2 Depreciation and Depletion PDF

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Lecture # 2

Depreciation Calculation Fundamentals W BV Co

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Depreciation Methods  Straight Line (SL) Method  Declining – Balance (DB) or

Double Declining Balance (DDB) Method  Unit of production Method

Straight Line Method The annual SL depreciation is determined by multiplying the first cost minus the salvage value by the depreciation rate. Dt = (B - S)d Dt = B – S / n Where Dt depreciation charge for year t (t 1, 2, . . . , n) B = First cost S = Estimated salvage value n = Recovery period d = Depreciation rate 1/n

Example 12-1 First cost, B $ 50,000 Depreciation life, in years, N 5 years Salvage Value $ 10,000 Solution: The depreciation each year for 5 years is Dt = B – S / n Dt = 50,000 – 10,000/5 = $ 8000

Example 12-1 Years

dt

∑dt

0

BV 50,000

1

$8000

$8000

42000

2

$8000

$16000

34000

3

$8000

$24000

26000

4

$8000

$32000

18000

5

$8000

$40000

10000

BV1 = 50,000 – 8000 = 42,000 BV2 = 50,000 – 16,000 = 34,000 . . . BVt = B –∑Dt Bv5 = 50,000 – 40,000 = 10,000

Example 12-1

Declining – Balance (DB) or Double Declining Balance (DDB) Method  Sometimes called fixed percentage or uniform

percentage Method  If DB method is twice the straight line rate. The rate dmax = 2/n called the DDB method  Another commonly used percentage for the DB method is 150% of the SL rate, where d= 1.5/n.

Declining – Balance (DB) or Double Declining Balance (DDB) Method  The depreciation for year “t”is the fixed rate d times the book

value at the end of the previous year. Dt =(d)BVt-1

 Book value in year t is determined by

BVt = B(1 - d )t  DB book value never goes to zero

Declining – Balance (DB) or Double Declining Balance (DDB) Method  Implied salvage value after n years is the BVn amount. Implied S = BVn = B(1 - d)n  If a salvage value is initially estimated, this value is not

used in the DB or DDB method.  If the implied S < estimated S, it is correct to stop charging further depreciation when the book value is at or below the estimated salvage value.

Example 12-2 First cost $80,000 Anticipated life 5 years Salvage value $10,000 Find out: (a) Compare the schedules for annual depreciation and book value using two methods: DB at 150% of the straight line rate and at the DDB rate. (b) How is the estimated $10,000 salvage value used?

Example 12-2 (a)  The DB depreciation rate is d= 1.5/5 = 0.30  while the DDB rate is dmax= 2/5 = 0.40.

Example 12-2 (a) Declining balance d= 0.30 Dt = (d)BVt-1 D1 = 0.30(80,000) = 24,000 D2 = 0.30(56,000) = 16,800 BVt = B(1-d)t BV1 = 80,000(1-0.30)1 =80,000 (0.70)1 = 56,000 BV2 = 80,000(1-0.30)2 = 80,000(0.70)2 = 39,200

Double declining balance d= 0.40 Dt = (d)BVt-1 D2 =0.40( 48,000) = 19,200 D3 = 0.40( 28,800) = 11,520 BVt = B(1-d)t BV2 = 80,000(1-0.40)2 = 80,000(0.60)2 = 28,800 BV3 = 80,000(1-.40)3 =80,000(0.60)3 = 17,280

Example 12-2 (a)

Example 12-2 (b)  The $10,000 salvage value is not utilized by the 150%

DB method since the book value is not reduced this far (BV5 = $13,446)  However, the DDB method reduces book value to $10,368 in year 4. Therefore, not all of the calculated depreciation for year 5, D5 0.40(10,368) $4147, can be removed; only the $368 above S can be written off.

Unit of production Depreciation  Useful is when the recovery of depreciation on an asset

more closely related to use than time.  Not considered an acceptable method for general use

Example A piece of equipment use in a business has a basis of $50,000 and is expected to have a $10,000 SV when replaced after 30,000 hours of use. Find its depreciation rate per hour of use, and find its BV after 10,000 hours of operation. Solution: Dt = 50,000 – 10,000/ 30,000 = $1.33 per hour BV = B – Dt = 50,000 -1.33(10,000) =$36,700

Depletion  Depletion is another method to write off investment

that is applicable only to natural resources.  Depletion is the exhaustion of natural resources as

a result of their removal.  When the resources are removed, they cannot be

replaced or repurchased in the same manner as can a machine, computer, or structure.

Depletion  Depletion is applicable to mines, wells, quarries,

geothermal deposits, forests

 Except for standing timber and most oil and gas wells,

depletion allowance is the larger of the two methods.

Methods of Depletion:  Percentage Depletion  Cost depletion

Percentage depletion  Depletion allowance is a certain percentage of the

property’s gross income during the year.  Cannot exceed 50% of the property’s taxable income computed without the depletion deduction. The annual depletion amount is Percentage depletion amount = percentage × gross income from property

Percentage Depletion Allowance  The annual percentage depletion for some common

natural deposits is listed below. These percentages may change from time to time.

Example 12-5  A gold mine was purchased for $10 million. It has an

anticipated gross income of $8.0 million per year for years 1 to 5 and $5.0 million per year after year 5.  Assume that depletion charges do not exceed 50% of

taxable income. Compute the annual depletion amount and determine how long it will take to recover the initial investment.

Example 12-5 A 15% depletion applies for gold. Years 1 to 5

=

0.15(8.0 million) = $1.2 million

Years thereafter = 0.15(5.0 million) = $750,000 A total of $6 million(1.2×5) is written off in 5 years, and the remaining $4 million is written off at $750,000 per year. Total recovery is attained in 5+ 4 million/750,000 = 5 + 5.3 = 10.3 years

Cost depletion  Cost depletion, also called factor depletion, is based on

the level of activity or usage.(unit of production)  It may be applied to most types of natural resources.  Cost of land must be excluded from the property cost.

Cost depletion The annual cost depletion factor pt is the ratio of the first cost to the estimated number of units recoverable.

 The total cost depletion cannot exceed the first cost of

the resource. If the capacity of the property is re estimated as higher or lower in the future, a new pt is determined based upon the new un depleted amount.

Example 12-6  Temple-Inland Corporation has negotiated the

rights to cut timber on privately held forest acreage for $700,000. An estimated 350 million board feet of lumber are harvestable.  Determine the depletion amount for the first 2 years if 15 million and 22 million board feet are removed.

Example 12-6 Solution:

Multiply pt by the annual harvest to obtain depletion of $30,000(2000 ×15) in year 1 and $44,000 (2000 × 22)in year 2. Continue using pt until a total of $700,000 is written off or the remaining timber requires a re estimate of total board feet harvestable.

Depletion  When allowed by law, the depletion each year may be

determined using either the cost method or the percentage method.  Usually, the percentage depletion amount is chosen because of the possibility of writing off more than the original investment.  However, the law does require that the cost depletion amount be chosen if the percentage depletion is smaller in any year....