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PW of machine with tax at 50%

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.

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

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

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.)

✓ Answer checked by Claude Opus 5.5 (high effort)

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