#### weighted average

**What Is a Weighted Average?**

Most people know how to do a simple average, but have trouble with a weighted average. Weighted averages are all around us, although you may not have realized it. In most classes, your grade is calculated using a weighted average. Not all assignments count the same when calculating your final grade. Some assignments count more than others. Your professor is giving more *weight* to tests than to homework. Your final exam might have more weight than a regular exam.

In accounting, weight is given based on the number of units. Say we sold two units last month, one was $100 and one was $500. What is the average cost? $500 + $100 = $600 / 2 = $300. How would the average change if we sold two units at $100 and one at $500? The average would be closer to $100 because there are two units pulling the average down. $500 + $100 + $100 = $700 / 3 = $233.33. We gave more weight to the $100 units because there were more of them.

When dealing with large numbers of units, rather than adding them up individually, we can calculate the total cost of the units and divide by the total number of units. What if we had 20 units at $100 and 10 units at $500. You might notice that the ratio of $100 units to $500 units is still the same (2:1). Let’s do the calculation to confirm that the weighted average will be the same.

The total cost of all the units is $7,000 and there are 30 units. Divide $7,000 by 30 and the weighted average is $233.33.

**Weighted Average Periodic**

Weighted average periodic is probably the easiest of all the inventory methods. Since the calculation is done at the end of the period, we figure out the total cost of goods available for sale and divide by the number of units. It is helpful to separate the purchases from the sales.

Goods available for sale is 415 units with a total cost of $3,394.00. If we divide $3,394.00 by 415, we get a weighted average cost of $8.18 (rounded) per unit. The rest of the calculation is very simple at this point. The company sold 245 units. We will use $8.18 as the cost of each unit, therefore the total cost of goods sold is $2.004.10. There are 170 units remaining in ending inventory (415 – 245). We will use $8.18 as the cost of those units as well which gives is an ending inventory balance of $1,390.60.

If we add cost of goods sold and ending inventory, the total is $3,394.70. Because we rounded up when calculating cost per unit, we should expect our total to be a bit higher than goods available for sale. When doing weighted average, always make sure to tie back to goods available for sale.

**Weighted Average Perpetual**

If weighted average periodic is the easiest of all the methods, weighted average perpetual is the hardest. It is not that the method is hard, it is just annoying because you must calculate a new weighted average cost for each sale, based on the units available for sale at that time. When doing weighted average perpetual, do not separate the purchases and sales.

Perpetual inventory systems require cost of goods sold to be calculated each time there is a sale. Therefore, at the time of each sale, we must calculate the weighted average cost of the units on hand at the time of the sale. On January 7, the company sold 100 units. We must calculate the average cost of the 225 units on hand as of that date.

We calculate the average cost by taking total cost divided by the number of units on hand. This gives us a weighted average cost of $8.03 per unit. Does this make sense? The simple average would be $8.05, but there are twice as many units at $8.00, so the weighted average should be closer to $8.00 than it is to $8.10. Doing a mental check to make sure your numbers make sense is a great habit to start!

Now we can calculate the cost of the sale by taking the average cost per unit multiplied by the number of units sold.

Next, calculate the value of the remaining units. There are 125 units left. We will assign $8.03 per unit because that is the weighted average cost of those units on January 7. We will use this figure in the calculation for January 17. For the sale on January 17, we need to do another weighted average calculation.

Add the 50 units purchased on January 12 to the 125 units remaining and calculate the total cost of all those units. Then divide cost by the total number of units. The weighted average cost on January 17 is $8.09. The inclusion of the units costing $8.25 increased the weighted average cost slightly. Using $8.09 as the unit cost, calculate the cost of the sale.

Cost of goods sold for the January 17 sale is $525.85.

One more sale on January 31, so we need to do this calculation one more time. Start with the remaining units at $8.09 then add in the additional purchases.

Cost of goods sold for the January 31 sale is $660.80.

We can now calculate total cost of goods sold for the month of January by adding cost of goods sold for each sale.

The value of ending inventory is the number of units remaining multiplied by the average cost at the time of the last sale, in this case $8.26. Add cost of goods sold and ending inventory to see if it matches goods available for sale. In this case, there was some rounding so things may not be exact.

Be patient when doing weighted average, especially under the perpetual method. Tie back to goods available for sale to ensure you did your calculations correctly. Do a quick mental check to make sure your weighted average cost per unit makes sense. If you take a few seconds to do these things, you will greatly increase the chance that your calculations are correct.

**Related Video:**

Weighted Average Inventory Calculation