3.2 Discounting and Discount Rates
In all but the simplest proposals, cashflows will occur at several different points in time. In general, it is not appropriate to treat cashflows in one period as having the same weight as cashflows in other periods. Rather, cashflows need to be discounted.
The term discounted means that cash flows which occur later are given less weight than flows which occur sooner, with larger reductions the further into the future the cash flows occur. The discounted value of cash flows is therefore the relevant assessment measure. The discounted value is also known as the present value.
An intuitive justification for discounting is that most people would prefer receiving a dollar today over receiving a dollar in a year’s time. This is referred to as time preference or the time value of money.
A second justification for discounting, and the one which is used in practice to derive the discount rate (r), is that when a person assesses a proposal, they will require a return at least as high as they can obtain from any other investment of equal risk.
By discounting, the net benefit or cost over and above the return for other proposals of equal risk can be determined. A net present value (NPV) above zero indicates a higher return than other proposals of equal risk, an NPV of zero indicates an equal return, and a negative NPV indicates a lower return.
Example 3.2: Discounting – The Rationale
The Ministry of Information Technology expects to receive a net cashflow of $45 million in the first year after they upgrade their system. However, the Ministry could also receive a net cashflow of $45 million in one years time by investing $40.9 million in high-yield corporate bonds now (assuming a 10% per annum real rate of interest on those bonds). So, assuming the IT proposal is approximately as risky as investing in the corporate bonds, the $45 million cashflow in one year’s time is really only worth as much as having $40.9 million now. The future cashflow is therefore discounted by the discount rate of 10%, to $40.9 million, for the purposes of proposal evaluation.
3.2.1 The Discounting Formula
The discounting can mostly easily be done in Excel (see Section 3.4). However, for the sake of completeness there is an explicit formula for the discount factor in period n:
Discounted value now = Future value in nth period × Discount factor
= Future value in nth period × (1 + Discount rate)-n
Example 3.3: Discounting Using the Formula
If the Ministry assesses that its proposal is as approximately as risky as other proposals with a real return of 10%, it will choose a discount rate of 10%. The discounted values of expected cash flows are calculated in the following table.
| Year (n) | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Forecast cash inflow | 0 | 65 | 65 | 65 |
| Less forecast cash outflow | 100 | 20 | 20 | 20 |
| Forecast net cashflow | -100 | 45 | 45 | 45 |
| Discount factor = 1 ÷ (1 + 10%)n | 1.000 | 0.9091 | 0.8264 | 0.7513 |
| Present value = net cashflow × disc. factor | -100 | 40.9 | 37.2 | 33.8 |
