3.4 Net Present Value
Given a set of cashflows, how are the net benefits of the proposal actually assessed? In practice, there are many stages of assessment, including both quantitative and qualitative methods.
However, one element of assessment that should be included in virtually all projects is a calculation of the Net Present Value (NPV) of the project. The NPV is the sum of discounted net cashflows over the period.[46] When properly calculated, the NPV is a relatively objective method of determining the improvement in national wealth resulting from a proposal. It is mechanistic, and because of this, starting assumptions need to be explicitly identified.
Once calculated, the NPVs of several projects can be compared. In a commercial setting, it is typical for the project with the highest NPV to be chosen, but in a government setting where many costs and benefits may be difficult to quantify, the NPV may be just one of the decision-making criteria.
Put simply, a proposal with a higher NPV ranks ahead of the alternative, assuming the proposals are otherwise equal. If the proposals are not the same in all other respects, a higher NPV is not conclusive. For example, one proposal may have much greater intangible net benefits. A negative NPV does not rule out proceeding with a proposal. There may be other qualitative influences on the decision to proceed, and these may be important.
The NPV of a proposal is to be compared to NPVs for alternative options, at least one of which should be the status quo (i.e. the costs and benefits if no action were taken).[47] Alternatively, all cash flows could be expressed as differences in cash flows compared to the cash flows from the status quo. If this alternative is used, an NPV greater than zero indicates that the net benefits of the proposed project are greater than the benefits from the status quo.
Note that NPV analysis is not the same as Cost Benefit Analysis. Cost Benefit Analysis is the wider process of proposal selection. NPV analysis is just one tool which may be applied in Cost Benefit Analysis.
Example 3.5: NPV Calculation
Using the table from Example 3.3 and adding the discounted net cashflows, gives:
| Year | 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 = future value × disc. factor | -100 | 40.9 | 37.2 | 33.8 |
| Cumulative sum of present values (i.e. NPV) | -100 | -59.1 | -21.9 | 11.9 |
The highlighted figure, the sum of all the present values, is the NPV. The NPV is greater than zero, which implies that the proposal will generate a greater return than other proposals with a similar level of risk (or equivalently, the proposal is superior to the status quo). On this basis, and for the moment ignoring non-monetary considerations, proceeding with the upgrade would be a good idea.
Recall that the cash flows were incremental – over and above the “do nothing” or “status quo” scenario. An alternative would have been to use two scenarios – one involving total net national cash flows assuming an upgrade, and one involving total net cash flows assuming the status quo. Using such an alternative approach, the project with the highest NPV would be chosen (non-monetary considerations aside).
Example 3.6: Using a Spreadsheet to Calculate an NPV.
While manual calculation of an NPV is relatively straightforward, it is likely to be simpler in practice to use the built-in NPV tools in a commercial spreadsheet package.
To calculate the NPV for the Ministry’s proposal in Excel (similar functions are available in other packages), follow this procedure:
In Cell A1, enter the formula as shown in the figure below:
=C1 + NPV(10%, C2:C4)
10% is the discount rate for the proposal (it may of course be varied – see Section 4, which covers sensitivity analysis). C1:C4 is the range of cells containing net cashflow data for each period (the areas with a bold outline). The NPV formula is applied to cells C2 to C4. The first cashflow (C1) is excluded from the NPV formula because it occurs immediately and should not be discounted.
Naturally, in cases where the first cashflow occurs one period into the future, rather than immediately, it should be discounted and the formula would be:
=NPV(10%, C1:C4)
Excel gives the answer, $11.9 million, the same figure we determined manually.
Notes
- [46]In the case of annual cashflows, and assuming the current year is ’year 0’, the formula for NPV is:
NPV = CF(0) + CF(1)/(1+r) + CF(2)/(1+r)2 + ..... + CF(n)/(1+r)n
where CF(n) is the net cashflow for NPV purposes in period n and r is the discount rate. Note that the initial cashflow is not discounted if it occurs very close to the beginning of the project (in period 0). - [47]Some sources recommend using the least-cost project as a benchmark. The Treasury recommends using the status quo. Note that the status quo option should not include sunk costs.
