# How to Calculate a Risk-Adjusted NPV

Probability adjustments can be made at the discount rate level or cash flow level.
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Net present value is equal to the sum of the present values of a project's anticipated cash outflows and inflows, netted against each other. The present value of the cash flows is calculated using a discount rate that reflects the project's required rate of return on investment. Risk-adjusted net present value accounts for the risk associated with the projected cash flow amounts varying from their forecast amount. Risk in this case is a measure of variation in results.

## Calculating Risk-Adjusted Net Present Value

The theoretical structure of a risk-adjusted NPV calculation is of a probability tree, which details all likely scenarios and the ensuing cash flows, as well as the probability of each likely scenario occurring. Incorporating probability into a cash flow estimate is relatively simple. If a hypothetical scenario results in a net cash inflow of \$100, and its probability of occurring is 50 percent, the value of the net cash flow is equal to probability, 50 percent, multiplied by the net cash flow, \$100, or \$50. All that is left is to calculate its present value, although this must be done for each potential cash inflow and outflow to be generated by the investment.

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## Crunching the Numbers

Use a spreadsheet to compile these calculations, making it easy to update changes in any assumptions. Apply a present value factor to each ensuing cash flow value, calculated as: 1/(1+r)^n, where "r" is the discount rate, and "n" equals the time period. For example, at month 6, n would equal 6 months divided by 12 months, or 0.5. Using a discount rate of 10 percent, this results in a present value factor of: 1/(1+0.1)^0.5, or 1/(1.1)^0.5, which equals 0.9535. Multiply this by the relevant cash flow, and repeat this step for all potential cash flows. The sum of all the individual present values is equal to the project's risk-adjusted NPV.