Because the numerator changes each year, the SYD depreciation rate changes each year.

True or False

**True.**

Every year, the numerator changes as it represents the years remaining in the asset's life. With each year that passes, the years left to depreciate the asset is reduced.

For example, if a company has a 4-year asset, at the beginning of Year 1, the assets remaining life is 4 years. At the beginning of Year 4, the assets remaining life is 1 year.

On May 1, 20x0 your firm purchased a 4-year asset at an acquisition cost of $42,000 and a residual value of $7,000.

Under the SYD method, what is depreciation for Years 1 and 2, respectively?

When an asset is purchased during the year, the company must use the depreciation rate for a full consecutive 12 months, even if that 12-month period falls within two different calendar years.

Solution: First, compute the denominator (sum-of-the-years-digits) which will be used each year:

__n(n+1)__ = __4(4+1) __ __4(5)__ = 10 **OR **(4+3+2+1) = 10

2 2 2

The annual depreciation rate in Year 1 and 2 is:

Year 1 = 4/10

Year 2 = 3/10

Depreciation expense = Depreciation Rate x Depreciable base

Because the asset was placed in service on May 1, the company can only recognize depreciation for the 8 out of 12 months for 20x0. Therefore, in the first 4 months of 20x2, the 4/10 rate will be used and starting May 1, 20x1, the 3/10 rate will be used.

**Year 1 = 4/10 x $35,000 = $14,000 x 8/12 = $9,333.33**

Year 2 = 4/10 x $35,000 = $14,000 x 4/12 = 4,666.67

Year 2 = 3/10 x $35,000 = $10,500 x 8/12 = $7,000

**Total year 2 depreciation = $11,666,67**

Which method of depreciation is the least used?

Sum-of-the-years-digits

When calculating the depreciation rate under the SYD method, the denominator represents?

__ Numerator __

**Denominator**

__Years Remaining in Assets life__

**SYD**

The formula to find the depreciation rate using the sum-of-the-years-digits method is found using this formula. After the depreciation rate is found, it is multiplied by the depreciable base to find the annual depreciation expense.

To compute depreciation under the SYD method, you simply multiply the depreciable base by the depreciation rate.

True or False

**True.**

What is the formula to calculate the SYD?

The SYD can be found using the formula below:

__ n(n+1) __ = SYD denominator

2

**OR**

The company can manually compute by adding the digits.

For example, a 6-year asset would have SYD denominator of 21.

__ 6(6+1) __ = __ 42 __ = 21 **OR** (6+5+4+3+2+1) = 21

2 2

The sum-of-the-years'-digits for an asset with an estimated life of 8 years is?

__n(n+1) __ = __8(8+1) __ __8(9)__ __72 __ = **36 ( SYD denominator)**

2 2 2 2

OR

(8+7+6+5+4+3+2+1) = **36 ( SYD denominator)**

To compute annual depreciation expense each year under the SYD method, every year the depreciation rate is multiplied by the ______.

Depreciable base.

The only method that multiplies the depreciation rate by the book value is the declining balance method.

On Sep 1, 20x1 your firm purchased a 5-year asset at an acquisition cost of $62,000 and a residual value of $2,000.

Under the SYD method, what is 20x1 depreciation?

When an asset is purchased during the year, the company must use the depreciation rate for a full consecutive 12 months, even if that 12-month period falls within two different calendar years.

Solution: First, compute the denominator (sum-of-the-years-digits) which will be used each year:

__n(n+1)__ = __5(5+1)__ __5(6)__ = 15 **OR **(5+4+3+2+1) = 15

2 2 2

The annual depreciation rate in Year 1 is:

Year 1 = 5/15

Depreciation expense = Depreciation Rate x Depreciable base

Year 1 = 5/15 x $60,000 = $20,000

Because the asset was not placed in service on January 1, the company can only recognize depreciation for the last 4 out of 12 months for 20x1. Therefore, in the first 8 months of 20x2, the 5/15 rate will be used and starting September 1, 20x2, the 4/15 rate will be used.

A company has a machine that is used for manufacturing purposes. If the company uses the SYD method of depreciation, omitting the dollar amounts, what would be the adjusting journal entry at year end to recognize depreciation?

Inventory - Work in Process Overhead (DR.)

Accumulated Depreciation (CR.)

With no regard to the depreciation method, whenever a company has an asset that is used for manufacturing purposes, the depreciation expense for the period is recorded in the Inventory Work in Process Overhead account. The depreciation expense account is used for assets that are used for nonmanufacturing purposes.

N is the formula below represents?

__n(n+1)__

2

N = number of years

The formula computes the SYD, the number that will be used in the denominator.

On January 1, MackCo which uses SYD depreciation acquired an asset with an estimated life of 9 years. The depreciation rate each year will be as follows:

Solution: First, compute the denominator (sum-of-the-years-digits) which will be used each year:

n(n+1) = 9(9+1) 9(10) = 45 **OR **(9+8+7+6+5+4+3+2+1) =45

2 2 2

The annual depreciation rate for the asset will be as follows:

Year 1 = 9/45

Year 2 = 8/45

Year 3 = 7/45

Year 4 = 6/45

Year 5 = 5/45

Year 6 = 4/45

Year 7 = 3/45

Year 8 = 2/45

Year 9 = 1/45

How is the sum-of-the-years-digits method similar to the declining balance method?

The sum-of-the-years-digits and declining balance method are both accelerated methods of depreciation.

*Accelerated means more depreciation is recognized in the earlier years of the asset's life and less in the later years.*

If a company has a 7-year asset, the fraction used to determine the depreciation rate at the end of Year 3 would be?

Under SYD method, the depreciation rate is a fraction that is used as follows

__Numerator - Years remaining in the asset's life__

Denominator - SYD

The denominator is found as follows: (7+6+5+4+3+2+1) **OR **__n(n+1)__

2

In the formula to find the sum of the digits in the assets life, n represents the number of years. In this case, the total SYD is 28. [7(7+1) = 56/2] Please note, **only **the numerator changes every year, the denominator stays the same.

**In Year 3, the fraction would be 5/28.**

- Year 1 = 7/28.
- Year 2 = 6/28.
**Year 3 = 5/28.**- Year 4 = 4/28.
- Year 5 = 3/28.
- Year 6 = 2/28.
- Year 7 = 1/28.

Under SYD depreciation, depreciation expense declines each year.

True or False

True.

Similar to the declining balance method, SYD is an accelerated method of depreciation which recognizes more depreciation expense in the earlier years of an asset's life and less in it's later years.

When calculating the depreciation rate under the SYD method, the numerator represents?

__ Numerator __

Denominator

**Years Remaining in Assets life**

SYD

The formula to find the depreciation rate using the sum-of-the-years-digits method is found using this formula. After the depreciation rate is found, it is multiplied by the depreciable base to find the annual depreciation expense.

The formula below represents:

__Years Remaining in Assets life __

SYD

__Years Remaining in Assets life __

SYD

The formula to find the * depreciation rate* using the sum-of-the-years-digits method is found using this formula.

After the depreciation rate is found, it is multiplied by the depreciable base to find the annual depreciation expense.

When an asset is purchased in the middle of the year and depreciated under the SYD, a new depreciation rate is computed each January 1 and applied for an entire calendar year?

True or False

**False.**

When an asset is purchased during the year, the company must use the depreciation rate for a full consecutive 12 months, even if that 12-month period falls within two different calendar years. For example, if Yahweh Co, purchased an asset on August 1st, 20x0 the company must use the same depreciation rate through July 31, 20x1.

On January 1, 20x1, your company acquired a machine for $500,000 with an estimated useful life of 7 years and a residual value of $45,000. Using SYD depreciation, the 20x2 depreciation expense?

Solution: First, compute the denominator (sum-of-the-years-digits) which will be used each year:

n(n+1) = 7(7+1) 7(8) = 28 OR (9+8+7+6+5+4+3+2+1) = 28

2 2 2

The annual depreciation rate in Year 1 and 2 are as follows:

Year 1 = 7/28

Year 2 = 6/28

The annual depreciation expense in Year 1 and 2 is as follows:

Depreciation rate x Depreciable base

Year 1 = 7/28 x $455,000 = $113,750

**Year 2 = 6/28 x $455,000 = $97,500**

If a company has a 4-year asset, the fraction used to determine the depreciation rate at the end of Year 2 would be?

Under the SYD method, the depreciation rate is a fraction that is used as follows

__Numerator - Years remaining in the asset's life__

Denominator - SYD

The denominator is found as follows: (4+3+2+1) OR __n(n+1)__

2

In the formula to find the sum of the digits in the assets life, n represents the number of years. In this case, the total SYD is 10. [4(4+1) = 20/2] Please note, only the numerator changes every year, the denominator stays the same.

In Year 2, the fraction would be 3/10.

Year 1 = 4/10.

**Year 2 = 3/10.**

Year 3 = 2/10.

Year 4 = 1/10.

How are partial-year assets depreciated under the SYD method?

When an asset is purchased during the year, the company must use the depreciation rate for a full consecutive 12 months, even if that 12-month period falls within two different calendar years.