The GATE Grind

GATE 2026 CH – Question 46

Plant Design and Economics · Depreciation, rate of return, payback period and discounted cash flow · 2 marks · Multiple choice

In a certain project, 15% of the total investment is the working capital. The minimum acceptable rate of return is 4.95% and the period of evaluation is 15 years. Which one of the following is the maximum acceptable project payback period (in years)?

  1. 5
  2. 8
  3. 12
  4. 15

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) 12

Explanation

Let the total investment be $I$, of which $0.15I$ is working capital that is recovered at the end of the project. Let the (uniform) annual cash flow be $A$. At the minimum acceptable rate, the present worth is zero: $A \cdot \frac{1 - (1.0495)^{-15}}{0.0495} + 0.15I(1.0495)^{-15} = I$. The annuity factor is 10.41 and $(1.0495)^{-15} = 0.4856$, so $10.41A = I(1 - 0.0728) = 0.927I$. The payback period is $\frac{I}{A} = \frac{10.41}{0.927} \approx 11.2$ years, so the maximum acceptable payback period is about 12 years (closest option).