# Prediction Error Evaluation in Cost Accounting

A *prediction error* occurs in cost accounting when actual costs differ from your estimates. This is an example of a *variance* — a variance being a difference between planned results and actual results.

You calculate the cost of a prediction error in these steps:

Compute the economic order quantity (EOQ).

The EOQ is calculated as the square root of [(2 x demand x ordering costs) ÷ carrying costs].

Calculate the relevant total cost based on your planned amounts.

Relevant total cost is calculated as [(demand x ordering cost) ÷ EOQ] + [(EOQ x carrying cost per unit) ÷ 2].

Because you determined that your estimate is incorrect, plug in the actual data and recalculate relevant total cost.

Compare the relevant total cost you planned with the relevant total cost using actual data.

Say you manage a large chain of sporting-goods stores that sells a light windbreaker. The jacket is popular with runners and bikers.

Here are your planned estimates for the month: Monthly demand is 10,000 jackets. The ordering cost is $70 per order. Carrying costs total $3 per unit. You calculate an economic order quantity (EOQ) of 683.13 units.

Here’s the formula for relevant total cost:

Relevant total cost = [(demand x ordering cost) ÷ EOQ] + [(EOQ x carrying cost per unit) ÷ 2]

The calculation is in the form of two fractions. Compute one fraction at a time and then add them to get relevant total cost. Here’s the monthly relevant total cost for the windbreaker:

Relevant total cost = [(demand x ordering cost) ÷ EOQ] + [(EOQ x carrying cost per unit) ÷ 2]

Relevant total cost = (10,000 x $70 ordering cost) ÷ 683.13 + (683.13 x $3) ÷ 2)

Relevant total cost = ($700,000 ÷ 683.13) + (2049.39 ÷ 2)

Relevant total cost = $1,024.70 + $1,024.70

Relevant total cost = $2,049.40

The relevant total cost for the windbreakers is $2,049.40 for the month. You can’t purchase a fractional unit, so you round down to from 683.13 to 683 units.

Note that you can simplify calculating relevant total cost. You get to the same total cost amount by multiplying EOQ by the carrying cost (with a slight rounding difference):

Relevant total cost = EOQ x carrying costs

Relevant total cost = 683.13 units x $3 carrying cost per unit

Relevant total cost = 683.13 x $3

Relevant total cost = $2,049.39

This version of the formula is easier, so consider using it.

But then you learn that there’s a prediction error. You determine that your actual ordering cost is $85. The cost is higher than the $70 in your plan. All of the other assumptions are correct. Your new relevant total cost is $2,258.32. That actual amount is $208.93 higher than the amount using the planned ordering amount ($2,049.39). The impact of the higher ordering cost is $208.93 for the month.

You could plug in actual results for any of the variables in the relevant total cost formula. When you recalculate the relevant total cost, you see the dollar impact of your prediction error.