As I mentioned in my prior post, the traditional ROI formula does not consider time. But in weighing the costs and benefits of a project, we must take into account the fact that neither costs nor benefits materialize instantaneously, each play out over time.

A dollar that you will receive a year from now is worth less than a dollar in your pocket today, because that dollar in your pocket could be invested to return a gain. The future dollar will need to be discounted based on an interest rate to determine its present value.

If we define R as the return that we expect to receive, t as the time period in which we expect to receive it, and i as the interest rate, then the following formula provides us with the present value:

In considering a project, its costs and benefits will be received over multiple periods, which form a time series of cash flows:

Time Period |
0 | 1 | 2 | 3 | 4 |

Benefit |
0 | 100 | 100 | 100 | 100 |

Cost |
200 | 100 | 0 | 0 | 0 |

Net |
-200 | 0 | 100 | 100 | 100 |

In the chart above, time period zero represents the present, which falls at the very beginning of a project when the first costs are encountered. All other costs and benefits are discounted to their present value so as to be made comparable with those of period zero.

To calculate the net present value of a project, calculate the net of the cash inflows and outflows of each period and then discount each period’s net:

Conveniently, Excel has a NPV function that takes an interest rate and a range of cells. (See http://office.microsoft.com/en-us/excel-help/npv-HP005209199.aspx.) Note that the Excel NPV function treats the first value in the range as period one rather than zero, meaning the first value gets discounted. You will need to add the value from period zero, which is usually a negative number, to the value returned by the function.

In deciding the period used in the calculation, note that longer periods introduce inaccuracies as the costs and benefits received get distributed throughout the period rather falling at the very beginning of the period as the formula assumes. Shorter periods decrease this inaccuracy but increase the difficulty of estimating in which period the costs and benefits will fall. Choose a period long enough to make the timing of cash flows feasible and short enough to render the inaccuracies immaterial. Most importantly, adjust the interest rate to match the period chosen.

Other than the obvious difficulty of estimating costs and benefits by period, a specific challenge with net present value as a decision tool is selecting an appropriate interest rate. The rate selected should at least equal the cost for the firm of borrowing money. But since there is always a limit to borrowing, the rate should ideally capture the opportunity cost, the rate that the money would have earned had it not been invested in the project.

One disagreement that exists over net present value is whether the interest rate should reflect the risk of the project. Should higher risk projects be discounted at higher rates just as high-risk consumers pay higher rates on their credit cards? Or should the risks be addressed more directly and incorporated into the expected costs and benefits? Generally, the latter approach is preferable, but the former could work as a crude adjustment for risk. Most importantly, projects must be compared using a consistent approach.

A limitation of NPV is that it does not in itself enable comparisons across projects with different levels of investment. Is a project with an NPV of $150,000 better than a project with an NPV of $100,000? Not if the first project requires a much larger investment. A common approach to get around this limitation and compare projects of different sizes is to divide the NPV by the present value of all costs.

NPV is a powerful decision making tool, but requires care in selecting an appropriate interest rate as well as in comparing projects of different sizes and levels of risk.

How does your organization select an interest rate for NPV calculations? Do you adjust the rate for risk?

Other posts in series: MIRR, IRR, Break-Even Analysis, NPV, ROI

## Leave a Reply