Payback Period (PBP)

The Payback Period is a simple financial metric used to determine the time it takes for an investment or project to "pay back" its initial cost. In other words, it represents the time it takes for the cumulative cash flows to equal the initial investment.

Formula

Given an initial investment ( C_0 ) and cash inflows for each period ( CF_t ), the Payback Period (PP) is the time ( t ) such that:

$$\sum _{i=1}^{t}C{F}_i\ge C_0$$

Where:

$$\begin{array}{rl}& C{F}_t=\text{Cash inflow during the period }t\\ & C_0=\text{Initial investment}\\ & t=\text{Time period}\end{array}$$

Interpretation

• A shorter Payback Period is generally preferred as it indicates quicker recovery of the initial investment.
• It helps in assessing the liquidity risk associated with an investment.

Strengths

• Simple and easy to understand.
• Useful for projects where liquidity is a concern or when dealing with high-risk investments.

Limitations

• Does not account for the time value of money.
• Ignores cash flows that occur after the Payback Period, hence may not consider the overall profitability of the project.

Example

If a project requires an initial investment of $100,000 and is expected to generate cash inflows of $50,000 each year, then the Payback Period is:

$$\text{Payback Period}=\frac{\text{\$100,000}}{\text{\$50,000/year}}=2\text{ years}$$

This means the project will take 2 years to recover the initial investment of $100,000.

Quiz

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