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.
Calculating Cost Using First-In, First-Out (FIFO)
The First-In, First-Out method, also called FIFO, is the most straight-forward of all the methods. When determining the cost of a sale, the company uses the cost of the oldest (first-in) units in inventory. This does not necessarily mean the company sold the oldest units, but is using the cost of the oldest ones. When I think of FIFO, it reminds me of milk being sold at the grocery store. In most grocery stores, the coolers are built to allow staff to put the new milk in from the back, pushing the old milk forward, and encouraging shoppers to purchase the older milk (first-in) before the new milk.
When the cost of inventory is rising, FIFO will ensure that the older, less expensive inventory cost is transferred to Cost of Goods Sold. This creates a lower expense on the income statement and higher profit. Higher profit also leads to higher income taxes. Inventory on the balance sheet will be higher than when using other inventory methods, assuming costs are rising.
The wonderful thing about FIFO is that the calculations are the same for both periodic and perpetual inventory systems because we are always taking the cost for the oldest units.
All periodic inventory systems calculate inventory at the end of the period. Therefore, we are not concerned about which units are on hand when a sale occurs. When calculating any inventory method under periodic, it is best to separate the purchases from the sales.
We now have a much clearer picture of what happened during the month of January. Our goods available for sale (beginning inventory plus purchases) is 415 units or $3,394. We know we sold 245 units during the month. When using FIFO, we pick the units that were acquired first and use the cost of those units first. We keep picking units until we have accounted for the cost of all the units sold, in this case 245 units.
First we select the units from beginning inventory.
That gives us 150 of the 245 units we need. We still need 95 more units. We move to the first purchase on January 3.
Taking all the units from January 3 still leaves us 20 units short of the 245 units we need. We will take those 20 units from the 50 purchased on January 12.
We have now accounted for all 245 units sold and have determined that the cost of those units is $1,972.50. We sold the units for $4,900. Now we can calculate gross profit. Gross profit is sales less cost of goods sold. Gross profit tells us how much profit we are making off the sale of our product before all other expenses.
Our gross profit is $2,927.50. Remember that as prices rise, FIFO will give you the lowest cost of goods sold because the oldest and least expensive units are being sold first. This also gives us the highest gross profit.
Now to calculate ending inventory. Remember that ending inventory is what is left at the end of the period. The units from beginning inventory and the January 3rd purchase have all been sold. The company also sold 20 of the 50 units from the January 12 purchase. That leaves 30 units from that purchase and the units purchased on January 22 and 26.
Ending inventory contains 170 units with a value of $1,421.50. To ensure we accounted for all the units and their value, add cost of goods sold and ending inventory.
This agrees to our original goods available for sale. While this check figure will not ensure that you picked the right units, it will ensure that you accounted for all the units and calculated the cost correctly.
As stated previously, FIFO periodic and FIFO perpetual will give you the same result for cost of goods sold and ending inventory. However, with perpetual inventory systems we must be concerned with calculating cost of goods sold at the time of each sale.
When calculating using the perpetual systems, do not separate purchases and sales. At the time of each sale, we must consider what units are actually available to be sold. Only consider units that are on hand at the time of the sale. Look at the sale on January 7. What units are on hand on that date? The company has the units from beginning inventory and the purchase on January 3rd.
If we take 100 units out of inventory, we would take them from beginning inventory.
The cost of goods sold for the January 7th sale is $800. That would leave 50 units from beginning inventory and 75 from the purchase on January 3rd. Now we can move on to the next sale on January 17. Update the list of goods available for sale to reflect what was sold and the additional purchase on January 12.
The company sold 65 units on January 17. Using FIFO, we would take the first units in, taking 50 units left from beginning inventory and an additional 15 from the purchase on January 3rd.
The cost of the January 17th sale is $521.50. We have now used up all the units from beginning inventory and 15 of the units from January 3rd. Now let’s look at the last sale, again updating what is on hand as of that date.
The sale on January 31 of 80 units would be taken from the purchase on January 3rd and the purchase on January 12th.
The total cost of the sale is $651.00. We can now figure out the total cost of goods sold for the month by adding the cost of goods sold from each transaction.
Cost of goods sold for the month of January is $1,972.50. Notice this is the same as the cost of goods sold calculated until FIFO periodic. We can also calculate ending inventory, which is just the sum of what is left over.
If we add cost of goods sold and ending inventory, we get $3,394.00 which is our goods available for sale.
Remember that under FIFO, periodic and perpetual inventory systems will always give you the same cost of goods sold and ending inventory. This will only occur under FIFO.
When doing this by hand, I always cross out the number of units and write in the remaining amount. This is much faster than rewriting the list. Keeping track of the number of units remaining will help to ensure that you take your units from the correct date and calculate ending inventory properly.
FIFO Inventory Calculations
FIFO Inventory Journal Entries
Calculating Inventory Cost
Inventory costs are constantly changing. Companies must decide how inventory costs will be calculated for the purposes of expensing that inventory when it is sold. There are a number of accepted methods and the method of calculation does not have to match how products actually leave the building. Companies pick a method based on profit and tax objectives. We will look at four methods of calculating costs and the advantages and disadvantages of each method.
There are a number of important terms that will be used when discussing inventory cost. It is crucial that you know this terminology in order to master this topic. All of these terms can be used to describe a dollar value or a number of units.
Beginning inventory is the amount of inventory a company has at the start of the period. Remember that inventory is an asset and appears on the balance sheet. Purchases are additional units of inventory that have been acquired during the period. If you add beginning inventory and purchases, the total is called Goods Available for Sale. Goods Available for Sale is an important concept because we can use this figure as a check figure when doing calculations.
Goods Available for Sale is the total of all the goods that could have been sold during the period. Some of those units will be sold, which is called Cost of Goods Sold. The items that were not sold are still in inventory. Since it is the end of the period, we refer to this as Ending Inventory. If you add cost of goods sold and ending inventory, it should match the amount in Goods Available for Sale. Whenever you are doing calculations involving inventory, you should make sure you have accounted for everything by adding Cost of Goods Sold and Ending Inventory to ensure it matches Goods Available for Sale.
Periodic and Perpetual Inventory
The rules for periodic and perpetual inventory methods still apply when we look at cost determination. Remember that under the periodic inventory system, cost of goods sold is determined at the end of the year via an adjusting entry. Therefore, when entering sales entries, inventory and cost of goods sold is not a factor. Companies that use the perpetual inventory system are always updating inventory balances. Every sales transaction includes the entry for cost of goods sold. Therefore, under the perpetual system, we must figure out the cost of inventory for every sales entry.
What Is a Discount?
We all love discounts, but why would a business offer offer a discount on their products? Typically, a business might offer a discount to increase sales, make an unhappy customer happy or incentivize a customer to pay quickly.
Understanding Payment Terms
Typically when customers purchase inventory, they are not expected to pay cash. The seller extends credit to the buyer, but extending credit comes at a cost for the seller. The seller does not have the cash and therefore must pay its bills from other sources, either cash reserves or borrowing. The seller may lose out on interest earned on cash reserves or possibly even pay interest on loans or lines of credit. In order to decrease the time a receivable is outstanding, a company may offer a discount for fast payment. When a company offers this type of discount, it is listed in the payment terms on the bill:
Payment terms: 2/10, n/30
What does this mean? Well, first notice the comma. That means there are two parts to the payment terms. So let’s look at each part, starting with 2/10. This does not mean that the bill is due on February 10. It means “2% discount if paid in 10 days”. Therefore, if the date of the bill is February 15 and you pay the bill on or before February 25, you get a 2% discount off the balance due. What happens if you don’t pay in the first 10 days? For that, we have to look at the statement after the comma: n/30. The “n” in the statement stands for net. So the statement tells us that the net, or entire, amount is due in 30 days. Taking it all together, the statement is as follows:
Payment terms: If paid within 10 days, we will give you a 2% discount, or you can pay the full balance within 30 days.
Can you see why businesses prefer 2/10, n/30? Takes up a lot less space on a bill. What happens if you don’t pay with bill within 30 days? After 30 days, your payment is now late and the seller can add on late charges or interest, depending on state law.
Let’s look at some examples using payment discounts.
Medici Music purchased instruments to sell in its stores from Whistling Flutes, LLC on August 13. The total purchase was $5,000 with terms 3/10, n/30. Medici paid for the purchase on August 20. Record the necessary journal entries for Medici Music.
The first step is to break down the information. Medici purchased inventory for $5,000 on August 13 and paid the bill on August 20. Looks like we have two transactions. Wait! We are dealing with inventory. Have you realized we are missing something? If not, take a second to see if you can figure it out. <Insert Jeopardy theme here> Is Medici using periodic or perpetual inventory? Remember, we are about to record an entry dealing with the movement or change in value of inventory! I know we are talking about payments here but we are still talking about inventory. That trumps the payment discussion!
We will look at this transaction under both methods so you can see the difference. Before we start looking at each method, let’s start by discussing what is the same under each of the methods. We have two transactions. The first transaction deals with the purchase of the inventory. The second transaction deals with the payment for the instruments already received.
When working with discounts, we generally calculate the discount and record it at the time of payment. Some textbooks may show you two different methods for recording the discount, one in which the discount is recorded at the time of the purchase and one where the discount is recorded at the time of the payment. I prefer the second method. When you record the discount at the time of the purchase and the discount is not taken because the buyer does not pay within the discount window, we must alter the payment entry to undo the discount taken in the first entry. By recording the discount at the time of the payment, we are only recording a discount that has actually been taken and we never need to undo something from the first entry.
First, we need to record the entry to show the purchase of the inventory.
Notice that we used Inventory, because under the perpetual method, whenever the value of inventory is changing, we must show that change in the account.
Now let’s look at the second transaction. We are paying off what is owed but we are receiving a discount. We must show the accounts payable fully paid off, so we must debit Accounts Payable for $5,000. How are we paying the balance? With cash, so we must credit Cash for the amount of cash being paid. Because of the discount, the amount will be less than $5,000. If we take 3% of $5,000, we calculate the discount as $150. Therefore, the amount of cash needed to fulfill the obligation is $4,850.
What do we do with the $150? Remember the rules for perpetual inventory. If the value of the inventory is changing, we need to target the inventory account. Is the value of the inventory changing? Currently, we have $5,000 in the Inventory account for this purchase. Did we actually pay $5,000 for the inventory? Well, no, we didn’t. We actually paid $4,850 for the inventory. Therefore, the value of the inventory is not $5,000 but $4,850. We need to reduce the value of the inventory by $150 to reflect the discount received. Now, we have all the information we need to complete the second entry.
Now the process is complete. The Accounts Payable balance is now zero and the Inventory balance is $4,850 which matches what we actually paid for the inventory.
Under the periodic method, we do not update the value in the inventory account until we do the adjusting entries at the end of the period. Therefore, we should never use the inventory account in purchase transactions for companies that use the periodic method. Instead, we use the purchases account.
Let’s look at the first entry.
Pretty similar to the perpetual method, except for the use of the purchases account. The second entry will also be similar to the perpetual method, except for one difference. Can you figure out what that difference would be?
We will not be using the Inventory account. Instead we will use an account related to the Purchases account. We do not use the Purchases account because we want to preserve the balance in that account, in case we need to match it up with purchase documents. In order to preserve the original balance in the Purchases account, we will use a contra account. A contra account is an account that is linked to an account but acts in the opposite way. It acts contrary to the account it is linked to. Since Purchases has a normal debit balance, the contra account will have a normal credit balance because it will be used to decrease the value in the Purchases account. The account we will use is called Purchase Discounts (very tricky, huh?). Here is the entry:
The Sales Side
So far, we have looked at the purchase side of the transaction. What about the sales side? Let’s look at our original example again. This time, we will look at it from the seller’s perspective.
Medici Music purchases instruments to sell in its stores from Whistling Flutes, LLC on August 13. The total purchase was $5,000 (with a cost of $3,000), terms 3/10, n/30. Medici paid for the purchase on August 20. Record the necessary journal entries for Whistling Flutes, LLC.
When recording sales transactions, we still must be concerned with whether the company uses perpetual or periodic inventory. We will review perpetual inventory first.
Under the perpetual method, when inventory changes or the value changes, we must record that change. When a business sells merchandise, inventory is leaving the building, therefore the amount and value of the inventory left is changing. There will be two parts to the August 13 entry. The first part will record the sale and increase in an asset (Accounts Receivable). The second part will record the change in Inventory and the cost of the sale. Let’s look at the entry:
The value of Inventory dropped $3,000, which moves to the income statement as an expense.
Now let’s look at the entry on August 20. This is the date that Whistling Flutes, LLC gets paid in full. However, because of the discount, the Company will not receive the full $5,000. Therefore, we must show the obligation fully paid even though the amount received is less than the amount in Accounts Receivable. The amount of the discount is 3% of $5,000 or $150. The amount of cash received is $4,850. Is Inventory changing? No, the payment on August 20 has no effect on Inventory. We will use a contra account, Sales Discounts, to record the discount amount.
By using a contra account, the company knows how much its sales were over the course of the year and how much was lost because of discounts and other items. This is good information for managers to have in order to make decisions about the effectiveness of company policy.
How would the entry be different under a periodic system? On the sales side, the only difference is the fact that we would not track the change in inventory at the time of the sale. The rest of the entry is exactly the same. Let’s look at both entries together, since we already discussed the methodology. Again, the only difference is that we do not track the changes in inventory under the periodic system.
Read Transactions Slowly!
The biggest problem students have with this topic is confusing purchase and sale transactions. I have had students do the problem perfectly, except they give me the journal entries for the purchase when I ask for the sale or vice versa. Spend extra time if needed to make sure that you understand what the transaction actually means. Do not jump right into the entries until you know what is happening in the transaction. Typically, a problem will state which company you should do the entries for. Go back through the transactions to see if the company is the buyer or seller. Sometimes, I will even note that when I am reading the problem. Read the transactions carefully or you may lose a lot of points on a problem you know how to do.
Sales Entries: Periodic and Perpetual Methods
Purchasing Inventory: Periodic and Perpetual Journal Entries