(a)
The
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 |
(b)
The depreciation schedule using straight line depreciation.
Answer to Problem 16P
The depreciation schedule using straight line depreciation is shown below.
| Year (t) | Depreciation dt=B−Sn |
| 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=B−Sn ...... (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=B−Sn |
| 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=B−Sn |
| 1 | $5,000 |
| 2 | $5,000 |
| 3 | $5,000 |
| 4 | $5,000 |
| 5 | $5,000 |
| 6 | $5,000 |
| 7 | $5,000 |
| 8 | $5,000 |
(c)
The depreciation schedule using SOYD.
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=n−t+1SOYD(B−S)dt=n−t+1[n(n+1)2](B−S) ...... (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=8−t+1[8(8+1)2]($50,000−$10,000)=(9−t)36×($40,000)=$1111.11(9−t) ......(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 |
(d)
The depreciation schedule using double declining balance depreciation.
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(B−Depreciation charge up to year t) ...... (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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Chapter 11 Solutions
Engineering Economic Analysis
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