Engineering Economic Analysis
Engineering Economic Analysis
13th Edition
ISBN: 9780190296902
Author: Donald G. Newnan, Ted G. Eschenbach, Jerome P. Lavelle
Publisher: Oxford University Press
Question
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Chapter 11, Problem 16P
To determine

(a)

The depreciation schedule using MACRS depreciation.

Expert Solution
Check Mark

Answer to Problem 16P

The depreciation schedule using MACRS is shown below.

Year (t) MACRS (rt) Cost (B) Depreciation dt=rt×B
1 14.29% $20,000 $7,145
2 24.49% $20,000 $12,245
3 17.49% $20,000 $8,745
4 12.49% $20,000 $6,245
5 8.93% $20,000 $4,465
6 8.92% $20,000 $4,460
7 8.93% $20,000 $4,465
8 4.46% $20,000 $2,230

Explanation of Solution

Given:

Cost of the crystal extraction device is $50,000.

Time period is 8 years.

Salvage value is $10,000.

Concept used:

Write the expression to calculate the depreciation value for the crystal extraction device.

dt=B×rt ...... (I)

Here, the depreciation value is dt, the cost of the crystal extraction device is B and the MACRS percentage is rt.

Calculation:

Crystal extraction device comes under MACRS GDS “all other property not assigned to another class” designation.

Using MACRS GDS 8 year property table calculate the depreciation for the crystal extraction device.

Calculate the depreciation for crystal extraction device.

Substitute $50,000 for B and 14.29% for rt in Equation (I).

dt=$50,000×14.29%=$7,145

Calculate the depreciation for 5 years and enter them in a table below.

Year (t) MACRS (rt) Cost (B) Depreciation dt=rt×B
1 14.29% $20,000 $7,145
2 24.49% $20,000 $12,245
3 17.49% $20,000 $8,745
4 12.49% $20,000 $6,245
5 8.93% $20,000 $4,465
6 8.92% $20,000 $4,460
7 8.93% $20,000 $4,465
8 4.46% $20,000 $2,230

Conclusion:

The depreciation schedule using MACRS is shown below

Year (t) MACRS (rt) Cost (B) Depreciation dt=rt×B
1 14.29% $20,000 $7,145
2 24.49% $20,000 $12,245
3 17.49% $20,000 $8,745
4 12.49% $20,000 $6,245
5 8.93% $20,000 $4,465
6 8.92% $20,000 $4,460
7 8.93% $20,000 $4,465
8 4.46% $20,000 $2,230
To determine

(b)

The depreciation schedule using straight line depreciation.

Expert Solution
Check Mark

Answer to Problem 16P

The depreciation schedule using straight line depreciation is shown below.

Year (t) Depreciation dt=BSn
1 $5,000
2 $5,000
3 $5,000
4 $5,000
5 $5,000
6 $5,000
7 $5,000
8 $5,000

Explanation of Solution

Concept used:

Write the expression to calculate the depreciation value for the crystal extraction device

dt=BSn ...... (II)

Here, the depreciation value is dt, the cost of the crystal extraction device is B, salvage value is S and number of years is n.

Calculation:

Calculate the depreciation for the crystal extraction device.

Substitute $50,000 for B, $10,000 for S and 8 for n in Equation (II).

dt=$50,000$10,0008=$5,000

Calculate the depreciation for 5 years and enter them in a table below.

Year (t) Depreciation dt=BSn
1 $5,000
2 $5,000
3 $5,000
4 $5,000
5 $5,000
6 $5,000
7 $5,000
8 $5,000

Conclusion:

The depreciation schedule using straight line depreciation is shown below.

Year (t) Depreciation dt=BSn
1 $5,000
2 $5,000
3 $5,000
4 $5,000
5 $5,000
6 $5,000
7 $5,000
8 $5,000
To determine

(c)

The depreciation schedule using SOYD.

Expert Solution
Check Mark

Answer to Problem 16P

The depreciation schedule using SOYD is shown below.

Year (t) Depreciation (dt)
1 $8,888.88
2 $7,778
3 $6,667
4 $5,556
5 $4,444
6 $3,333
7 $2,222
8 $1,111

Explanation of Solution

Concept used:

SOYD is known as sum of year’s digits depreciation.

Write the expression to calculate the depreciation of the crystal extraction device.

dt=nt+1SOYD(BS)dt=nt+1[n(n+1)2](BS) ...... (III)

Here, the depreciation value is dt, total number of years is n, cost of the crystal extraction device is B, particular year is t and salvage value after depreciable life is S.

Calculation:

Calculate the depreciation using SOYD for the crystal extraction device.

Substitute 8 for n, $50,000 for B and $10,000 for S in Equation (III).

dt=8t+1[8(8+1)2]($50,000$10,000)=(9t)36×($40,000)=$1111.11(9t) ......(IV)

Calculate the depreciation value for 5 year.

Year (t) Depreciation (dt)
1 $8,888.88
2 $7,778
3 $6,667
4 $5,556
5 $4,444
6 $3,333
7 $2,222
8 $1,111

Here, the depreciation is calculated from Equation (IV).

Conclusion:

The depreciation schedule using SOYD is shown below.

Year (t) Depreciation (dt)
1 $8,888.88
2 $7,778
3 $6,667
4 $5,556
5 $4,444
6 $3,333
7 $2,222
8 $1,111
To determine

(d)

The depreciation schedule using double declining balance depreciation.

Expert Solution
Check Mark

Answer to Problem 16P

The depreciation schedule using double declining balance depreciation is shown below.

Year (t) Depreciation (dt)
1 $12,500
2 $9,375
3 $7,031
4 $5,273.5
5 $3,955.125
6 $2,966.35
7 $2,224.75
8 $1,668.56

Explanation of Solution

Concept used:

Write the expression to calculate the depreciation using double declining balance depreciation

dt=2n(BDepreciationchargeuptoyeart) ...... (V)

Here, the depreciation is dt, number of years is n, cost is B.

Calculation:

Calculate the depreciation of the crystal extraction device for the first year.

Substitute 8 for n, $50,000 for B and 0 for depreciation charge up to year t in Equation (V).

dt=28($50,000$0)=28×$50,000=$12,500

Calculate the depreciation of the crystal extraction device for 5 years and enter it in a table below.

Year (t) Depreciation charge up to year t Depreciation (dt)
1 0 $12,500
2 $12,500 $9,375
3 $21,875 $7,031
4 $28,906 $5,273.5
5 $34,179.5 $3,955.125
6 $38,134.625 $2,966.35
7 $41,101 $2,224.75
8 $43,325.75 $1,668.56

Conclusion:

The depreciation schedule using double declining balance depreciation is shown below.

Year (t) Depreciation (dt)
1 $12,500
2 $9,375
3 $7,031
4 $5,273.5
5 $3,955.125
6 $2,966.35
7 $2,224.75
8 $1,668.56

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