# NPV and Interest Rates for Discount Purposes

## Net Present Value and Sensitivity to Interest Rates

This post continues a discussion about cash flow and net present value which you can read by clicking on the specific links. This post deals with a major factor on NPV which is the fluctuating interest rate. This variable can change outlook in a hurry.

The NPV (net present value) of any project is very sensitive to the interest rate used for discounting cash flows (costs, which usually occur at time 0, are not discounted, while cash inflows closer to the end of the project are heavily discounted). Therefore choosing the appropriate interest rate is very important.

The interest rate used for discounting should equal the opportunity cost of money / capital which is:

â€¢ the best return if this money would be invested in another project (in case the investor owns the initial capital)

â€¢ the lowest cost of financing (if the project is financed through a loan).

This is also referred to as the required rate of return.

So how can you be sure to discover the RRR? After determining the appropriate rate of return that the project should generate, there are two other elements that we should consider: inflation and risk. Thus the rate of interest for discount purposes, r, should reflect:
â€¢ the (real) required return component: rr (or the opportunity cost of money),
â€¢ the inflation component: s,
â€¢ the uncertainty component: u.

(l + r) = (l + rr) (l + i) (l + u)
So: r = (1 + rr)(l + i)(l + u) - 1

Sometimes r is calculated approximately as r = rr + i + u. This approximation works reasonably well for small values but it creates discrepancies when rr, i and u are rather large percentages, thus the multiplicative formula is the correct one.

If the appropriate interest rate is still hard to calculate, the project can be evaluated separately for different interest rates. If the NPV is positive in all cases then the profitability of the project is relatively robust to changes in the interest rate and the project should be adopted.

This post is part of a series of articles on cash flow analysis. Visit our cash flow analysis page to find a summary of each method.