### Allocating the expense of an asset over its life with straight-line and double-declining depreciation.

Depreciation can be a tricky concept to understand. It is basically a way of allocating the expense of an asset over its life. So let’s say for example you bought a piece of equipment for $25,000, and the equipment is good for 5 years. That means that every year you are using up $5000 worth of the value of that equipment. You can basically allocate $5000 each year as an expense: you are allocating the expense over the life of the asset and that is what depreciation does.

We can go over a few examples of depreciation. First there is straight-line depreciation. Straight-line depreciation basically says that you are going to evenly allocate the cost of the asset over its useful life. You’ll need a few pieces of information before you can allocate depreciation. First of all, you need to know how much the piece of equipment cost. So if you bought a truck for $25,000, that will be the acquisition cost. You need to know the useful life of the asset in years: how long is that truck going to last for? maybe it’s five years, maybe it’s more. And at the end of its useful life, what is the salvage value? What is it worth? A truck may only live for 5 years, but you can sell it for parts: there is a salvage value to it. The equation to figure out annual depreciation is the acquisition cost minus the salvage value all over its useful life.

Let’s say we buy that truck for $25,000: it has a useful life of 5 years and a salvage value of $5000. What is the value depreciated every year? We are going to take the purchase price minus the salvage value, and that means that we are going to depreciate a total of $20,000 over the course of five years. That is going to be the annual depreciation, the total amount depreciated divided by the number of years it’s depreciated. $20,000 divided by 5 means that every year you are going to have $4000 in annual depreciation for that truck.

Double-declining depreciation means that you want to accelerate the value of the depreciation. Basically the piece of equipment that you purchased is going to lose a lot of value in the first couple of years, and less value each year [after that]. So what do you need to know before you can calculate double declining depreciation? You need to know the acquisition cost, the useful life of the asset in years, and the salvage value. And the depreciation calculation is done like this: you have to figure out what the rate is; that is going to be 100% divided by its useful life times 2. So for example with straight-line depreciation, if you were depreciating something over five years, you would depreciate 20% percent of the value every year. Double declining means that if you are depreciating something over 5 years, you are going to depreciate it 40% each year, and that value is going to change each year.

So how do you figure that out? Annual depreciation equals book value times the depreciation rate, and in the final year the depreciation is going to equal the book value minus the salvage value. Let’s work through the numbers. In the first year, the beginning value of your truck is $25,000; you’ll depreciate it 40%. 40% times $25,000 is $10,000. So the ending value of the truck and the end of the first year after it has been depreciated is $25,000 minus $10,000, which equals $15,000. In year two, the beginning value of the truck is $15,000 which coincidently is the ending value in year 1. $15,000 times 40% is $6,000. With a beginning value of $15,000, minus the depreciation of $6000, the ending value of the truck at the end of year 2, is $9000, which will be the beginning value of your truck in year 3. $9000 times 40% is $3600, so at the end of the third year the value of your truck is $5400. Now in the fourth year we can’t do 40% because we can’t depreciate the value of the truck below $5000 because we know that is the salvage value. So in the forth year, we are just going to depreciate $400, and we will end the year at $5000 for the value of the truck.