calculations

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

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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.

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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.

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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.

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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.

LIFO Perpetual

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.

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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.

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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.

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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.

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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.

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One more sale remaining. Again, we will update the remaining units before considering the sale.

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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.

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To calculate total cost of goods sold, add the cost of each of the sales.

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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.

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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.

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LIFO Calculations

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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.

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FIFO Periodic

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.

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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.

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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.

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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.

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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.

 FIFO5

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.

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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.

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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.

FIFO Perpetual

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.

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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.

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If we take 100 units out of inventory, we would take them from beginning inventory.

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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.

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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.

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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.

 FIFO13

The sale on January 31 of 80 units would be taken from the purchase on January 3rd and the purchase on January 12th.

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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.

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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.

 FIFO16

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.

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FIFO Inventory Calculations

FIFO Inventory Journal Entries

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Choosing a Method of Depreciation

There are various ways to depreciate an asset and each company must determine which method to use. There are a number of items to consider when making this determination, including ease of calculation, the speed of cost recovery and predictability of the expense.

While all methods are fairly easy to calculate, the units-of-production method is based on usage of the asset and therefore requires usage to be tracked. This would be easy to calculate for a vehicle (mileage) but would be more difficult for a computer. I know I wouldn’t want to track exactly how many hours I used my computer each year, would you?

Most companies consider speed of cost recovery to be the most important consideration because how fast the cost is recovered affects many aspects of business. If the business paid cash for the asset, typically it would like to recover that cost as an expense as quickly as possible. However, if the company financed the asset over a longer period of time, the company may wish to match the cash expenditures of the loan payments to the expensing of the asset.

The speed of cost recovery also affects profit and taxes. A method like straight-line, where the depreciation is the same each year, will cause higher profit in the early years but lower profit in later years when compared to an accelerated method like double-declining balance. Double-declining balance generates a large amount of depreciation in early years of asset ownership, which lowers profit and lowers taxes. Later in the asset’s life, the amount of depreciation is lower than straight-line and causes higher profit and taxes. Some argue that an asset is more efficient when it is newer and generates more revenue, therefore accelerated methods, like double-declining balance, are the way to go. It could also be argued that units-of-production will most closely match revenue because it is based on the output of machinery, equipment and vehicles.

Being able to predict the amount of expense is important to some businesses for consistency in the financial statements. For some companies, that means using straight-line depreciation to evenly depreciate an asset. For some companies, that means using units-of-production to more closely match higher revenue with higher depreciation. Others argue that trying to match cash expenditures and expenses more closely is more consistent and therefore accelerated methods should be used for assets purchased with cash.

As you can see, there are no easy answers when deciding which method of depreciation to use. Luckily, the calculations are much easier than the decision making!

Important Terminology

Like most areas of accounting, there are a number of important terms to learn in order to correctly calculate depreciation. It is critical to know these terms and how to apply them to the calculations.

Most depreciation methods use cost in the calculation. Asset cost is the total cost of the asset, including costs to acquire, deliver, and get the asset ready to use. Both straight-line and units-of-production use cost in the calculation. Double-declining balance uses book value rather than cost. Book value is the cost of the asset less any accumulated depreciation on that asset. In the first year, book value is equal to cost because no depreciation has been recorded yet. As depreciation is recorded, the book value of the asset decreases. Book value can also be called basis.

When a company purchases an asset, the company typically has a plan to keep the asset for a certain period of time. At the end of that time, the company will usually sell the asset and use the proceeds toward the acquisition of a new asset. The amount the asset will probably be worth at the end of that time is called salvage value. Because there is value left at the end of the asset’s life, the company should only depreciate the asset so the book value at the end of the life equals the salvage value. Salvage value is not perfect, but it is an estimate at the time of purchase to help minimize gains or losses at the time of sale. Salvage value is used in all depreciation calculations, in one way or another, so that the asset is never depreciated below salvage value.

How long the asset will be useful is the last key to the calculation. Useful life is the period used to depreciate an asset. In most cases useful life is expressed as a measure of time, usually years. In the case of units-of-production, useful life is expressed in a unit of measure associated with the asset. For a vehicle, we typically use mileage when using units-of-production. For a copier, we might use number of copies we expect to be able to make over the life of the copier. For machinery, we could use the expected number of units that could be manufactured with the machine. Useful life has little connection to the actual life of an asset. The Internal Revenue Service has an extensive list of asset lives, which is used by most companies for depreciation purposes. For example, the useful life of a building used in business is 39 years. We all know of perfectly good buildings much older than that!

Calculating Straight-line Depreciation

Straight-line depreciation is the easiest of the three major depreciation methods. This method creates an equal amount of depreciation for each full year. Another perspective is to say that an equal percentage of the asset is depreciated each year. If an asset has a five year life, 20% of the depreciable value would be depreciated each year (100% / 5 years = 20% per year). As discussed earlier, a company cannot depreciate below salvage value; therefore, salvage value is subtracted from the cost of the asset. This depreciable basis is then spread out over the life of the asset to calculate annual depreciation. The formula for calculating straight-line depreciation is:

Annual straight-line depreciation = (cost – salvage value) / life in years

Example #1: On January 1, 2013, Beans R’ Us purchases a van at a cost of $27,000. The company believes the van will have a useful life of five years or 250,000 miles. The salvage value is estimated to be $4,000. Calculate the annual depreciation, using straight-line depreciation, for the five years Beans R’ Us plans to own the vehicle and the journal entry to record the depreciation for 2013.

Since we are using straight-line and the van was purchased on January 1, the depreciation will be the same amount each year. Plug the information given into the formula to calculate the annual depreciation.

($27,000 – $4,000) / 5 =$23,000 / 5 =$4,600 per year

Does this make sense?

depr1

At the end of the fifth year, the asset has been depreciated to the point where book value is equal to salvage value. The accumulated depreciation is equal to the depreciable value of the asset. If the company continues to keep the asset, there will be no additional depreciation, unless the company believes that the salvage value has changed.

Using Straight-line Depreciation with a short year

What if the asset as instead purchased on March 1? The depreciation for the first year would be less than $4,600 because the company only owned the van for 10 months. When this is the case, we must adjust the depreciation to reflect the short year. There are a few ways we could do this. We could calculate the monthly depreciation then multiply the monthly amount by the number of months the asset was owned. We could also use a ratio of the number of months owned to the number of months in the year. In this case, the ratio would be 10/12. Either way, you will get the same answer.

$4,600 * 10/12 = $3,833 (rounded to the nearest whole dollar)

This would be the amount of depreciation for the first year. The remaining full years would still be $4,600. Because the van was purchased in March of 2013, we would need to depreciate in January and February of 2018 to record all of the depreciation. Although this is a five-year asset, in order to depreciate five full years, we need six years to do it.

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* There are two months of deprecation remaining in 2018. $4,600 * 2/12 = $767 (rounded to the nearest whole dollar). You could also take the book value of $4,767 at the end of 2017 and subtract the salvage value of $4,000, which would also give you $767.

Calculating Units-of-Production Depreciation

Units-of-production is very similar to straight-line, but very rarely used. We are still looking at depreciable value and dividing that amount by the life of the asset. With units-of-production, we are not using years for the life. Instead we use a quantity of units. For vehicles, this quantity is typically mileage. It makes sense because the life of a vehicle is more closely tied to miles driven than age.

Using the depreciable value and units for the life, we can calculate a rate per unit that can then be applied to the actual usage for each year. Because depreciation is based on usage rather than life in years, partial year depreciation is not a factor in units-of-production. If the asset was acquired at any time other than the first of the year, actual activity would reflect that fact. The formula for calculating the rate is very similar to formula used in straight-line.

Depreciation per unit = (cost – salvage value) / life in units

Remember that an asset can never be depreciated below salvage value. This is critically important when using units-of-production because it is very easy to underestimate the life of an asset. If there is more activity than predicted, the company would just stop depreciating once the estimated life in units is reached.

Example #2: On January 1, 2013, Beans R’ Us purchases a van at a cost of $27,000. The company believes the van will have a useful life of five years or 250,000 miles. The salvage value is estimated to be $4,000. The actual miles driven for the first five years are as follows:

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Calculate annual depreciation using the units-of-production method for 2013 – 2017.

The first step to solving a problem like this is to calculate the rate that the company will use to apply depreciation. Using the formula above we calculate the rate.

($27,000 – $4,000) / 250,000 = $0.092 per mile

This rate will be used for the life of the asset, unless the company believes that the life will be dramatically increased or decreased. Now that we have the rate, we can apply it to the actual activity for each year to calculate the annual depreciation. When calculating rates, label the rate! In the past, I have had students tell me that the depreciation is $0.092 per year because they did not label the rate and therefore did not apply it correctly. Get in the habit of labeling numbers you calculate.

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Although we calculated the 2017 depreciation to be $3,956, that would drop the book value below $4,000 (the salvage value). Therefore, in the fifth year, the depreciation is limited to $2,484. Make sure to watch the accumulated depreciation and book value when doing these calculations so you do not over-depreciate the asset.

Calculating Double Declining Balance

Double declining balance is an accelerated method of depreciation. Companies use double declining balance when they want to quickly depreciate an asset. Those who use the method argue that the value of an asset falls quickly in the first few years and believe that the depreciation method selected should match. It can also be said that companies get more life out of an asset in the first few years of ownership.

The asset will depreciate much faster under this method than straight-line because we double the percentage that would be depreciated each year under straight-line. This does not mean we just calculate straight-line and double it. Instead, we calculate the straight-line percentage and double it. We then multiply that percentage by the book value of the asset. When using double declining balance, do not subtract salvage value when calculating depreciation. However, you must make sure to watch the book value as you do the calculations to ensure you do not depreciate the asset too much.

The formula for double declining balance is:

Annual depreciation = Book value * 100% / life * 2

or

Annual depreciation = Book value * 200% / life

When doing these calculations, calculate the percentage that should be used first. Once the percentage is calculated, it is the same for the rest of the asset’s life. For a five-year life, the percentage would always be 40% (200% / 5). For a four-year asset, the percentage is 50%. Many of the percentages are easy to calculate in your head.

Example #3: On January 1, 2013, Beans R’ Us purchases a van at a cost of $27,000. The company believes the van will have a useful life of five years or 250,000 miles. The salvage value is estimated to be $4,000. Calculate annual depreciation, using double declining balance, assuming the company plans to keep the vehicle for five years.

Since this asset has a five-year life, the percentage used is 40%. We will multiply the book value by this percentage. Book value in year one is $27,000 because no depreciation has been taken on the asset yet.

$27,000 * 40% = $10,800

As you can see, double declining balance results in a lot more depreciation than straight-line. It is more than twice straight-line because we did not subtract salvage.

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When calculating the depreciation for 2014, use the book value of $16,200.

$16,200 * 40% = $6,480

For 2014, the amount of depreciation is significantly less than 2013 but still more than the annual depreciation under straight-line.

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Keep running the calculations until you get close to salvage value.

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We are only $1,832 from salvage. Calculate the depreciation for 2016.

$5,832 * 40% = $2,332.80

The annual depreciation for 2016 is more than the amount of remaining depreciation we are allowed to take on the asset. Therefore, we cannot take the full amount of depreciation calculated. Instead, we are limited to $1,832 in 2016. Since we have hit salvage value, there is no depreciation in 2017.

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Because depreciation is accelerated, often the asset finishes depreciating before the end of its life. Make sure to watch book value!

Using Double Declining Balance with a short year

What if the asset was purchased June 1? If that is the case, use the same rules used for straight-line. Calculate the first year’s depreciation and then adjust it based on the number of months the company owned the asset. If the asset was purchased June 1, the company owned the asset for seven months in year 1.

$27,000 * .40 = $10,800 * 7/12 = $6,300

Once you calculate the first year’s depreciation, continue on as normal, depreciating the asset until book value is reached.

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For 2017, the amount of depreciation calculated was $1,788.48 but we are limited to $471.20 because of the salvage value.

Final Thoughts

When completing depreciation calculations, know when to use salvage value in the calculation and always make sure to stop depreciating once you reach salvage value. For partial years, only depreciate for the months that the company owned the piece of equipment. Multiply the annual depreciation by the ratio of months owned to months in the year. This is not necessary for units-of-production since the calculation is based on units rather than time.

Related Videos

Straight-line depreciation

Double-declining balance depreciation

Partial year double declining balance depreciation

Units of production depreciation

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