The sensitive type

It's a fact of life that people have to make choices that are not certain. Whole Life Cost (WLC) calculations depend on numerous assumptions, all of which are subject to a degree of uncertainty. Without a crystal ball it is hard to accurately forecast the cost and frequency of future events. However, certain techniques can help, including sensitivity analysis, which tests the impact of the uncertain assumptions used in your WLC model.

Because various activities will take place at different times to maintain an asset, the incremental costs must be converted to present day value using a discounted cash flow technique.

It is necessary to discount costs occurring later relative to those occurring sooner because money has an opportunity cost - money received now can be invested and converted into a larger future amount. Therefore WLC requires future cash flows incurred over the lifetime of the project to be discounted and expressed in present values. The formula used to do this is:

X/ (1+r) n

When X= input value, r = rate of interest or discount rate, n = number of years

(Discount equation, Treasury, 1997)

There is often confusion as to why we must discount. People suppose it is because of the existence of inflation, but rather the origin stems from our psychological preference to receive goods today rather than tomorrow - time-preference for money.

What about inflation?

One can either use real or nominal discount rates in a WLC calculation.

If one uses real discount rates, each expected future cash flow is forecasted at today's prices. The discount rate used to convert these ‘constant price' cash flows to their present value is based on the real rate of interest (this is the nominal rate of interest - expected rate of inflation) plus a risk premium.

Nominal discount rates, however, see future cash flow forecasted in terms of the expected quantity of goods or services multiplied by the unit price expected to prevail at the time of the expenditure (future prices). The discount rate used to convert these cash flows to their present value is based upon the nominal rate of interest (required real rate of interest plus expected rate of inflation) plus the risk-premium.

Contingency allowance

A common method of allowing uncertainty is to add a percentage figure to the most likely estimate of predicted cost. The amount added is usually called a contingency. The value of this is usually expressed as a percentage mark-up on the base estimate, but there are weaknesses:

Sensitivity analysis is not a crystal ball, but it does highlight the most significant assumptions in your WLC model

• The percentage figure is usually arbitrarily arrived at and not appropriate for the specific project

• There is a tendency to double-count risk as some estimators include contingencies in their best estimate

• The percentage added indicates the potential for detrimental or downside risk; it does not indicate any potential for cost reduction

• It does not encourage creativity in estimating practice, allowing it to become mundane, which can cause oversights.

Using this method, forecasts can therefore be too conservative or pessimistic.

Sensitivity analysis

Sensitivity analysis can be used to assess which of the uncertain input values have the greatest significance and potential impact on the forecast. It is a way of estimating the cost if one or more of the input parameters changed value. An advantage here is that you can pick out a specific cost item, thereby acknowledging that uncertainty and price variances might exist in the model.

It is essential to test the WLC forecast for both ‘optimistic' and ‘pessimistic' scenarios. This can be done by changing the values of key variables in the analysis and measuring the impact of the change on the WLC. You can change both the cost and frequency assumptions and the discount rate.

Undertaking a ‘one at a time' sensitivity analysis involves changing each assumption to a chosen optimistic value, recording the WLC result and then repeating the process with a chosen pessimistic value. One way to show the results is to construct a Tornado diagram (as shown below). This graphically uncovers which variables have the most influence on the WLC. It is known as a Tornado diagram because when one ranks the results in order of importance, the shape of the graph looks like a whirlwind.

Sensitivity analysis is not a crystal ball, but it does highlight the most significant assumptions in your WLC model and it shows you what the WLC forecast would be should any input assumption take on a different value.

Anthony Waterman is head of research at Sense Cost Consultancy. He can be reached at awaterman@sense-limited.co.uk