- Depreciation is the decrease in value of an asset over time due to wear and tear. It allows a company to allocate the cost of the asset over its useful life. - There are several methods of calculating depreciation, including straight-line, declining balance, sum-of-years digits, and annuity methods. Each method allocates the depreciation expense differently over the life of the asset. - Public projects are evaluated based on their benefit-cost ratio, which compares the present value of benefits to present value of costs. A project is acceptable if the benefit-cost ratio is equal to or greater than 1.

2. Depreciation
• Any equipment which is purchased today will not work for ever.
– Due to Wear & Tear, Becoming out of Date
• Successful company has to take the decision, when to replace the
old equipment
• Replacement Involves Money.
– This should be internally generated from the earnings of the equipment.
(depreciation Fund).
• Depreciation means decrease in value of any physical asset
with the passage of time.
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3. • Fixed sum is charged as the depreciation amount
throughout the life time.
• Accumulated sum at the end of life is equal to the
purchase value of the asset. MG6863 S.BALAMURUGAN, AP/MECH AAACET
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4. Straight Line Method of Depreciation
• Himalaya Drug Company has just purchased a capsulizing machine for Rs. 10, 00,000.
The plant engineer estimates that the machine has a useful life of 5 years and a salvage
value of Rs. 10,000 at the end of its useful life. Compute the depreciation schedule for
the machine by each of the following depreciation methods : i) Straight line method of
depreciation.
• Solution:
• P = Rs. 10,00,000 n=5 years F = Rs. 10,000
• Depreciation Dt =
𝑷−𝑭
𝒏
= =
10,00,000 − 10,0000
𝟓
= Rs. 1,98,000
End of Year Depreciation (Dt ) Book Value (Bt = Bt-1 - Dt )
0 10,00,000
1 1,98,000 8,02,000
2 1,98,000 6,04,000
3 1,98,000 4,06,000
4 1,98,000 2,08,000
5 1,98,000 10,000
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5. • More realistic approach, the depreciation charges decreases
with the life of the asset which matches the earning potential of
the asset.
• Constant percentage of the book value of the previous period of
the asset will be charged as the depreciation amount for the
current period.
• Depreciation, Dt = K × Bt-1 Book Value (Bt) = Bt-1 - Dt
• Fixed Percentage K = limited to 2/n.
• Generally Assume K = 0.2
Declining Balance method of depreciation
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6. Declining Balance method of depreciation
• A company has purchased an equipment whose first cost is Rs.1,00,000 with an
estimated life of eight years. The estimated salvage value of the equipment at the
end of its lifetime is Rs.20,000. Determine the depreciation charge and book value
at the end of various years using decline balance method of depreciation by
assuming K=0.2
• Solution: P = Rs.1,00,000 F = Rs.20,000 n = 8 Years K=0.2(Assume)
Depreciation, Dt = K × Bt-1 Book Value (Bt) = Bt-1 - Dt
End of Year (n) Depreciation (Dt ) (Rs.) Book Value (Bt) (Rs.)
0 1,00,000
1 1,00,000 × 0.2 = 20,000 10,00,000 - 2,00,000= 80,000
2 80,000 × 0.2 = 16,000 80,000 – 16,000 = 64,000
3 64,000 × 0.2 = 12,800 64,000 – 12,800 = 51,200
4 51,200 × 0.2 = 10,240 51,200-10,240 = 40,960
5 40,960 × 0.2 = 8,192 40,960 – 8,192 = 32,768
6 32,768 × 0.2 = 6,553.60 32,768 – 6,553.60 = 26,214.40
7 26,214.40 × 0.2 = 5,242.88 26,214.40 – 5,242.88 = 20,971.52
8 20,971.52 × 0.2 = 4,194.30 20,971.52 – 4,194.30 = 16,777.22
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7. Sum of Years Digit Method of Depreciation
• In this method, it is assumed that the book value of the asset
decreases at a decreasing rate.
• Step 1 – Find Sum of Years
– Example – 5 Years life
– Sum of Years = 1+2+3+4+5 = 15 =
𝒏(𝒏+𝟏)
𝟐
• Rate of depreciation for the years 1-5 = 5/15, 4/15, 3/15, 2/15, 1/15
• Step 2
– Depreciation, Dt = Rate × (P-F)
– Book Value (Bt) = Bt-1 - Dt
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8. Sum of Years Digit Method of Depreciation
• The cost of the machine is Rs.1,00,000 and its scrap value is Rs.40,000.
Estimate life 5 years. Using sum of years digit method, determine
depreciation charges for each year.
• Solution
– 5 Years life
– Sum of Years = 1+2+3+4+5 = 15 =
𝒏(𝒏+𝟏)
𝟐
– Rate of depreciation for the years 1-5 = 5/15, 4/15, 3/15, 2/15, 1/15
• Depreciation, Dt = Rate × (P-F) Book Value (Bt) = Bt-1 - Dt
End of
Year
Depreciation (Dt )
(Rs.)
Book Value (Bt = Bt-1 - Dt )
(Rs.)
0 - 1,00,000
1 Rate (5/15) = (5/15) × (1,00,000 – 40,000) = 20,000 =1,00,000 –20,000=80,000
2 Rate (4/15) = (4/15) × (1,00,000 – 40,000) = 16,000 = 80,000 – 16,000 = 64,000
3 Rate (3/15) = (3/15) × (1,00,000 – 40,000) = 12,000 = 64,000 – 12,000 = 52,000
4 Rate (2/15) = (2/15) × (1,00,000 – 40,000) = 8,000 = 52,000 – 8,000 = 44,000
5 Rate (1/15) = (1/15) × (1,00,000 – 40,000) = 4,000 = 44,000 – 4,000 = 40,000
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9. Annuity Method or Sinking Fund Method of
Depreciation
• In this method of depreciation, the book value decreases at increasing
rates with respect to the life of the asset.
• Step 1
– Find Equal depreciation amount for Loss in value of asset (P – F)
– A = (P – F) × [A/F, i ,n]
• Step 2
– Depreciation Dt = (P – F) × (A/F, i ,n) × (F/P, i, t – 1)
– Book Value (Bt) = P – (P – F) × (A/F, i ,n) × (F/A, i, t )
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10. Annuity Method or Sinking Fund Method
of Depreciation
• Find the depreciation annuity by Annuity method after three years,
when the initial cost of the machine is Rs.8,00,000 and the salvage
value at the end of three years is Rs.4,00,000. Rate of interest 10%.
• Solution:
• A = (P – F) × (A/F, i ,n)
= (8,00,000 – 4,00,000) × (A/F, 10% ,3) =(4,00,000 × 0.3021)
A = Rs.1,20,840
• Method 1
• Depreciation Dt = (P – F) × (A/F, i ,n) × (F/P, i, t – 1)
At Year 1, D1 = 1,20,840 × (F/P, i, 1 – 1) = Rs. 1,20,840
At Year 2, D2 = 1,20,840 × (F/P, i, 2 – 1) = 1,20,840 × (F/P, i, 1)
= 1,20,840 × (1.100) = Rs. 1,32,924
At Year 2, D2 = 1,20,840 × (F/P, i, 3 – 1) = 1,20,840 × (F/P, i, 2)
= 1,20,840 × (1.210) = Rs. 1,46,216.4MG6863 S.BALAMURUGAN, AP/MECH AAACET
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11. Annuity Method or Sinking Fund Method of Depreciation
• Find the depreciation annuity by Annuity method after three years,
when the initial cost of the machine is Rs.8,00,000 and the salvage
value at the end of three years is Rs.4,00,000. Rate of interest 10%.
• Solution:
• A = (P – F) × (A/F, i ,n)
= (8,00,000 – 4,00,000) × (A/F, 10% ,3) =(4,00,000 × 0.3021)
A = Rs.1,20,840
• Method 2
End of
Year
Fixed
Depreciation
(Rs.)
Net Depreciation (Dt)
(Rs.)
Book Value
(Bt = Bt-1 - Dt )
(Rs.)
0 8,00,000
1 1,20,840 1,20,840 =8,00,000 – 1,20,840 = 679160
2 1,20,840 1,20,840 + 1,20,840(0.10) = 132924 =679160 – 1,32,924 = 546236
3 1,20,840 1,20840 + (1,20,840 + 1,32,924) (0.10)
= 1,46,216.4
=5,46,236 – 1,46,216.4 = 4,00,019.6
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12. Service Output Method of Depreciation
• This method of depreciation based on Service provided by the
asset. Not based on Time Period.
• Depreciation / unit of service =
𝑷−𝑭
𝑿
• Depreciation for x units of service in a period =
𝑷−𝑭
𝑿
(x)
• Example – Printer Toner – Initial Cost (P) – Salvage
Value (F)– Capacity (𝑿)1000 Pages
• At present 500 pages(x) completed,
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13. • The first coat of a road laying machine is Rs.80,00,000. its salvage value after five years is
Rs.50,000. the length of road that can be laid by the machine during its life time is 75,000
km. in its third year of operation, the length of road laid is 2,000 km. Find the
depreciation of the equipment for that year.
• Solution:
• P = 80,00,000, F = Rs.50,000, X = 75,000km, x = 2,000 km
• Depreciation for x units of service in a period =
𝑷−𝑭
𝑿
(x)
• Depreciation for 3 years (or) for 2,000 km =
𝟖𝟎,𝟎𝟎,𝟎𝟎𝟎−𝟓𝟎,𝟎𝟎𝟎
𝟕𝟓,𝟎𝟎𝟎
(2000)
• Depreciation for 3 years (or) for 2,000 km = Rs.2,12,000
Service Output Method of Depreciation
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14. • For private organizations – the selection of alternative is based on
Maximum profit. The main goal is to provide goods/service as per
specifications with Maximum Profit.
• For Public Organizations / Government Organizations / Govt. Projects
• The same condition is not applicable for Evaluation of Public Alternatives.
• The main objective of any public alternative is to provide goods/service to
the public at the minimum cost.
• In this case, the benefits of the public alternative are at least equal to its
costs. (BC ratio = 1 or >1) If yes, then the public alternative can be taken
for implementation.
• BC Ratio =
𝑬𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝑩𝒆𝒏𝒆𝒇𝒊𝒕𝒔
𝑬𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝑪𝒐𝒔𝒕𝒔
=
𝑩 𝑷
𝑷+𝑪𝑷
=
𝑩 𝑭
𝑷 𝑭
+𝑪𝑷
=
𝑩 𝑨
𝑷 𝑨
+𝑪
Evaluation of Public Alternatives
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15. • Two mutually exclusive projects are being considered for investment. Project A1 requires an initial
outlay of Rs. 30, 00,000 with net receipts estimated as Rs. 9, 00,000 per year for the next 5 years.
The initial outlay for the project A2 is Rs. 60, 00,000, and net receipts have been estimated at Rs.
15, 00,000 per year for the next seven years. There is no salvage value associated with either of the
projects. Using the benefit cost ratio, which project would you select? Assume an interest rate of
10%.
• Solution:
Evaluation of Public Alternatives
Alternative A1 Alternative A2
Initial Cost (P) = Rs.30,00,000
Net Benefit / year (B) = Rs.9,00,000
Life (n) = 5 years
Annual Equivalent of Initial Cost = P (A/P, i, n)
= 30,00,000 (A/P, 10%, 5)
= 30,00,000 (0.2638)
= Rs.7,91,400
Benefit – Cost ratio =
𝑨𝒏𝒏𝒖𝒂𝒍 𝑬𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝑩𝒆𝒏𝒆𝒇𝒊𝒕𝒔
𝑨𝒏𝒏𝒖𝒂𝒍 𝑬𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝑪𝒐𝒔𝒕𝒔
=
𝟗,𝟎𝟎,𝟎𝟎𝟎
𝟕,𝟗𝟏,𝟒𝟎𝟎
= 1.137
Initial Cost (P) = Rs.60,00,000
Net Benefit / year (B) = Rs.15,00,000
Life (n) = 7 years
Annual Equivalent of Initial Cost = P (A/P, i, n)
= 60,00,000 (A/P, 10%, 7)
= 60,00,000 (0.2054)
= Rs.12,32,400
Benefit – Cost ratio =
𝑨𝒏𝒏𝒖𝒂𝒍 𝑬𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝑩𝒆𝒏𝒆𝒇𝒊𝒕𝒔
𝑨𝒏𝒏𝒖𝒂𝒍 𝑬𝒒𝒖𝒊𝒗𝒂𝒍𝒆𝒏𝒕 𝑪𝒐𝒔𝒕𝒔
=
𝟏𝟓,𝟎𝟎,𝟎𝟎𝟎
𝟏𝟐,𝟑𝟐,𝟒𝟎𝟎
= 1.217
BC Ratio, Alternative A2 > Alternative A1, So Alternative A2 is selected.
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16. Inflation
• The rise in prices of goods & services in a given
period of a country is called Inflation.
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17. deflation is a decrease in the general price level of goods and services. It occurs when the inflation
rate falls below 0% (a negative inflation rate). Inflation reduces the value of currency over time,
but deflation increases it.
Deflation
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18. MG6863 S.BALAMURUGAN, AP/MECH AAACET
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19. MG6863 S.BALAMURUGAN, AP/MECH AAACET
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