Expected Monetary Value (EMV)

Expected monetary value (EMV) analysis is a mathematical concept that calculates the average outcome when the future includes scenarios with probabilities of possibilities.

The EMV of opportunities will usually be expressed as positive values, while those of threats will be negative

Let’s learn EMV using an example:

You have the following data:

You are doing expedition for wildlife photography. You are carrying very expensive equipment with you. There is a risk of high winds of high probability and high impact.  You decided to buy tents for the risk response. Please select which tent to buy. You have following information:

Cost

Heavy tent: $350/-

Lighter Tent: $130

Chance of High Winds: 35%

Loss expected if you buy Heavy Tent:

High Winds: $48

Low Winds: $10

Loss expected if you buy Light Tent:

High Winds: $953

Low Winds: $15

By analyzing this data, you can infer that you need to buy a specific tent but think about the scenarios that may be more complex and will contain complex scenarios and paths with different probabilities and values.

Let’s draw the data using EMV:

  

Don’t get scared by the picture. It’s very easy.

First of all, we need to represent the data.

The first node is the DECISION NODE. In this node just write the decisions.

The second part is the decision node, Draw rectangles and write the alternate decisions, One node for one decision.

The third node is Probability or Chance. In the current case, the winds have a probability associated. Write the probability for the High Winds and Low Winds.

Now we write all the values that are provided to us. For example, if we buy a heavy tent, how much money is spent. Write that value. In the case of high winds, there are losses, write the value provided here.

We draw the NET PATH VALUE as the last nodes.

Now at any point of time, only one path can be true.

So let’s calculate one of the paths say what if we buy light tent:.

If we buy a light tent than we spend $130.  Since money is out, it should be shown as negative. If on that day, there are LOW WINDS then losses are  -$15.

If this path becomes TRUE, the total money out from the project is (-130)+(-15) = -145.

Now calculate all the other paths individually.

Arriving at the total cost of the decision:

If you select a decision, say buying a heavy tent.

Then the TOTAL COST OF THE DECISION is the addition of all path values with its probability distribution.

What does it mean?

Buy HEAVY TENT:

Net path value for HIGH winds is -398

Net path value for LOW winds is -360.

The probability of high winds is 35%, and low winds is 65%

TOTAL EMV = probability1 * net path value + …..+ PraboabilytyN* Net path value

EMV for HEAVY tent = (35% * -398 ) + (65% * -360) =  – 373.3

Similarly

EMV for LIGHT tent = (35% * -1083) + (65% * -145) =  – 473.3

Which decision would you select?

The one where EMV Is MOST POSITIVE

OR

The one where EMV Is LEAST NEGATIVE

So which decision will we take?

Buying the heavy tent is a better decision, given the data.

Leave a Reply

X
%d bloggers like this: