Thursday, September 19, 2013

Pension Potholes: Mei and the Curse of Exponentiation

"We need to do something about this pension plan" the CFO exclaimed. "It has created us a real problem in terms of hitting our performance targets and is causing us to lag our industry peers. I need you to look at this issue and make a recommendation as to what we should do about it. Can you get me something before our Board meeting early next week?"

"Of course" Mei replied.

Her mind was racing as she left the CFO's office...she had a lot of work ahead of her, without any indication of where it would end up.

What is Defined?

In general, there are two types of retirement plans that can be offered - Defined Benefit plans and Defined Contribution plans.

Emphasis on the word "defined".

A defined benefit plan is one that pays out a - you guessed it! - defined amount of benefits to the employee. The word "defined" in this context means "known with certainty". For example, should Marie be retiring tomorrow under a defined benefit plan she would know that she is going to recieve $400 every month for the rest of her life. Marie does not know (i.e. what is undefined) how much money the firm made in investments to produce this amount.

Figure A
Plan Comparison

Under a defined contribution plan, on the other hand, what is known is the amount placed into the plan. For example, Marie knows that every month the company paid into her retirement account 5% of her wages. What Marie does not know (i.e. what is undefined) is the amount of payments her retirement account will produce.

Figure A shows the comparison of the two plans and identifies where the certainty and uncertainty lies.

"A lot of companies are converting their DB plans to DC plans these days. Perhaps that would help your issue?" Stacy said. Mei had met her at a conference last year and they had stayed in touch since then.

Objective advice was always valuable.

"That seems like a pretty dramatic change!" Mei replied.

"It is for sure, but more and more seem to be doing it. The general consensus is that DB plans are going the way of the dinosaur."

If that were to be the solution, Mei decided she better check in with the Human Resources group and see what they had to say about this issue.

The Projected Benefit Obligation

An organization incurs a liability when it has a defined benefit plan because it is realizing the benefits of the employees' labor now in exchange for a payment that will be made later.

Figure B
Example Pension Payout Formula
According to this formula, a retiree will receive an annual payment equal to 2% multiplied by their final salary and years of service. The retiree in the example calculation will recieve 20,000 per year (2% x 50,000 x 20).

In order to achieve the matching principle - one of the pillars of the accounting process - there need to be methods and techniques to associate the current period's labor costs with this deferred obligation.

The Projected Benefit Obligation (PBO) is the measure of the current state of this liability.

Let's examine how this is calculated through an example.

We will assume that Joe's Agricultural Empire, LLC sponsors a defined benefit plan for their employees. The annual pension payout is determined by the formula shown in Figure B. The example shows an employee who will receive annual payments of 20,000. Note that applying the math to a single employee helps to make these factors more understandable, which is why we will use this approach in the blog post. In real life, we would apply these calculations to the entire employee group as a whole.

Figure C
Net Present Value Equation
The Net Present Value is equal to the sum of the n cash flows discounted at rate r

Knowledge of the annual benefit payment is the first step in being able to quantify the amount of the liability. In order to value these payments at a point in time, we also need to know the number of payments that will be made and a discount rate to apply to them.

For the sake of our example, let's say that Joe's employee is expected to receive 10 payments in retirement, and the current discount rate applicable to these is 10%. Using the Net Present Value formula (shown in Figure C), we can determine that the value of these payments at the employee's retirement date is 122,891 (see Figure D).

Figure D
Net Present Value Calculation
The Net Present Value of 10 payments of 20,000 discounted at 10% equals 121,891, verified using Excel's PV() function

At this point we have established the value of the payments made to the retiree at their retirement date. However, we have not dealt with the 20 years of employment the person works prior to that point.

In order to do that, we need to make a second series of NPV calculations, only now going back in time rather than forward. This second calculation needs to take into account the employee's actual years of service in order to assign the correct final value of the payments to the period when the labor was performed.

In the first year of employment, for example, the present value of the final amount is 1,005. The calculation of this amount is shown in Figure E.

The amount of the final PV attributable to the current work period is known as the Service Cost.

Figure E
Service Cost Calculation
The amount of the final value of retirement pay attributable to the first year of service (i.e. Service Cost) is 1,005.

There is a slight twist in the second year. Using the same methodology as in Figure E (substituting 18 years until retirement for 19) will yield a Service Cost of 1,105. However, the amount of retirement pay the employee earned in the first year has not been paid out. Because it has been earned and not yet paid, we calculate an interest cost associated with this balance. At our 10% rate, interest on the first year balance of 1,005 is 100 (rounded amount).

Figure F
PBO Through Time
The PBO is increased each year by Service Cost and Interest Cost

With these two years calculated we can see how the Projected Benefit Obligation "rolls forward" through time. This is shown in Figure F.

Figure G shows the PBO calculation for each of the years of service, along with some of the intermediate values involved (e.g. percent of years of service completed, etc.). Figure H takes the service cost and PBO calculations, adds interest cost, and shows the PBO in "roll-forward" format.

Figure G
PBO Through Time
The underlying assumptions and intermediate calculations that generate the PBO. Note that as a check on our work the final amount of the PBO (122,891) is equal to the net present value of retirement payments we calculated earlier.

Figure H
PBO Through Time
The PBO in rollforward format. The ending value equals the beginning value plus the service cost plus the interest cost.

Since we are using a single active employee as our example, we do not see any reduction in the PBO. Naturally, as payments are made (i.e. the employee has retired and begins realizing the benefit) the PBO will be reduced by these amounts.

Because the PBO relies on a lot of actuarial assumptions (years in retirement, service years, final salary, etc) firms routinely engage professional actuarial firms who specialize in these assessments and calculations.

"According to this PBO data, our costs increase the longer the employee has been here, is that correct?" Mei asked.

On her way to HR she had stopped by the office of Scott, one of the company's accountants - the one who always found time to discuss issues and questions in a sincere attempt to help out. Mei liked it when she had the opportunity to discuss problems and situations with him because some new tidbit of knowledge or a deeper understanding always seemed to result.

"Yes. That is going to be due to the geometric nature of the calculation." he told her. "Since the PBO equation involves exponents in the formula, it will have an increasing effect. David Waltz, who writes the Treasury Cafe blog, calls this 'the curse of exponentiation'!"

"So that is one of the reasons why this is becoming a larger issue!" she exclaimed. "Our workforce is aging, so we are farther out the curve where the exponent effect really picks up."

"Exactly!" he beamed. Scott loved it when people understood what he was saying and they could share the insights. "And there are other factors too. For example, average lifespan has been increasing, so that increases the PBO as well since there will be more payments in retirement."

"Yes, that makes sense" said Mei. "I suppose any of the factors that we use the actuary for can increase it, higher wages due to higher inflation for instance?"

"Yes. There is a lot of uncertainty involved in the calculation."

"Doesn't make earnings any easier to predict, does it?"


Asset Returns

The PBO addresses the liability side of the pension equation. We now turn to the asset side.

In order to avoid large, "chunky" payment streams in later years, firms generally fund specific accounts that are held in trust for the sole purpose of making future payments to retirees. In the US certain levels of retirement plan funding are required for some entities.

Since investments earn returns, firms are also able to use these in the pension expense calculation.

Figure I
Pension Expense
Pension expense involves service cost, interest cost and assumed return on plan assets.

In order to determine this amount, an assumption about how much invested plan assets will earn is also required. For example, if Joe's Agricultural Empire were to place 1,000 into the trust account in year 1, and it assumed that 10% would be earned on these investments, then in year 2 expected returns of 100 (1000 x 10%) would be reflected in the pension expense calculation. Figure I builds on the prior PBO example and adds returns to come up with pension expense.

Mei ran into Miguel in the elevator. A long-time employee of the Treasury department, he was involved in investing the pension plan's assets and coordinated this activity both internally and with external parties such as consultants, investment managers and banks.

Another fortuitous encounter!

After explaining her project, Miguel opined "I can see why this is becoming a bigger issue. So long as the stock market was healthy, we were in a pretty good position with respect to funding our obligations. That has gotten a lot worse lately, so we are faced with raising a significant amount of cash to fund the plan."

"But the market has gotten better lately."

"Yes it has, but the effects of the past few years are catching up to us since we did not hit our return assumptions for several really bad years, and what is happening now will take a while to work its way into the financials. It is the difference between actual results and our assumed results that matter." he replied.

"Wait a sec, why do we use assumed returns? We know what they actually are, don't we?" Mei asked.

The Impact of Assumptions

In order to keep pension expense a little less volatile, the procedures involved with its calculation, on both the PBO side and the asset side, allow for changes to be "smoothed in" over a period of time (generally the remaining service years).

In addition, accounting rules do not require amortization of changes that are less than 10% of the PBO or the assets (whichever is larger). Only when the net changes are greater than this amount are amortizations required, and then only enough to get back within the 10% band.

Let's go back to the example in Figure F and Figure I. Let's say actual plan returns in year 2 were 0% rather than 10% (earnings were 0 vs. the assumed of 100). These differences are not immediately recognized anywhere. The amount of the beginning Year 2 PBO (from Figure F) is 1,005 and the beginning Year 2 Assets were 1,000. Since PBO is larger, we calculate the 10% "corridor" amount using that number, which equals a little bit more than 100. Since the return deficit compared to the 10% assumption is within (just barely!) the 10% corridor, no amortization is required.

Figure J
Amortization of Gains and Losses
Changing the discount rate from 10% to 8% results in a PBO that is higher by 550. In addition, investment returns were 100 lower than assumed. After adjusting for the 10% corridor, 550 will be amortized over the remaining service life.

Items such as asset returns, which replace an assumption because of the fact that time has passed, are called Experience Gains and Losses. Items that reflect changes in assumptions, such as the discount rate, are called Actuarial Gains and Losses.

All Experience and Actuarial Gains and Losses are combined when determining the amortization, and one net amount is added to the pension expense calculation.

For example, Figures F, G and H showed the calculation of PBO for one of Joe's Agricultural Empire, LLC's employees. At the beginning of year 2 the PBO, as shown in those figures was 1,005. Had we been calculating the PBO at the 8% rate from the beginning, the beginning PBO would be larger by 550. This is the amount that will need to be amortized over the remaining service life of the employee (which was 19 years at the beginning of the period).

Figure J shows the calculation of the amortization amount reflecting both the Actuarial Loss due to the discount rate change and the Experience Loss resulting from the investment performance of the assets.

The Balance Sheet

Up to this point we have considered expense, which is an income statement item. We now turn to the balance sheet perspective.

The offsetting entry to pension expense will be a liability account, such as Accrued Pension Cost, Benefits Payable, etc.

If the organization contributes cash into the pension trust during the year, the other side of the cash entry will be to the liability account mentioned in the previous paragraph, or if contributions have exceeded the liability, into an asset account (Prepaid Benefits, etc.).

Figure K
Balance Sheet Adjustments
The Accrued Pension Cost reflects the difference between the PBO and Assetsr

Finally, a comparison is made between the PBO and the value of the assets. If the PBO is greater, the liability is increased by this amount (net of tax) and the offsetting entry debits Other Comprehensive Income, which is in the Equity category. If the assets are greater, than the asset side is increased (net of tax) and the corresponding entry credits Other Comprehensive Income.

Figure K shows this calculation for year 1 using Joe's employee as the example. In this year no adjustment is required because the difference between the assets and the PBO is completely reflected in the accrued liability account (Accrued Pension Cost).

Figure L shows the calculation for year 2. With the impacts of the Actuarial and Experience Losses, the liability on the balance sheet does not initially reflect the entire difference between the PBO and the assets. For this reason, an entry is required to increase the liability, with the other side of the entry going towards the tax impact and equity (via Other Comprehensive Income).

Figure L
Balance Sheet Adjustments
The Accrued Pension Cost category does not reflect the entire difference between the PBO and Assets. An entry increasing this amount and reducing Equity via Other Comprehensive Income is required. This example assumes a 40% tax rate.

There are a couple of other items that can impact pension expense and its balance sheet impact which we are not going to cover since they are a little more 'esoteric'.

The first of these is called 'Prior Service Cost', which arises if changes are made to the pension benefit formula which is attributed retroactively. Say for example that Joe's changed their payout formula to 3% from 2%. The increase in the liability due to this change would be accounted for under this category. Another category relates to changes in accounting rules a few decades ago, which companies could amortize over a period of time (usually called 'Transition Costs" or something similar). Finally, there are specific accounting requirements when changes to the plan result in reduced benefits to some or all employees (usually termed 'Curtailment' or 'Termination'). These usually involve recognition on the financials of a lot of the items that are amortizing under normal circumstances.

Miguel continued "Our OCI has taken a hit because of this, which is a problem because that impacts our Debt to Equity ratios. It puts us in danger of breaking loan covenants - even if we've done everything by the book!"

A Cornucopia of Potholes

The consequences of the pension accounting methodology can create a wide array of problems and counter-intuitive results, many of which may lead to poor decisions being made. Among them are:

Valuation Confusion - an important point to keep in mind is that the pension accounting rules are designed to reflect proper accounting, not necessarily economic reality. If we are valuing our company, or determining the lifetime economic cost of an employee, then we are concered with the Net Present Value of our cash flows. These are not reflected in the income and expense items correctly until the point of retirement. In the Figure G example, we assume that the employee is going to work 20 years and retire. Because of this, we fully expect to incur the full dollar amount of the pension obligation on day 1 - the date of hire! Thus, we should reflect the NPV of our future outlays immediately, which would be 18,267 (the year 1 ending present value of 20,094 discounted an additional 10%). Simply looking at the income statement and balance sheet does not reflect our true expected obligation.

Figure M
Pension Expense at 2 Firms
Pension expense calculation favors the poorly managed company. Average annual salary increase of 3.72%, both employees beginning at 25,000. Employees at MBC finish the final 10 years at different firms.

Reward Bad Leadership - good leadership generally results in highly engaged employees who are motivated, causing them to want to stick around. Bad management, on the other hand, generally results in higher turnover. Many of our pension expense components, chief among them the benefit payout formula, relate to average service life. Consider two firms - ManageGoodCo (MGC) and ManageBadCo (MBD). MGC has an average service life of 20 years. MBC has an average service life of 10 years. Figure M shows the pension calculations at these two firms. MBC has lower pension expense! Because of this, activities such as benchmarking, valuation ratio comparisons based on earnings (such as PE), cannot be relied upon without adjusting for differences.

Figure N
Excess of Assets Over PBO
The amount of Assets at a level funding level always exceeds the PBO until the retirement year, peaking in year 13.

Management Discipline - since the NPV of the ultimate pension obligation can be calculated at the time of employment, it is possible for firms to evenly fund this obligation annually over the employee's career in order to prevent large funding requirements. In our Figure G example, an annual payment of 2,146 (assuming 10% returns, the same as PBO) will create a future value at the employee's retirement exactly equal to the PBO. However, the consequence of this is that the Assets of the plan will always exceed the PBO until the final year. The amount of this difference is shown in Figure N. Maintaining this payment level during the entire time will be extraordinarily difficult. It is quite easy to rationalize skipping a few payments in favor of 'more pressing' items such as an acquisition, a pet project, returning funds to shareholders, and a host of other things. Managers making these decisions in the early years are unlikely to be around to 'suffer the consequences' in the later years, increasing the likelihood that these types of decisions will be made.

Figure O
The Curse of Exponentiation
Using the Joe's employee as an example, we see that Pension Expense (Service Cost and Interest Cost) increases the longer the employee has worked there and the less Remaining Service Life there is.

Mismatched Timing - every industry progresses through various stages as time goes on, from introduction, then to growth, then to maturity, and finally decline. During the introduction and growth phases, the firms will need to hire more and more workers in order to accommodate market demand. This results in a lot of new workers, with long service lives ahead of them, and populating the very left hand side of the exponential curve (such as point A in Figure O). This translates into lower service cost, lower interest cost, and longer time frames to amortize experience and actuarial gains and losses. However, once the maturity stage is reached, worker attrition sets in, where hiring occurs only as those already employed leave. This moves the firm towards the right along the exponential curve (such as Point B in Figure O), resulting in higher service cost, higher interest cost, and reduced amortization periods (making these higher, for better or worse) as remaining average service life decreases. This all occurs at the same time as the firms need to become more cost conscious. Without rapid growth to offset costs, firms shift into optimizing expense at current levels and investigating ways they can reduce costs in order to maintain their current levels and avoid the decline phase as long as possible. Once the decline phase is reached, the pension expense factors become even more exacerbated. All at a time when they can least affort it.

Mei finally reached the office of Aisha, the VP of HR, and briefly explained her project.

"Wow, converting plans would be a big change. Morale is not the best around here right now anyway...this could hurt it even more! It makes it seem like the company is reneging on its promises."

"You mean because people have worked under that expectation for their entire time here and now they won't get it?"

"It's not quite as bad as that. Whatver they have earned up to this point has been earned, we can't go back in time and change things. But going forward we can. So someone who has worked here 16 years will be expecting to retire with 20 years in the payout formula, whereas if we change the plan it will only and forever be 16 years. So they will have less retirement payments than they expected."

"But if we replace it with a different form, such as a DC plan, won't that make them not care about the change?"

"Maybe, but it is very difficult to compare the one type to the other. There are a lot of factors - how financially savvy they are, how long they live, differences in salary levels used between the two options, a lot of other things..."

"Hey, maybe we should do a Monte-Carlo simulation of these differences. What do you think?"

"That sounds interesting and might be helpful, but I am not sure you have the time to do that prior to your recommendation deadline. I think you need to have a recommendation ready even if that is not done. Do you know what it would be?"

Key Takeaways

The calculation of a Defined Benefit plan's pension expense is a complex operation. The nature of the methodology creates long-term biases that are difficult to avoid when management has shorter term priorities. Due to the "Curse of Exponentiation", pension expense and funding become larger issues at exactly the wrong times. In order to correct for these factors, a long-term view of total value rather than accounting metrics can help correct for some of these drawbacks.

You May Also Like

For accounting "potholes" in other situations:

Cash Conversion Cycle: A Good Measure?

For NPV methodology and how it diverges from accounting treatment:

Does Your Accountant Speak Finance?

    ::What would you recommend if you were in Mei's shoes? Why?
    ::In what other ways does the "curse of exponentiation" manifest itself in the pension expense context?

Add to the discussion with your thoughts, comments, questions and feedback! Please share Treasury Café with others. Thank you!

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