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 1P
To determine

The depreciation and book value over the asset’s 10 year life of use in a table.

Expert Solution & Answer
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Answer to Problem 1P

The depreciation and book value over the asset’s 10 year life of use in a table is shown below.

Year (t) MACRS (rt) Cost basis (B) Depreciation dt=rt×B CumulativeDepreciation (Cumdt) Book value at the end of the year BVt=BCumdt
1 14.29% $20,000 $2,858 $2,858 $17,142
2 24.49% $20,000 $4,898 $7,756 $12,244
3 17.49% $20,000 $3,498 $11,254 $8,746
4 12.49% $20,000 $2,498 $13,752 $6,248
5 8.93% $20,000 $1,786 $15,538 $4,462
6 8.92% $20,000 $1,784 $17,322 $2,678
7 8.93% $20,000 $1,786 $19,108 $892
8 4.46% $20,000 $892 $20,000 $0
Total 100% $20,000

Explanation of Solution

Given:

The cost basis of the asset is $20,000.

Concept used:

MACRS is known as modified accelerated cost recovery system and is a modified method to calculate depreciation.

Write the expression to calculate the depreciation value.

dt=B×rt ...... (I)

Here, the depreciation value is dt, the cost is B and the MACRS percentage is rt.

Write the expression to calculate the book value at the end of the year.

BV=BCumdt ...... (II)

Here, book value at the end of the year is BV, cost is B, and the cumulative depreciation is Cumdt.

Calculation:

The asset fits into MACRS “all property not assigned to another class” designation. Thus it is considered as 7 year property. Use MACRS GDS 7 year property percentages.

Calculate the depreciation.

Substitute $20,000 for B and 14.29% for rt in Equation (I).

dt=$20,000×14.29%=$2,858

Calculate the book value at the end of the year.

Substitute $20,000 for B and $2,858 for Cumdt in Equation (II).

BV=$20,000$2,858=$17,142

Calculate the depreciation and book value for 7 years and enter them in a table below.

Year (t) MACRS (rt) Cost basis (B) Depreciation dt=rt×B CumulativeDepreciation (Cumdt) Book value at the end of the year BVt=BCumdt
1 14.29% $20,000 $2,858 $2,858 $17,142
2 24.49% $20,000 $4,898 $7,756 $12,244
3 17.49% $20,000 $3,498 $11,254 $8,746
4 12.49% $20,000 $2,498 $13,752 $6,248
5 8.93% $20,000 $1,786 $15,538 $4,462
6 8.92% $20,000 $1,784 $17,322 $2,678
7 8.93% $20,000 $1,786 $19,108 $892
8 4.46% $20,000 $892 $20,000 $0
Total 100% $20,000

Conclusion:

The depreciation and book value over the asset’s 10 year life of use in a table is shown below.

Year (t) MACRS (rt) Cost basis (B) Depreciation dt=rt×B CumulativeDepreciation (Cumdt) Book value at the end of the year BVt=BCumdt
1 14.29% $20,000 $2,858 $2,858 $17,142
2 24.49% $20,000 $4,898 $7,756 $12,244
3 17.49% $20,000 $3,498 $11,254 $8,746
4 12.49% $20,000 $2,498 $13,752 $6,248
5 8.93% $20,000 $1,786 $15,538 $4,462
6 8.92% $20,000 $1,784 $17,322 $2,678
7 8.93% $20,000 $1,786 $19,108 $892
8 4.46% $20,000 $892 $20,000 $0
Total 100% $20,000

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