Whole life cost measures

Costs over a given period of time - cumulative costs

The cost over a given period of time, say 30 years, measures the acquisition and installation costs, as well as the cumulative costs of maintenance, disposal and component replacement.

Generally in pure financial terms the best value option would be the one with the lowest cumulative cost. However, cumulative costs do not provide a level playing field when comparing future costs. For example, £10,000 spent in 10 years' time does not have the same value as £10,000 spent in 20 years' time.

Nor does the cumulative cost measure allow comparison between schemes compared over different time spans.

To enable fair comparison of future expenditures the net present value is used.

Net present value

Net present value (NPV) allows a comparison of future costs at present values. HM Treasury guidance (The Green Book - Appraisal and Evaluation in Central Government, 2003) is for a discount rate of 3.5% to compare alternative options for periods up to 30 years. For periods longer than this the discount rate decreases. A discount rate of 3.5% has been used in this assessment.

HM Treasury's The Green Book (2003) defines net present values as follows:

'The discount rate is used to convert all costs and benefits to "present values", so that they can be compared. Calculating the present value of the differences between the streams of costs and benefits provides the net present value (NPV) of an option. The NPV is the primary criterion for deciding whether government action can be justified.' (Clauses 5.49 and 5.50)

'Discounting is a technique used to compare costs and benefits that occur in different time periods. It is a separate concept from inflation, and is based on the principle that, generally, people prefer to receive goods and services now rather than later. This is known as "time preference".' (Clause 5.48)

The mathematical expressions used to calculate discounted present values are set out below.

Year 0 is the present. Accordingly, the present value, at the middle of year 0, of a payment of £1 made at the middle of year n is given by:

Dn = 1/(1 + r)n

where r is the discount rate and Dn is the discount factor. For example, a payment of £150 at the middle of year 5 has a present value at the middle of year 0 of:

Dn = £150 x 1/(1 + 0.035)5 = £150 x 0.8420 = £126.30

Lower total net present value options give the best value options in cost terms.

Alternative approaches to calculating net present value

Net present value at 'real' discount rates:

This is more of a business appraisal method - typically a discounted rate, which could be obtained from 'safe' investments such as government gilts or stocks, is used for this calculation. The formulae used are as above.

Allowance for inflation:

An alternative approach is to use a discount rate with an adjustment for inflation:

1 + R = (1 + r) + (1 + i),

this may be approximated to: R = r + i.

A view needs to be taken of the rate - typically this could be calculated using the Bank of England inflation target. Interest rates on investment depend on the level of risk investors are prepared to take. Again, typically a 'safe' investment is selected.

However, calculating the net present value on this basis tends to give high discount rates with opportunity costs which would only be realised in the equity markets with a high risk factor. It is unlikely that institutions would base their calculations on these risk factors.

Calculating life cycle costs for a series of expenditures

Life cycle costs for say a building can be calculated using the following equation:

                     t           Ct
LCC = Co + sum   ________  
                    t=0      (1+r)t

Units = £/functional unit/year for t years at r discount rate

Where

LCC   = Life cycle cost

Ct     = Values at year t

r       = Discount rate

t       = Time or number of years

Co    = Capital costs

More typically a life cycle cost per unit area is calculated which is achieved by dividing the result from the above equation by the area of the asset in question.

Annualised costs

Annualised costs give a cost per unit per year. This may be based on an area (such as the cost per square metre of school per year) or a functional unit (such as the cost per pupil per year). It is based on the cumulative cost over years. It is a typical measure for whole life costs in the construction industry and is a useful overview figure.

The same caution attached to cumulative costs should be taken, as annualised costs may not be a fair comparison of future expenditure.