Last edited 08 Jan 2021

#  Introduction

Cost-benefit analyses can be used not only to examine the current benefits and costs of a project, but also the future benefits and costs.

Discounting is a way of comparing the value of costs and benefits over different time periods to their present values. It provides a means for accurately assessing the economic impact of a project over time and helps to calculate net present value (NPV - the difference between the present value of cash inflows and the present value of cash outflows for a long-term investment that can be used to assess the likely profitability of investments).

The principle of discounting is based around the time value of money. This is the concept that money is worth less in the future than it is in the present because of its reduced capacity for generating a return, such as interest, and because of inflation. Discounting is a means of assessing how much less an amount is worth in the future than it is now.

This is the opposite of the concept of ‘compounding’, which describes the rate at with an amount will grow over time due to the accumulation of returns such as interest.

#  Example

A construction project has initial costs of £1.7m. It is expected to generate the following cash inflow:

• End of year 1 = £120,000.
• End of year 2 = £250,000.
• End of year 3 = £550,000.
• End of year 4 = £1.3m.

To calculate the discount value at a rate of 5% you use the following equation:

120,000/1.05¹ = £114,285.70 (Year 1).

250,000/1.05² = £226,757.37 (Year 2).

550,000/1.05³ = £475,110.68 (Year 3).

1,069,512.22/1.05^4 = £1,069,513.22 (Year 4).

NPV = £1,885,666.97

NPV = £1,885,666.97 – £1.7m

NPV = £185,666.97

So there is still economic justification for the project to go ahead. However, if the discount rate is increased to 10% the result is:

120,000/1.1¹ = £109,090.91 (Year 1).

250,000/1.1² = £206,611.57 (Year 2).

550,000/1.1³ = £413,223.14 (Year 3).

1,069,513.22/1.1^4 = £887,917.49 (Year 4).

NPV = £1,616,843.11

NPV = £1,616,843.11 – £1.7m

NPV = -£83,156.89

In this scenario there does not appear to be economic justification for the project to go ahead.

#  Other definitions

The Green Book, Central Government Guidance On Appraisal And Evaluation, Published by HM Treasury in 2020, suggests discounting: ‘…is a technique that converts future values occurring over different periods of time to a present value by taking account of the human preference for value now rather than later. This concept is known as “social time preference”, and it is applied to real prices expressed in base year values and has nothing to do with inflation.’

Guide to developing the project business case, Better business cases: for better outcomes, published by HM Treasury in 2018, defines discounting as: ‘A method used to convert future values occurring over different periods of time to a present value so that alternative future values can be compared on the same basis.’

The SuDS Manual published by CIRIA in 2015 defines discounting as: ‘A method to compare the benefits and costs that arise over the appraisal period. The discount rate converts all costs and benefits to the present day to determine the present value (PV) or whole life costs (WLC) so that they can be evaluated consistently.’

#  External references

## Designing Buildings Anywhere

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