In U.S. public pension and OPEB modes, the liability calculation date, funding asset valuation date and accounting asset measurement date are specified in the Initial Asset Values topic of the Asset & Funding Policy.  If the funding asset valuation date or accounting asset measurement date is later than the liability calculation date, ProVal rolls the liabilities forward from the liability calculation date to the appropriate asset measurement date.

 

In all cases, ProVal will not roll liabilities backward, so any asset measurement date cannot be specified to be earlier than the liability calculation date.

Below are the details of the roll forward calculations. The examples demonstrate rolling forward accounting liabilities from the liability calculation date to the asset measurement date. In U.S. public and OPEB modes, the same formulas are used when rolling funding liabilities from the liability calculation date to the funding asset valuation date.

Liability roll forward method, where roll forward period is 1 year or less:

where:

The subscript rf denotes "rolled forward" and the subscript vd denotes "as of the valuation date".

PBO is the projected benefit obligation.

Rate is the underlying liability interest rate. When a yield curve is used as the discount rate assumption, Rate is set equal to the effective interest rate.

T is the fraction of the year from the valuation date to the measurement date, calculated as: (number of days from valuation date to measurement date) / (365 + 1 if a leap year)

PBONC is the beginning of year service cost.

PBOEeNC and ABOEeNC are the beginning of the year portion of projected benefit obligation normal cost (a.k.a. service cost) and accrued benefit obligation normal cost, respectively, assumed paid via employee contributions. These employee normal costs, PBOEeNC and ABOEeNC, may have different values. Note that their values are calculated as of the valuation date, whereas Valuation Set and forecast output display values that reflect interest to the middle of the year (when employee contributions are assumed paid.). Thus the PBOEeNC and ABOEeNC values used in the roll-forward calculation will differ from the values displayed in output.

BP is expected cash benefit payments, which are assumed to be paid, on average, in the middle of the year beginning on the valuation date. An override in the Asset & Funding Policy allows you to reflect actual benefit payments for the term BP during the roll forward period to the first measurement date.

NAPBO is the non-active (retired, terminated vested, disabled or survivor) component of the PBO.

NAABO is the non-active component of the ABO and is equal to NAPBO.

EBO is the expected benefit obligation, also known as the accounting present value of all future benefits.

ABO is the accumulated benefit obligation.

VABO is the vested benefit obligation.

V is the assumed vested ratio.

EAN is the liability under then entry age normal level % of pay cost method.

EANNC is the normal cost under the entry age normal level % of pay cost method.

salary is the assumed salary scale.

Liability roll forward method, where roll forward period is greater than 1 year :

Liability is either the funding or accounting liability.

rate is the is the underlying liability interest rate. When a yield curve is used as the discount rate assumption, Rate is set equal to the effective interest rate.

PVNC is the present value, as of the valuation date, of normal cost accruing during the roll forward period.

PVBPs is the present value, as of the valuation date, of the expected benefit payments during the roll forward period.  The expected benefit payments may be overwritten in the Asset & Funding Policy for the roll forward to the first and second measurement dates.  When using an override, the roll forward to the first measurement date will use the benefit payments as entered (prorated for the fractional year if annualized amounts were entered). When using an override, the roll forward to the second measurement date will be adjusted to combine the portion of the override applicable with the expected benefit payments for the period.

Expected benefit payments for the first complete year following the valuation date used to roll forward to the second measurement date when using overrides:

The formula above calculates benefit payments for the complete year following the valuation date by reflecting the override applicable to the period and using ProVal's expected benefit payments for the remainder of the period.  

Normal Cost roll forwards

Where:

PBONC is the normal cost under a projected unit credit cost method.

EANNC is the normal cost under the entry age normal level percent of pay method.

UCNC is the normal cost under the unit credit cost method.

rate is the is the underlying liability interest rate. When a yield curve is used as the discount rate assumption, Rate is set equal to the effective interest rate.

salary is the assumed salary scale.

The liability roll forward method and plan changes 

For a Valuation Set, any liability changes resulting from accounting plan changes are calculated based on already rolled-forward liabilities. During a forecast, however, changes in liability attributed to plan changes are calculated as of the valuation date and adjusted, as follows, to roll forward to the measurement date:

Where:

PC is the change in projected benefit obligation attributable to the plan change.

NCCHG is the change in the beginning of year service cost attributable to the plan change.

Thus, during a forecast, there will be a spurious gain or loss, attributable to the approximation used to roll the change in liability forward to the measurement date.

Benefit payment roll forward method (used for the spot rate interest cost method):

This method works by rolling forward the benefit payment stream underlying the liability as of the valuation date to the measurement date.  Once the benefit payment stream as of the measurement date is determined, ProVal takes the present value to calculate the liability.

Benefit payments are adjusted to the measurement date as follows:

BP_t+z = {(BP_t x (1 – z)) + (BP_t+1 x z)} + {[(BPNC_t x (1-z)) + (BPNC_t+1 x z)] x z} 

where:

t is the valuation date 

z is the fraction of the year between the valuation date and the measurement date. If the roll forward period is greater than 1 year, the first term of the benefit stream determined as of the valuation date will drop out and z will be adjusted by subtracting 1 year.

BP_t is the liability benefit payment at time t

BPNC_t is the normal cost benefit payment at time t

Calculating the PBO

Once the benefit payments have been determined as of the measurement date, the liability is determined as:

​

where:

k is the average benefit timing factor and is assumed to be the same as the average benefit timing factor calculated at the valuation date

Other notes regarding this method:

1. ABO and EBO, for which projected benefit payments are available, are rolled forward in the same manner as described for PBO above.
2. For liabilities where there are no projected benefit payments available, the liabilities are determined based on the relationship to the closest proxy. For example,
   • The active fully eligible APBO is determined by first calculating the total APBO at the measurement date, and then  assuming that active fully eligible APBO at the measurement date bears the same ratio to the total APBO at the measurement date as it did at the valuation date.
   • The active participant VBO at the measurement date is assumed to remain in the same proportion to the active participant ABO as it bore to it on the valuation date.
3. As all calculations are done in total, the split of projected benefit payments between actives and inactives is an estimation. Component pieces of results at the measurement date are assumed to bear the same relationship to their corresponding result at the valuation date as the total. 
4. Expected benefit payments at the measurement date are assumed to be equal to the first projected benefit payment at the measurement date.
5. The liabilities associated with plan changes and assumption changes are estimated the same way as for the liability roll forward method described in the section above (in other words, ProVal does not determine the liability change as the difference between the present values of two sets of adjusted benefit payment streams.  The change is determined based on the liability difference as of the valuation date and then rolled forward in aggregate to the measurement date).
6. Employee contributions are approximated at the measurement date by assuming they are equal to the value at the valuation date.

   Adjusting the PBO for actual benefit payment override

If you have defined a benefit payment override for the accounting roll forward on the Benefits and Rounding topic of the Asset & Funding Policy, the liability and its corresponding benefit payment stream will be further adjusted. 

The PBO will be adjusted to reflect the actual benefit payments as follows:

 PBO_adj = PBO_initial + BP Adjustment 

where:

If the roll forward period is 1 year or less and the override is annualized

If the roll forward period is 1 year or less and the override is the actual amount paid during the roll forward period

If the roll forward period is greater than 1 year and the override is the actual amount paid during the roll forward period

​

z is the fraction of the year between the valuation date and the measurement date

Override BP₀ is the benefit payment override entered in the Asset & Funding Policy for the first year

Override BP₁ is the benefit payment override entered in the Asset & Funding Policy for the second (only applicable if roll forward is greater than 1 year)

BP₀ is the expected benefit payments for the first year

BP₁ is the expected benefit payments for the second year (only applicable if the roll forward is greater than 1 year)

i is the first term from the spot rate yield curve

PBO_initial is the PBO calculated in the section above prior to adjustment for actual benefit payments

Benefit payment overrides in forecasts when the roll forward period is greater than 1 year

When using benefit payment overrides for a roll forward period that is greater than 1 year, the roll forward to the measurement date for the second year will also be adjusted.  For example, if the actual benefits (not annualized amount) have been entered for a 13 month roll forward, 

​

Adjusting the benefit payment stream for actual benefit payment override

Next the underlying benefit payment streams are adjusted accordingly.  If you have selected to spread the override over all future benefit payments (which might be appropriate, for example, if there are significant lump sums), then each term of the PBO benefit payment stream will be adjusted by the ratio of PBO_adj to PBO_{initial.  Similar adjustments are made to the benefit streams underlying the other accounting liabilities, EBO & ABO.}

If you have selected to adjust the first year benefit payment only, then the first term of the benefit payment stream will be adjusted as follows:

​

where:

k is the average benefit timing factor

Annuity substitution benefit payments​

If you are also using the annuity substitution benefit payment method, the annuity substitution benefit payments are adjusted to the measurement date as follows:

1. Adjust the annuity substitution benefit payments to the measurement date:      BP_t+z = {(BP_t x (1 – z)) + (BP_t+1 x z)} + {[(BPNC_t x (1-z)) + (BPNC_t+1 x z)] x z} 
2. Calculate the present value of the benefit payments determined in 1.
3. Calculate the ratio of the actual PBO (which was determined based on upon the actual benefit payment stream underlying the PBO as of the measurement date) to the present value determined in step 2.
4. Adjust each cash flow in 1. by the ratio determined in 3.