 In this presentation, we will take a look at the depreciation calculation for a partial year. When considering depreciation calculations, we typically think of whole months or whole years in order to simplify that process and learn the different types of methods, including straight line, double declining, units of production. However, it's often the case where the depreciation needs to take place or something has been purchased in the middle of the time period, the middle of the month or the middle of the year. To account for that, we could take a fraction of the time period, and that's what we'll do here. We'll be using a straight line depreciation method, but a similar principle will apply to all types of depreciation methods. We've got the cost here, the salvage value being 1000. We purchased it on 10-1 October 1st, and the useful life is 3 years. So if we go through our normal kind of straight line calculation here, we're going to say that the cost is 10,000, and note where we're starting from. We're just going to start and get that depreciation per year. We're not going to try to figure out from 0.1 what this fraction of the first year is. First, we're going to figure out depreciation for an entire year, and then we'll try to figure out, okay, what are we going to do about this fact that we bought it in the middle of the year and deal with that issue. Of course, how we're going to deal with that is that we're going to have part of the depreciation in year 1 and then part of the depreciation in the final year. And therefore, the 3-year property is going to really be running through 4 years, which is half of year 1, half of year 4, a full year 2 and 3. So let's see how that'll work. We're going to do the normal calculation, which will be the cost. So we'll take the cost, 10,000. We will subtract out the salvage value in our normal type calculation. That will give us the amount that needs to be depreciated, 9,000 in this case. So 10,000 minus 1,000 gives us the 9,000. That's how much we need to depreciate over the useful life of 3 years. So we're going to take that 9,000 and just divide it by 3. That will give us the depreciation per year. So here's our depreciation per year. Now our problem is that we didn't buy it at the beginning of the year in this case. We bought it in October. Now when you figure out the number of months that it was used, note that we have to figure out, okay, it's October 1st. That's by the beginning of the month. So you have to include October when you do the counting. So when you count, if you count on your fingers, October, November, December, we got the three months there. October, November, December. Just make sure to include October. If it was October, the end of October, then you may not include. You may just have November and December and have two months. So how are we going to account for that? We could say, okay, there's 3,000 per year. Why don't we see how much per month we need now? So we're going to break this down into a monthly amount by dividing by 12 months. And that will give us a monthly depreciation of 250. So we got a 250 monthly depreciation and we bought it in October. October, November, December means we had it for three months. So we can then take the three months and multiply it times the 250 per month depreciation to give us 750. Now note, if you see that in a book, they might simplify this calculation. Or actually, I think this is the easiest way to think about it, but they may represent it with a fraction because they could say, well, we had it for three months divided by or over compared to 12 months, which would be 0.25 times the 3,000. And if you were to write something out, if you were to just write it out in a book, that would be the shortest way to do it, 3 over 12 times 3,000. And you could even write it even quicker by saying 3 over 12 can be simplified down to 1 over 4. So if you see a problem that says 1 over 4 times 3,000, that's the most simplified term in order to record this portion of the year. However, it's probably more confusing than if you write out the long way here. Say, okay, I have 3,000 a year. I'm going to break it out into units of months divided by 12 to get the units of months, 250. And then there's three months in the current year that we had used this three and then you get to the 750. So I think that's the easiest way to think through your own calculations. If you look at other people's calculations, especially book calculations, they will also often simplify the process down to write it as shortly as possible, not to be able to go back and read it as easily as possible. Okay, so if we have that then we're going to say that the book value will be calculated in year one as the cost of 10,000 minus the accumulated depreciation, which is just the depreciation for year one. That's all we have now. It gives us the book value in year one of 9,250. Remember that you really need, they can ask you for the depreciation here and it's great to get to that point, but it's really common even for multiple choice questions to ask for the book value or the accumulated depreciation just to give a little extra level of complexity. So make sure to be able to calculate both depreciation in at least a couple years of the accumulated depreciation and book value. So in year two, we would take the 10,000 and then we have a full year of depreciation, 3,000 plus the 750 from the prior period, meaning the accumulated depreciation is 750 from last year plus this year's full year of depreciation, not the 750 partial year, and that gives us 3,750. 10,000 minus 3,750 gives us 6,250. Then we're going to do this for year three. We've got 10,000, same cost. Accumulated depreciation is now the 3,750 prior years accumulated depreciation plus another 3,000. You can also think of it as just the depreciation that has been calculated over the three year period which is 750 plus 3,000 plus 3,000. That's the same thing as saying the prior years accumulated depreciation plus the current year's depreciation expense gives us 6,750. 10,000 minus 6,750 leaves us at 3,250. Now in year four, of course, we have this partial year again. So we're going to have the same 10,000, but now we've got this partial year. If there was 750 recorded in year one, the other half of or the other portion of the 3,000 is going to have to be recorded in year four. Let's go through the same calculation one more time to get to that. We're going to say that the straight line calculation is the 10,000 cost. This is the exact same calculation until we get to the green part here. Divided or minus the salvage value gives us the amount to be depreciated 9,000 and then we're going to take that and divide it by the number of years three and remember that's how we got to our 3,000. So here's our 3,000 per year. Now we need to figure out the partial year for the last year. So in other words, if we had it for 10, 11, 12 and year one three months then 12 minus 3, what happened there? 12 minus 3, we had it for nine months in the final year in year four. So we'll do the same calculation as 3,000 and divided by 12 gives us 250 per month and now we're going to multiply that not times three which happened in year one but by nine which happened in year four and that'll give us the 2,250. The other way you can do this of course is to just say well if this is a full year of depreciation 3,000 and we already depreciated 750 in year one then we need to get the other part of that 3,000 to get to the full year between year one and year four so we can subtract minus the 750 gives us that 2,250. So then we can complete this. We're going to say that we have the 10,000 here minus the 9,000 which is the accumulated depreciation of 6,750 from last year plus the current years 2,250 that'll give us the 9,000. You can also think of it as just adding up all the depreciation over the life which started out with the 750 and then we added 3,000 plus 3,000 plus now 2,250 so what have we done accumulated over the life we had 750 in year one plus 3,000 in year two plus 3,000 in year two three plus now 2,250 in year four or we already did that all the way through year three so we had accumulated depreciation of 6,750 in year three plus year four depreciation expense 2,250 that'll give us our 9,000 then if we subtract that out not the 10,000 minus the 9,000 we get to the 1,000 which should be and is our salvage value and it's great to be able to go through the whole problem so that you can have that you can get to that check figure where you should remain at and get to the salvage value