---
title: "Book value by SOYD and sinking fund"
subject: "Engineering Economics"
chapter: 7
key: "semester_6/engineering_economics:book-value-soyd-sinking-fund"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/book-value-soyd-sinking-fund
site: BCT Engineering
---

# Book value by SOYD and sinking fund

Engineering Economics · Chapter 7: Depreciation and Corporate Income Taxes

- Asked in: 2076 Shrawan, 3+3 marks
- Video: [Depreciation by SOYD and sinking fund method|| Numerical Engineering Economics](https://www.youtube.com/watch?v=v_jOTrB5agE) — OPengineer
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/book-value-soyd-sinking-fund
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-7

## Question

A machine was bought two years ago at Rs 50000. Its salvage value is estimated to be Rs 10000 after three years. Calculate its book value now using (i) sum of year digits method and (ii) sinking fund method. Assume MARR = 10%.

## Short answer

For a machine with cost Rs50,000, salvagge Rs10,000, life 3 yearss, after 2 years: book value by SOYD is Rs 16,667; by sinking-fund method at 10%, book value is Rs 24,622.

## Answer

**Assumption:** the machine was bought for P = Rs 50,000 and will have S = Rs 10,000 after 3 years, so its life is N = 3 years. "Now" is the end of year 2 (two years after purchase).

#### (i) Sum-of-the-years'-digits (SOYD)
Sum of digits = N(N + 1)/2 = 3(4)/2 = 6; P − S = 40,000.
```text
D₁ = 40,000 × 3/6 = 20,000
D₂ = 40,000 × 2/6 = 13,333
Book value after 2 years = 50,000 − 20,000 − 13,333 = Rs 16,667
```
#### (ii) Sinking-fund method (i = 10%)
Yearly deposit = (P − S)(A/F,10%,3) = 40,000(0.30211) = Rs 12,085. Depreciation in year k = deposit × (F/P,10%,k − 1).
```text
D₁ = 12,085
D₂ = 12,085(1.10) = 13,293
Book value after 2 years = 50,000 − 12,085 − 13,293 = Rs 24,622
```
| Method | Total depreciation (2 yr) | Book value now |
|---|---|---|
| SOYD | 33,333 | 16,667 |
| Sinking fund | 25,378 | 24,622 |

**Answer:** Book value now = **Rs 16,667** by SOYD and **Rs 24,622** by the sinking-fund method.

## Check yourself

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

1. With N = 3, what is the SOYD year-1 depreciation for P = 50,000, S = 10,000?
   A. Rs 20,000
   B. Rs 13,333
   C. Rs 13,333 x 3
   D. Rs 40,000/3 = 13,333
   Answer: A. Sum of digits is 6, so D1 = 40,000 x 3/6 = 20,000. (Key point: SOYD depreciation)

2. What is the book value after 2 years by SOYD?
   A. Rs 24,622
   B. Rs 16,667
   C. Rs 26,667
   D. Rs 10,000
   Answer: B. 50,000 - 20,000 - 13,333 = 16,667. (Key point: SOYD book value)

3. How is the yearly sinking-fund deposit found?
   A. P(A/F,10%,3)
   B. (P - S)(A/P,10%,3)
   C. (P - S)(A/F,10%,3) = 40,000(0.30211) = Rs 12,085
   D. (P - S)/3
   Answer: C. The deposit grows at the interest rate to reach P - S after N years. (Key point: Sinking-fund deposit)

4. What is the book value after 2 years by sinking fund?
   A. Rs 16,667
   B. Rs 25,378
   C. Rs 37,915
   D. Rs 24,622
   Answer: D. Depreciation 12,085 + 13,293 = 25,378; 50,000 - 25,378 = 24,622. It exceeds SOYD because early charges are smaller. (Key point: Sinking-fund book value)

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