### Using Expected Values in Forecasting

There are many turns and twists when it comes to forecasting cash flows and other amounts. The last thing you need in your analysis is statistical errors that distort your estimates. The problem is what amount do I use? Do I use the average amount? Do I use the most likely amount? Or do I use the expected value?

In order to come up with a realistic estimate of what amount will occur in the future, you should use expected value. Expected value is not the same as average value or most likely value. Expected value is derived by looking at all possibilities and taking into account the probability of occurrence. Using expected value has statistical merit over other approaches since you are forced to give consideration to all possible outcomes. And the difference you get in estimates can be extremely significant.

Let's say you need to estimate the cash inflows for next month. You have three customers who have outstanding receivable balances. Based on past histories, you can assign probabilities to receiving payment next month.

Customer A owes $ 10,000, there is a 60% probability of receiving payment next month. Customer B owes $ 20,000, there is a 30% probability of receiving payment next month.

Customer C owes $ 30,000, there is a 10% probability of receiving payment next month.

Total Expected Value next month = ($10,000 x .60) + ($20,000 x .30) + ($30,000 x .10) = $ 15,000. Total Average Value = ($10,000 + $20,000 + $30,000) / 3 = $ 20,000.

Total Most Likely Value = $ 10,000 + $0 + $0 = $10,000.

As you can see, it makes a difference in which approach you take in coming up with your estimate. We can use an expected value of $ 15,000, an average value of $ 20,000, or a most likely value of $ 10,000. Therefore, it is very to go through a decision based approach to estimation. You accomplish this by calculating expected values.

Written by: Matt H. Evans, CPA, CMA, CFM | Email: matt@exinfm.com | Phone: 1-877-807-8756