---
title: "Define depreciation; list methods"
subject: "Engineering Economics"
chapter: 7
key: "semester_6/engineering_economics:depreciation-define-methods-list"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/depreciation-define-methods-list
site: BCT Engineering
---

# Define depreciation; list methods

Engineering Economics · Chapter 7: Depreciation and Corporate Income Taxes

- Asked in: 2069 Bhadra, 4 marks
- Video: [#E5 Depreciation | Straight line method | Constant Percentage method | Sinking Fund Method |](https://www.youtube.com/watch?v=pb8uKs5Cn_8) — Kivip Tech 【 Civil Engineering 】
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/depreciation-define-methods-list
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-7

## Question

Define depreciation and list out important methods of calculating depreciation deductions.

## Short answer

Depreciation is the decrease in asset value due to wear, use, and obsolescence, allocated over useful life. Important methods: straight-line, declining balance (including double declining), sum of years’ digits, sinking fund, units of production, MACRS, and depletion.

## Answer

**Depreciation** is the decrease in the value of a physical asset with the passage of time and use, caused by wear, deterioration and obsolescence. In accounting it is the systematic allocation of the cost of the asset (less salvage value) over its useful life, and it is a non-cash expense that is deductible from taxable income.

#### Important methods of calculating depreciation
| Method | Annual depreciation | Nature |
|---|---|---|
| Straight line | (P − S)/N | equal each year |
| Declining balance (and double declining balance, rate 2/N) | R × opening book value | accelerated |
| Sum of years' digits | (P − S)(N − k + 1)/[N(N + 1)/2] | accelerated |
| Sinking fund | (P − S)(A/F,i,N)(F/P,i,k − 1) | small early, large later |
| Unit of production (service output) | (P − S) × units this year / total units | based on use |
| MACRS | cost basis × table percentage | accelerated tax method |
| Depletion (cost or percentage) | for mines, wells and quarries | based on extraction |

Here P is the first cost, S the salvage value, N the useful life, k the year number and i the interest rate.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is depreciation defined?
   A. Decrease in value of an asset with time and use; allocation of cost less salvage; non-cash and tax-deductible
   B. A cash outflow each year
   C. Increase in book value
   D. Purchase price of a new asset
   Answer: A. It is a non-cash deduction from taxable income. (Key point: Definition)

2. Which is the SOYD formula?
   A. (P - S)/N
   B. (P - S)(N - k + 1)/[N(N+1)/2]
   C. R x opening BV
   D. (P - S)(A/F,i,N)(F/P,i,k-1)
   Answer: B. Fraction is largest in year 1. (Key point: SOYD formula)

3. On what is unit-of-production depreciation based?
   A. Years of life
   B. Interest rate
   C. Units produced this year / total expected units
   D. Book value
   Answer: C. It suits machinery whose wear depends on use. (Key point: Unit of production)

4. For which assets is depletion used?
   A. Vehicles
   B. Computers
   C. Buildings
   D. Mines, wells and quarries
   Answer: D. It is based on extraction. (Key point: Depletion)

## Related in Engineering Economics

- [Short note: methods of calculating depreciation](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Ashort-note-depreciation-methods) — Engineering Economics, chapter 7, asked 2×

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