Annualisation

Annualisation of Capital Costs in Economic Evaluation

Annualisation lets an economic evaluation charge equipment, buildings and training to the years in which they are used, rather than to the year in which they are paid for. In its economic form the annual sum is set so that its present value over the asset's useful life, at the evaluation's discount rate, equals the purchase price less the present value of any resale value. Most evaluations report costs per year, per patient or per test, so a one-off outlay has to be turned into a yearly figure before it can sit beside staff, drug and consumable costs. The method matters, because dividing by the number of years treats money locked into an asset as free and understates the cost of capital-intensive services.

Capital inputs and the cost of tying up funds

The Global Health Cost Consortium (GHCC) reference case defines a capital cost as any input with a useful life of more than one year, including non-equipment inputs such as training and bed linen, and adds that start-up costs can also be treated as capital. Turner and colleagues explain that because such resources are bought in one year but used over several, their cost has to be spread over their useful life, and they call this adjustment annualisation.

Turner and colleagues identify two components in the spread cost. The first is depreciation, the loss in value of the asset through wear and tear. The second is the opportunity cost of tying up funds in the capital item, since the money could have generated gains elsewhere. An economic cost aims to capture both, and annualisation is the step in cost valuation that does so for capital. In the WHO-CHOICE costing methods described by Johns and colleagues, capital costs were annualised over each input's useful life as standard practice, and a programme's start-up costs were treated as a capital investment annualised over 10 years to allow comparison across sub-regions. How a shared asset is split between services is covered on the capital cost page.

The annuity factor and the equivalent annual cost

The calculation needs four inputs, which are the price, the resale value, the discount rate and the useful life. The standard health economics form divides the outlay, net of the discounted resale value, by an annuity factor.

$$E = \frac{K - S(1+r)^{-n}}{A(n,r)}$$

where $E$ is the equivalent annual cost, $K$ is the purchase price paid at the start of year 1, $S$ is the resale or residual value at the end of the useful life, $r$ is the annual discount rate, and $n$ is the useful life in years.

The annuity factor is the present value of one unit of currency received at the end of each year for $n$ years. It is the sum of a geometric series, which has the closed form shown below.

$$A(n,r) = \sum_{t=1}^{n} (1+r)^{-t} = \frac{1-(1+r)^{-n}}{r}$$

where $A(n,r)$ is the annuity factor, $t$ indexes the years of use, and $n$ and $r$ are as above.

With no resale value, $E = K/A(n,r)$. Otherwise the formula can be rearranged to show how the resale value is treated.

$$E = \frac{K - S}{A(n,r)} + rS$$

where the first term recovers the value used up, $K - S$, together with a return on it while it remains tied up, and the second term, $rS$, is a yearly charge for the part of the outlay that is recovered at the end. The rearrangement follows from $A(n,r) = (1-(1+r)^{-n})/r$, so the resale value attracts only the opportunity cost of holding it, not any wear.

The formula assumes the annual sums fall at the end of each year. If they are treated as falling at the start of each year, the factor becomes $(1+r)A(n,r)$ and the annual figure is slightly lower. A model with $m$ cycles a year can annualise per cycle at the rate $(1+r)^{1/m} - 1$ over $nm$ cycles.

Straight-line depreciation and why the two differ

Straight-line depreciation divides the price less the resale value by the number of years of life. The GHCC reference case states that financial cost estimates should use straight-line depreciation, while economic costs should use an annualisation factor that adjusts the years of life for opportunity cost by means of a discount rate. Turner and colleagues make the same distinction and note that, because the annualisation factor is smaller than the expected lifespan, the annualised economic cost is higher than the annualised financial cost even from a provider or payer perspective.

The gap depends on the useful life and the rate. With no resale value, the ratio of the equivalent annual cost to the straight-line charge is $n/A(n,r)$, and the table gives $A(n,r)$ for four lives at two rates, with the ratio at 3.5%.

For a five-year device the economic charge is about 11% above straight-line depreciation at 3.5%. For a building with a 60-year life it is about 2.4 times as high, which is why the choice of method has its largest effect on services that occupy purpose-built space. As $r$ approaches zero, $A(n,r)$ approaches $n$ and the two methods converge.

HM Treasury's Green Book (2026) keeps depreciation out of appraisal and in a proposal's financial dimension, and annualisation at the discount rate is consistent with that, because its equal annual sums have the same present value as paying the full price at the outset.

Choosing the rate, the useful life, the price and the resale value

Each input is a judgement, and the GHCC reference case asks for the method, the discount rate and the useful life to be reported for each major category of capital input. The usual choice is the rate used to discount the evaluation's other costs, so that capital and recurrent costs are valued on one basis. Section 4.5.1 of the NICE technology appraisal manual (PMG36) sets the reference-case rate at 3.5% a year, and section 4.5.2 allows alternative analyses at 1.5% in specific circumstances. The rate must be paired with real prices. For international comparison the GHCC reference case asks for 3% in all cases, with local rates in addition where available.

UK unit cost tables apply the same logic to buildings. In the Unit Costs of Health and Social Care 2025 manual, notes to the building cost entries state that capital costs have been depreciated over 60 years at a discount rate of 3.5 per cent, declining to 3 per cent after 30 years, and the glossary defines annuitising as converting a capital investment such as a building into its annual equivalent cost.

The GHCC reference case notes that useful life can depend on the setting, such as the availability of repair and maintenance, and is hard to judge for novel technologies. For training, its glossary gives the example that training repeated every five years would be spread over five years.

The GHCC reference case notes that economic evaluations may need replacement prices to capture current opportunity cost. The Green Book states that an asset's residual value should be included to reflect its opportunity cost, whether or not the asset is actually sold.

Worked example of a retinal camera and screener training (illustrative)

All figures in this example are illustrative. A community eye screening service buys a retinal camera for GBP 50,000, expects to use it for 5 years and expects a resale value of GBP 5,000. Training the screeners costs GBP 12,000 and has to be repeated every 4 years. The service performs 2,500 screens a year, and the evaluation discounts costs at 3.5%.

1. The annuity factor for the camera. With $r = 0.035$ and $n = 5$, $(1.035)^5 = 1.18769$ and $(1.035)^{-5} = 0.84197$.

$$A(5, 0.035) = \frac{1 - 0.84197}{0.035} = 4.5151$$

where 0.84197 is the present value of GBP 1 received in 5 years and 4.5151 is the present value of GBP 1 received at the end of each of the 5 years.

2. Without resale value. GBP 50,000 divided by 4.5151 gives an equivalent annual cost of GBP 11,074. The straight-line charge would be GBP 50,000 divided by 5, or GBP 10,000.

3. With resale value. The present value of the resale value is GBP 5,000 multiplied by 0.84197, or GBP 4,210, so the net outlay is GBP 45,790. Dividing by 4.5151 gives GBP 10,142 a year. The rearranged formula gives the same answer, since GBP 45,000 divided by 4.5151 is GBP 9,967 and the charge on the resale value is 0.035 multiplied by GBP 5,000, or GBP 175.

4. Straight-line depreciation with resale value. GBP 45,000 divided by 5 is GBP 9,000 a year. The economic charge is GBP 1,142 a year higher, which is the opportunity cost of the capital tied up in the camera.

5. Where the difference comes from. The annual charge without resale value behaves like a loan repayment at 3.5%. Each year it pays a return on the balance still tied up and recovers part of the price.

With figures rounded to the nearest pound, the returns sum to GBP 5,370 and the recovered amounts to GBP 50,000, matching five payments of GBP 11,074. Straight-line depreciation charges the GBP 50,000 and nothing for the return.

6. The training cost. With $n = 4$, $(1.035)^{-4} = 0.87144$ and $A(4, 0.035) = 3.6731$. GBP 12,000 divided by 3.6731 gives GBP 3,267 a year, against GBP 3,000 on a straight-line basis.

7. The capital cost per screen. The annual capital charge is GBP 10,142 plus GBP 3,267, or GBP 13,409, which is GBP 5.36 per screen over 2,500 screens. Straight-line figures give GBP 12,000, or GBP 4.80 per screen. The economic figure is about 12% higher, and the gap would be far larger if a building were included.

When an evaluation needs annualisation

Annualisation fits when results are reported per year, per patient or per unit of service, when costing is based on a typical year of a running programme, or when the asset outlives the time horizon, so that only the years of use within the horizon are charged. Published unit costs can already include an annualised building element, which should not be charged twice.

A model whose horizon covers the asset's whole life can instead enter the price and the resale value when they occur, as set out on the capital cost page, and at the same rate both routes give the same present value.

In a budget impact analysis the camera appears as GBP 50,000 in the year it is bought, because a budget holder pays at purchase, and the capital cost page shows how the budget and cost-effectiveness treatments of one asset fit together.

Boundaries with discounting and annuity payments

Annualisation and discounting are inverse operations at the same rate. Discounting converts a future stream into a single present value, while annualisation converts a present outlay into a stream of equal annual sums, and the discount rate links the two. Net present value applies discounting to a whole stream of costs and benefits, while annualisation in health economic costing is usually applied to a single capital input.

An annuity payment for a one-off therapy is a contract under which instalments are paid, whereas annualisation is a costing device that moves no money.

Limitations and common errors

Annualisation assumes the asset gives the same service in every year of its life and that the rate reflects the opportunity cost of capital. Equipment can become obsolete before it wears out, and a life set too long lowers the annual charge, so the useful life, rate and resale value belong in sensitivity analysis when capital is a large share of cost.

Several errors recur. Straight-line depreciation from provider accounts is used in an analysis that claims to measure economic costs, omitting the return on capital. A nominal rate is applied to real prices. The purchase price is entered at the start of a model and an equivalent annual cost is added for the same asset later. Equipment bought in earlier years is treated as costless, although the GHCC reference case notes that such capital can still be resold and so still has an opportunity cost.

Sources

• Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance GW. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford: Oxford University Press; 2015.
• Global Health Cost Consortium. Reference Case for Estimating the Costs of Global Health Services and Interventions. 2017. Principles 11 and 12, and Glossary. https://ghcosting.org/pages/standards/principles/pricing_and_valuation.php
• HM Treasury. The Green Book (2026). London: HM Treasury; updated 5 February 2026. Sections on depreciation and assets.
• Johns B, Baltussen R, Hutubessy R. Programme costs in the economic evaluation of health interventions. Cost Effectiveness and Resource Allocation. 2003;1:1. doi:10.1186/1478-7547-1-1
• Jones K, Weatherly H, Barker A, et al. Unit Costs of Health and Social Care 2025 Manual. Canterbury and York: University of Kent and University of York; 2026. https://kar.kent.ac.uk/115569/
• National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). London: NICE; published 31 January 2022, last updated 13 October 2026. Sections 4.5.1 and 4.5.2.
• Turner HC, Sandmann FG, Downey LE, Orangi S, Teerawattananon Y, Vassall A, Jit M. What are economic costs and when should they be used in health economic studies? Cost Effectiveness and Resource Allocation. 2023;21:31. doi:10.1186/s12962-023-00436-w