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Annuity Payment

A reimbursement structure paying a treatment's total cost to the manufacturer in a series of instalments over time, rather than as a single upfront sum.

Last reviewedDarrin Baines IP Ltd

Concept Architecture

Concept


Theoretically, Annuity Payment is the fixed periodic payment required to amortise a present value or generate a future value over a specified number of periods at a constant interest or discount rate. It is founded on the mathematics of annuities and the time value of money, recognising that money available today differs in value from money received in the future. The concept exists to determine equal periodic cash flows that are financially equivalent to a present or future lump sum.

Mathematically, the annuity payment is derived by rearranging the present value or future value equation of an annuity to solve for the periodic payment. The calculation depends on the interest rate, number of payment periods and whether payments occur at the beginning or end of each period. In health economics, the ordinary annuity formulation is typically used for annualised capital costs and equivalent annual cost calculations.

In practice, annuity payments are calculated using financial calculators, spreadsheet functions or economic evaluation software. In health economics, they are used to annualise capital investments, spread equipment acquisition costs over useful lives, estimate recurring financing obligations and compare interventions with different asset lives through equivalent annual cost methods.

Purpose


Used to calculate equal periodic payments that are financially equivalent to a present or future value, supporting capital costing, equivalent annual cost analysis and long-term financial planning in health economic evaluations.


Mathematical Formulae

Primary Formula

PMT = PV ? r / (1 ? (1 + r)?�)

Supporting Formulae

Present value of an annuity:

PV = PMT ? (1 ? (1 + r)?�) / r

Future value of an annuity:

FV = PMT ? ((1 + r)� ? 1) / r

Equivalent annual cost:

EAC = PV ? r / (1 ? (1 + r)?�)

Related Mathematical Methods

  • Discounting
  • Present Value
  • Future Value
  • Equivalent Annual Cost
  • Net Present Value
  • Capital Recovery Factor

Example

A hospital purchases diagnostic equipment costing �500,000 with a useful life of 10 years. Using a discount rate of 3.5%, the equivalent annual payment is:

PMT = 500,000 ? 0.035 / (1 ? (1.035)???)

PMT = �60,965 per year

This annual payment represents the equivalent annual cost of owning the equipment over its useful life.


Excel Implementation

FunctionExample FormulaHealth Economics Application
PMT=PMT(3.5%,10,-500000)Calculates the equivalent annual payment for a capital investment.
PV=PV(3.5%,10,-60965)Calculates the present value of an annuity stream.
FV=FV(3.5%,10,-60965)Calculates the future accumulated value of periodic payments.
RATE=RATE(10,-60965,500000)Estimates the implied discount or financing rate.
NPER=NPER(3.5%,-60965,500000)Determines the number of payment periods.

VBA (Optional)

VBA can automate annuity payment calculations for multiple capital investment scenarios and generate equivalent annual cost schedules for health economic models.


Sources

  • Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes.
  • Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
  • Boardman AE, Greenberg DH, Vining AR, Weimer DL. Cost-Benefit Analysis: Concepts and Practice.
  • Brealey RA, Myers SC, Allen F. Principles of Corporate Finance.
  • NICE. Health Technology Evaluation Manual.

Frequently Asked Questions (6)

  • What is an annuity payment?

    A reimbursement structure paying a treatment's total cost to the manufacturer in a series of instalments over time, rather than as a single upfront sum.

    Source: Jørgensen & Kefalas 2015

  • How does an annuity payment structure spread a treatment's cost?

    An annuity payment spreads the total cost of a treatment across a series of instalments over time, rather than settling it in a single upfront sum. The manufacturer receives regular payments over several years, which eases the immediate strain on a payer's budget and can be linked to the treatment continuing to work. This structure was devised chiefly for one-time therapies whose huge prices would otherwise land all at once. Paying over time instead of all at once is its principle. Drummond and colleagues (2015) discuss such arrangements.

    Source: Drummond et al. 2015

  • Why are annuity payments used?

    Annuity payments are used because some treatments, particularly one-time gene and cell therapies, carry very high upfront costs that strain budgets, and spreading the cost over instalments improves affordability and can align payment with the period over which the benefit is realised. So annuity payments are used to manage the affordability of large upfront costs and, when tied to ongoing benefit, to share the risk that a durable therapy may not last as expected, which is why they are proposed for high-cost, potentially curative treatments, converting a single large payment into a manageable stream that can be linked to continued performance.

    Source: Jørgensen & Kefalas 2015

  • How does an annuity payment work?

    An annuity payment works by dividing a treatment's total agreed cost into periodic instalments paid over a set period, sometimes with the instalments conditional on the treatment continuing to demonstrate benefit in the patient. If the benefit ceases, payments may stop or be adjusted. So an annuity payment works by spreading reimbursement over time and potentially linking each instalment to ongoing evidence of benefit, which converts a large upfront cost into a series of payments, easing budget impact and, when performance-linked, sharing durability risk, though it requires arrangements to track outcomes and manage payments over the period.

    Source: Jørgensen & Kefalas 2015

  • What challenges do annuity payments face?

    Annuity payments face challenges including tracking outcomes over time if instalments are linked to benefit; patient mobility between payers, which complicates who pays remaining instalments if a patient changes insurer; the accounting and budgeting treatment of future payment commitments; and administrative complexity. So annuity payments face practical obstacles around continuity of payment across payers, financial treatment of the obligations, and the administration of instalments, which is why, despite easing affordability, they are not straightforward to implement, requiring solutions to these issues, and their adoption depends on the health system's capacity to support such arrangements over time.

    Source: Jørgensen & Kefalas 2015

  • How do annuity payments relate to one-time treatments?

    Annuity payments relate to one-time treatments as a payment model designed for them: because one-time treatments deliver durable benefit from a single administration at high upfront cost, paying in instalments over time spreads that cost and can match payment to the period of benefit. So annuity payments are proposed specifically for one-time treatments, whose single high-cost, potentially long-lasting nature makes a large upfront payment difficult and a spread-out, possibly performance-linked payment attractive, which is why the two are closely linked in discussions of how to fund advanced therapies such as gene and cell treatments.

    Source: Jørgensen & Kefalas 2015

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Verified by Dr Darrin Baines

British health economist

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Verification date: 8 Apr 2026

Content version: 1.0.0

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