5. Double Declining Balance

Let's talk about the double declining balance method. The double declining balance method is not as straightforward as the straight line method. The straight line method, if you'll remember, was cost minus salvage over useful life. So if we say that the useful life is five years, then you end up with cost minus salvage over 5.

And this is for straight line, and if you say that it's that, you could also say it's 1 over 5 times cost minus salvage. Right? Do you see how these are all the same? Cost minus salvage over useful life. If our useful life is five, then it's the same thing as saying 1 over 5 times cost over salvage, and essentially, this is our slope. This becomes the rate at which we depreciate. So when you're doing straight line depreciation, you're depreciating it at this rate. Now, why am I talking about straight line depreciation when I told you we were gonna be talking about double declining balance?

Because double declining balance is double the straight line rate. Double declining balance looks like this: double the straight line depreciation rate times book value, and that's gonna give you your depreciation expense for that year. This is where that double comes from. It's two times the straight line rate times this book value. Now, if you don't know what book value is, book value is pretty simple. Book value is the asset's cost minus any accumulated depreciation we have for that asset, and that is the book value. The book value is what the value of the asset is according to our books. So we take whatever we have for the original cost, and this never changes, right?

We put this in, and then we start adding to accumulated depreciation. So it's the asset's cost minus whatever accumulated depreciation we've added. That becomes our book value. So we say that the book value of an asset is the value after depreciation. So the book value is constantly changing because the accumulated depreciation is constantly changing. Year over year, accumulated depreciation is going up, and the book value is going down until eventually this reaches either salvage value or zero. So that's what we're gonna use in the double declining balance, is that book value. I think it's easiest probably to do a problem. Let's say the acquisition cost was $8,000, salvage value is $2,000, life of five years, and we're gonna use the double declining balance method.

Now, what is the straight line rate on this problem? Well, if we were doing straight line depreciation, we would say cost less salvage value over useful life is the same as 1 over 5 times cost less salvage value. So what we can say is the straight line rate is gonna be 1 over the useful life. So this is our straight line rate, and you can use this every time. I just wanted to explain up here how you can get there without having to memorize this. It's the rate at which we are depreciating on a straight line method.

So we're gonna take 2, 'cause it's double declining, 2 times 1 over 5, 1 over the useful life or the straight line rate. Then what's our book value? If this is Year 1, what's our book value? Well, you know, it doesn't really matter that it's Year 1. The formula still applies. $8,000 minus zero in accumulated depreciation gives us $8,000. So you may have some teachers that say, "Well, in the first year, just do the acquisition cost, and the year after that, do acquisition cost minus accumulated depreciation." Meh. Just use the book value all the time. That's always going to be right. It just so happens that in the first year, your accumulated depreciation is zero, so your book value and your cost are gonna be the same thing.

So in the first year, we take 2 times 1 over 5 times $8,000, and that's gonna give us $3,200 in Year 1. Now, unfortunately, the double declining balance method is unlike the straight line method in that each year the amounts are gonna be different. Why would that be? Well, two never changes, and the straight line rate never changes, but this $8,000, this is actually a formula of cost minus accumulated depreciation. The cost never changes, but the accumulated depreciation changes year after year, doesn't it? So in Year 1, we said depreciation expense is $3,200. Accumulated depreciation is $3,200. So we added $3,200 to the accumulated depreciation account.

So the next year, the book value is going to be $8,000 minus this $3,200. So the next year, it's gonna look like this: 2 times 1 over 5 times our book value. And what's our book value? It's gonna be the $8,000 less our accumulated depreciation. That one I'm gonna need a calculator for. So let's do 2 times 1 over 5 times $8,000 minus our accumulated depreciation, and we get $1,920. So you can see that this is much less than the year before, and that's why they call this one an accelerated depreciation method, because you take a lot in the first years and you take less in the later years.

So in these first years, you have these massive drops, and then they start to slow down, and then at the end, you're barely taking any depreciation at all. So this front-loads your depreciation in the first couple of years. Now, the depreciation method you use is supposed to match the useful life and the output production of the machine. Now, whether that's the case, I don't really know. But if on your test it says the machine is going to produce a lot in the first few years and not as much in the last years, well, don't use straight line because that doesn't really match. What they're probably going for there is you need to use an accelerated method.

Realistically, they're gonna tell you what method to use, but it should match the production output of the machine. Okay, let's do Year 3 on this guy. So on Year 2, we decided the depreciation expense was $1,920. So now what we do is we say Year 2: depreciation expense, 1,920; accumulated depreciation, 1,920. And we add that to our accumulated depreciation account.

So you can see that our accumulated depreciation account is still going up, which means our book value is still going down. So now we're at $5,120 for accumulated depreciation. So what is Year 3 gonna look like? Well, it's gonna be 2 times 1 over 5 times $8,000. Now you have to add in this $1,920. $8,000 less $5,120, and that gives us $1,152. Don't worry, I used a calculator. So that gives us $1,152 for Year 3. So now we go over to accumulated depreciation, and the journal entry is gonna look just like this, except we're gonna add in $1,152.

Now, if you add in $1,152, you're gonna get $6,272. And this looks good, I mean, as good as $6,272 can look. But what's the problem with this? What's our book value when accumulated depreciation is $6,272?

Our book value is $1,728. What's the problem with that? Well, the problem with that is we said that the salvage value was $2,000, and now our book value is below the salvage value. What's the depreciable base for this asset? The depreciable base for this asset, the amount that we are able to depreciate, is $6,000. So we should never have more in the accumulated depreciation account than the amount that we are able to depreciate. So we've gone too far. $6,272 is too much. So we know that it cannot be $1,152, because if we take this $1,152, and if we put this $1,152 in here, we end up at $6,272, which is too much.

You just can't over-depreciate like that. So you need to undo that $1,152, because that's too much. And what you need to do is say, "Okay, well, that entry made it too much, so I know that I'm gonna hit $6,000 on this entry, because $6,000 is my max and my last entry took me over $6,000. So I gotta figure out what number goes here such that I get $6,000." And your depreciation for Year 3 becomes $880. So even though we calculated it to be $1,152, the rule still applies that you can't depreciate over your salvage value.

So Year 3 becomes $880. Now, this is the absolute worst part about double declining balance, is that it doesn't take into account salvage value at all. In the straight line, we say cost minus salvage over the useful life, such that you get some amount you can depreciate per year, and you know based on the fact that math is math, you're never gonna go over salvage value because you took out salvage value in the beginning. But you'll notice this equation doesn't involve salvage value at all. You have a 2, you have a one-fifth rate, and then you have book value, which has nothing to do with salvage value.

Book value is just cost minus accumulated depreciation. So when you're doing double declining balance, when the problem says double declining balance, step one, and put a big star next to it, is figure out depreciable base. So in this problem, you should figure out the depreciable base, and you say depreciable base is $6,000. Circle it and put a star next to it. And then when you're doing your accumulated depreciation account, you need to realize my accumulated depreciation can never go above $6,000. I can never depreciate more than I'm able to depreciate. So in this problem, when we got up to, here it is, $6,272, if you had had $6,000 written next to accumulated depreciation like this, and you ended up with $6,272, you would look at that and go, "Huh, okay, well, that's the end of double declining balance, so let me take that amount out and figure out what gets me to $6,000."

So on double declining balance, unfortunately, you just have to be on guard. When you see double declining balance, the first thing, number one always, is find out how much am I able to depreciate, because the formula won't do it for you. On straight line, the formula, math itself, takes care of doing it for you. But on double declining balance, you have to do it. So figure out how much are you able to depreciate, and then write that in big numbers next to your accumulated depreciation, and maybe even put, "Don't go over $6,000." So that when you write in $2,000 right here and it comes out to $7,120, you don't think you've done it correct.

You look over here and go, "You're right, I haven't done this correct. Let me back that out and figure out the missing amount." And then you just take that missing amount and you say, "Okay, for Year 3, it's actually gonna be $880." And you know what? If you wanna do this on every problem, regardless of what method you're using, that is not a bad idea. It's not a bad idea to know how much can I depreciate, how much am I able to depreciate, so that when you're doing depreciation, you don't ever get over this amount. Because no matter what method you're using, you can never depreciate beyond salvage value.

So if it helps and if it makes sense and it makes it easier to understand, start every problem by identifying your depreciable base.