Question

Which of the following is correct statement of payout time?

• A. Payout period and the economic life of a project are the same.
• B. Payout period is affected by the variations in earnings after the recovery of the investment
• C. Payout period is not important for business decision making
• D. Payout period is the length of time over which the earnings on a project equal the investment

Hint:

The payback period is a metric of risk, not of profitability.
It ignores all cash flows after the payback point as well as the time value of money, which is why modern analysis combines it with Net Present Value (NPV) and Internal Rate of Return (IRR).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks for the correct definition of "payout time" (also known as the payback period or payout period) in the context of capital investment and project feasibility analysis.
The payout period is a primary metric used to evaluate the economic risk of a project.

Step 2: Key Formula or Approach:
For a project with an initial fixed capital investment \(FCI\) and uniform annual cash inflows (net earnings after taxes plus depreciation) \(CF\), the payout period (\(PP\)) is defined as:
\[ PP = \frac{\text{Initial Capital Investment}}{\text{Annual Net Cash Flow}} = \frac{FCI}{CF} \] When the annual cash inflows are non-uniform, the payout time is the value of \(t\) that satisfies the integral or cumulative sum equation:
\[ \int_{0}^{t} CF(t) \, dt = FCI \]

Step 3: Detailed Explanation:
Let us evaluate each statement to determine the correct one:
- Option (A) states that the payout period and economic life are the same. This is incorrect because the economic life of a project is the total duration over which the plant can operate profitably, which is typically much longer than the time required to recover the initial investment.
- Option (B) states that the payout period is affected by the variations in earnings after the recovery of the investment. This is incorrect because the payout period calculation stops once the initial investment is recovered; any cash flows occurring after the payback point have no influence on the payback time itself.
- Option (C) states that the payout period is not important. This is incorrect because payout time is an essential risk indicator; projects with shorter payback periods are highly favored because they expose the invested capital to market risks for a shorter duration.
- Option (D) states that the payout period is the length of time over which the earnings on a project equal the investment. This is the exact, standard economic definition of the payback period.

Step 4: Final Answer
Thus, the correct statement is option (D).