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Sum-of-Years’-Digits Example. Assume depreciable asset is a car with:. 4 year useful life Original cost of $22,000 Salvage Value of $7,000. First, compute Depreciable Base = Cost – Salvage Value. = $22,000 - $7,000. = $15,000. Then, depreciate base x Sum of Years’ Digits Multiplier.

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slide1

Sum-of-Years’-Digits Example

  • Assume depreciable asset is a car with:
  • 4 year useful life
  • Original cost of $22,000
  • Salvage Value of $7,000

First, compute Depreciable Base = Cost – Salvage Value

= $22,000 - $7,000

= $15,000

Then, depreciate base x Sum of Years’ Digits Multiplier

slide2

Sum-of-Years’-Digits Example

Sum of Year’s Digits

slide3

Sum-of-Years’-Digits Example

This was corrected on July 16, 2002.

Depr. Fraction = Remaining Life/Sum of Years’ Digits

slide4

Sum-of-Years’-Digits Example

This was corrected on July 16, 2002.

slide5

Sum-of-Years’-Digits Example

This was corrected on July 16, 2002.

slide6

Sum-of-Years’-Digits Example

This was corrected on July 16, 2002.

slide7

Sum-of-Years’-Digits Example

This was corrected on July 16, 2002.

slide8

Double Declining Balance Example

  • Assume depreciable asset is a car with:
  • 4 year useful life
  • Original cost of $22,000
  • Salvage Value of $7,000
slide9

Double Declining Balance Example

Straight Line %age = 100%/Useful Life

slide11

Double Declining Balance Example

Start with cost (not cost – salvage value)

slide14

Double Declining Balance Example

Too much depreciation—below salvage value!

slide15

Double Declining Balance Example

Throw out these final year computed values.

slide16

Double Declining Balance Example

Make this enough to arrive exactly at ending salvage value.

slide17

Double Declining Balance Example

Note that depreciation is complete after two years even

though asset has four year useful life.

slide18

Partial Period Depreciation

Note that the prior examples assumed that the assets were put in use on January 1st of the year they were bought for use. Therefore, we took a full first year of depreciation expense.

In reality, assets are usually put into use at all times throughout the year. So, we need to prorate the first year’s depreciation expense and adjust the following years’ depreciation expense accordingly.

slide19

Partial Period Depreciation

This is easy to do with straight-line:

JoePa bought a car for $20,000, 4 yr. life, $4,000 salvage value. He started driving the car on July 1.

Normal annual depreciation = $16,000 / 4 = $4,000 per year

Year 1 use = 6 months/12 months = ½ year

slide20

Partial Period Depreciation

This is easy to do with straight-line:

JoePa bought a car for $20,000, 4 yr. life, $4,000 salvage value. He started driving the car on July 1.

Normal annual depreciation = $16,000 / 4 = $4,000 per year

slide21

Partial Period Depreciation

This is easy to do with straight-line:

JoePa bought a car for $20,000, 4 yr. life, $4,000 salvage value. He started driving the car on July 1.

Normal annual depreciation = $16,000 / 4 = $4,000 per year

slide22

Partial Period Depreciation

This is easy to do with straight-line:

JoePa bought a car for $20,000, 4 yr. life, $4,000 salvage value. He started driving the car on July 1.

Normal annual depreciation = $16,000 / 4 = $4,000 per year

slide23

Partial Period Depreciation

This is easy to do with straight-line:

JoePa bought a car for $20,000, 4 yr. life, $4,000 salvage value. He started driving the car on July 1.

Normal annual depreciation = $16,000 / 4 = $4,000 per year

slide24

Partial Period Depreciation

This is easy to do with straight-line:

JoePa bought a car for $20,000, 4 yr. life, $4,000 salvage value. He started driving the car on July 1.

Normal annual depreciation = $16,000 / 4 = $4,000 per year

slide25

Partial Period Depreciation

This is easy to do with straight-line:

JoePa bought a car for $20,000, 4 yr. life, $4,000 salvage value. He started driving the car on July 1.

Normal annual depreciation = $16,000 / 4 = $4,000 per year

slide26

Partial Period Depreciation

This is harder to do with accelerated (Sum-of-Year’s Digits or Double-Declining Balance):

The idea for prorating in a partial period asset placement is the same regardless of the method used for accelerated depreciation.

slide27

Partial Period Depreciation

This is harder to do with accelerated (Sum-of-Year’s Digits or Double-Declining Balance):

First, compute normal annual depreciation as if the asset were used the entire year.

Example: JoePa bought a car for $20,000, 4 yr. life, $4,000 salvage value. He started driving the car on July 1. He uses double-declining balance method.

slide28

Partial Period Depreciation

Example: JoePa bought a car for $20,000, 4 yr. life, $4,000 salvage value. He started driving the car on July 1. He uses double-declining balance method.

slide29

Partial Period Depreciation

Example: JoePa bought a car for $20,000, 4 yr. life, $4,000 salvage value. He started driving the car on July 1. He uses double-declining balance method.

slide30

Partial Period Depreciation

Example: JoePa bought a car for $20,000, 4 yr. life, $4,000 salvage value. He started driving the car on July 1. He uses double-declining balance method.

slide31

Partial Period Depreciation

Example: JoePa bought a car for $20,000, 4 yr. life, $4,000 salvage value. He started driving the car on July 1. He uses double-declining balance method.

Since the car was place in service for only ½ the first year, we need to prorate and adjust the depreciation schedule.

We effectively do this by taking ½ the first year’s depreciation, and then rolling the rest of the depreciation schedule forward.

slide32

Partial Period Depreciation

Example: JoePa bought a car for $20,000, 4 yr. life, $4,000 salvage value. He started driving the car on July 1. He uses double-declining balance method.

Normal Schedule

½ Use First Year Schedule

slide33

Partial Period Depreciation

First, take ½ of the first year’s normal depreciation.

Normal Schedule

½ Use First Year Schedule

x 1/2

slide34

Partial Period Depreciation

First, take ½ of the first year’s normal depreciation. Then roll forward the second ½ of the first year’s normal depreciation.

Normal Schedule

½ Use First Year Schedule

x 1/2

slide35

Partial Period Depreciation

Then add ½ of the second year’s normal depreciation to the roll forward amount.

Normal Schedule

½ Use First Year Schedule

x 1/2

slide36

Partial Period Depreciation

Then add ½ of the second year’s normal depreciation to the roll forward amount.

Normal Schedule

½ Use First Year Schedule

slide37

Partial Period Depreciation

Then roll forward ½ of the second year’s normal depreciation to the third year schedule.

Normal Schedule

½ Use First Year Schedule

x 1/2

slide38

Partial Period Depreciation

Then add ½ of the third year’s normal depreciation to the roll forward amount.

Normal Schedule

½ Use First Year Schedule

x 1/2

slide39

Partial Period Depreciation

Then add ½ of the third year’s normal depreciation to the roll forward amount.

Normal Schedule

½ Use First Year Schedule

slide40

Partial Period Depreciation

Finally, roll forward ½ of the third year’s normal depreciation to the fourth year schedule.

Normal Schedule

½ Use First Year Schedule

x 1/2

slide41

Yr 1

Yr 2

Yr 3

Yr 4

Partial Period Depreciation

Another way to look at it conceptually is with a timeline.

slide42

Yr 1

Yr 2

Yr 3

Yr 4

Partial Period Depreciation

Another way to look at it conceptually is with a timeline.

$10,000

$5,000

$1,000

slide43

Yr 1

Yr 2

Yr 3

Yr 4

Partial Period Depreciation

Another way to look at it conceptually is with a timeline.

$10,000

$5,000

$1,000

$5,000

$5,000

slide44

Yr 1

Yr 1

Yr 2

Yr 2

Yr 3

Yr 3

Yr 4

Yr 4

Partial Period Depreciation

Another way to look at it conceptually is with a timeline.

$10,000

$5,000

$1,000

$5,000

$5,000

slide45

Yr 1

Yr 1

Yr 2

Yr 2

Yr 3

Yr 3

Yr 4

Yr 4

Partial Period Depreciation

Another way to look at it conceptually is with a timeline.

$10,000

$5,000

$1,000

$5,000

$5,000

$5,000

slide46

Yr 1

Yr 1

Yr 2

Yr 2

Yr 3

Yr 3

Yr 4

Yr 4

Partial Period Depreciation

Another way to look at it conceptually is with a timeline.

$10,000

$5,000

$1,000

$5,000

$5,000

$5,000

$5,000

slide47

Yr 1

Yr 1

Yr 2

Yr 2

Yr 3

Yr 3

Yr 4

Yr 4

Partial Period Depreciation

Another way to look at it conceptually is with a timeline.

$10,000

$5,000

$1,000

$2,500

$2,500

$5,000

$5,000

slide48

Yr 1

Yr 1

Yr 2

Yr 2

Yr 3

Yr 3

Yr 4

Yr 4

Partial Period Depreciation

Another way to look at it conceptually is with a timeline.

$10,000

$5,000

$1,000

$2,500

$2,500

$5,000

$5,000

$2,500

$2,500

slide49

Yr 1

Yr 1

Yr 2

Yr 2

Yr 3

Yr 3

Yr 4

Yr 4

Partial Period Depreciation

Another way to look at it conceptually is with a timeline.

$10,000

$5,000

$1,000

$2,500

$2,500

$5,000

$5,000

$2,500

$2,500

$7,500

slide50

Yr 1

Yr 1

Yr 2

Yr 2

Yr 3

Yr 3

Yr 4

Yr 4

Partial Period Depreciation

Another way to look at it conceptually is with a timeline.

$10,000

$5,000

$1,000

$500

$500

$5,000

$7,500

$2,500

slide51

Yr 1

Yr 1

Yr 2

Yr 2

Yr 3

Yr 3

Yr 4

Yr 4

Partial Period Depreciation

Another way to look at it conceptually is with a timeline.

$10,000

$5,000

$1,000

$500

$500

$5,000

$7,500

$2,500

$500

$500

slide52

Yr 1

Yr 1

Yr 2

Yr 2

Yr 3

Yr 3

Yr 4

Yr 4

Partial Period Depreciation

Another way to look at it conceptually is with a timeline.

$10,000

$5,000

$1,000

$5,000

$7,500

$3,000

$500

slide53

Fixed Asset Impairment Example

  • Assume Company A has equipment:
  • Original cost of $120,000
  • Accumulated depreciation of $20,000
  • Market value of $97,000
  • Market interest rate of 8%
  • Expected cash flows:
    • $24,000 for four years (paid at end of yr.)
slide54

Fixed Asset Impairment Example

Recoverability Test (do we need to record an impairment?)

  • Book value = $120,000 – 20,000 = $100,000

Orig. Cost

Accum. Depr.

slide55

Fixed Asset Impairment Example

Recoverability Test (do we need to record an impairment?)

  • Book value = $120,000 – 20,000 = $100,000
  • Net future cash flows = $24,000 x 4 = $96,000

Not discounted for interest rate

slide56

Fixed Asset Impairment Example

Recoverability Test (do we need to record an impairment?)

  • Book value = $120,000 – 20,000 = $100,000
  • Net future cash flows = $24,000 x 4 = $96,000
  • NFCF < BV, so we need to record an impairment
slide57

Fixed Asset Impairment Example

Recoverability Test (do we need to record an impairment?)

  • Book value = $120,000 – 20,000 = $100,000
  • Net future cash flows = $24,000 x 4 = $96,000
  • NFCF < BV, so we need to record an impairment

Amount of Impairment Loss

  • Market value is determinable, so use BV – FMV:
  • $100,000 - $97,000 = $3,000
slide58

Fixed Asset Impairment Example

Recoverability Test (do we need to record an impairment?)

  • Book value = $120,000 – 20,000 = $100,000
  • Net future cash flows = $24,000 x 4 = $96,000
  • NFCF < BV, so we need to record an impairment

Amount of Impairment Loss

  • Market value is determinable, so use BV – FMV:
  • $100,000 - $97,000 = $3,000

3/31 Loss on Impairment 3,000

Accum. Depr, Equipment 3,000

Note: Record impairment to equipment

slide59

Fixed Asset Impairment Example

Recoverability Test (do we need to record an impairment?)

  • Book value = $120,000 – 20,000 = $100,000
  • Net future cash flows = $24,000 x 4 = $96,000
  • NFCF < BV, so we need to record an impairment

Amount of Impairment Loss

  • Market value is determinable, so use BV – FMV:
  • $100,000 - $97,000 = $3,000
  • If FMV is undeterminable, use BV – Discounted CF
slide60

1/1/01

12/31/01

12/31/02

12/31/03

12/31/04

Fixed Asset Impairment Example

Discounted Cash Flows

slide61

1/1/01

12/31/01

12/31/02

12/31/03

12/31/04

Fixed Asset Impairment Example

Discounted Cash Flows

$24,000

$24,000

$24,000

$24,000

slide62

1/1/01

12/31/01

12/31/02

12/31/03

12/31/04

1

Each year’s discount rate =

(1 + int rate)year

Fixed Asset Impairment Example

Discounted Cash Flows

$24,000

$24,000

$24,000

$24,000

slide63

1/1/01

12/31/01

12/31/02

12/31/03

12/31/04

x

x

x

x

1

1

1

1

1

Each year’s discount rate =

(1.08)3

(1.08)1

(1.08)2

(1.08)4

(1 + int rate)year

Fixed Asset Impairment Example

Discounted Cash Flows

$24,000

$24,000

$24,000

$24,000

slide64

1/1/01

12/31/01

12/31/02

12/31/03

12/31/04

1

(1.08)1

Fixed Asset Impairment Example

Discounted Cash Flows

$24,000

$24,000

$24,000

$24,000

x 0.926

x 0.857

x 0.794

x 0.735

slide65

1/1/01

12/31/01

12/31/02

12/31/03

12/31/04

Fixed Asset Impairment Example

Discounted Cash Flows

$24,000

$24,000

$24,000

$24,000

x 0.926

x 0.857

x 0.794

x 0.735

= 22,224

= 20,568

= 19,056

= 17,640

slide66

1/1/01

12/31/01

12/31/02

12/31/03

12/31/04

Fixed Asset Impairment Example

Discounted Cash Flows

$24,000

$24,000

$24,000

$24,000

x 0.926

x 0.857

x 0.794

x 0.735

= 22,224

= 20,568

= 19,056

= 17,640

Net Discounted Cash Flows = 22,224 + 20,568 + 19,056 + 17,640 = $79,488

slide67

1/1/01

12/31/01

12/31/02

12/31/03

12/31/04

Fixed Asset Impairment Example

Discounted Cash Flows

$24,000

$24,000

$24,000

$24,000

x 0.926

x 0.857

x 0.794

x 0.735

= 22,224

= 20,568

= 19,056

= 17,640

Net Discounted Cash Flows = 22,224 + 20,568 + 19,056 + 17,640 = $79,488

Note: We can arrive at the same answer by using the Annuity formula:

slide68

Fixed Asset Impairment Example

Present Value of $1 Annuity

slide69

Fixed Asset Impairment Example

Present Value of $1 Annuity

slide70

1/1/01

12/31/01

12/31/02

12/31/03

12/31/04

Fixed Asset Impairment Example

Discounted Cash Flows

$24,000

$24,000

$24,000

$24,000

x 0.926

x 0.857

x 0.794

x 0.735

= 22,224

= 20,568

= 19,056

= 17,640

Net Discounted Cash Flows = 22,224 + 20,568 + 19,056 + 17,640 = $79,488

Note: We can arrive at the same answer by using the Annuity formula:

$24,000 x 3.312 = $79,488

slide71

Fixed Asset Impairment Example

Recoverability Test (do we need to record an impairment?)

  • Book value = $120,000 – 20,000 = $100,000
  • Net future cash flows = $24,000 x 4 = $96,000
  • NFCF < BV, so we need to record an impairment

Amount of Impairment Loss

  • Market value is determinable, so use BV – FMV:
  • $100,000 - $97,000 = $3,000
  • If FMV is undeterminable, use BV – Discounted CF:
  • $100,000 – 79,488 = $20,512
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