Module 11 Depreciation

Module 11: Depreciation SI-4251 Ekonomi Teknik Muhamad Abduh, Ph.D.

Introduction  Asset will eventually loss its value due to age, wear (physical depreciation) and obsolescence (functional depreciation) over its useful life.  The loss of value through the time must be considered in economic evaluation of (asset) investment .  Thus, the loss in capital investment (equipment, building, machinery, vehicle) must be recovered through tax-allowed expense deduction, called deprecation.  The act of recovery loss of value of asset is known as (cost) capital recovery.  EXAMPLE:  2

It is common to consider loss of value of an investment as partSI-4251 of expenses that would bePh.D. Ekonomi Teknik Muhamad Abduh, recovered from revenue (volume x unit price)

Introduction Depreciation ( in relation to business and tax purposes )

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Is an artificial (non cash) accounting entry intended to capture the consumption of a capital asset over its economic life. Depreciation increases after-tax profit

What can be depreciated? Property that meets the following criteria: 

 Used in business and/or held for the production of income  Must expected to last for more than one year (must be substantially beyond the year it was placed in service)  It losses on values caused by natural causes.

What cannot be depreciated?

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    3 

Property put in placed into service and disposed in the same year Land (can never be depreciated) Inventory (property held for resale during the normal course of business) Leased property (in accounting this was placed under SI-4251 Ekonomi TeknikMuhamad Abduh, Ph.D. expenses)

Terminology 

Depreciation (D) aka Capital Recovery

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Book Value (BV)

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Market Value aka Realized Value

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Basis Cost aka First Cost (B) 

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Recovery Period aka Depreciable Life (n)

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Depreciation Rate aka Recovery Rate (d)

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Salvage Value (SV)

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SI-4251 Ekonomi TeknikMuhamad Abduh, Ph.D.

Depreciation BV

B

Book Value

BV 1

D BV 2 BV 3 SV

0 5

1

2

3

4

Time

n

SI-4251 Ekonomi TeknikMuhamad Abduh, Ph.D.

Straight Line Depreciation B − SV Dt = n

B

BV

1 dt = d = n

SV

0

1

2 Where:

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3 t n Dt dt B BVt SV

4 = = = = = = =

n

BVt = BVt −1 − Dt  B − SV  BVt = B − t    n 

year (t = 1, 2, 3, …n) estimated service life annual depreciation depreciation rate (the same for each year) first cost / basis cost book value at end of year t salvage value = BVn SI-4251 Ekonomi TeknikMuhamad Abduh, Ph.D.

Declining Balance Depreciation  In this method, an asset is depreciated faster early than in the latter portion of its service life  The depreciation is calculated based on a fixed percentage of the book value at the D = α .BV t −1 beginning of anyt year of the service life

 since

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

then

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BVt = BVt −1 − Dt BVt = BVt −1 − αBVt −1 = (1 − α ) BVt −1 Dt = α (1 − α ) B t −1

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therefore,

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BVt = (1 − α ) B t

SI-4251 Ekonomi TeknikMuhamad Abduh, Ph.D.

Double Declining Balance Depreciation Under the US tax law, an asset can only be depreciated at the maximum rate of twice the rate 0f straight line depreciation method.  Double declining balance method: 2 α=  

n

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SI-4251 Ekonomi TeknikMuhamad Abduh, Ph.D.

Sum-of-Year-Digits Depreciation Under this method, an asset is depreciated faster on the first one-third of the recovery period.  The depreciation value at any end of the year: D =  n − t + 1( B − SV ) 

  

t

 S  n ( n + 1) S= = dt 2 where

 

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thus

 t ( n − t / 2+ 0.5)  ( B − SV ) BVt = B −   S  

SI-4251 Ekonomi TeknikMuhamad Abduh, Ph.D.

Graphical Representation of Depreciation Methods

Book Value

B SLD

SYD DDB

SV 0 10

1

2

3

4

5

6

n

SI-4251 Ekonomi TeknikMuhamad Abduh, Ph.D.

Exercise A man just bought a Mercedes for Rp 675.000.000,-. He expects to use that car for 6 years after which he hopes to sell it for Rp 450.000.000, Calculate the book value of that piece of car each year for the next six years using SLD, DB @ 175%, and SYD methods EOY SLD DB@175% SYD 

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0 1 2 3 4 5 6 11

Dt

BVt

Dt

BVt

Dt

BVt

SI-4251 Ekonomi TeknikMuhamad Abduh, Ph.D.

Other Reduction in Values of Asset UNITS - OF - PRODUCTION DEPRECIATION

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 Sometimes calculating recovery of capital cost in accordance to theoretical value-time approach is undesirable.  Alternatively, it can be assumed that depreciation occurs based on unit of production  example: 

A tractor was bought 3 years ago for $ 2,400,000. The owners has estimated the equipment to be used for another 4 years, and to be sold for $ 950,000. During 7 years of ownership the tractor is expected to help moving 6 million cm of dirt. If in its 3 years of operation that tractor has excavated 2.5 millions cm of dirt, what is the current book value?

 answer: dv = (B-SV)/Volume = ($2,400,000 - $ 950,000)/6.000.000 = $ 0.24/cm D = dv x Vol = $ 0.24 x 2,500,000 = $ 0.6 25m . millions BV = B – dv x Vol = $ 2,400,000 - $ 0.24 x 2.5 m 25m . 12= $ 1.8 millions SI-4251 Ekonomi TeknikMuhamad Abduh, Ph.D.

Other Reduction in Values of Asset 

DEPLETION

This term refers to activity that tends to exhaust a supply (of resources)

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COST METHOD :  This method is similar to the units-of-product depreciation method, where the depletion charge is based on the amount of resources consumed and the initial investment.  example:  A coal mining site worth $ 3.5 billions is estimated to produce 20 million tons of coal. Last year the mine produce 2,2 million ton of coal.  The unit depletion rate = $ 3.5 billions/20 million tons = $ 175 / ton  Depletion charge = 2.2 million to x $ 175/ton = $ 33 millions 

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PERCENTAGE METHOD :  This method is based on the application of a fixed percentage of depletion rate for individual type of natural resource, e.g., oil, gas. copper, etc. (max charge is 50%)  example:  The fixed percentage of depletion for coal is 10%. The coal can be sold for $ 195 /ton.  The gross depletion income = 2.2 million tons x $ 195 /ton = $ 429 millions.  Depletion rate = 10% x $ 429 millions = $ 42.9 millions  

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SI-4251 Ekonomi TeknikMuhamad Abduh, Ph.D.

Other Reduction in Values of Asset REDUCED BALANCE METHOD

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 This method assumes assets are used more in early years, thus larger depreciation charges made in early years  Depreciation is calculated by applying a fixed rate to the “net book value” (reduced balance) of the asset.  Where: R r = depreciation rate  r = 1− n n = estimated service life C  R = residual value (BVt) C = historic cost (B)  example:  The installed cost of an asphalt mixing plant is $ 1,150,000 and is estimated to serve for 12 years. After 5 years in service this piece of plant has recorded book value of $ 725,000. Calculate the book value at the end of 7th , 10th , and 12th year 

 14

SI-4251 Ekonomi TeknikMuhamad Abduh, Ph.D.

Exercise/Homework 1. A scraper was bought for $ 1,375,000. Service life was estimated

at 12 years, and would then be resold for 485,000. Compute the annual depreciation charge for 4th , 7th , and 10th year using a) straight line and b) double declining balance method. Compare the book value of both method.

2. A gold mine that is estimated to produce 300,000 ounces of gold is purchased for $45 million. The gold can sold for $620 per ounce. If 28,500 ounce was produced this year, what will be the depletion for a) cost depletion, and b) percentage depletion where the fixed percentage for gold is 22,5%? For what price should the gold be sold so that percentage depletion will be advantageous than cost depletion?

3. A truck bought for Rp 675,000,000 was to be used for 6 years on

an average of 2,000 hours per year. So far the truck has accumulated 5,400 operating hours. What was the depreciation charge?

4. An investor is considering to choose applying depreciation method 15

between DDB and SYD for an asset he bought 2 years Abduh, ago for Rp SI-4251 Ekonomi TeknikMuhamad Ph.D. 1,175 million. At that time he estimated the service life of 9