---
title: "DDB with switchover to straight line"
subject: "Engineering Economics"
chapter: 7
key: "semester_6/engineering_economics:ddb-switchover-30000-7yr"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/ddb-switchover-30000-7yr
site: BCT Engineering
---

# DDB with switchover to straight line

Engineering Economics · Chapter 7: Depreciation and Corporate Income Taxes

- Asked in: 2076 Shrawan, 6 marks
- Video: [Engineering Economics | Depreciation | DB Method Switchover To SL Method Numerical | Ninja Guru](https://www.youtube.com/watch?v=jHDl-OA2GDU) — Ninja Gurukul
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/ddb-switchover-30000-7yr
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-7

## Question

Compute the annual depreciation allowances and the resulting book value using the double declining balance method with switchover to straight line method. Cost of asset = Rs 30,000, useful life = 7 years, salvage value = 0.

## Short answer

Using DDB with switchover to straight-line, annual depreciation is Rs 8,571, 6,122, 4,373, 3,124, 2,603, 2,603, 2,603 for years 1–7. Book values end at Rs 0. Switch occurs in year 5 when SL charge (2,603) exceeds DDB.

## Answer

Data: P = 30,000; N = 7; S = 0. DDB rate = 2/N = 2/7 = 28.57% of the opening book value. Switch to straight-line (SL) in the first year where the SL charge on the remaining book value, BV/(remaining years), is at least the DDB charge.

```text
DDB charge_k = (2/7) × BV_(k−1)
SL charge_k  = BV_(k−1) / (7 − k + 1)
Depreciation = larger of the two
```
| Year | Opening BV | DDB | SL on remaining | Depreciation | Closing BV |
|---|---|---|---|---|---|
| 1 | 30,000 | 8,571 | 4,286 | 8,571 | 21,429 |
| 2 | 21,429 | 6,122 | 3,571 | 6,122 | 15,306 |
| 3 | 15,306 | 4,373 | 3,061 | 4,373 | 10,933 |
| 4 | 10,933 | 3,124 | 2,733 | 3,124 | 7,809 |
| 5 | 7,809 | 2,231 | 2,603 | 2,603 | 5,206 |
| 6 | 5,206 | 1,487 | 2,603 | 2,603 | 2,603 |
| 7 | 2,603 | 744 | 2,603 | 2,603 | 0 |

Switchover occurs in **year 5**, where SL = 7,809 / 3 = 2,603 exceeds DDB = 2,231. The charge stays at 2,603 for years 5, 6 and 7, and the book value reaches 0 at the end of year 7.

**Answer:** Annual depreciation = 8,571, 6,122, 4,373, 3,124, 2,603, 2,603, 2,603 for years 1 to 7; book values = 21,429, 15,306, 10,933, 7,809, 5,206, 2,603, 0.

## Check yourself

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

1. What DDB rate is used for N = 7?
   A. 2/7 = 28.57% of opening book value
   B. 1/7 = 14.29% of cost
   C. 2/7 of cost
   D. 28.57% of (P - S)
   Answer: A. DDB uses 2/N on the declining book value. (Key point: DDB rate)

2. When does the switch to SL occur?
   A. When book value reaches 50% of cost
   B. In the first year where BV/(remaining years) is at least the DDB charge
   C. In the last year only
   D. When DDB charge becomes zero
   Answer: B. The larger of the two charges is taken each year. (Key point: Switch rule)

3. In which year does the switch occur?
   A. Year 4
   B. Year 6
   C. Year 5 (SL = 7,809/3 = 2,603 > DDB = 2,231)
   D. Year 3
   Answer: C. Year 4: DDB 3,124 > SL 2,733; year 5: SL 2,603 > DDB 2,231. (Key point: Switch year)

4. What are book values at end of years 5 and 7?
   A. 7,809 and 2,603
   B. 5,206 and 2,603
   C. 2,603 and 0
   D. 5,206 and 0
   Answer: D. Year 5 depreciation 2,603 leaves 5,206; with S = 0 it reaches zero at year 7. (Key point: Book values)

## Related in Engineering Economics

- [Double declining balance depreciation, 15000 machine](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Addb-15000-salvage-900) — Engineering Economics, chapter 7
- [Depreciation, causes; declining balance for 50,000](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Adepreciation-causes-db-50000) — Engineering Economics, chapter 7, asked 2×
- [After-tax cash flow, DDB with switchover](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aafter-tax-cash-flow-ddb-switchover) — Engineering Economics, chapter 7
- [Depreciation and book value by four methods](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Adepreciation-sl-db-soyd-sf-7000) — 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
- [Define ESL; find ESL of 50,000 asset](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aesl-define-50000-15-percent-growth) — Engineering Economics, chapter 5

## Related in other subjects

- [EPS and book value; ABC project Rs 6,00,000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeps-bv-abc-project-600000-b79) — Project Engineering, chapter 6
- [EPS and book value; capital Rs 5,00,000](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeps-bv-capital-500000-2000-shares) — Project Engineering, chapter 6
- [EPS and book value; Rs 10,00,000, 3500 shares](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeps-bv-capital-1000000-3500-shares) — Project Engineering, chapter 6
- [EPS and book value; 500 shares, EBIT 40,000, tax 40%](https://www.bctengineer.com/question.md?key=semester_7%2Fproject_engineering%3Aeps-bv-500-shares-300-pref) — Project Engineering, chapter 6