# Expected NPV

Expected net present value is a capital budgeting technique which adjusts for uncertainty by calculating NPVs under different scenarios and probability-weighting them to get the most likely NPV.

For example, instead of relying on a single NPV, companies calculate NPVs under a range of scenarios; say base case, worst case and best case. They then estimates probability of occurrence of each scenario and then weight the NPVs calculated according to their relative probabilities to find the expected NPV.

Expected NPV is a more reliable estimate than the traditional NPV because it considers the uncertainty inherent in projecting future scenarios.

## Formula

Expected NPV is the sum of the product of NPVs under different scenarios and their relevant probabilities. The following formula is used to calculate expected NPV.

Expected NPV = Σ (p × Scenario NPV)

Scenario NPV is the NPV under a specific scenario while p stands for the probability of occurrence of each scenario.

## Example

Logar Investments invests in public infrastructure projects in Afghanistan. The company is considering building a viaduct on the highway linking Kabul, the Afghan capital, with Landi Kotal, the town across the border with Pakistan. It expects to earn revenue by collecting a fee from the users of the viaduct.

You are the Corporate Finance specialist in the company and Omar Hotak, the CFO, has requested you to calculate expected NPV of the project. There are three scenarios: base case scenario assumes that the trade between Afghanistan and outside world routed through Peshawar will remain the same, the best case scenario assumes the trade will increase and worst scenario assumes the trade will decrease.

Your associate calculated the following NPVs for each scenario:

NPV (in '000 AFN) | Probability | |

Best | 40,000 | 0.4 |

Base | 30,000 | 0.2 |

Worst | 10,000 | 0.4 |

__Solution__

Expected NPV

= Best Case NPV × Probability of Best Case Scenario

+ Base Case NPV × Probability of Base Case Scenario

+ Worst Case NPV × Probability of Worst Case Scenario

= 40,000 × 0.4 + 30,000 × 0.2 + 10,000 × 0.4 = AFN 26,000 thousand

The expected NPV of the viaduct project is 26 million Afghanis (the Afghanistan's currency).

Written by Obaidullah Jan, ACA, CFA