What is Present Value of an Annuity?
The present value of an annuity (PVA) is the current value of a series of equal periodic future payments, discounted at a specified interest rate. It is used to value loans, leases, pensions, structured settlements, and any stream of equal cash flows over a fixed term.
How It Works
- PVA = PMT * [1 – (1 + r)^-n] / r, where PMT is the periodic payment.
- r is the discount rate per period; n is the number of periods.
- For an annuity due (payments at start of period), multiply PVA by (1 + r).
- Higher discount rates lower the present value.
- Used in loan amortization, lease accounting (IFRS 16), and pension obligation measurement.
Saudi Context
Under IFRS 16 (mandatory in KSA via SOCPA), lessees compute lease liabilities as the present value of fixed lease payments at the implicit rate or incremental borrowing rate. End-of-service benefits under IAS 19 are similarly measured at present value. Saudi banks also disclose loan amortization schedules where PVA arithmetic determines installment payments.
Example
A company signs a five-year lease at SAR 200,000 annual rent, discount rate 6%. PVA = 200,000 * [1 – (1.06)^-5] / 0.06 = 200,000 * 4.2124 = SAR 842,473. This amount is capitalized as a right-of-use asset and lease liability on day one.