Straight-Line Depreciation

In one sentence: Straight-line depreciation spreads the cost of an item you use for years into equal yearly amounts of expense, so the whole cost is not counted in the year you buy it.

$D = \frac{C - S}{L}$

Read it out loud: “D equals C minus S, divided by L. D is the depreciation, the expense recorded each year. C is the cost of the item when it was bought. S is the salvage value, what the item is expected to be worth at the end. L is the useful life, the number of years the item is expected to be used.”

Before you start

The ideas and signs this page uses, explained from zero. For powers of ten, Greek letters and other notation in general, see Math basics.

Fractions and the fraction bar: A fraction is one number divided by another. The line between the two numbers is the fraction bar, and it means divide. So $\frac{6}{3}$ means 6 divided by 3, which is 2. The whole top part of a fraction is divided by the whole bottom part, so $\frac{C - S}{L}$ means the difference between C and S, divided by L.
Cost, salvage value and book value: The cost of an asset is what the business paid to buy it and get it ready to use. The salvage value is what the business expects to get for it at the end of its use, which can be zero. The book value is the cost still shown on the company’s records after the depreciation recorded so far has been taken away.
Useful life: The useful life is the number of years a business expects to use an asset to earn money. It is an estimate, not a promise, and it is measured in years. A machine with a useful life of 5 years is expected to be used for 5 years, which is 60 months.
An asset and an expense: An asset is something a business owns that helps it earn money over several years, such as an oven, a van or a computer. An expense is a cost counted against the profit of one year. Depreciation turns part of an asset’s cost into a yearly expense, so the cost is matched to the years in which the asset is used.

What each symbol means

Symbol	Meaning
$D$	Depreciation expense per year, the share of the asset’s cost that is counted as an expense in one year. It is measured in dollars per year. With the straight-line method this amount is the same in every year of the useful life.
$C$	Cost, what the business paid to buy the asset and get it ready for use, measured in dollars. It includes the price plus any delivery or setup charges needed before the asset could be used.
$S$	Salvage value, the amount the business expects to receive for the asset at the end of its useful life, measured in dollars. Some assets are expected to be worth nothing at the end, so S can be 0. It is an estimate made when the asset is bought.
$L$	Useful life, the number of years the business expects to use the asset, measured in years. It is an estimate of how long the asset will be useful to the business, not how long it will physically last.

The formula piece by piece

$C - S$: Start with the part of the cost that will be used up. The salvage value is expected to come back at the end, so it is taken away from the cost. What is left, the cost minus the salvage value, is the amount that gets spread over the years of use.
$\frac{C - S}{L}$: Divide the amount used up by the number of years. The division splits that amount into equal shares, one for each year, so each year gets the same expense. A longer useful life gives a smaller share, and a shorter life gives a bigger one.
$D = \frac{C - S}{L}$: The whole formula in one sentence: the yearly depreciation expense equals the cost minus the salvage value, divided by the useful life in years. Nothing else appears on the right side, so the same yearly amount is recorded every year.

What the formula is doing, and why

A coffee chain buys an espresso machine for a large sum, and the machine will be used for several years. If the whole cost were counted as an expense in the year of purchase, that year would look very expensive and later years would look free, which does not match the years in which the machine helps earn money. Depreciation spreads the cost across those years. The formula gives the yearly share, which is the depreciation expense for each year.

Why subtract the salvage value? The machine will still be worth something at the end, so that part of the cost is not used up. Only the cost that is really used up, the cost minus the salvage value, is spread over the years. If the machine costs 6000 dollars and is expected to be worth 600 dollars at the end, then 5400 dollars is the amount that gets used up.

Why divide by the useful life? Dividing splits the used-up amount into equal shares, one per year. A longer useful life gives a smaller yearly expense, because the same cost is spread over more years. A shorter life gives a bigger expense each year. The name straight-line comes from the fact that the same amount is taken each year, so the book value falls in a straight line when it is plotted against time.

The formula gives an accounting estimate, not a cash payment. The machine’s price was paid when it was bought, but the depreciation expense is recorded each year to match the cost to the years of use. Because the answer depends on the estimates for salvage value and useful life, a change in either estimate changes the yearly expense.

An everyday picture

Imagine you buy a bicycle for 300 dollars, plan to use it for 3 years and expect to sell it for 60 dollars at the end. You do not treat the whole 300 dollars as spent on the day you buy it. The 240 dollars you expect to use up is split into 3 equal parts of 80 dollars each. That is the formula at work: (300 minus 60) divided by 3 gives 80 dollars per year.

Worked example: Depreciating an espresso machine over 5 years

Blue Kettle Coffee, a made-up coffee chain used for illustration, buys an espresso machine for 6000 dollars including delivery and setup. The owners expect to use it for 5 years and to sell it for 600 dollars at the end. We want the depreciation expense for one year, and the book value after 3 years.

Find the cost that will be used up. The machine costs 6000 dollars, but the owners expect to get 600 dollars back when they sell it at the end, so only the rest is used up. We subtract the salvage value from the cost: $C - S = 6000\ \text{dollars} - 600\ \text{dollars} = 5400\ \text{dollars}$ .
Divide by the useful life to get one year’s share. The machine is used for 5 years, so the 5400 dollars is split into 5 equal parts, one for each year. $D = \frac{5400\ \text{dollars}}{5\ \text{years}} = 1080\ \text{dollars per year}$ . Dividing dollars by years leaves dollars per year, which is the unit of a yearly expense.
Check that the unit matches the answer. The cost is in dollars and the useful life is in years, so dividing dollars by years gives dollars per year. That is the unit we want, because the expense is a dollar amount recorded each year and not one lump sum. If the life had been given in months, we would have to convert it to years first.
Find the total depreciation after 3 years. Each year adds the same 1080 dollars, so after 3 years the total depreciation recorded is $3 \times 1080\ \text{dollars} = 3240\ \text{dollars}$ . Multiplying the yearly amount by the number of years is the reverse of dividing the used-up amount into equal shares.
Find the book value after 3 years. Book value is the cost minus the depreciation recorded so far. So $6000\ \text{dollars} - 3240\ \text{dollars} = 2760\ \text{dollars}$ . The company still shows 2760 dollars for the machine on its records, and that number falls by 1080 dollars each year.
Check the end of the useful life. After 5 years the total depreciation is 5 times 1080, which is 5400 dollars. The book value is then $6000 - 5400 = 600$ dollars, exactly the salvage value the owners expected. The schedule ends where it was planned to end, so the numbers agree.

Answer: The espresso machine adds 1080 dollars per year of depreciation expense for 5 years. After 3 years its book value is 2760 dollars, and after 5 years it falls to the expected 600 dollar salvage value.

The numbers in this example are recomputed by script every time the site is built.

Common mistakes

Forgetting to subtract the salvage value. Dividing the full 6000 dollars by 5 years gives 1200 dollars a year, which spends more of the cost than the machine is expected to use up.
Mixing units. A useful life given in months must be converted to years first, or the answer comes out as a monthly expense. Five years is 60 months, and dividing by 60 gives a monthly amount, not a yearly one.
Thinking depreciation is money paid out each year. The cash was paid when the machine was bought, and depreciation is an accounting record that spreads that cost across the years of use.
Subtracting the salvage value every year. The salvage value is taken off once, from the whole cost, before the division by the useful life.

Where you will meet it

Yearly accounting for equipment such as ovens, vans and computers in a small business.
Financial statements, where the book value of each asset is shown below its original cost.
Tax calculations in some countries, which set their own rules for how quickly an asset may be written off.
Comparing the yearly profit of two shops that bought equipment at different times or for different amounts.

Questions people ask

Why is it called straight-line?

Because the same amount is recorded each year. If the book value is drawn on a graph against time, it falls along a straight line. Other methods record bigger amounts in the early years, which makes the line curve instead.

Does depreciation mean the machine lost that much cash?

Not exactly. Depreciation is an accounting record that spreads the cost of an asset over its useful life. The cash was paid when the asset was bought. The book value is a record, and the asset may sell for more or less than its book value.

What happens if the estimates change?

The yearly expense is recalculated using the new estimates for the years that are left. A longer life or a higher salvage value lowers the yearly expense, while a shorter life or a lower salvage value raises it.

Accounting Equation: The accounting equation says everything a business owns equals what it owes to others plus what belongs to its owners.
Return on Investment (ROI): Return on investment says how much profit you made for each dollar you spent, so you can compare a small investment with a large one.