Sum Of Years Digits Depreciation: Concept, Formulas & Solved Problem | PMP Exam - YouTube

In this lesson we will talk about Sum of Years Digits method of depreciation. We

also have solved problems at the end of the lesson. Let's get started ...

You bought an asset, a car for $20,000. The car will be in use for five years

and has a salvage value of dollar 500. The first step in this approach is to

find the depreciation base. In this example the useful life of the asset is

five years. We start with 1 and keep adding the consecutive numbers till the

end of useful life. Depreciation base for this example is

simply 1 plus 2 plus 3 plus 4 plus 5. Fifteen is the depreciation base.

What happens if the useful life of the asset is 10 years? We have to add a lot

of numbers until we reach 10. There is a easier way to add these numbers. Here is

the formula ...

In this example useful life is five. 5 divided by 2 multiplied by 1 plus

5 gives us 15. It works!

Next we find the depreciable value, the value that has to be depreciated

across the useful life of the asset. It is simply asset cost minus the

salvage value. 20,000 minus 500 ...

We have $19,500 as depreciable value. How do we split this depreciable

value across the useful life of the asset? We have a base of 15. In the year 1, we

use 5 out of 15

5 by 15 of 19,500 is the depreciation in year 1

The number is $6,500 We should put a minus sign. Depreciation

decreases the value of the asset. The asset value after one year is 20,000 minus

6500 or $13,500

In second year the depreciation is 4 by 15 of depreciable value

or $19,500, that is $5,200

Asset value after two years is $8300

We continue ...

until we reach the 5th year. We consume the remaining depreciable

value here, that is, 1 by 15 of total depreciable

value. The asset value after five years the

useful life is $500, the salvage value

Finally Sum of Years method belongs to a special category of depreciation

techniques called accelerated depreciation.

In Sum of Years method, the annual depreciation is much more in the initial

years. It decreases with time. This is evident in our example too.

Depreciation is $6,500 in year 1 but drops to $5,200 in year 2. It keeps

decreasing across the lifetime of the asset.

These characteristics are unique to accelerated depreciation

Double Declining method also belongs to accelerated depreciation

This is unlike straight-line depreciation where the annual

depreciation is constant across the useful life of the asset. We will look at

a sample problem now. You bought a high-end computing machine

for $1,700. You have decided to use the sum of years digits method for

depreciation. The machine will be used for five years. The salvage value of the

machine is $200. Which of the following is incorrect?

A. The value of the computing machine after five years is $200

B. The value of depreciation in first-year is $500

C. The depreciation in value will be more in initial years and will gradually decline over the useful life of the machine

D. The value of the computing machine after two years is $680

Please pause the video and try to find the correct choice

The problem provides us the asset acquisition cost of $1700.

Useful life of five years and salvage value of $200

Sum of Years Digits is used for depreciation. We have to identify the

incorrect statement, not the correct statement. I hope you got that right!

Let's look at the first choice. The value of the computing machine after five

years is $200. Five years is the useful life of the

asset. After five years we should be left with salvage value.

$200 is the salvage value.

So, A is correct. The next choice says that the value of

depreciation in the first year is $500

Let's check that. First, the depreciable value is asset

cost minus the salvage value, or $1,500.

Sum of Years Digits is 1 plus 2 plus 3 plus 4 plus 5, or 15

So, the depreciation in year 1 will be 5 by

15 times $1,500, or

$500 B is also a correct statement.

C says that the depreciation in value will be more in initial years and will

gradually decline over the useful life of the machine.

This is definitely true for Sum of Years approach, an accelerated depreciation

technique. C is also correct.

We are only left with D. This has to be the incorrect statement and our answer.

Still, we will have a look at this. The value of the computing machine after

two years is $680

We have the depreciation for year 1. Let's do that for year 2 also

It is 4 by Sum of Years or 4 by 15 times $1500

or $400 The asset value after two years will be

initial value of $1700 minus $500, depreciation in year 1 minus

$400, depreciation in year 2, or $800

D says $680, which is incorrect. D is our choice.