## Weighted Average

### Learning Outcomes

• Illustrate the use of weighted average cost flow assumption

Let’s apply the weighted-average cost flow assumption to our baseball bat example, using a periodic inventory system.

To calculate the weighted average cost of bats, we are going to toss them all together like a baseball bat salad, so we don’t need any color coding. Other than that, this is the same data we used for our analysis of specific identification.

Again, here is the list of sales, by date:

All Revenue 6 $120 6$120 19 $380 31Double line$620Double line

And here are the purchases:

Product ID Description Cost Quantity Purchases NewCo Sporting Goods Slugger purchased 10/15/20XX 10.00 10 100.00 Slugger purchased 11/15/20XX 12.00 25 300.00 Slugger purchased 12/15/20XX 15.00 8 120.00 $520.00 We’ll use the same worksheet format as before and do our calculations step by step, tracking purchases, COGS, and inventory on hand for each date that something happens, this time using a weighted average method of assigning costs to inventory. Purchases Cost of Goods Sold Inventory on Hand Date Quantity Unit Cost 0$0 $0 10$10 $100 10$10 $100 Right now, the average cost of inventory is$10 because we have $100 in total cost divided by 10 units. When we sell six units, we assign$60 in costs and move that much from inventory to COGS. So far, this method is the same as specific identification because we only have one batch of bats to draw from.

Purchases Cost of Goods Sold Inventory on Hand Date Quantity Unit Cost Total Cost Quantity Unit Cost 0 $0$0 10 $10$100 10 $10$100 6 $10$60 4 $10$40

We had ten, sold six, and now there are four left, and the average cost is still $10 each. On November 15, we bought 25 more bats for$300. We now have 29 bats at a total cost of $340 (the four bats at$10 each and the 25 bats at $12 each). The average of the two prices is$11 (10 + 12 divided by 2) but the weighted moving average is $340 divided by 29 (total cost of inventory on hand divided by units) which is, in this case,$11.72. The average is much closer to $12 than to$10 because there are so many more of the $12 units. Purchases Cost of Goods Sold Inventory on Hand Date Quantity Unit Cost Total Cost Quantity Unit Cost 0$0.00 $0 10$10 $100 10$10.00 $100 6$10 $60 4$10.00 $40 25$12 $300 29$11.72 $340 When we next sell bats on November 20th, we use the new cost for COGS: Purchases Cost of Goods Sold Inventory on Hand Date Quantity Unit Cost Total Cost Quantity Unit Cost 0$0.00 $0.00 10$10.00 $100.00 10$10.00 $100.00 6$10.00 $60.00 4$10.00 $40.00 25$12.00 $300.00 29$11.72 $340.00 6$11.72 $70.32 23$11.73 $269.68 We had 29, sold six, and now we have 23 left (the cost changed slightly due to rounding). Total cost was$340.00, but we removed six bats at $70.32 total, so we have$269.68 total cost to spread evenly over 23 units. (269.68 / 23 = 11.725…)

On the 15th of December, NewCo bought eight more bats for $120 total ($15 each) and then had 31 bats on hand for a total cost of $389.68 (that’s 269.68 + 120). The weighted (moving) average is now$12.57.

Do you see the pattern?

Hint: Every time we purchase inventory, we recalculate the average cost by taking total cost of inventory on hand and dividing it by total units on hand.

That’s the formula to memorize: total cost / total units = weighted average cost.

Purchases Cost of Goods Sold Inventory on Hand Date Quantity Unit Cost Total Cost Quantity Unit Cost 0 $0.00$0.00 10 $10.00$100.00 10 $10.00$100.00 6 $10.00$60.00 4 $10.00$40.00 25 $12.00$300.00 29 $11.72$340.00 6 $11.72$70.32 23 $11.73$269.68 8 $15.00$120.00 31 $12.57$389.68 19 $12.57$238.83 12 $12.57$150.85 43 $520 31$369.15

It’s called a moving average because we are always recalculating it. In the periodic system, we took total cost for the year and divided it by total units (for each individual item). Here, in the perpetual system, we have to recalculate the weighted average every time we purchase more of the product.

At the end of December, we have 12 bats on hand at an average cost of $12.57. Notice that because beginning inventory of this item was zero, total costs of items sold ($369.15) plus cost of ending inventory ($150.85) is equal to purchases. If we had a beginning inventory, the calculation is still the same, and ending inventory plus COGS would equal purchases plus beginning inventory. Here are the results after all our journal entries are posted, the trial balance is run, adjusting journal entries made and posted, the adjusted trial balance checked over one last time, and financial statements produced: NewCo Sporting Goods Gross Profit Calculation Weighted Average (perpetual) Description Amount Total Gross sales$ 620.00
Beginning inventory $- Purchases$520.00
Less ending inventory $150.85 Costs of goods sold$396.15
Gross profit Single Line\$250.85Double Line
Gross profit % 40.46%

This method may look easier than the other methods, but it is not ideal for large ticket items like cars, boats, yachts, or even appliances and anything one of a kind or unique in some way. If you had a boutique store that sold fancy olive oil from 5-gallon jugs with spigots, this method could be ideal since the oils get mixed together in the jug. It would be really hard to use specific identification with oils and other fungible items. However, there is no rule that says you have to use a cost flow assumption that matches the physical flow of goods.