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Depreciation

Depreciation allocates the cost of an asset over its useful life. Straight-line depreciation gives the same depreciation amount each year.

$$D=\frac{C-S}{n}$$

Straight-Line Book Value

A machine costs Php 1,200,000, has a salvage value of Php 200,000, and a life of 10 years. Find the annual depreciation and book value after 4 years.

$$D=\frac{1,200,000-200,000}{10}=100,000$$
$$BV_4=1,200,000-4(100,000)=800,000$$

Final answer: annual depreciation is Php 100,000 and book value after 4 years is Php 800,000.

Exam Generator Problems

Additional board-style practice items for this topic.

Question Bank: q229

MSTE - Engineering Economy / Depreciation / Engr. Janclyde Espinosa (Clidez)

Using a straight line method of depreciation, find the annual depreciation and book value at the end of the 3rd year for a truck loader having an initial cost of P50,000, a salvage value of P5,000, and an expected life of 5 years.

Answer:

  1. Annual depreciation = 9000, BV at the end of the 3rd year = 23000
  2. Annual depreciation = 8000, BV at the end of the 3rd year = 23000
  3. Annual depreciation = 9000, BV at the end of the 3rd year = 24000
  4. Annual depreciation = 8000, BV at the end of the 3rd year = 24000
Annual SL depreciation: $d = \frac{C_o - S}{n} = \frac{50{,}000 - 5{,}000}{5} = $ P9,000/yr
Book value at end of Year 3: $BV_3 = 50{,}000 - 3 \times 9{,}000 = 50{,}000 - 27{,}000$
$\boxed{BV_3 = \text{P}23{,}000}$

Question Bank: q230

MSTE - Engineering Economy / Depreciation / Engr. Janclyde Espinosa (Clidez)

CE Board May 2019
A machine was purchased at an original cost of P400,000 with a salvage value of P20,000. Life of this machine is expected to last for 6 years. It was used for 4000 hrs. in the first year, 6000 hrs. in the second year, and 8000 hrs. on the 3rd year. The machine is expected to last for 38000 hrs. in a period of 6 yrs.
Which of the following gives the depreciation at the end of the second year?

Answer:

  1. 60000
  2. 70000
  3. 65000
  4. 75000
Method: Units of Production (hours)
$C_o = $ P400,000; $S = $ P20,000; total life = 38,000 hrs
Depreciation rate = $\frac{400{,}000 - 20{,}000}{38{,}000} = \frac{380{,}000}{38{,}000} = $ P10/hr
Hours in Year 2 = 6,000 hrs
Depreciation$_2 = 6{,}000 \times 10$
$\boxed{= \text{P}60{,}000}$

Question Bank: q231

MSTE - Engineering Economy / Depreciation / Engr. Janclyde Espinosa (Clidez)

A truck loader has an initial cost of 50,000 dollars and a salvage value of 5000 dollars. Its expected life is 5 years. Find the book value of the truck loader at the end of its life. Use sum of years digit method.

Answer:

  1. 5000
  2. 45000
  3. 6000
  4. 44000
By definition, any depreciation method (SYD, SL, DDB, etc.) depreciates the asset
from its initial cost $C_o$ to its salvage value $S$ over its estimated life.
At end of life (year 5): $BV_5 = S$
$\boxed{BV_5 = \$5{,}000 = \text{salvage value}}$

Question Bank: q232

MSTE - Engineering Economy / Depreciation / Engr. Janclyde Espinosa (Clidez)

A truck loader has an initial cost of 50,000 dollars and a salvage value of 5000 dollars. Its expected life is 5 years. Find the book value at the end of the third year. Use Double Declining Balance Method.

Answer:

  1. 10800
  2. 72000
  3. 12300
  4. 71500
$C_o = \$50{,}000$; $S = \$5{,}000$; $n = 5$ yr; DDB rate $= \frac{2}{n} = \frac{2}{5} = 40\%$
Year 1: $d_1 = 0.40 \times 50{,}000 = 20{,}000$; $BV_1 = 30{,}000$
Year 2: $d_2 = 0.40 \times 30{,}000 = 12{,}000$; $BV_2 = 18{,}000$
Year 3: $d_3 = 0.40 \times 18{,}000 = 7{,}200$; $BV_3 = 18{,}000 - 7{,}200$
$\boxed{BV_3 = \$10{,}800}$

Question Bank: q233

MSTE - Engineering Economy / Depreciation / Engr. Janclyde Espinosa (Clidez)

A truck loader has an initial cost of 50,000 dollars and a salvage value of 5000 dollars. Its expected life is 5 years. Find the book value at the end of the third year. Use the Modified Accelerated Cost Recovery System (MACRS) method.

Answer:

  1. 14400
  2. 35600
  3. 10000
  4. 9600
For 5-year MACRS property, the first three depreciation rates are 20%, 32%, and 19.2%. Accumulated depreciation after year 3 is:
$50{,}000(0.20+0.32+0.192)=35{,}600$
Book value:
$50{,}000-35{,}600=14{,}400$
$\boxed{14400}$

Question Bank: q234

MSTE - Engineering Economy / Depreciation / Engr. Janclyde Espinosa (Clidez)

A truck loader has an initial cost of 50,000 dollars and a salvage value of 5000 dollars. Its expected life is 5 years. Find the book value at the end of the third year using declining balance method.

Answer:

  1. 12502.35
  2. 37497.65
  3. 12205.53
  4. 37947.56
Using the declining-balance rate based on the given cost, salvage, and life gives a rate of about 37% per year. Book value after 3 years:
$BV_3=50{,}000(1-0.37)^3$
$\boxed{BV_3\approx12502.35}$

Question Bank: q235

MSTE - Engineering Economy / Depreciation / Engr. Janclyde Espinosa (Clidez)

A machine costs P200,000 with a salvage value of P15,000 at the end of its life of 8 years. Determine the book value of the machine at the end of 6 years using Sinking Fund Method if money is worth 6%.

Answer:

  1. 69619.86
  2. 61916.86
  3. 18691.64
  4. 130380.14
For sinking fund depreciation, accumulated depreciation after 6 years is:
$D_6=(C-S)\frac{(1+i)^6-1}{(1+i)^8-1}$
$D_6=(200{,}000-15{,}000)\frac{(1.06)^6-1}{(1.06)^8-1}$
Book value:
$BV_6=200{,}000-D_6$
$\boxed{69619.86}$

Question Bank: t1066

MSTE - Engineering Economy / Engineering Economy / Gemini mapped Chapter 7 to 10

A machine costing P620,000 is estimated to have a salvage value of P320,000 when retired at the end of 5 years. Depreciation cost is computed using a constant percentage of the declining book value. What is the annual rate of depreciation in %?

  1. 14.57%
  2. 11.47%
  3. 10.24%
  4. 12.39%

Solution pending in psadquestions/t1066.json.

Question Bank: t1073

MSTE - Engineering Economy / Engineering Economy / Gemini mapped Chapter 7 to 10

A machine costing P550,000 has an estimate scrap value of P85,000 at the end of its economic life of 8 years. Using the Double-Declining Balance Method of depreciation, what is its book value after four years of service?

  1. P130,518
  2. P174023
  3. P216,217
  4. P214167
Double-declining rate $= \dfrac{2}{n} = \dfrac{2}{8} = 0.25$ (scrap value is not used in the DDB book-value formula):
$$BV_4 = FC(1 - 0.25)^4 = 550{,}000(0.75)^4$$
$$\boxed{BV_4 = \text{P}174{,}023}$$

Question Bank: t2114

MSTE - Engineering Economy / Depreciation / Besavilla CE Pre-Board Math & Surveying

A new bldg. costing P300M, excluding equipment, has an estimated useful life of 40 yrs., with no salvage value. The equipment cost P50M and has an estimated useful life of 15 yrs. with a salvage value of P5M. Using straight line method, what will be the book value of the bldg. and equipment at the end of 10 yrs.

  1. P245M
  2. P232M
  3. P248M
  4. P237M
  5. P240M
Use straight-line depreciation separately for the building and equipment.
Building annual depreciation: $\frac{300-0}{40}=7.5$ M/yr
Building book value after 10 years: $300-10(7.5)=225$ M
Equipment annual depreciation: $\frac{50-5}{15}=3$ M/yr
Equipment book value after 10 years: $50-10(3)=20$ M
Total book value $=225+20$
$\boxed{\text{P}245\text{M}}$

Question Bank: w40

MSTE - Engineering Economy / Depreciation / MSTE May 2019

A machine was purchased at an original cost of P400,000 with a salvage value of P20,000. The life of this machine is expected to last for 6 years. It was used for 4000 hours in the first year, 6000 hours in the second year, and 6000 hours in the third year. The machine is expected to last for 38000 hours in the period of 6 years. Which of the following gives the depreciation at the end of the second year?

  1. P300,000
  2. P100,000
  3. P200,000
  4. P150,000
Depreciation per hour:
$d = \frac{400{,}000 - 20{,}000}{38{,}000} = P\,10/\text{hr}$
Hours used in 2 years $= 4000 + 6000 = 10{,}000\text{ hrs}$
Depreciation $= 10{,}000 \times 10 = \boxed{P\,100{,}000}$

Problem: Straight-Line Depreciation

An asset costs P900,000, has salvage P120,000, and life 8 years. Find annual depreciation.

$$D=\frac{900000-120000}{8}=97500$$

Answer: Annual depreciation is P97,500.

Problem: Straight-Line Book Value

Using annual depreciation P97,500 on a P900,000 asset, find book value after 5 years.

$$BV_5=900000-5(97500)=412500$$

Answer: Book value is P412,500.

Problem: Sum-of-Years Digits Fraction

For a 5-year asset, find the SYD depreciation fraction for year 2.

$$SYD=\frac{5(6)}{2}=15,\qquad \text{Year 2 fraction}=\frac{4}{15}$$

Answer: The year-2 SYD fraction is 4/15.

Problem: Double-Declining Balance Rate

Find the double-declining balance rate for an asset with 10-year life.

$$r=\frac{2}{n}=\frac{2}{10}=0.20$$

Answer: The DDB rate is 20% per year.

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