our simulation results suggest that the new funding provisions may actually be less harmful than initially suggested, a finding consistent with the results of Warshawsky (2007).

The paper proceeds in the following manner. Section I provides background information on defined benefit pension plans including a brief history of funding requirements and a review of the relevant literature. The structure of the Monte Carlo simulation model is described in Section II. Sections III-VI describe the results of the simulation analysis including an application of the simulation methodology to a collection of individual companies with severely underfunded plans. The seventh and final section provides our conclusions.

I. Corporate Pension Policy and Firm Value

A. Brief History

The funding and investment policies of defined benefit pension plans are subject to varying levels of influence by three stakeholder groups: 1) the plan beneficiaries, 2) the shareholders of the plan sponsor, and 3) the federal government. Plan beneficiaries seek conditions that reduce the risk that promised benefits will not be paid. A fully funded plan holding securities with low price volatility and promising benefits that are underwritten by a federal agency (PBGC) support that objective. The interests of the shareholders, who seek to minimize the cost of sponsoring the plan, are often opposite of those of the beneficiaries. As a consequence, their actions are constrained by regulations written to protect the interests of both the beneficiaries and the federal government.

The role of the federal government in the design of funding and investment policy is dominant and consists of three distinct components. First, the Internal Revenue Code provides valuable tax incentives to defray the cost of plan sponsorship. Additionally, the PBGC (under the Department of Labor) insures annual vested benefits for each plan participant up to $56,000. Finally, federal law sets both minimum annual funding requirements and the liability of the plan sponsor in the event of a plan termination.

Subject to meeting specified minimum contribution requirements, wealth-maximizing shareholders determine the speed with which plan obligations are funded and have a large amount of discretion in determining how accumulated contributions are invested. In the first decades following the passage of Employee Retirement Income Security Act (ERISA), minimum funding requirements were relatively unbinding and the liability of a plan sponsor for unfunded obligations was virtually zero. Those conditions created the (now familiar) moral hazard problem in which financially weak plan sponsors had an incentive to minimize the funding level and maximize the risk of the plan assets. Under that approach, as first formally recognized by Sharpe (1976) and Treynor (1977), the shareholders of the plan sponsor would enjoy the upside investment gains on the pension plan while holding a valuable option to transfer an underfunded plan to the PBGC.

The prescribed optimal funding and investment policy for financially strong plan sponsors in the early ERISA period was diametrically opposite. Viewing the pension assets as a component of the shareholder portfolio, the value-maximizing policy combination called for maintaining a fully funded plan invested entirely in bonds (Black, 1980; Tepper, 1981). Under the assumption that the option to transfer the plan to the PBGC is virtually worthless for viable firms, maximizing the funding level and holding only fixed claims fully exploits the tax arbitrage available to a levered firm by holding the security facing the greatest tax disadvantage (bonds) in a tax shelter. (1)

A succession of legislative activity over two decades, beginning in 1986, steadily reduced, but did not eliminate the moral hazard problem. That reduction was achieved through a combination of changes that increased the employer liability for unfunded obligations, required higher annual contributions for severely underfunded plans, and reduced the gain on overfunded plan terminations. The most recent modification to pension funding rules (the Pension Protection Act of 2006) further alters the amortization of unfunded obligations. (2)

B. Pension Funding and Internal Finance

The early prescriptions for optimal pension policy assumed (explicitly or otherwise) that corporate-level investment would be unaffected by the activity of the pension plan. The confining nature of that assumption has become more apparent with the development of the literature on the convex costs of external financing and the related importance of internal funds (Hennessy, Levy, and Whited, 2007). Large sample empirical studies have examined the connection between unfunded pension liabilities, available internal finance and capital expenditures, but the nature of the conclusions from those studies is mixed.

Three empirical studies collectively suggest that mandatory contributions to defined benefit pension plans reduce internal finance to the point that plan sponsors are unable to accept all high value investment opportunities. Franzoni and Marin (2006) report that the long-run abnormal investment performance of firms with severely underfunded pension plans is significantly negative, a finding they attribute to a failure on the part of investors to properly anticipate higher future mandatory contributions. A concurrent study by Rauh (2006) provides evidence of a corporate-level investment effect by demonstrating that increases in mandatory pension contributions reduce capital expenditures. (3)

Franzoni (2009) subsequently finds that limitations on internal financing suggest a link between the investment effect documented by Rauh (2006) and the underperformance reported by Franzoni and Marin (2006). He examines the correlation between the long-run abnormal returns to defined benefit plan sponsors and the level of mandatory pension contributions. Under the assumption that long-run abnormal performance will reflect any corporate-level investment effect, Franzoni's (2009) evidence points to the fact that underperformance is more pronounced when mandatory contribution levels are higher. The implication is that higher mandatory contributions deprive firms of the funds required to finance high value capital expenditures, resulting in poorer investment performance. (4)

The general state of financial weakness among firms with severely underfunded pension plans suggests an alternative explanation for those poor investment returns that is connected to the distressed firm effect (the investment performance of distressed firms is poor) documented by Campbell, Hilscher, and Szilagyi (2008). Further, while the disclosure process for pension contributions renders an examination of abnormal announcement returns infeasible, the use of long-run abnormal returns to estimate the valuation impact of new information relies on a strictly gradual price adjustment that is absent in semi-strong form efficient markets. (5) In other words, since firms with severely underfunded pension plans are also financially weak, Franzoni's (2009) results may be a manifestation of the distressed firm effect and, therefore, less informative about the influence of underinvestment.

Independent of the difficulties inherent in the estimation and interpretation of long-run abnormal returns, two other studies have produced results that are inconsistent with the notion that pension funding requirements have the capacity to choke off corporate investment. An event study by McFarland, Pang, and Warshawsky (2009) finds virtually no evidence that freezing or closing a defined benefit plan removes a source of value destruction. More generally, Gatchev, Pulvino, and Tarhan (2010) report that an examination of pooled cross-sectional and time series data fails to demonstrate that capital expenditure activity is constrained by the amount of internal funds available. Their results would appear to question whether corporate-level investment is at all sensitive to internal cash flow constraints, a finding that would imply that corporate pension policy is irrelevant.

C. Pension Policy and the Value of Corporate-Level Investment

Separate and apart from the question of whether pension funding requirements interfere with the financing of capital expenditures is the issue concerning the extent to which pension liabilities diminish the value of corporate-level investment to the shareholders. Pension obligations are legal liabilities of the firm, which means that a portion of the value created by corporate-level investment might also be shared with the pension fund. Myers (1977) demonstrated that firms have a rational incentive to underinvest if a portion of the gains from capital expenditures accrue to the bondholders. Those gains are shared through an increase in the amount and duration of the payments made to the bondholders from resources generated by the project.

A different form of debt overhang may also exert an influence on the investment activity of defined benefit plan sponsors. Shareholders own an option to default on any unfunded pension liabilities because a plan sponsor can terminate its pension plan in bankruptcy, leaving the excess of the accumulated benefit obligation over pension assets to the PBGC. The value of that default option will be reduced to the extent that a portion of the gains from high value projects are shared with the pension fund. That sharing of value will occur if the project allows the firm to make greater contributions to the fund for longer periods of time, thus creating a pension overhang effect.

When compared to conventional debt overhang, however, the overhang effect of a defined benefit pension plan exhibits several unique characteristics. First, unlike a bond issue, the liability to the pension fund is not fixed; rather, it is contingent upon the level of interest rates and stock prices, as well as the flow of contributions and benefit payments. (6) Perhaps more importantly, the unfunded pension liability is pro-cyclical as it is likely to change in the opposite direction of the plan sponsor's net worth and growth options. As a consequence, the extent to which pension overhang influences the value of corporate investment to the shareholders may be greater than in the case of conventional debt, given that the overhang condition worsens when the firm is weaker. (7)

II. The Simulation Model

The study employs a Monte Carlo simulation to gauge the extent of pension overhang. We do so by examining the incremental value of corporate-level investment to the fixed and residual claimants of a defined benefit pension plan sponsor. The study estimates how the incremental value of the project to each of the claimant classes (fixed coupon sinking fund debt, pension liability, and common equity) is affected by various funding and investment policies of the defined benefit pension plan.

A. The Plan Sponsor

The plan sponsor has an infinite life with operating assets generating a varying income stream for 30 years. Pre-tax operating income (earnings before interest, taxes, and pension fund contributions or EBITP) is the difference between revenue and operating expenses, but those operating expenses exclude any contribution to the pension fund. Starting in Year 31, Year 30 pre-tax operating cash flow is normalized as a fixed perpetual stream. The initial level of pre-tax operating income (time zero) is $1,000. Changes in operating income from year to year are generated by a stock market factor (in proportion to the asset beta) and a normally distributed random factor.

The firm invests in a single project. The pre-tax operating cash flow from the project follows a random walk with no drift and is independent of the pre-tax cash flow of the operating assets already in place. The initial level of pre-tax operating income from the project (time zero) is $100.

The initial capital structure of the firm consists of subordinated sinking fund debt with a 30-year maturity and common equity. The initial amount of outstanding subordinated debt is set at 25% of the expected value of the levered firm (the average leverage ratio of defined benefit plan sponsors as documented by Shivdasani and Stefanescu, 2009). The bonds have a 6.29% fixed coupon (based on an initial risk flee rate of 4.5% and a 1.79% risk premium) with a sinking fund provision that amortizes the principal in 30 equal installments. The issuance of 100-year bullet maturity bonds finances sinking fund redemptions. (8) The bullet maturity bonds carry a fixed coupon that is determined by the total debt-to-income ratio of the firm at the time of issue. (9) Total debt (for credit rating purposes) includes any unfunded pension liability and the coupon rate on newly issued bullet maturity debt increases as the credit quality of the firm declines, as described in the following table.

Ratio of Total Debt to EBITP    Bond Rating/Risk Premium (percent)

1.39 or less                                AAA / 0.79%
1.40 to 1.99                                AA / 1.38%
2.00 to 2.99                                 A / 1.79%
3.00 to 4.49                                BBB / 2.50%
4.5 and higher                              BB / 5.19%


The US Treasury bond rate is 4.5% at time zero. The US Treasury bond rate ([R.sub.t]) in subsequent years is determined by the following stochastic process:

[R.sub.t] = [R.sub.t-i] + .3(.045 - [R.sub.t-1]) + .3[R.sup.1.1.sub.t-1] (0, 1), (1)

where 2% < = [R.sub.t] < = 20% and N(0,1) is a standard normal random variable. The stochastic process is representative of the one factor interest rate model examined by Chan et al. (1992). The use of a stochastic interest rate is critical to the analysis as fluctuating interest rates determine corporate-level interest expense, the present value of pension benefits, and the value of bonds held in the pension fund.

The firm can also borrow from the bank to finance cash shortfalls. Along with the bullet debt, bank debt is senior to all other claims in liquidation and has the same interest cost as the latest issue of bullet maturity debt. Bank borrowing is limited to financing interest payments and negative operating cash flows (but not pension contributions) in the face of insufficient income. Thus, the bank borrowing convention that we employ allows the firm to (temporarily) avoid default when operating income is low, but cannot be used to fund the pension plan.

The decision to terminate the firm's operations is contingent upon the relation between two measures: 1) the amount of senior debt and 2) the liquidation value of the firm. The liquidation value of the firm for every trial is equal to the expected present value of future after-tax operating income at time zero. We adopt a protocol for liquidation that is similar to the one adopted by Parrino and Weisbach (1999). The firm is dissolved if the combined total of bank and bullet maturity debt just exceeds the liquidation value. This condition imposes a rule that delays liquidation until the point at which the stake of the senior claimants just begins to be impaired.

Liquidation is assumed to occur without the PBGC having filed a prior claim leaving the PBGC holding an unsecured subordinated claim for the difference between the value of the accumulated benefit obligation and the value of the assets in the pension fund at the liquidation date. Its claim is on par with that of the sinking fund debt and is therefore assumed to be worthless should liquidation occur. (10) If the firm liquidates when the pension plan has a surplus, the simulation assumes it is captured by income and excise taxes. (11)

Following Jin et al. (2006), the value of debt includes the initial pension liability. The unlevered beta coefficient of the plan sponsor without the project is 0.75, an estimate that results from assuming an equity beta of 1.0, a marginal tax rate of 35%, and a consolidated (conventional debt plus the pension liability) leverage ratio of 34%. The standard deviation of the annual change in EBIT is 66%, which is the median value for all firms on Compustat over the 10-year period 2001-2010. We assume that the riskless return is 4.50% and estimate the market risk premium to be 3.4%, which is the average estimate reported in a survey of Chief Financial Officers by Graham and Harvey (2010). The unlevered cost of capital is estimated using the Capital Asset Pricing Model.

B. The Pension Plan

The pension plan is assumed to have been established a sufficient amount of time before the simulation period to create a stable age and years of service distribution for both current and prior employees. (12) Two measures of the pension liability are required for the analysis.

The first is the accumulated benefit obligation, which is the present value of pension benefits owed to the plan participants based on current salary and service levels. That measure of the pension obligation is the single payment that the plan sponsor would be required to make in order to satisfy all future benefit obligations were the plan terminated immediately. The other measure of the pension liability is the projected benefit obligation. It estimates the present value of the pension benefits owed to the plan participants based on current service, but projecting the impact of future salary increases on the benefit stream. The initial projected benefit obligation is equal to 9% of the value of the firm, which is the average pension liability of defined benefit plan sponsors as documented by Shivdasani and Stefanescu (2009).

The present value of the accumulated benefit obligation must be computed using a three-segment investment grade corporate bond yield curve. In practice, the segments are defined at maturity breaks of five and 15 years, and the discount rate applied from each segment is specified by the Secretary of the Treasury based on the average of recent historical yields. Our model employs an initial discount rate of 5.82%, which is the average of the initial AAA, AA, and A yields. It assumes a flat yield curve and a riskless interest rate that follows a random walk over time, as described earlier. Variation in interest rates is essential to the analysis as it contributes to variation in the required amortization of the unfunded pension obligation.

The assets in the pension fund accumulate investment earnings on a pretax basis and are strictly dedicated to financing the stream of benefits. In any given year, pension assets are increased by contributions from the plan sponsor to the pension fund and by positive investment earnings. The level of pension assets declines due to benefit payments and investment losses. Thus, the change in the value of the pension fund from year to year is equal to: 1) the beginning value times the realized investment return, 2) plus contributions, 3) less benefit payments. Pursuant to the rules governing the computation of the minimum required contribution, the actuarial (smoothed) value of plan assets is employed (instead of the actual current market value) as the measure of the value of the plan assets in determining the amortization of any funding deficiency. (13)

Investment earnings are the product of pension fund assets as of the beginning of the year and a rate of return generated by the respective return distributions for corporate bonds and equity securities. Stochastic market returns are modeled on the historical experience of the US financial markets. The equity exposure of the pension fund consists of a position in the market portfolio. The expected return on stocks is 7.90% (the sum of a 4.50% riskless yield and the 3.40% market risk premium). The standard deviation of return on stocks is 20.2% (the historical average over the period 1900-2008 as reported by Brealey, Myers, and Allen, 2011.)

Fixed claims in the pension fund are assumed to consist of a portfolio of 10-year constant maturity Treasury bonds with an initial coupon rate of 4.50%. The yield changes over time based on the stochastic interest rate model. The return on the portfolio in a given year is determined by the combination of the coupon payment and any capital gain or loss generated by the change in yield.

We simulate six different investment policies: 1) an "all bonds" portfolio, 2) a 100% equity position, and 3) four different stock/bond mixes: 20/80, 40/60, 60/40, and 80/20.

C. Minimum Funding Requirements

The priority for the distribution of operating cash flow is, in order: 1) pension fund, 2) bank debt, 3) bondholders, and 4) stockholders. Therefore, the minimum required annual contribution to the pension fund plays a crucial role in the analysis as it determines how much cash flow is available for the bank lenders, bondholders, and the stockholders. Our simulation assumes that the plan sponsor contributes only the minimum required amount to the pension fund in any year. In practice, firms can and do contribute more than the required minimum, but allowing that to happen in the simulation would create a buffer in the pension fund and, in the process, dilute the impact of the minimum requirement.

The minimum annual contribution to the pension fund consists of two components: 1) to fund the benefits accruing in the current period (normal cost) and 2) to amortize any funding shortfall (the difference between the funding target and the value of pension assets). The initial analysis computes the minimum annual contribution under the rules that have applied since the enactment of the Pension Protection Act of 2006. A subsequent analysis examines how the simulation results are affected by the changes introduced by the new law. We do that by repeating the simulation under the prior law funding rules and examining the difference in the valuation results. The specific rules for computing the minimum required contribution under both prior law and the current funding rules are contained in the Appendix.

D. Valuation of Claims

For each simulation trial, the 30-year time series of EBITP (earnings before interest, taxes, and pension contributions) is determined by a combination of systematic and nonsystematic changes. We compute the changes in the value of the original debt, the pension liability, and common equity that result from acceptance of the project.

For each year that the firm is a going concern, the original bondholders receive their coupon payment plus the principal amount of the retired bonds. If the firm continues as a going concern for the entire 30-year horizon, the outstanding value of the original debt is zero at t = 30. If the firm liquidates, those same bondholders are assumed to receive nothing. The value of the bonds at the beginning of each trial is the present value of the coupon and principal payments, discounted at the yield to maturity. The yield to maturity for each trial is determined by the ratio of total debt (inclusive of the unfunded pension liability) to expected EBITP.

The cash flow to the pension fund is the annual contribution. The present value of the pension claim is the discounted value of the stream of annual contributions. Under the assumption that the risk of the pension fund contribution stream is equivalent to the business risk of the plan sponsor, the discount rate is the unlevered cost of capital (7.05%).

The common stockholders are assumed to receive a dividend equal to the amount of any free cash flow. If the firm is liquidated, the free cash flow is zero. If the firm continues as a going concern, the free cash flow is computed as surplus cash flow (pre-tax operating income reduced by interest expense, the pension contribution, and income taxes) less net bank borrowing. If there is an outstanding bank loan balance, any surplus cash is used to reduce the outstanding bank loan balance causing net new bank borrowing to be negative in those years. Free cash flow can be positive if and only if the bank loan balance has been eliminated.

The project is financed entirely with equity and the value of the project is computed using the adjusted present value method. The all-equity value of the project is the present value of the incremental free cash flow generated by the project, discounted at the risk-adjusted rate of return as determined by the unlevered systematic risk of the firm. That rate is used because the ultimate risk to the continuation of the project is the risk of the firm.

The all-equity value of the project is augmented or diminished by the incremental amounts of usable tax shields (interest and pension) that are generated by the project cash flows. Under the assumption that the tax shields are as risky as the cash flow stream to the stockholders, the discount rate applied to the incremental tax shields is the expected return on the levered equity of the plan sponsor. Thus, the adjusted present value of the project for any simulation estimates the value added to the firm by the project. The value of the project to the shareholders is the adjusted present value augmented or diminished by wealth transfers to or from the sinking fund bondholders and the pension fund.

III. Project Valuation with an "All Bonds" Pension Fund

We first examine the valuation of a project under the current rules for minimum pension funding, which have been in effect since the enactment of the Pension Protection Act of 2006. In order to provide a benchmark for subsequent results, our initial analysis considers a defined benefit plan with pension assets that are entirely invested in bonds. This is an appropriate starting point for investment policy as it provides a set of results generated when the performance of the pension fund is independent of the same (stock market) factor that affects the operating cash flow of the plan sponsor. Subsequent simulations consider the impact of different amounts of equity exposure in the fund.

The simulation results are presented in a collection of tables and figures that contain the average value from 5,000 trials, for varying levels of project risk, for two measures of project value: 1) the value of the project to the entire firm (the adjusted present value) and 2) the value of the project to the shareholders (the NPV). We also present two wealth transfer measures related to the acceptance of the project: 1) the change in the value of the original sinking fund debt and 2) the change in the value of the contributions to the pension fund. The project NPV is the project adjusted present value (APV) plus or minus any wealth transfers to or from the original bondholders and or the pension fund.

The simulation exercise analyzes both a mature pension plan that is fully funded at the outset and a mature plan that is severely (20%) underfunded. Our objective is to gauge the impact of varying levels of project risk on the value of a project to the firm, the original bondholders, the pension fund, and the shareholders for different funding levels. Holding investment policy constant, we are able to observe whether project risk affects how much the shareholders would be willing to pay for the project cash flows and, if so, to what extent. The results to the simulation are presented in Table I.

Summary of results: Both the pension fund and the bondholders gain from corporate-level investment. For a fully funded plan, the pension fund expropriates an average of 1.35% (the quotient of $10.16 and $753.62) of the value of a riskless project. The comparable figure for a severely underfunded plan is 1.87%. The gains decline as project risk increases. The gains to the pension fund range from 25% to 40% of the corresponding wealth transfer to the bondholders.

A. Mature Fully Funded Pension Plan

Panel A contains the simulation results for a firm with a mature pension plan that is fully funded on an initial basis. The results indicate that the adjusted present value of the project increases as project risk rises. The riskless project adds $753.62, on average, to the value of the firm. At the highest level of project risk (100% standard deviation), the project increases the value of the firm by $820.93. Increased project risk adds value because the more volatile project payoffs result in a net reduction in the frequency of financial distress. In this setting, the project has the characteristics of a call option.

The bondholders experience an average gain of $35.71 when the firm accepts the riskless project. Bondholder gains decline with increased project risk, falling to $29.49 at the highest project risk level. Increased project risk harms the bondholders as they don't benefit from high value outcomes, but are harmed by poor project performance.

The results in Panel A also report how the pension fund is affected by the addition of the project. The pension fund gains $10.16 from the riskless project. The gain declines to $10.06 for the project with a standard deviation of 5%, and then falls further to $7.49 with the highest risk (standard deviation of 100%) project. The share of project value accruing to the pension fund is only a fraction (approximately 25%) of the incremental value enjoyed by the bondholders. However, similar to the fixed claimants, the pension fund receives less value as project risk increases as low value outcomes impair the ability of the firm to make the minimum required contribution.

The greater propensity for risk sharing also affects the relation between project risk and its value to the shareholders. As demonstrated in Panel A, shareholder NPV climbs with increasing project risk, a change explained by the simple fact that the value of the project to the firm increases with project risk and share accruing to the senior claimants declines, leaving a greater portion for the stockholders.

B. Severely Underfunded Plan

Next, we examine the case of a mature plan that is severely underfunded. The ratio of plan assets to plan liabilities in Year Zero is 80%, meaning that the plan is 20% underfunded. Panel B contains the simulation results and reports that the same relationship between project risk and the value received by the claimants holds. The bondholders and pension fund are worse off when project risk is higher, while the shareholders benefit.

A more detailed comparison of Panels B and A confirms that the value of the project to the firm is slightly lower when the pension plan is underfunded. The average adjusted present value of the riskless project in Panel B is $751.30 compared to $753.62 in Panel A. That pattern holds for project risk levels up through 100%. Said differently, the shareholders of an unlevered firm would be willing to pay approximately 0.31% less for the project cash flows when it faces the financial constraints imposed by a severely underfunded pension plan. The reduction in project value is caused by a modest loss of tax shields and slight increase in liquidation frequency when the plan is severely underfunded.

When compared to the gains to the pension fund, the results in Panel B of Table I indicate that the share of project value accruing to the original bondholders changes very little when the pension plan is severely underfunded. The average gain to the bondholders from the adoption of the project is $0.05-$0.10 lower than when the plan is fully funded. The underlying cause of the decline is straightforward. The higher minimum contributions required for the severely underfunded plan drain operating cash that would otherwise be available for debt service.

Also, as expected, when the funding ratio is cut to 80%, the pension fund receives contributions with a greater present value and the project itself provides more value to the pension fund. The average gain to the severely underfunded pension fund when the firm accepts the riskless project is $14.05. The value of the project is $3.89 (38%) greater than the average gain for the mature fully funded pension plan (Panel A). What's more, the gain realized by the underfunded plan remains higher as project risk increases through the 100% standard deviation level. Those changes make economic sense. An underfunded plan requires a higher minimum contribution stream, but higher risk projects produce downside outcomes that sometimes impair the ability of the plan sponsor to fund those higher required contributions. That in turn causes the project to be more valuable on average.

The value of the project to the shareholders is lower across all levels of project risk with the underfunded pension plan, primarily because the original bondholders and the pension fund receive greater wealth transfers. When the pension plan is underfunded, the average NPV of the riskless project is $701.64 vs. $707.04 when the plan is initially fully funded for a difference of $5.40. At the highest level of project risk, the average NPV is reduced by $4.52. Severe underfunding encourages the stockholders to pay less for project cash flows as a significant amount of the project gains are shared with the pension fund and, to a lesser extent, the bondholders.

IV. Leverage, Pension Liability, Asset Allocation, and Project Valuation

We conduct simulations on the value of the project to the claimants of the firm while varying the amount of financial leverage, the size of the projected benefit obligation, and the asset allocation of the pension fund.

A. Financial Leverage

The degree of financial leverage influences the risk of financial distress and plan termination. Here, the leverage ratio is varied from zero to 80% of the value of the levered firm in increments of 20%.

Summary of results: The share of project value accruing to both the pension fund and the sinking fund bonds increases as the degree of financial leverage rises.

Figure 1A displays the average increase in the present value of contributions to the pension fund. As shown in the figure, the share of project value accruing to the pension fund increases with the leverage ratio and declines as project risk increases. The pension fund receives a greater share of project value for high leverage ratios because the incremental operating income from the project is more critical to financing required contributions. For a given leverage ratio, higher project risk reduces the frequency with which the firm can make the required minimum contribution.

Figure 1B displays the average increase in the present value of payments to the bondholders. (For the sake of brevity, the term "PV of sinking fund payments" is used to describe the present value of payments to the sinking fund bondholders.) The share of project value paid to the bondholders also increases with the leverage ratio and declines as project risk increases. The bondholders receive a greater share of project value for high leverage ratios as the incremental operating income from the project is more critical to paying the debt service. Higher project risk reduces the frequency with which the firm can service its debt. The project is more important to the fortunes of the bondholders because the bond issue is larger than the pension obligation in these simulations.

Figure 1C displays the average increase in the present value of payments to the stockholders. The (untabulated) value of the project to the firm (APV) increases with the leverage ratio because project income becomes more essential to the survival of the firm as the debt load rises. Holding the level of project risk constant, the relation between the change in shareholder NPV and the leverage ratio depends upon how the reduction in distress costs compares with the incremental wealth transfers reported in Figures 1A and 1B. When the leverage ratio is between zero and 60%, more leverage generally means a smaller portion of project value accrues to the shareholders, although the relation is not monotonic. (14) For a given leverage ratio, shareholder NPV increases with project risk due to the effect of limited liability and the fact that the wealth transfers to senior claimants decline as project risk rises.

B. Projected Benefit Obligation

The size of the pension obligation determines the level of annual contributions to the pension fund and the amount of investment earnings that it generates. Here, the size of the projected benefit obligation is varied from zero to 25% of the value of the levered firm, in increments of 5%.

Summary of results: The pension fund and the sinking fund bonds both receive a greater share of the value of the project when the pension obligation is larger. As project risk increases, the share of project value expropriated by both claims falls, but the decline is more pronounced for the bondholders given that required pension contributions are paid first. Shareholder NPV declines with higher levels of the projected benefit obligation. For a given projected benefit obligation, the shareholder NPV increases with the level of project risk.

Figure 2A displays the average increase in the present value of contributions to the pension fund. In order to avoid visual congestion, the figure only reports the results for pension benefit obligation (PBO) levels of 5%, 15%, and 25%. The share of project value accruing to the pension fund is higher when the PBO is greater as the operating income from the project is more critical to the ability of the firm to finance the required contribution stream. Higher project risk reduces the frequency with which the firm can make the required minimum contribution causing the value accruing to the pension fund to decline with project risk.

Figure 2B illustrates the average increase in the present value of payments to the bondholders. As shown in the figure, the share of project value they receive increases with the PBO and declines as project risk increases. The bondholders receive a greater share of project value when the pension obligation is larger because the required pension contribution is senior in the payment priority schedule. Higher project risk reduces the frequency with which the firm can service its debt, thereby lowering the incremental value of the project to the bondholders. A comparison with Figure 2A demonstrates that the pension fund expropriates a greater amount of project value than the bondholders once the PBO exceeds 20% of firm value.

Figure 2C displays the average increase in the present value of payments to the stockholders. The residual share of project value available to the shareholders strictly declines with increases in the size of the pension obligation and project risk. The stockholders receive a lesser share or the project value when the projected benefit obligation is higher because project income is more critical in financing the commensurately higher contribution stream. Shareholder NPV increases with project risk because the shareholders enjoy limited liability and the wealth transfers to the senior claimants decline as project risk increases.

C. Asset Allocation

Next, we examine the simulation results for a firm that deviates from the "All Bonds" pension fund and instead invests some or all of its pension assets in a broad equity market index. The amount of equity exposure in the pension fund is varied from zero to 100% of the value of pension assets in increments of 20%.

Increased equity exposure in the pension fund causes two important changes. First, the expected return on pension assets rises, reducing the net cost of sponsoring the plan. Additionally, the increased correlation between the performance of the pension fund and the operating performance of the plan sponsor (working off an asset beta of 0.75) enhances the procyclical characteristics of the pension fund and, by extension, the countercyclical tendencies of the required contribution stream. In specific terms, that means an increase in the frequency with which required contributions rise when EBITP declines. The impact of that change will be reflected in the value of the project to the firm and its claimants.

Summary of results: The project adds more value to the pension fund when it is less diversified as a concentrated asset allocation produces more downside outcomes that need to be offset by incremental project income. Corporate-level investment is marginally less valuable to the original bondholders with increased equity exposure in the pension fund because more stocks in the pension fund increases firm risk with no benefit to the fixed claimants. Since wealth transfers to the pension fund are mitigated with balanced asset allocations, corporate-level investment is more valuable to the shareholders when the pension fund holds a combination of stocks and bonds.

Figure 3A displays the average increase in the present value of contributions to the pension fund. In contrast to Figures 1 and 2, the degree of equity exposure is measured on the horizontal axis and the individual graphs represent various levels of project risk (as measured by the standard deviation of the change in project operating income). Thus "0% risk" refers to the riskless project, etc.

The graph indicates that the share of project value accruing to the pension fund is higher when the pension assets are invested solely in stocks or bonds. That gain occurs because project income is more critical with an undiversified portfolio, either because of a greater need to offset investment losses (on equities) or to compensate for lower long-run expected returns (on bonds). For any given level of project risk, the expropriation of value from corporate-level investment by the pension fund declines as the stock/bond mix moves closer to being even. Holding the asset allocation constant, higher project risk reduces the frequency with which the firm can make the required minimum contribution causing the value accruing to the pension fund to decline.

Figure 3B displays the average increase in the present value of payments to the bondholders. The asset allocation of the pension fund exerts very little influence on the bondholder position here because the pension fund is small in relation to the size of the firm. The slight downward slope of the graphs shows indicates that for a given level of project risk, the gains to the bondholders from adopting the project decline by very small amounts as the equity exposure in the pension fund increases. That reduction occurs due to risk shifting. Holding a fixed claim, the bondholders can only lose when the firm adds risk to the pension fund. As before, higher project risk reduces the frequency with which the firm can service its debt, thereby lowering the incremental value of the project to the bondholders.

Figure 3C displays the average increase in the present value of payments to the stockholders. As before, the residual share of project value available to the shareholders increases with project risk. However, the most important finding comes from the fluctuation of the NPVs. The figure indicates that shareholder NPV is greatest for risky projects when equities comprise 40% of pension fund assets and the least when the fund holds only equities, an ordering driven by wealth transfers to the pension fund that are minimized (maximized) when the equity position is 40% (100%). The figure demonstrates that shareholder NPV is maximized for the riskless project at an equity allocation of 60%.

How large is the variation in shareholder project value? Table I (Panel B) reports that the project NPV is $706.28 at a project risk level of 15% when the pension fund holds only bonds. The corresponding (untabulated) result from the simulation when the pension fund is entirely invested in stocks is $704.66. The highest shareholder NPV ($707.11) occurs at the same level of project risk when the asset allocation in the pension fund is 40% stocks. Similar comparisons occur at higher levels of project risk.

Thus, the empirical effect is small (0.35%), empirically consistent across varying levels of project risk, but, perhaps most important, consistent with the observed tendency of defined benefit plan sponsors to hold balanced asset allocations (Rauh, 2009).

Comprehensive summary. In order to compare the economic effect of changes in pension plan characteristics on shareholder NPV, we computed the elasticity of shareholder NPV with respect to changes in the funding level, size of the pension plan, and asset allocation. (15) The estimated elasticity measures for those three variables are 0.036, -0.014, and 0.001, respectively. The implication of the relation among those numbers indicates that plan sponsors can control the pension overhang problem most effectively by reducing the level of plan underfunding. Absent that alternative, controlling the size of the pension liability (perhaps through a plan freeze) provides the second most effective form of relief, followed by modifying the degree of equity exposure in the pension fund.

V. Comparing the Pension Protection Act of 2006 (PPA) with Prior Law

The Pension Protection Act of 2006 was designed to enhance the funding levels of defined benefit plans. In this section, we report the results of an examination of the incremental effect of the new law on the value of: 1) the payment stream to the sinking fund bondholders and 2) contributions to the pension fund due to project adoption. The incremental effect is calculated as the difference between the mean value from the original simulations and the corresponding values estimated under pension funding rules that existed prior to the enactment of PPA. We frequently refer to the values in these tables as "changes caused by the new law."

The incremental effect is not influenced by random factors because we compute the components of project value in a particular trial under both the old and new laws using the same randomly generated values for firm EBITR project operating income, and equity and bond market returns. As a result, the differences reported here solely reflect the impact of the changes caused by the switch to the new method for computing required contributions. We examined the changes for the severely underfunded plan for six different levels of equity exposure: zero, 20%, 40%, 60%, 80%, and 100%. In order to present a clearer picture of the simulation results, the figures demonstrate changes caused by the new law for only three different levels of project risk: 1) zero, 2) 25%, and 100%.

Summary of results: The changes to funding requirements caused by the Pension Protection Act of 2006 generally mitigate wealth transfers to the pension fund, and that mitigating effect increases with the degree of equity exposure in the pension fund. On a relative basis, the stricter funding rules imposed by the new law lead to a reduction of as much as 20% in the overhang problem.

Figure 4A displays the change in the amount of project value accruing to the pension fund due to the changes in minimum funding requirements imposed by the new law. As illustrated in the figure, the changes in funding requirements cause the share of project value transferred to the pension fund to increase by a small amount ($0.25) when the pension fund is entirely invested in bonds. Increases in the equity exposure of the pension fund make the project less critical than before in terms of financing pension contributions for all levels of project risk. At the highest levels of equity exposure, the pension fund receives between $2.00 and $3.00 less under the new law than under the funding rules mandated by prior law.

While the impact on project value is small in terms of dollars, the proportional increase in investment efficiency comes to as much as 20% of the original wealth transfer found in Panel B of Table I. The dollar changes in Figure 4A are also comparable to the change in wealth transfers to the pension fund induced by changes in equity exposure, as noted in Figure 3A.

Consulting actuaries we spoke with told us that the overall impact of the changes in funding requirements imposed by the Pension Protection Act of 2006 is to make the stream of contributions to the pension plan higher and less volatile. The simulation analysis here is consistent with that observation, and suggests that changes in the minimum funding requirements result in a higher average level of funding. As equity exposure in the pension fund increases, higher realized investment returns (on greater accumulated contributions) cause the additional income provided by the project to become less crucial to the ability of the firm to fund the plan. In other words, changes caused by the new law create less need for the pension fund to rely on the value created by corporate-level investment as the pension fund becomes more self-sufficient with increases in the level of equity exposure.

Figure 4B demonstrates how changes in funding requirements affect the value of the project to the bondholders. The effect is minimal. If the pension fund holds only bonds, the change in the wealth transfer to the sinking fund bondholders fluctuates around zero across the different levels of project risk. As the equity exposure of the pension fund increases, the more stringent funding requirements of the new law cause the share of project value accruing to the bondholders to rise by a small amount. When the pension fund is fully invested in stocks, the share of project value received by the bondholders is slightly greater by $0.03-$0.16 depending upon the level of project risk. Our takeaway from Figure 4B is that the bondholders expropriate slightly more project value under the new law because the more stringent minimum pension funding requirements drain a slightly greater amount of corporate cash flow as the risk of the pension fund increases.

The changes in overhang demonstrated by Figures 4A and 4B reflect the same underlying dynamic. More equity exposure in the pension fund increases average investment earnings, thereby making the pension fund less dependent on the success of corporate-level investment. However, that same increased equity exposure increases the frequency with which the plan sponsor must contribute more money to the pension fund in order to compensate for disappointing equity returns. Since the new law requires a greater and more immediate response by the plan sponsor to changes in funded status, money that would have otherwise been available to the bondholders must go to the pension fund. That makes the project more important to the bondholders since increased equity exposure adds to the downside risk with no upside benefit.

We find no evidence to support the notion that the stricter funding requirements imposed by the Pension Protection Act of 2006 cause the pension fund to expropriate a greater share of the value created by capital expenditures. Since the reduction in wealth transfers to the pension fund dominates the slight increase in wealth transfers to the sinking fund bondholders, the provisions of the new law reduce overhang losses on a net basis.

VI. Case Analysis

The final segment of our analysis involves the application of the simulation model to 23 public companies with severely underfunded defined benefit plans. Similar to Parrino and Weisbach (1999), we assemble a set of inputs so that the Monte Carlo simulation can function as a tailor-made valuation model for each firm that we examine. We confine our analysis to firms with severely underfunded plans as the earlier analysis suggests that any empirical effect will be more apparent among those companies.

The firms selected for this portion of the simulation exercise were required to have a fiscal year that ended between September 30, 2010 and December 31, 2010. The financial data employed were gathered in mid-October 2011 and companies in the financial sector (standard industrial classification (SIC) Codes 6000-6999) were excluded. In addition, the available set of information accessible at the end of fiscal year 2010 needed to include the accumulated benefit obligation, the projected benefit obligation, the allocation of the pension fund among debt and equity, operating income, capital expenditures, long-term debt, and market capitalization. Firms were also required to have a bond rating and an equity beta that was available on Value Line. The final set of firms selected had: 1) a projected benefit obligation of at least 10%, but not more than 50%, of the plan sponsor's invested capital and 2) a funding ratio of 80% or lower.

This protocol left us with companies that faced severe funding shortfalls, but limited the extent to which valuation considerations might be overwhelmed by the unfunded pension obligation. For each trial, the one-factor model generated the time series of operating income (EBITP) with an upward drift. The mean value of the distribution for a particular firm was set to the sum of reported EBIT and the pension contribution for fiscal year 2010. The standard deviation of the distribution was the actual standard deviation of the percentage change in EBIT over the prior 10 years. The drift term was backed out of a two-stage growth model with parameters set to equal the value of the firm at December 31, 2010. Expected project income is the product of capital expenditures and the return on invested capital in 2010. The amount of financial leverage was determined by the face value of long-term debt outstanding at the end of the fiscal year, and the model incorporated the expected maturing amounts of debt for the first five years, after which the remaining debt was assumed to mature on a straight-line basis through the life of the bond issue with the most distant maturity date.

Table II contains the financial characteristics of the 23 firms examined. The table reports the name of each firm along with measures that describe the features of the pension plan: l) the size of the projected benefit obligation in relation to invested capital, 2) the ratio of plan assets to the accumulated benefit obligation, and 3) the percentage of pension fund assets invested in equities. The latter measure is normalized to reflect the relative amounts of debt and equity. Table II also describes the financial risk of the plan sponsor: 1) the leverage ratio, 2) the equity beta coefficient (as estimated by Value Line), and 3) the credit risk of bonds outstanding.

The untabulated average size of the projected benefit obligation is 27% of invested capital. The mean funding ratio is 73% and the average equity exposure is 58%. Among the 23 firms selected, the mean leverage ratio is 44% and the median bond rating is BBB. In relation to the general simulation model (with a 25% leverage ratio, a projected benefit obligation equal to 9% of firm value, and a funding ratio of 80%), our public companies use more financial leverage and sponsor pension plans that are both larger and more underfunded.

The sample companies also display a great amount of variation with respect to their individual characteristics. Each is drawn from a different industry (defined on the basis of two-digit SIC codes). The companies have funding ratios as low as 52%, equity allocations that vary from 25% to 71%, leverage ratios that range from zero to more than 100%, and equity beta coefficients as low as 0.70 and as high as 1.60.

Table III displays the percentage of project value expropriated by the pension fund for varying levels of project risk. The figures are computed by dividing the change in the present value of contributions to the pension fund by the adjusted present value of the project. Consistent with patterns produced by the general simulation model, the incremental value of the project to the pension fund tends to decline as project risk increases. With the exception of Con-Way and Jack in the Box, the proportion of project value transferred to the pension fund is always less than 20%. What's more, the correlation between the wealth transfer as a percentage of the riskless project value and the size of the projected benefit obligation is 0.52, which is consistent with the results reported in Figure 2A.

The variation in the percentages reported in Table III is influenced not only by the varying characteristics of the plan sponsor and of the pension plan, but also by the variation in operating profitability and scale of corporate investment. In conjunction with the fact that the inputs are imperfect estimates of the true valuation parameters, the individual estimates of project value expropriation are expected to be very noisy. In order to see through the influence of the noise, we report the mean and median values of the figures for each level of project risk in Table IV. As reported in the table, the average (median) estimated portion of project value transferred to the pension fund is 7.0% (5.3%) when the sample firms adopt a riskless project. Both the mean and median values decline as the level of project risk increases.

In order to put those summary statistics in perspective, we compare them to an untabulated value from Figure 3A, which indicates that the average change in the present value of contributions to the pension fund is $12.17 when: 1) the project is riskless, 2) the pension fund holds 60% of its value in stocks, 3) the leverage ratio is 25%, and 4) the projected benefit obligation is 9% of firm value. That figure is 1.62% of the adjusted present value of the project. Given that the public firms we examine have greater leverage and larger unfunded pension obligations, the higher 7.0% average wealth transfer doesn't appear to be unreasonable.

As added standard for comparison, we also report the results to a final simulation with the general model for a hypothetical plan sponsor that has the average attributes of the 23 public companies: 1) a projected benefit obligation equal to 27% of invested capital, 2) a 73% funding ratio, 3) a 44% leverage ratio, and 4) a pension fund with a 58/42 stock-bond mix. The results are reported in the bottom line of Table IV. Across all levels of project risk, the pension fund expropriates from 8.1% to 8.4% of the adjusted present value of the project. As expected from the tenor of the simulation results presented in Section IV, the pension overhang effect is greater for that composite firm given that it employs more financial leverage and has a larger unfunded pension obligation.

Finally, we estimated the portion of project value expropriated by the bondholders of the 23 public companies. In untabulated results, the average wealth transfer is 2.3% of the project value, regardless of the level of project risk. That value is smaller than the amounts observed for the pension fund, but appears to be sensible for two reasons. First, the projected benefit obligations among the public firms are relatively large. Additionally, the average maturity of debt for the 23 public companies is 15 years resulting in a duration level that is much shorter than the duration of the pension plan.

VII. Conclusion

The impact of corporate pension policy on the efficiency of corporate-level investment has received scant attention in the literature. Here, we employ Monte Carlo simulation to examine the impact of pension funding levels and investment allocations on the incremental value of capital expenditures. The issue is important as the need to manage pension overhang may be a factor in the formulation of any optimal pension policy.

Our simulation results demonstrate that the overhang of pension obligations reduces the value of corporate-level investment to the shareholders. We also find that the switch to new funding rules imposed by the Pension Protection Act of 2006 serves to mitigate those wealth transfers.

The examination of both hypothetical firms and individual public companies suggests that the magnitude of the effect ranges from 1% to 8% of project value, depending upon the level of project risk, the financial risk of the plan sponsor, and the degree of equity exposure in the pension fund. How the wealth transfer to the pension fund compares to corresponding bondholder wealth transfers depends on the relation between the projected benefit obligation and the amount and duration of conventional borrowing. Therefore, we conclude that a measureable pension overhang effect exists, and that it can equal or exceed the overhang problem posed by ordinary debt for plan sponsors with severe funding shortfalls.

Having established the empirical properties of pension overhang, the next logical question pertains to any policy implications. Specifically, what can firms do to minimize the extent of the problem? Here, our analysis provides a clear recommendation. Maintain a fully funded pension plan that holds a balanced asset allocation. Our elasticity measures indicate that the funding level of the plan has the greatest effect between the two.

Additional support for that proposition would appear to exist in the literature. Rauh (2009) finds that a majority of firms select an allocation of assets that includes both fixed and residual claims. Weak firms select a higher fixed income allocation, which Rauh (2009) attributes to an attempt to limit expected distress costs. Our analysis suggests that an additional motivation for a balanced asset allocation may stem from a desire to limit the extent to which gains from corporate-level investment accrue to the pension fund. This problem could be particularly acute for firms with high leverage and low profitability--the same set of firms that have a need to realize the full potential of the capital expenditure program.

Appendix

1. Funding Requirements under the Pension Protection Act of 2006

The minimum required contribution is equal to the normal cost of the plan (which is the present value of benefit accruals for the period) plus an amount designed to amortize any unfunded pension liability. The funding target is the accumulated benefit obligation (the present value of pension benefits that have been earned). If the value of the assets in the pension fund is less than the funding target, the difference must be amortized as an annuity due over no more than seven years. Further, the plan sponsor is required to make an additional contribution during years in which the pension plan is deemed to be "at risk." The "at risk" designation is assigned when the funding ratio (actuarial value of plan assets to the accumulated benefit obligation) is less than 80%. If the pension plan merits that designation, it is required to contribute an additional $700 per plan participant, plus 4% of the sum of the funding target and normal cost.

The tax shelter provided to qualified defined benefit pension plan sponsors is valuable. In order to prevent abuse, plan sponsors must observe the full funding limitation, which imposes a maximum amount that can be contributed to the pension fund in any given year. Consistent with the provisions of the Pension Protection Act, the annual contribution is limited to an amount that would cause pension fund assets to exceed 150% of the accumulated benefit obligation. Our simulations do not involve contributions in excess of the minimum required, so the full funding limitation becomes binding only as a result of superior investment performance. The simulation model also allows the plan sponsor to receive a funding waiver, meaning that the required minimum contribution can be skipped if internal finance is insufficient. All other things equal, the missed contribution causes the value of pension assets to be lower than otherwise, and the incremental shortfall is amortized as an annuity due over seven years.

2. Funding Requirements under Prior Law

Under our prior law simulations, the actuarial value of pension assets is computed as the arithmetic average of prior year-end market values. That average is computed going back five years, and the actuarial value is used to establish is subject to a wider collar. It is bounded from below by 80% of the current market value and from above by 120% of the current market value. In relation to the simulations under the new law, this valuation regime will reduce fluctuations in pension asset values.

The minimum funding requirement simulated under prior law consists of three separate components. The first component is the normal cost of the plan. Another component of the minimum required contribution simulated under prior law is the five-year amortization of experience gains and losses. Experience losses (gains) occur when the investment performance of the pension assets fall short (exceeds) of expectations, augmenting (reducing) the difference between the value of pension assets and liabilities. The simulation model applied here computes an experience gain or loss for a given year as the difference between the actual market value of the pension assets and the pro forma value under the assumption that the expected rate of return was realized over the just completed period. For example, if the investment earnings on the pension assets over the just completed year were $100,000 less than expected, an additional $100,000 would be contributed in present value to the pension fund in equal installments over the next five years, with the first contribution required immediately. The simulation model also allows the plan sponsor to receive a funding waiver, and the waived contribution must be amortized over five years.

Consistent with prior law, if the firm in our simulation finds itself with a severely underfunded plan, it is required to substitute an amount known as the deficit reduction contribution (DRC) for the sum of the three amortization components of the minimum required contribution described above. The DRC is based, in part, on a measure known as the funded current liability percentage (FCL), which is equal to the current liability divided into the actuarial value of the pension assets. The value of the current liability is approximated by the accumulated benefit obligation. The DRC is equal to the difference between the funding target and the actuarial value of pension assets times the quantity [0.30 - 0.40* (FCL - 0.60)]. In practice, the DRC amortized the unfunded current liability over a period of three to five years.

The plan sponsor makes the DRC in place of the sum of the ordinary amortization amounts if the ratio of the current liability to the value of plan assets is less than 80%. As such, the minimum required contribution in our simulation under prior law is a complex function of both the mix of the various components of the unfunded liability and the relation of their total to the value of the plan assets.

Prior law also allowed the plan sponsor to receive funding credits for any amounts contributed in excess of the minimum required contribution. Those credits are then used to offset the minimum required contributions in future years, thus allowing the plan sponsor to substitute funding credits for cash contributions. This practice has the effect of lowering funding levels following an increase in unfunded liabilities because as the plan sponsor is able to claim credit for surplus contributions made in prior years, even though the value of the assets contributed may have fallen in relation to the value of plan obligations.

Finally, the contribution to the pension fund in our prior law simulations cannot exceed an amount that would cause the value of the pension assets to exceed the projected benefit obligation.

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Treynor, J., 1977, "The Principles of Corporate Pension Finance," Journal of Finance 32, 627-638.

Warshawsky, M., 2007, "The New Pension Law and Defined Benefit Plans: A Surprisingly Good Match," Journal of Pension Benefits 14, 14-27.

(1) If the pretax risk-adjusted return on bonds is adjusted upward to compensate for the fact that equities are subject to a lower effective tax rate (Miller, 1977), the "All Bonds" strategy would also allow the shareholders of the plan sponsor to fully capture any available tax premium.

(2) Changes in financial reporting requirements over the same period served to enhance the transparency of the pension plan. The major changes in pension accounting included the promulgation of two separate pension obligation measures (accumulated and projected) and the requirement that the unfunded portion of the accumulated benefit obligation (and since FAS 158, the projected benefit obligation) appear on the balance sheet.

(3) Campbell, Dhaliwal, and Schwartz, Jr. (20 12) find that the cost of capital is the transmission mechanism for the reduction in capital expenditures documented by Rauh (2006). However, Bakke and Whited (2012) re-examine Rauh's (2006) results and find that the correlation between capital expenditures and pension contributions is driven by only a small subset of the sample.

(4) Petersen (1994) finds that firms with high operating leverage avoid DB plans, perhaps anticipating this effect.

(5) These observations are consistent with the general characteristics of long run abnormal returns leading both their estimation and use for inference to be referred to as "treacherous" (Lyon, Barber, and Tsai, 1999; Mitchell and Stafford, 2000).

(6) An exception would occur among firms that immunize their pension liabilities (by holding bonds in equal value and with equal duration). Subject to making adequate contributions each year, immunization would eliminate the risk of underfunding, but at the expense of earning the equity risk premium.

(7) Recent studies have identified other influences on the value of corporate-level investment. Marchica and Mura (2010) find that a form of financial flexibility similar to a fully funded pension plan (unused debt capacity) leads to higher future capital expenditures. Simutin (2010) reports a similar finding with respect to surplus cash.

(8) The 100-year bullet maturity bond is adopted for one practical purpose: to factor in a layer of borrowing costs that reflect the financial condition of the firm as of each sinking fund redemption and to maintain them for the life of the firm.

(9) Source: Standard and Poor's Corporate Criteria (Analytical Methodology). Average yield premiums are option-adjusted yield spreads as of May 28, 2010 and were obtained from the St. Louis Federal Reserve FRED database.

(10) Following Parrino and Weisbach (1999), the sinking fund bondholders are subordinated to all other claims and are completely wiped out in bankruptcy. The stockholders hold a residual claim that receives net income after bank repayment in any year that the firm is a going concern and nothing in the event of liquidation.

(11) In practice, the surplus on a terminated defined benefit plan is subject to taxation at both the ordinary rate (35%) and a 50% excise tax, not including any portion transferred to fund retiree health care liabilities.

(12) The base pension liability is estimated for a hypothetical firm with I0,000 employees. The firm is assumed to be mature. As such, the pension benefit obligation (PBO) and accumulated benefit organization (ABO) are the present value of a series of declining payments. The PBO includes benefits based on estimated salary growth and the ABO does not. Both are determined by assuming a hiring age distribution ranging from 20 to 65 with a mode of 25, an employee turnover rate declining linearly from 13% at age 21 to 3% at age 65, and a mortality rate based on Life Tables for the Total US Population from the US Centers for Disease Control. The benefit for each employee is set at 2% of their final salary times years of service with full vesting after five years. Employees are assumed to have a starting salary of $30,000 and receive a salary increase of 1% a year equal to their productivity increase. Once the PBO and ABO were determined for the 10,000 employee pool, the number of employees was scaled up or down to achieve the targeted percentage relationship between the PBO and firm value.

(13) The actuarial value of the pension assets (frequently referred to as the smoothed value) is based on the average of prior year market values over the prior two years, and is bounded below by 90% of the current market value of the pension assets and bounded above by 110% of the current market value. The purpose of this convention is to smooth out changes in the value of pension assets and reduce the volatility of required pension contributions.

(14) In order to scale the vertical axis in a way that avoids too much clustering, the graph for the highest leverage ratio (80%) is not shown. It would be positioned high above the others, owing to the fact that the reduction in distress costs from adoption of the project dominates the wealth transfer causing a sharp increase in shareholder NPV.

(15) Elasticity was computed by measuring the percentage change in NPV in relation to the percentage change in one of the simulated attributes, and was estimated at the base case value for all of the other variables. For example, the elasticity of the equity allocation was estimated for a project with a standard deviation of 25% (close to the standard deviation of equity returns), a leverage ratio of 25%, and the PBO equal to 9% of firm value.

We thank John T. Alderson of Towers Watson, Brian Betker, Bidisha Chakrabarty, Bill Christie (Editor) and an anonymous reviewer for helpful comments and suggestions. We are also grateful to John Graham for providing us with the marginal income tax rates used in the study. An earlier version of this paper was presented at the 2011 FMA Conference (Denver). All errors remain our own.

Michael J. Alderson and Neil L. Seitz *

* Michael J. Alderson is a Professor of Finance in the Department of Finance at Saint Louis University in St. Louis, MO.

Neil L. Seitz is a Professor of Finance in the Department of Finance at Saint Louis University in St. Louis, MO.

Table I. Project Risk and Project Valuation with an "All Bonds"
Pension Fund Asset Mix for Different Pension Plan Profiles

Debt, pension fund, and equity claim values as project risk changes.
The simulations are for a firm with a 25% leverage ratio, an all
equity financed project with cash flows that are independent of the
cash flows from the firm's existing assets, and a marginal tax rate
of 35%. Each simulation is based on 5,000 draws from the cash flow
distribution for both the firm and the project. Project risk is
measured as the standard deviation of the change in project cash
flows in relation to the initial $100 cash flow.

                                       0%         5%        15%

Panel A. Mature Plan, Fully Funded at Outset

                                        Project Risk (standard
                                    deviation of annual change in
                                         project cash flows)

Adjusted present value of the         753.62     752.35     756.24
  project
Value of original debt with         2,295.63   2,295.33   2,295.19
  project
Value of original debt without      2,259.92   2,259.92   2,259.92
  project
Change in value of original debt       35.71      35.41      35.28
  due to project
Value of contribution stream to       285.54     285.44     285.14
  pension fund with project
Value of contribution stream to       275.38     275.38     275.38
  pension fund without project
Change in value of pension fund        10.16      10.06       9.76
  contributions due to project
Shareholder project value net of      707.74     706.88     711.21
  wealth transfers

Panel B. Severely Underfunded Mature Plan

                                        Project Risk (standard
                                    deviation of annual change in
                                         project cash flows)

Adjusted present value of the         751.30     750.86     754.84
  project
Value of original debt with         2,295.42   2,295.16   2,295.04
  project
Value of original debt without      2,259.82   2,259.82   2,259.82
  project
Change in value of original debt       35.60      35.34      35.21
  due to project
Value of contribution stream to       460.47     460.21     459.76
  pension fund with project
Value of contribution stream to       446.42     446.42     446.42
  pension fund without project
Change in value of pension fund        14.05      13.79      13.35
  contributions due to project
Shareholder project value net of      701.64     701.73     706.28
  wealth transfers

                                      25%        50%        100%

Panel A. Mature Plan, Fully Funded at Outset

                                        Project Risk (standard
                                    deviation of annual change in
                                         project cash flows)

Adjusted present value of the         759.12     774.32     820.93
  project
Value of original debt with         2,294.86   2,293.48   2,289.40
  project
Value of original debt without      2,259.92   2,259.92   2,259.92
  project
Change in value of original debt       34.94      33.56      29.49
  due to project
Value of contribution stream to       284.95     284.31     282.87
  pension fund with project
Value of contribution stream to       275.38     275.38     275.38
  pension fund without project
Change in value of pension fund         9.57       8.93       7.49
  contributions due to project
Shareholder project value net of      714.61     731.82     783.95
  wealth transfers

Panel B. Severely Underfunded Mature Plan

                                        Project Risk (standard
                                    deviation of annual change in
                                         project cash flows)

Adjusted present value of the         757.59     772.05     819.28
  project
Value of original debt with         2,294.70   2,293.31   2,289.23
  project
Value of original debt without      2,259.82   2,259.82   2,259.82
  project
Change in value of original debt       34.88      33.49      29.41
  due to project
Value of contribution stream to       459.66     458.80     456.85
  pension fund with project
Value of contribution stream to       446.42     446.42     446.42
  pension fund without project
Change in value of pension fund        13.24      12.39      10.43
  contributions due to project
Shareholder project value net of      709.46     726.17     779.43
  wealth transfers

Table II. Select Financial Characteristics of the 23 Public
Companies with Severely Underfunded Defined Benefit Pension Plans

Company                PBO/         Funding       Pension
                     Invested        Ratio         Fund
                      Capital                     Equity
                                                Allocation

ALCOA INC               50%           79%           41%
BALL CORP               19%           71%           31%
CBS CORP                26%           75%           25%
CHARLES RIVER           10%           76%           68%
  LABS INTL INC
CON-WAY INC             49%           79%           57%
DOLE FOOD CO INC        15%           52%           59%
DOW CHEMICAL            35%           79%           56%
DUN &                   34%           77%           66%
  BRADSTREET
  CORP
EXELON CORP             32%           76%           52%
EXXON MOBIL             11%           77%           61%
  CORP
GENERAL                 32%           70%           66%
  DYNAMICS CORP
HANESBRANDS INC         21%           68%           66%
HAVERTY                 26%           80%           64%
  FURNITURE
JACK IN THE BOX         25%           76%           64%
  INC
MAUI LAND &             46%           65%           71%
  PINEAPPLE CO
MOTOROLA                33%           72%           67%
  SOLUTIONS INC
NEWELL                  20%           74%           61%
  RUBBERMAID
  INC
OWENS CORNING           28%           76%           49%
SAFEWAY INC             18%           76%           68%
TYCO                    11%           74%           59%
  INTERNATIONAL
  LTD
URS CORP                19%           72%           55%
WESTMORELAND            25%           77%           66%
  COAL CO
WOLVERINE               15%           66%           71%
  WORLD WIDE

Company                Value          S&P          Bond
                     Leverage        Line         Rating
                       Ratio         Beta

ALCOA INC                   56%          1.45          BBB
BALL CORP                   46%          0.95          BB+
CBS CORP                    46%          1.50          BBB
CHARLES RIVER               33%          0.90           BB
  LABS INTL INC
CON-WAY INC                 40%          1.20          BBB
DOLE FOOD CO INC           131%          1.15           B+
DOW CHEMICAL                52%          1.25          BBB
DUN &                       24%          0.75            A
  BRADSTREET
  CORP
EXELON CORP                 44%          0.85          BBB
EXXON MOBIL                  3%          0.80          AAA
  CORP
GENERAL                      9%          0.95            A
  DYNAMICS CORP
HANESBRANDS INC             81%          1.20           BB
HAVERTY                      3%          0.90           AA
  FURNITURE
JACK IN THE BOX             31%          0.95           AA
  INC
MAUI LAND &                 49%          1.20           AA
  PINEAPPLE CO
MOTOROLA                    10%          1.00          BBB
  SOLUTIONS INC
NEWELL                      39%          1.25          BBB
  RUBBERMAID
  INC
OWENS CORNING               42%          1.25          BBB
SAFEWAY INC                 52%          0.70          BBB
TYCO                        20%          1.05            A
  INTERNATIONAL
  LTD
URS CORP                    19%          1.25           AA
WESTMORELAND               170%          1.60           AA
  COAL CO
WOLVERINE                    0%          0.85           AA
  WORLD WIDE

Table III. Percentage of Project Value Expropriated by the
Pension Fund by Varying Levels of Project Risk

                                Project Risk (standard deviation of
                               annual change in project cash flows)

Company                              0%        5%       15%

ALCOA INC                           14.5%     14.5%     13.6%
BALL CORP                            4.4%      4.4%      2.0%
CBS CORP                             4.8%      4.6%      4.7%
CHARLES RIVER LABS INTL INC          4.7%      4.7%      4.7%
CON-WAY INC                         22.1%     22.2%     21.6%
DOLE FOOD CO INC                     7.6%      7.6%      7.8%
DOW CHEMICAL                        14.9%     15.0%     14.7%
DUN & BRADSTREET CORP                5.3%      5.5%      5.0%
EXELON CORP                          2.2%      2.1%      2.1%
EXXON MOBIL CORP                     1.1%      1.1%      1.1%
GENERAL DYNAMICS CORP                5.6%      5.7%      5.2%
HANESBRANDS INC                      7.2%      7.3%      7.7%
HAVERTY FURNITURE                    1.8%      1.8%      1.8%
JACK IN THE BOX INC                 20.2%     20.3%     20.5%
MAUI LAND & PINEAPPLE CO             2.2%      2.1%      2.1%
MOTOROLA SOLUTIONS INC               7.3%      7.4%      7.1%
NEWELL RUBBERMAID INC                6.0%      6.1%      6.4%
OWENS CORNING                       10.3%     10.3%     10.3%
SAFEWAY INC                          3.5%      3.4%      3.4%
TYCO INTERNATIONAL LTD               3.0%      3.0%      3.1%
URS CORP                             3.1%      3.2%      3.1%
WESTMORELAND COAL CO                 5.4%      5.4%      5.5%
WOLVERINE WORLD WIDE                 2.6%      2.5%      2.6%

                                Project Risk (standard deviation of
                               annual change in project cash flows)

Company                             25%       50%       100%

ALCOA INC                           13.8%     13.7%     13.6%
BALL CORP                           10.8%      4.0%      2.7%
CBS CORP                             4.6%      4.7%      5.0%
CHARLES RIVER LABS INTL INC          4.9%      4.6%      5.0%
CON-WAY INC                         21.6%     21.9%     20.2%
DOLE FOOD CO INC                     7.7%      7.8%      7.9%
DOW CHEMICAL                        14.9%     15.4%     14.6%
DUN & BRADSTREET CORP                6.2%      7.6%      7.1%
EXELON CORP                          2.1%      2.2%      2.2%
EXXON MOBIL CORP                     1.1%      1.0%      0.7%
GENERAL DYNAMICS CORP                5.0%      5.1%      5.3%
HANESBRANDS INC                      7.6%      7.4%      6.9%
HAVERTY FURNITURE                    1.7%      1.7%      1.8%
JACK IN THE BOX INC                 20.5%     19.5%     16.0%
MAUI LAND & PINEAPPLE CO             2.1%      2.2%      2.2%
MOTOROLA SOLUTIONS INC               6.8%      7.6%      7.7%
NEWELL RUBBERMAID INC                6.2%      6.5%      6.4%
OWENS CORNING                       10.3%      9.8%      9.3%
SAFEWAY INC                          3.3%      2.9%      1.8%
TYCO INTERNATIONAL LTD               3.0%      3.1%      2.6%
URS CORP                             3.2%      3.1%      2.7%
WESTMORELAND COAL CO                 5.6%      5.4%      5.3%
WOLVERINE WORLD WIDE                 2.6%      2.1%      2.3%

Table IV. Summary Statistics for the Percentage of Project Value
Expropriated by the Pension Funds of Public Companies

                              Project Risk (standard deviation of
                              annual change in project cash flows)

                           0%      5%     15%     25%     50%    100%

Mean                     7.0%    7.0%    6.8%    7.2%    6.9%    6.5%
Median                   5.3%    5.4%    5.0%    5.6%    5.1%    5.3%
Composite simulation     8.1%    8.4%    8.3%    8.2%    7.9%    8.0%
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Author:Alderson, Michael J.; Seitz, Neil L.
Publication:Financial Management
Article Type:Report
Geographic Code:1USA
Date:Jun 22, 2013
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