---
title: "Depreciation and book value by four methods"
subject: "Engineering Economics"
chapter: 7
key: "semester_6/engineering_economics:depreciation-sl-db-soyd-sf-7000"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/depreciation-sl-db-soyd-sf-7000
site: BCT Engineering
---

# Depreciation and book value by four methods

Engineering Economics · Chapter 7: Depreciation and Corporate Income Taxes

- Asked in: 2072 Asoj, 1+2+3+2 marks
- Video: [Engineering Economy - Four Depreciation Methods](https://www.youtube.com/watch?v=d_YBhDsdDgY) — Adair Garrett
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/depreciation-sl-db-soyd-sf-7000
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-7

## Question

Considering the following information, compute the annual depreciation and book value of each year by (i) SL method (ii) DB method (iii) SOYD method and (iv) Sinking fund method.
| Cost basis | Salvage Value | Useful Life | MARR |
|---|---|---|---|
| \$ 7,000 | \$ 2,000 | 5 years | 10% |

## Short answer

SL: $1,000/yr, BV $6,000 to $2,000. DB (22.16%): $1,551, $1,208, $940, $732, $569, BV ends $2,000. SOYD: $1,667, $1,333, $1,000, $667, $333. Sinking fund (10%): $819, $901, $991, $1,090, $1,199. All end with BV $2,000.

## Answer

Data: cost basis P = \$7,000; salvage S = \$2,000; N = 5; depreciable amount P − S = \$5,000; MARR (sinking-fund rate) = 10%.

#### (i) Straight line
D = (7,000 − 2,000)/5 = **\$1,000 per year**. BV_k = 7,000 − 1,000k.

#### (ii) Declining balance
The rate that brings the book value to S is R = 1 − (S/P)^(1/N) = 1 − (2,000/7,000)^(1/5) = 1 − 0.7784 = **22.16%**. D_k = R × BV_(k−1). Year 1: 0.2216 × 7,000 = 1,551; BV₁ = 5,449.

#### (iii) Sum of years' digits
Sum = 5(6)/2 = 15. D_k = 5,000 × (6 − k)/15: 1,667; 1,333; 1,000; 667; 333.

#### (iv) Sinking fund (10%)
Deposit = 5,000(A/F,10%,5) = 5,000(0.16380) = 819. D_k = 819(1.10)^(k−1).

#### Summary (depreciation D and end-of-year book value BV, in \$)
| Year | SL D | SL BV | DB D | DB BV | SOYD D | SOYD BV | SF D | SF BV |
|---|---|---|---|---|---|---|---|---|
| 1 | 1,000 | 6,000 | 1,551 | 5,449 | 1,667 | 5,333 | 819 | 6,181 |
| 2 | 1,000 | 5,000 | 1,208 | 4,241 | 1,333 | 4,000 | 901 | 5,280 |
| 3 | 1,000 | 4,000 | 940 | 3,301 | 1,000 | 3,000 | 991 | 4,289 |
| 4 | 1,000 | 3,000 | 732 | 2,569 | 667 | 2,333 | 1,090 | 3,199 |
| 5 | 1,000 | 2,000 | 569 | 2,000 | 333 | 2,000 | 1,199 | 2,000 |

All four methods end with BV = \$2,000 at year 5. DB and SOYD are accelerated (large early charges); the sinking-fund method gives small early and large late charges.

## Check yourself

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

1. What is SL depreciation for P = 7,000, S = 2,000, N = 5?
   A. $1,000 per year
   B. $1,400
   C. $1,800
   D. $800
   Answer: A. (7,000 - 2,000)/5 = 1,000. (Key point: Straight line)

2. How is the DB rate that reaches S found?
   A. R = 2/N
   B. R = 1 - (S/P)^(1/N) = 22.16%
   C. R = (P - S)/P
   D. R = 1/N
   Answer: B. This fixed rate brings book value to S at year N. (Key point: DB rate)

3. What is SOYD depreciation in year 1?
   A. $1,000
   B. $1,333
   C. $1,667
   D. $2,500
   Answer: C. 5,000 x 5/15 = 1,667. (Key point: SOYD year 1)

4. Which method gives small early and large late charges?
   A. SOYD
   B. Declining balance
   C. Straight line
   D. Sinking fund (819 rising to 1,199)
   Answer: D. Sinking fund charge grows by factor 1.10 each year. (Key point: Sinking fund)

## Related in Engineering Economics

- [Book value by SOYD and sinking fund](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Abook-value-soyd-sinking-fund) — Engineering Economics, chapter 7
- [After-tax cash flow, sinking fund depreciation](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aaftertax-cash-flow-sinking-fund-25000) — Engineering Economics, chapter 7
- [PW and IRR after tax with SL depreciation](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Apw-irr-sl-tax-20-million) — Engineering Economics, chapter 7
- [Depreciation causes; SOYD and declining balance](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Adepreciation-causes-soyd-declining-150000) — Engineering Economics, chapter 7
- [Depreciation, causes, methods; DB schedule for 60,000](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Adepreciation-causes-methods-60000-db) — Engineering Economics, chapter 7, asked 2×
- [Sensitivity on initial cost and life; interpret](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asensitivity-30-initial-cost-life-25) — Engineering Economics, chapter 6

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