PVLI

PVLI calculates the present value of single life level income annuity – this is a multi-purpose function that also returns several other values used in the level income calculation, depending on the TypeOfCalc parameter.

Syntax

PVLI(TypeOfCalc, CurrentAge, CommencementAge, LevelAge, CurrentBenefit, SSBenefit, InterestRate, MortalityTable, [AgeSetback], [Frequency], [COLA], [CalculationMethod], [NoPreRetMort], [AnnTiming])

Parameter Name

Description

TypeOfCalc

Type of calculation to perform.
default = 0.

Type	Description
0	PVF = present value factor, calculated such that the present value of the level income annuity = PreBen × PVF.
1	Factor1 = DAF / IAF
2	Factor2 = IAF / TAF
3	PreBen = pre-leveling benefit = CurrentBenefit + SSBenefit × Factor1
4	PostBen = post-leveling benefit = PreBen – SSBenefit
5	LevelingFactor = PostBen / PreBen
6	conversion from single life = PreBen / CurrentBenefit
7	present value of benefit = PreBen × PVF
8	IAF = immediate annuity factor = single life annuity factor valued at CurrentAge, of $1 per year starting at CommencementAge.
9	TAF = temporary annuity factor = single life temporary annuity factor of $1 per year, valued at CurrentAge, starting at CommencementAge, and stopping at LevelAge.
10	DAF = deferred annuity factor = single life deferred annuity factor of $1 per year, valued at CurrentAge, starting at LevelAge.

CurrentAge

Current age of the annuitant (i.e. the age at the valuation date). May be provided as an integer, or as a fractional amount (e.g. years & months).

CommencementAge

Age of annuitant at benefit commencement.

· If CommencementAge > CurrentAge then it will be valued as a deferred annuity.

· If CommencementAge is missing or zero, then CommencementAge is assumed to be = CurrentAge and it will be valued as an immediate annuity

LevelAge

Age at which amount of annuity changes for the leveling option.

CurrentBenefit

Amount of the annuity benefit (in the normal form) before adjustments for "level income" payment form.

SSBenefit

Social Security monthly benefit payable at the leveling age.

InterestRate

The interest rate(s) to discount future payments to calculate the present value. May be a number, a percentage, a text string, a named range, or reference to a range.

· Rates can be defined using these interest definitions.

· Note: A value that is greater than 25% (i.e. 0.25) will be divided by 100; e.g. if you enter 2.75 it will be treated as .0275 or 2.75%.

MortalityTable

Mortality table definition text string.

YearsCertain

Number of years guaranteed payments. May be an integer, or a factional amount (e.g. years & months).
Optional, default = 0

AgeSetback

Mortality table age set-back. A negative number is a set-forward.
Note that you can also define a setback using the "/sb" option in the table definition (or "/sf").
Optional, default = 0.

Frequency

Number of payments per year:
Optional, default = 12

Frequency	Description
1	annual
2	semi-annual
4	quarterly
6	bi-monthly
12	monthly
99	continuous

COLA

Periodic cost-of-living adjustment applied to the benefit amount.
Optional, default = 0
Rates can be defined using these COLA definitions.

CalculationMethod

Method of calculation
Optional, default = 0

Method	Calculation Approach	How to Handle
Method	Calculation Approach	Fractional Ages	Frequency of Payments
0	discounted cash flow	interpolate on whole ages	Woolhouse
1	discounted cash flow	exact	exact
2	discounted cash flow	exact	Woolhouse
8	commutation functions	interpolate on 𝑙𝑥	Woolhouse
9	commutation functions	interpolate on 𝐷𝑥	Woolhouse

NoPreRetMort

The defines the application of pre-retirement mortality for a deferred annuity.
Optional, default = 0.

NoPreRetMort	Description
0	use pre-retirement mortality
1	no pre-retirement mortality

StopAge

Age when the annuity benefit stops -- no payment at this age.
Optional, default = to end of the mortality table.

AnnTiming

Defines when the payments are made in the period.
Optional, default = 0.

AnnTiming	Description
0	beginning of period
1	end of period
0 to 1	fraction of period, e.g. .5 means paid in middle of the period