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.
Weighted Average Inventory Calculation
Last-in, first-out (LIFO) is an inventory method popular with companies that experience frequent increases in the cost of their product. LIFO is used primarily by oil companies and supermarkets, because inventory costs are almost always rising, but any business can use LIFO. Remember, there is no correlation between physical inventory movement and cost method.
To visualize how LIFO works, think of one of those huge salt piles that cities and towns keep to salt icy roads. The town gets a salt delivery and puts it on top of the pile. When the trucks need to be filled, does the town take the salt from the top or bottom of the pile? The trucks are filled from the top of the pile. The last delivery in is the first to be used. This is the essence of LIFO. When calculating costs, we use the cost of the newest (last-in) products first.
When costs are rising, LIFO will give the highest cost of goods sold and the lowest gross profit. LIFO will also result in lower taxes than the other inventory methods.
LIFO Using a Periodic Inventory System
For all periodic methods we can separate the purchases from the sales in order to make the calculations easier. Under the periodic method, we only calculate inventory at the end of the period. Therefore, we can add up all the units sold and then look at what we have on hand.
We sold 245 units during the month of January. Using LIFO, we must look at the last units purchased and work our way up from the bottom. Start with the 50 units from January 26th and work up the list. We would then take the 90 units from January 22nd, and 50 units from January 12th. That gives us 190 units. We are still 55 short, so we will take 55 from January 3rd.
The cost of goods sold for the 245 units, using LIFO, is $2,032.00. Now we need to look at the value of what is left in ending inventory. We have 20 units left from the January 3rd purchase and all the units from beginning inventory.
Gross profit (sales less cost of goods sold) under LIFO is $2,868.00. Under LIFO, our cost of goods sold is higher than it was under FIFO and our ending inventory is lower than under FIFO. Gross profit is lower under LIFO than FIFO, which would result in lower income taxes because overall profit would be lower.
Adding cost of goods sold and ending inventory gives us $3,394.00 which ties back to goods available for sale. Everything has been accounted for in our calculation.
Under a perpetual inventory system, inventory must be calculated each time a sale is completed. The method of looking at the last units purchased is still the same, but under the perpetual system, we can only consider the units that are on hand on the date of the sale.
Imagine you were actually working for this company and you had to record the journal entry for the sale on January 7th. We would do the entry on that date, which means we only have the information from January 7th and earlier. We do not know what happens for the rest of the month because it has not happened yet. Ignore all the other information and just focus on the information we have from January 1st to January 7th.
LIFO means last-in, first-out. Based on the information we have as of January 7th, the last units purchased were those on January 3rd. We will take the cost of those units first, but we still need another 25 units to have 100. Those units will come from beginning inventory.
The cost of the January 7th sale is $807.50. Now, we can move on to the next sale, updating our inventory figures. There are no units remaining from the January 3rd purchase and 125 left in beginning inventory. Before the January 17th sale, we purchased 50 units on January 12th.
We need 65 units for this sale. Since we are using LIFO, we must take the last units in, which would be the units from January 12th. Then we would take the remaining 15 units needed from beginning inventory.
One more sale remaining. Again, we will update the remaining units before considering the sale.
The company sold 80 units on January 31st. Which units should we use for cost using LIFO? The last units in were from January 26th, so we use those first, but we still need an additional 30. We take those from January 22nd.
To calculate total cost of goods sold, add the cost of each of the sales.
You could also add $807.50 plus $532.50 plus $673.00 which also equals $2,013.00.
You may have noticed that perpetual inventory gave you a slightly lower cost of goods sold that periodic did. Under periodic, you wait until the end of the period and then take the most recent purchases, but under perpetual, we take the most recent purchases at the time of the sale. Under periodic, none of the beginning inventory units were used for cost purposes, but under perpetual, we did use some of them. Those less expensive units in beginning inventory led to a lower cost of goods sold under the perpetual method. You will also notice that ending inventory is slightly higher. Look at the differences in the units that are left in ending inventory.
Under perpetual we had some units left over from January 22nd, which we did not have under periodic.
When using a perpetual inventory system, dates matter! Make sure to only consider the units on hand at the time of the sale and work backwards accordingly.