Expected Monetary Value

The Estimated Monetary Value (EMV) formula is probabilty multiplied by impact. If that sounds like a simple one step calculation, that's because it is. It's only weakness is in having accurate impact and risk values. This is crusial since it is used in risk management. As the project manager it's your responsibility to determine and constantly recheck those values. Under the assumptiuon that those values are accurate this formula is used to select options among courses of action aka quantitatively prioritize a risk within a set of known risks. This is calculated in dollars because we are using probability to determine value, not vice versa. Note: generally the opportunities will be expressed as positive values and threats as negative values. The steps are simple:

1. Assign a probability of occurrence for the risk.
2. Assign monetary value of the impact of the risk when it occurs.
3. Multiply the values produced by step 1 and step 2.

The formula is expesssed as EMV = (Probability) x (Impact)
These sums are them added to the project cost to calculate total EMV.

Risks can be hard to quantify. It is best to begin by listing them in the risk register with its cause and effect. A risk probability and impact matrix can help you gauge their signifigance. It is assumed that any project with a positive EMV is worth doing.

A note on randomness: Iterative simulations can be performed with a "Monte Carlo" method. This stochastic simulation was developed in 1947 by John Von Newman and Stanislew Ulam to approximate the highly random output of neutron diffusion. The Monte Carlo method uses random and pseudo-random numbers to obtain the distribution of an unknown probability. Btu it's not your only option. In 1981 the Generalised Point Estimation Method was developed by RosenBleuth and can be used to calculate mean and standard deviation. In more recent years the Latin Hyper Cube has also seen some use. Assuming you've quantified your risks lets look at an example of how this would be applied.

Assume the project's total cost (aka cost baseline)is $500,000.
Risk #1: Your lead programmer will be poached. Cost of replacement $10,000. Probability 50%
So $10,000 x 0.5 = -$5,000.
So the total EMV of the project is now $495,000.

PROJECT A - cost baseline= $175,000
Risk #1 cost of $85,000 probability = 0.01 | EMV = -$850
Risk #2 cost of $7,000 probability = 0.3 | EMV = -$2,100
Risk #3 cost of $50,000 probability = 0.2 | EMV = -$10,000
Risk #4 opportunity of $3,000 probability = 0.9 | EMV = $2,700
Risk #5 cost of $13,000 probability = 0.5 | EMV = -$6,500
TOTAL EMV= $175,000 + (-16,750)= $158,250

Project B - cost baseline= $65,000
Risk #1 cost of $50,000 probability = 0.25 | EMV = -$12,500
Risk #2 cost $1,500,000 probability = 0.75 | EMV = -$1,125,000
Risk #3 cost of $900 probability = 0.95 | EMV = -$855
Risk #4 opportunity of 10,000 probability = 0.6 | EMV = $6,000
Risk #5 opportunity of 1,000 probability = 0.7 | EMV = $700
TOTAL EMV= $65,000 + (-$1,138,355) = -1,073,355


There is a lot more to quantifying and qualifying your risk assessments than computing this formula. The formula for EMV is very simple. The difficulty here is knowing how to produce reliable risk metrics, and what do do with the output of the EMV formula. There are a variety of quantitative risk analysis and modeling Techniques that can used to produce the probability and cost figures. As a project manager, you may apply different techniques to minimize risk. Often the proper course is to account for the risk in the project's contingency reserve.


These examples may make EMV look simple but larger projects will have much larger data sets and be more difficult to compute. As simple as this formula is, the risk side of the equation has been greatly expounded upon in the area of "game theory." It has brought us a whole array of mathmatical models: the Wald criterion, the Hurwicz-criterion, the Laplace criterion, the Savage criterion, and Probabilistic Dominance model among others. You may ultimately find simpler models have greater utility. While this is not generally considered part of the PM cannon, I expect it to be mined extensively in the future. This mathmatical arena takes a more rigorous statistical approach and truly develops the concepts beyond our contemporary PM tools.