---
title: "ATCF and IRR with given depreciation schedule"
subject: "Engineering Economics"
chapter: 7
key: "semester_6/engineering_economics:atcf-irr-pw-macrs-style-1000000"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/atcf-irr-pw-macrs-style-1000000
site: BCT Engineering
---

# ATCF and IRR with given depreciation schedule

Engineering Economics · Chapter 7: Depreciation and Corporate Income Taxes

- Asked in: 2070 Magh, 6 marks
- Video: [#ECO_8.8 BTCF and ATCF Calculation on MACRS Depreciation 017 Fall 5b Solved - Shiva Gyawali](https://www.youtube.com/watch?v=BMtUEv6R0uU) — Shiva Gyawali
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/atcf-irr-pw-macrs-style-1000000
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-7

## Question

Suppose an equipment purchased for Rs. 10,00,000. It is expected to generate income of Rs. 3,50,000 per year during 5 years. Corporate income tax rate is 25% per year. The recovery period depreciation amounts are as follows.
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Depreciation amount | 1,00,000 | 2,00,000 | 2,00,000 | 2,00,000 | 3,00,000 |
Calculate ATCFs and determine profitability (IRR) when MARR is 15% by using PW method.

## Short answer

After-tax cash flows: year 1 Rs 2,87,500; years 2–4 Rs 3,12,500; year 5 Rs 3,37,500. PW at 15% = Rs 38,239 > 0; IRR = 16.6% > MARR, so the investment is profitable.

## Answer

Data: P = Rs 10,00,000; income = Rs 3,50,000/yr for 5 years; tax rate = 25%; MARR = 15%. The depreciation totals Rs 10,00,000, so the book value at year 5 is 0; **assume no salvage value.**

#### After-tax cash flow
Taxable income = 3,50,000 − depreciation; tax = 25% × taxable income; ATCF = 3,50,000 − tax.
| Year | Depreciation | Taxable income | Tax (25%) | ATCF |
|---|---|---|---|---|
| 1 | 100,000 | 250,000 | 62,500 | 287,500 |
| 2 | 200,000 | 150,000 | 37,500 | 312,500 |
| 3 | 200,000 | 150,000 | 37,500 | 312,500 |
| 4 | 200,000 | 150,000 | 37,500 | 312,500 |
| 5 | 300,000 | 50,000 | 12,500 | 337,500 |

```text
Year   0          1        2        3        4        5
CF  −10,00,000  287,500  312,500  312,500  312,500  337,500
```
#### Present worth at 15%
```text
PW = −10,00,000 + 2,87,500(P/F,15%,1) + 3,12,500[(P/F,15%,2) + (P/F,15%,3) + (P/F,15%,4)] + 3,37,500(P/F,15%,5)
   = −10,00,000 + 2,87,500(0.8696) + 3,12,500(0.7561 + 0.6575 + 0.5718) + 3,37,500(0.4972)
   = −10,00,000 + 2,50,000 + 6,20,438 + 1,67,800 = Rs 38,239
```
#### Profitability (IRR)
Solve PW(i) = 0:
```text
PW(15%) = 38,239
PW(18%) = -33,018
IRR = 15% + 3% × 38,239/(38,239 + 33,018) ≈ 16.6%
```
**Answer:** After-tax PW at 15% = Rs 38,239 > 0 and after-tax IRR ≈ 16.6% > MARR = 15%, so the investment is **profitable**.

## Check yourself

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

1. How is ATCF found?
   A. ATCF = 3,50,000 - 25% x (3,50,000 - depreciation)
   B. ATCF = 3,50,000 - depreciation
   C. ATCF = 3,50,000 - 25% x depreciation
   D. ATCF = 25% x 3,50,000
   Answer: A. Tax is charged on income after deducting depreciation. (Key point: Tax formula)

2. What is the year-1 ATCF?
   A. Rs 250,000
   B. Rs 287,500
   C. Rs 62,500
   D. Rs 350,000
   Answer: B. Taxable 250,000; tax 62,500; ATCF 287,500. (Key point: Year-1 ATCF)

3. What is the PW at 15%?
   A. Rs -38,239
   B. Rs 0
   C. Rs 38,239
   D. Rs -33,018
   Answer: C. Positive PW means return above MARR. (Key point: PW)

4. What is the IRR by interpolation?
   A. About 18%
   B. About 15%
   C. About 14%, reject
   D. About 16.6%, profitable
   Answer: D. 15% + 3% x 38,239/(38,239 + 33,018) = 16.6%. (Key point: IRR)

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