Expected Value/Cost

Understanding of Expected Value/Cost

Expected Value/Cost is a method for examining the relative potential costs or benefits of multiple options;   also it helps to make the decisions in various areas of business. This is often performed with both positive and negative outcomes as well as with the probability with any particular outcome to occur.  Decision makers are mainly involved in this process and critical parameters which have impact on this process are project requirements, building prototypes and initial decision for a particular product (or project) to pass the UAT or not (refer to 2ndexample).

expected value cost

 

Let us consider a very general example for better understanding,

Example 1:-

A lumber wholesaler is planning on purchasing a load of lumber.  He calculates that the probabilities of reselling the load for $9500, $9000, or $8500 are .25, .60, and .15, respectfully.  In order to ensure an expected profit of at least $2500, how much can he afford to pay for the load?

The expected revenue from sales can be found below.

Note :- please refer to figure 1

Expected revenue: E(x) = $9050

Profit = revenue – cost or cost = profit – revenue

To have an expected profit of $2500, he can pay up to $9050 – $2500 = $6550.

Now for in detail understanding lets us consider a real time situation,

Example 2:- Impact of Prototype on Expected cost/ value

Should a prototype of the new airport security X-ray product be built? Project requirements were poorly defined. As a result, there is the risk that the final product will not pass the user acceptance test. However, a prototype also would substantially reduce the cost of rework for failures at user acceptance test.

  • Cost to build the prototype $98,000
  • Probability of passing user acceptance test

With prototype 90%

Without prototype 20%

  • Cost of rework after user acceptance test

With prototype $20,000

Without prototype $250,000

In this discussion, the cost to build the prototype may easily be more tangible to decision makers than the potential cost of the failure to build the prototype.

There is a main conclusion for this scenario,

Build the Prototype at an initial cost of $98,000 or do not build one at an initial cost of $0.

There are two options with associated probabilities and costs;

Pass Acceptance Testing and incur no additional costs; (90% probability) or Fail Acceptance Testing, but perform better, therefore incurring smaller additional testing cost of $20,000. There is a 10% probability of this occurring if the prototype is built; therefore the Expected Value of this outcome is $2,000 (the cost of the outcome times the probability that it will occur).

Total expected value for upper branch of tree is

$98,000 + $0 + $2,000 = $100,000

Total expected value for lower branch of tree is

$0 + $0 + $200,000 = $200,000

Note:- Please refer figure 2 (branch tree) for clear understanding

Based on this analysis, the organization can expect to spend twice as much if they fail to build the prototype. This example shows a fairly simple application of the expected value decision making approach.  But when many often decisions in real life are significantly more complex, thereby considering more than two initial options and nested financial amounts and probabilities.

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