---
title: "PW of machine with tax at 50%"
subject: "Engineering Economics"
chapter: 7
key: "semester_6/engineering_economics:pw-machine-save-4-million-tax"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/pw-machine-save-4-million-tax
site: BCT Engineering
---

# PW of machine with tax at 50%

Engineering Economics · Chapter 7: Depreciation and Corporate Income Taxes

- Asked in: 2066 Magh, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/pw-machine-save-4-million-tax
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-7

## Question

A machine costs Rs. 20 million and is expected to save Rs. 4 million/year. Tax rate = 50%, MARR = 10%. Evaluate the PW.

## Short answer

After-tax annual cash flow is Rs 3 million (saving Rs 4M minus 50% tax on saving less depreciation). PW at MARR 10% over 10-year life is -Rs 1.57 million, so the machine is not acceptable.

## Answer

**Assumptions (not stated):** useful life N = 10 years, salvage value zero, straight-line depreciation, and the saving is taxable like income. Figures in Rs million.

#### After-tax cash flow
```text
Depreciation = 20/10 = 2 per year
Taxable income = saving − depreciation = 4 − 2 = 2
Tax = 0.50 × 2 = 1
ATCF = 4 − 1 = 3 per year (years 1 to 10)
```
#### Present worth at MARR = 10%
PW(after tax) = −20 + 3(P/A,10%,10) = −20 + 3(6.1446) = −20 + 18.43 = **−1.57 million**

For comparison, before tax: PW = −20 + 4(6.1446) = +4.58 million. Tax at 50% turns an attractive project into an unattractive one.

**Answer:** After-tax PW = **−Rs 1,566,299** (about −Rs 1.57 million) < 0, so the machine is **not economical** after tax at 10%. (The result depends on the assumed life: with straight-line depreciation the after-tax PW becomes positive only for lives above about 14 years.)

## Check yourself

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

1. Which assumption does the answer make because the question omits life and depreciation?
   A. Life 10 years, zero salvage, straight-line depreciation
   B. Life 5 years, salvage 20%, DDB depreciation
   C. Life 20 years, no depreciation
   D. Life 10 years, MACRS depreciation
   Answer: A. The answer assumes N = 10, S = 0 and straight-line depreciation, giving 2 million per year. (Key point: Assumptions)

2. What is the yearly after-tax cash flow?
   A. 4 million
   B. 3 million
   C. 2 million
   D. 1 million
   Answer: B. Taxable income = 4 - 2 = 2; tax = 1; ATCF = 4 - 1 = 3 million. (Key point: ATCF)

3. What is the after-tax PW at 10%, and the decision?
   A. +4.58 million; accept
   B. +1.57 million; accept
   C. -1.57 million; reject
   D. -4.58 million; reject
   Answer: C. PW = -20 + 3(6.1446) = -1.57 million, so the machine is not economical after tax, though before tax it was +4.58 million. (Key point: After-tax PW)

## Related in Engineering Economics

- [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
- [Sensitivity of PW to investment and MARR](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Asensitivity-investment-marr-10-50) — Engineering Economics, chapter 6, asked 2×
- [IRR evaluation, MARR 20%](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Airr-60000-cash-flow-20) — Engineering Economics, chapter 3
- [ERR with MARR = ε = 10%](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Aerr-six-year-cash-flow) — Engineering Economics, chapter 3
- [Car loan interest rate and lump sum at year 3](https://www.bctengineer.com/question.md?key=semester_6%2Fengineering_economics%3Acar-loan-installments-lump-sum-year3) — Engineering Economics, chapter 2
- [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

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