Depreciation: Units-of-Activity - Online Tutor, Practice Problems & Exam Prep

The units of production method, also known as the units of activity method, calculates depreciation based on the asset's output rather than time. Key variables include the asset's cost, estimated useful life in units (e.g., miles for a truck), and residual value (or salvage value). The formula for depreciation per unit is: $(\mathrm{Cost}-\mathrm{Residual\; Value})/\mathrm{Total\; Units}$. This method effectively allocates the asset's cost over its productive capacity.

Units-of-Activity Depreciation

All right. Let's talk about a common depreciation method here, the units of production method. So the units of production method, sometimes it's called the units of activity method. It means the same thing. So depreciation, remember, why do we use depreciation? Well, it's because we bought some fixed asset that we're going to use for a long time, more than a year. And what we did is we probably spent a lot of money on this asset and we want to break up that cost. We spent all this money on the asset, we want to break it up over its useful life. Okay? And that's what depreciation does, it breaks up that upfront cost over the useful life of the asset.

So whenever we calculate depreciation in all the different methods, we're always going to be concerned about 3 variables. Cost, which is what we spent on it, right? The initial cost of the asset, then we're going to have to estimate a useful life and this is how long the company expects the asset to help us generate revenue. Now in this method, it's a little different than we're used to. This method, we're not talking about units of time like how many years is this gonna help us. We're talking about the useful life is gonna be in a number of units. So depending on the asset, it could be different. If it's let's say a truck, well, it could be how many miles are we gonna get out of the truck. If it's a machine in our factory, how many units is it going to produce for us? Is it going to produce 100,000 units in our factory? 200,000 units? What is that estimate of the amount of units? Okay? So it's a number of units not a measurement of time. So that's the difference in this method.

And lastly, we have our residual value, that's our 3rd variable here. How much the company expects the asset to be worth at the end of the useful life. So once we're done using it, how much is it going to be worth? And remember that these 2 variables, useful life and residual value, they're both estimated by the company, okay? So residual value, well it has other names like we've said it has salvage value, scrap value, they all mean the same thing, right?

So let's go ahead here into our, depreciate our units of production method and let's see our formula that we use in this method. So in this method, what we calculate is a depreciation per unit of output, okay? So what we're gonna do is like if it's a truck per mile that we drive, how much depreciation is it? Or if it's a machine that's producing units, how much depreciation per unit it produces. Okay? So it's a similar formula to our straight line formula. In our numerator, we have cost minus residual value and remember this is our depreciable base. So this is the total amount of depreciation that we're going to take over the useful life, right? We paid some cost for it and then we subtract out what it's worth at the end. And everything else in the middle, well that's the depreciation.

But notice in the denominator, it's no longer a unit of time. It's units of output like those total number of miles or the total number of units it's going to produce in the factory, right? So it's going to be like that. So why don't we pause here and then we'll go into an example of how we do the units of production in the next video. Alright, let's do that now.

Units-of-Activity Depreciation

On January 1st, year 1, Johnson and Johnson and Johnson Company purchased a delivery truck for $42,000. The truck has a useful life of 120,000 miles and a residual value of $2,000. We think that after 120,000 miles, this truck will not be operational anymore. During year 1, the truck was driven 36,000 miles. This information tells us how much depreciation we're going to take in the first year based on the units driven.

The first step is to calculate our depreciation per unit. We have our cost of $42,000 minus $2,000, our residual value. Depreciation per unit is calculated as follows:

40000 120000 = 0.33333

This calculation gives us a per unit (or per mile) depreciation rate of approximately 0.33333. It is crucial to use precision in this calculation, especially on tests, to avoid errors. Thus, it's advisable to use several decimal places in calculations.

To find the depreciation expense for year 1, we consider the miles driven:

36000 × 0.33333 = 12000

The result is a depreciation expense of $12,000 for the first year. The entry to record depreciation is as follows:

• Debit Depreciation Expense $12,000
• Credit Accumulated Depreciation $12,000

This standard journal entry affects both the expense and accumulated depreciation accounts.

Finally, the net book value at the end of the first year is calculated by subtracting the accumulated depreciation from the cost of the truck:

42000 - 12000 = 30000

Thus, the net book value is $30,000 at the end of the first year. With this method, each year's depreciation expense is simply the miles driven multiplied by the depreciation rate. Exact mileage must be provided each year to calculate the correct expense.

In the next video, we will continue to follow this truck through its entire useful life using the units of production method.

Units-of-Activity Depreciation

Alright, so let's go ahead and follow this truck through its entire useful life, using the units of production method. So I've got some of the data from above and remember we estimated we had an estimated useful life. In this case, it's not in years. It's in miles, right? This is 120,000 miles. And we have figured out our rate per mile above, which is the first step was going to be 0.33 repeating, right? 3 is forever per mile. So for each mile driven each year, we're going to take that much depreciation. Now, remember that the one trick here is that we have to find once we've used up the entire useful life. Because the useful life that we're depreciating over is 120,000 miles. So once we've gone through 120,000 miles, we don't take any more depreciation. So let's go ahead and start here. In January 1st year 1, well that's when we bought the truck. We haven't driven it yet. Our net book value is going to be the entire value of the truck, which is 42,000, right? I'll write that over here, 42,000. Cool?

And then we calculated during year 1, right? We already did year 1's calculation where we drove 36,000 miles times the 0.333¢ per mile, we got a depreciation expense of 12,000, right? So this gave us accumulated depreciation of 12,000 and this brings our net book value from 42,000 minus the 12,000 down to 30,000, right? So let's keep on going here. During year 2, we drove it for 24,000 miles. So let's see what that comes out to. 24,000 divided by 3. Well, that's how I do it. 24,000 divided by 3 because really this is one-third, right? So that's another way to do it, but if you don't know, if you can't deal with those fractions like that, you could just do times 0.33333 and you wanna make sure you max out those threes and you're gonna round it here. You'll see you're right at 8,000, right? So this is 24,000 times the rate of 0.33 repeating and that'll give us 8,000 in depreciation expense for the 2nd year. Notice it's not going in any particular order, it just matters how many miles you drove it. Look in year 3, we drove it more miles than in year 2. So it's not like it's going to keep decreasing over time or increasing. It just matters how many miles we drove the truck. So with 8,000 in depreciation for year 2, our total accumulated depreciation is going to increase to 20,000, right? So now we've got 42,000 minus the 20,000 in accumulated gets us to a value of 22,000 in net book value. Cool?

What about in year 3? So now year 3, we drove it another 30,000 miles. Have we reached that estimated useful life yet? No, it doesn't look like it. It looks like we've still got some space, so we don't have to really worry about that just yet. So another 30,000 miles, so let's find out what that rate going to be. 30,000 times 0.33 repeating and that's going to give us 10,000 in depreciation for year 3, right? So if we do our previous accumulated depreciation of 20,000 plus another 10,000, well that gets us to 30,000 in total accumulated depreciation and it brings our net book value down to 12,000, Right? 12,000. So let's keep going here in year 4. Well, why don't we calculate how many miles we've driven the truck just to make sure we're not run out of miles here. 36,000 plus 24,000 plus 30,000. So we've driven the truck 90,000 miles after 3 years. So we have another 30,000 to go. Right? Our total estimated useful life is 120,000 miles and that's what we are depreciating this truck over, is those 120,000 miles. So we just want to make sure we don't go over that amount. So in year 4, we've got space for Let's do the entire 18,000 here. 18,000 times 0.33 repeating and that gives us 18,000 divided by 3 really is 6,000. Cool. So 6,000 is added to our accumulated depreciation plus 6,000 is equal to 36,000. There we go. Alright. So now let's see what our remaining net book value is, And we're left with 6,000 in remaining net book value. And we're trying to get to an estimated residual value of 2,000, right? So we are getting pretty close to running out of miles here in our estimated useful life. So let's go ahead and remember, this estimated useful life, it's just an estimate. It might last longer, it might last shorter. So we just wanna make sure that we depreciate only over that estimate that we made. So 36 plus 24 plus 30, plus the 18 from year 4, gets us to 108,000 miles. We've already driven it 108,000 miles before we get to year 5. So how many miles are left in its estimated useful life? There's only 12,000 left. Right? 120,000 minus the 108 that we've driven from these 4 years. We had already driven 108,000 miles. Well, there's only 12,000 miles left. But in year 5, we drove it 16,000. So are we going to multiply 16,000 times 0.33? No, no, no. We can only depreciate it with the amount of miles left in its estimated useful life. If we use the whole 16,000, well, we would go under the residual value and we don't want to do that. So all we're going to do is we're going to depreciate it for the 12,000 miles left in its useful life times the 0.333 and that's going to give us 4,000 in depreciation and that gets us to 36,000. Look at look what happens in our accumulated depreciation, it equals 40,000. Remember that our depreciable base, that's the 42,000 minus the 2,000. So the total amount of depreciation we can take is 40,000. Okay? And that's exactly what's happened here when we reduced it in year 5. So actually, I'm going to write this 12,000 in a different color so that it stands out a little bit because we used a little bit of math to get to that 12,000. Okay? So we want to make sure that our total depreciation is equal to our depreciable base of 40,000. And then what's going to be left in our net book value? Well, just our residual value. Right? 42,000 minus 40,000 gets us to 2,000. Now, what about in year 6 when we continue to drive the truck for another 8,000 miles? Well, we've already fully depreciated. We're not going take any more depreciation expense. Our accumulated depreciation still 40,000 on our books and our net book value still going to be the 2,000 in residual value there. Cool? Alright. So now that you guys have seen the units of production method, why don't you guys try some practice problems. Alright. Let's do that now.

ABC Company purchased a new machine on January 1, Year 1 for $44,000. The company expects the machine to produce 50,000 units. The company thinks it could sell the scrap metal from the machine for $4,000 at the end of its useful life. If the company uses the units-of-production method for depreciation, what will be the net book value of the machine on December 31, Year 1, if 15,000 units are produced with the machine during the year?

• A. $12,000
• B. $13,200
• C. $30,800
• D. $32,000

DBQ Company purchased a machine on January 1, Year 1 for $60,000. The company estimated a 300,000 unit production useful life and $8,000 residual value. During Year 1, the company produced 90,000 units. During Year 2, the company produced 30,000 units. If the company uses the units-of-production method for depreciation, what will be the amount of accumulated depreciation on December 31, Year 2?

• A. $5,200
• B. $6,000
• C. $20,800
• D. $24,000

XYZ Company purchased a machine on January 1, 2018 for $110,000. The company estimated a 20,000 unit useful life and $10,000 residual value. XYZ produced 8,000 units in 2018; 6,000 units in 2019; and 10,000 units in 2020. If the company uses the units-of-production method for depreciation, what will be the amount of depreciation expense for the year 2020?

• A. $30,000
• B. $40,000
• C. $50,000
• D. None of the above

Here’s what students ask on this topic:

What is the units of production method of depreciation?

The units of production method, also known as the units of activity method, calculates depreciation based on the asset's output rather than time. This method is particularly useful for assets whose wear and tear is more closely related to usage than the passage of time. Key variables include the asset's cost, estimated useful life in units (e.g., miles for a truck), and residual value (or salvage value). The formula for depreciation per unit is:

$\frac{(\mathrm{Cost}-\mathrm{Residual\; Value})}{\mathrm{Total\; Units}}$

This method effectively allocates the asset's cost over its productive capacity.

How do you calculate depreciation using the units of production method?

To calculate depreciation using the units of production method, follow these steps:

1. Determine the asset's cost.
2. Estimate the residual value (salvage value) at the end of its useful life.
3. Estimate the total number of units the asset will produce over its useful life.
4. Use the formula:

$\frac{(\mathrm{Cost}-\mathrm{Residual\; Value})}{\mathrm{Total\; Units}}$

This gives you the depreciation per unit. Multiply this by the number of units produced in a given period to find the depreciation expense for that period.

What are the advantages of using the units of production method?

The units of production method has several advantages:

• Accuracy: It provides a more accurate reflection of an asset's usage and wear and tear.
• Cost Allocation: It aligns depreciation expense with the actual use of the asset, making it more relevant for assets with variable usage.
• Financial Reporting: It can improve the matching of expenses with revenues, leading to more accurate financial statements.

This method is particularly useful for manufacturing equipment, vehicles, and other assets where usage varies significantly over time.

What are the key variables in the units of production method?

The key variables in the units of production method are:

• Cost: The initial cost of the asset.
• Estimated Useful Life in Units: The total number of units the asset is expected to produce over its useful life (e.g., miles for a truck, units produced by a machine).
• Residual Value: The estimated value of the asset at the end of its useful life, also known as salvage value or scrap value.

These variables are used in the formula:

$\frac{(\mathrm{Cost}-\mathrm{Residual\; Value})}{\mathrm{Total\; Units}}$

to calculate depreciation per unit of output.

How does the units of production method differ from the straight-line method?

The units of production method differs from the straight-line method in how it allocates depreciation. The straight-line method spreads the cost of the asset evenly over its useful life in years, using the formula:

$\frac{(\mathrm{Cost}-\mathrm{Residual\; Value})}{\mathrm{Useful\; Life\; in\; Years}}$

In contrast, the units of production method allocates depreciation based on the asset's output, using the formula:

$\frac{(\mathrm{Cost}-\mathrm{Residual\; Value})}{\mathrm{Total\; Units}}$

This makes the units of production method more suitable for assets whose wear and tear is more closely related to usage than time.