Whole life cost calculation

There are 3 approaches to the selection of discount rates. They are:

• the test discount rate;
• the no risk return discount rate; and
• the average risk premium discount rate.

In each example below, the future costs are priced at today's prices.

Test discount rate

In the absence of better information, it is recommended that a test discount rate be used.

This recommendation is based on the assumption that when inflation rates are reasonably low, i.e. less than 15%, there is a relatively stable relationship between inflation and the bank base-interest rate, implying a real discount rate of between 4% and 5% (i.e. the interest rate is 4-5% greater than inflation). It is recommended that where no better information is available, a test discount rate of 4% is used. This method is often adopted in the public sector, where minimal risk associated with the investment is assumed.

According to The Green Book by the HM Treasury, the recommended discount rate is 3.5%. Where the appraisal of a proposal depends materially upon the discounting of effects in the very long term, the received view is that a lower discount rate for the longer term (beyond 30 years) should be used.

The main rationale for declining long-term discount rates results from uncertainty about the future. This uncertainty can be shown to cause declining discount rates over time. In light of this evidence, it is recommended that for costs and benefits accruing more than 30 years into the future, appraisers use the schedule of discount rates provided below.

These recommended discount rates may not be appropriate in the following circumstances.

• For international development assistance projects, a discount rate derived from estimates of the social time preference rate appropriate to the recipient economy should be used.
• When undertaking sensitivity analysis, the impact of changing the precise value of the discount rate can be analysed in the same way as for other parameters in the appraisal. The rationale for undertaking sensitivity analysis on the discount rate should be clearly explained.

No risk return discount rate

Investment in long-term Treasury Bonds can be assumed as having no risk, and is a good reflection of the return to be expected on other investments where there is no risk. Therefore, the discount rate in this approach can be taken as the Treasury Bond rate less an allowance for the expected rate of inflation. On this basis, the discount rate would be assessed as:

Average risk premium discount rate 

The average return on equities reflects the interest required on an average risk. The excess of this rate of return over that expected from the above Treasury Bonds can be taken as the premium expected for the average risk. On this basis, the average risk premium can be calculated as:

Therefore, if construction is deemed to be half as risky as equities, the discount rate for construction investment could be assessed as:

A further approach to establishing a discount rate is to analyse transactions involving the sale of comparable properties, and to use the 'all risks' yield as the discount rate.

Using the methodology

In the above examples of the calculation of discount rates, concurrent interest and inflation rates have been added and subtracted in order to clarify the methodology. This is mathematically imprecise. The actual calculation will need to be compounded.

In the 'no risk return discount rate' method, for example, the calculation should be as follows:

The same methodology should be adopted for actual calculations using other methods. As an approximation, however, this may be ignored.

The effect of future payments on a whole life cost (WLC) calculation is in inverse proportion to the level of discount rates. That is, the higher the discount rate, the less effect future payments have on the WLC calculation. For example, a risk-taking client is less likely to spend money on a building to reduce future costs, as they can use this money to obtain a high return elsewhere.

Selection of a suitable discount rate is crucial, as it can overwhelm all other decisions.

Once the discount rate is established, valuation tables can be used to convert future payments to present value. For example, the present value of £100 to be paid in 5 years' time at a discount rate of 4% =

£100 x 0.82192 (from the discount factor tables, page 46 in Part 2, section 2 of the old Surveyor's Construction Handbook, 'present worth of £1') = £82.19.

Such conversion of future payments to present value provides a basis for comparing alternative expenditure.