Present Value of a Growing Annuity Formula

Formula

PV = Pmt x (1 - (1 + g)n x (1 + i)-n ) / (i - g)
Variables used in the annuity formula
PV = Present Value
Pmt = Periodic payment
i = Discount rate
g = Growth rate
n = Number of periods

Use

The present value of growing annuity formula shows the value today of series of periodic payments which are growing or declining at a constant rate (g) each period. The payments are made at the end of each period for n periods, and a discount rate i is applied.

A growing annuity is sometimes referred to as an increasing annuity or graduated annuity.

The formula discounts the value of each payment back to its value at the start of period 1 (present value).

When using the formula, the discount rate (i) should not be equal to the growth rate (g).

Present Value of a Growing Annuity Formula Example

If a payment of 8,000 is received at the end of period 1 and grows at a rate of 3% for each subsequent period for a total of 10 periods, and the discount rate is 6%, then the value of the payments today is given by the present value of a growing annuity formula as follows:

PV = Pmt x (1 - (1 + g)n x (1 + i)-n ) / (i - g)
PV = 8,000 x (1 - (1 + 3%)10 x (1 + 6%)-10 ) / (6% - 3%)
PV = 66,550.43

Present Value of a Growing Annuity Formula if i = g

The above formula will not work when the discount rate (i) is the same as the growth rate (g). In this situation, the formula shown below should be substituted.

PV = Pmt x n / (1 + i)
Variables used in the annuity formula
PV = Present Value
Pmt = Periodic payment
i = Discount rate
n = Number of periods

For example, if a payment of 8,000 is received at the end of period 1 and grows at a rate of 3% for each subsequent period for a total of 10 periods, and the discount rate is also 3%, then the value of the payments today is given by the present value of a growing annuity formula as follows:

PV = Pmt x n / (1 + i)
PV = 8,000 x 10 / (1 + 3%)
PV = 77,669.90 

The present value of a growing annuity formula is one of many annuity formulas used in time value of money calculations, discover another at the link below.

Present Value of a Growing Annuity Formula November 6th, 2016Team

You May Also Like


Related pages


services rendered accounting entryexcel function npvhow to enter contra entry in tallymirr finance ratebalancing of ledger accountsmaterial requisition slipgross profit journal entryaverage account receivablesstockholders equity balance sheetopposite of unearned revenueprofitability index formulaformula for annuity present valuecalculating accounting rate of returninventory count templateleasing calculator formulahow to calculate straight line depreciation ratewhat is sunk cost in accountingtime sheet samplepercentage of completion method formulaaccrual accounting entrypresent value growing annuityfinancial forecast templatecalculate lease payment formulaprofitability index calculator financialcash operating cycle definitionunder perpetual inventory systempayback period formula excelaccrued interest on notes receivablematerial price variance formulaebit interest coverage ratioaccounting conventions and principlesending inventory formula accountinghow to calculate direct materials used in productiongross margin percentage formulafinished goods inventory calculationwhat is stockholders equity in accountingexample retained earnings statementdifference between profit margin and markupplant assets examplesin a perpetual inventory systempetty cash excel templateperpetual inventory income statementbad debt journal entry exampledefine deferred revenue expendituresubsidiary ledger accountsjournal entry for common stock issuedbudgeted overhead absorption rateexcel pmt exampleinternal control checklist templatestandard cost variance definitionfob value definitioninterest rate formula compounded continuouslydiminishing balance method depreciationfuture value annuity due calculatorcalculate future value of annuitydouble declining calculatorassets liabilities equationvalue of perpetuity formulabookkeeping definitionspreadsheet for small businessoutstanding loan calculatorissuing preferred stockgeneral ledger paperpresent value of a bond calculatorperpetual vs periodicgearing in accountingdouble declining balance calculationformula for gearingfuture value of annuityshipment terms fobmark up in accountingallowance for loan losses journal entrieshow to calculate predetermined manufacturing overhead rate