8.2 Payback Period and Profitability Index

Capital budgeting techniques help businesses decide which projects to invest in. Payback period and profitability index are two key methods used to evaluate potential investments. These tools help managers assess how quickly they'll recoup their initial outlay and the overall profitability of a project.

Understanding these metrics is crucial for making smart investment choices. Payback period focuses on timing, while profitability index considers the project's overall value. Both methods have their strengths and limitations, which we'll explore in this section.

Payback Period Methods

Calculating Payback Periods

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• Payback period measures the time it takes for the cumulative cash inflows from a project to equal the initial investment (cash outflows)
• Calculated by dividing the initial investment by the annual cash inflow $\text{Payback Period} = \frac{\text{Initial Investment}}{\text{Annual Cash Inflow}}$
• For projects with uneven cash flows, the payback period is found by adding up each year's cash flows until the initial investment is recovered (takes 3 years to recoup a $10,000 investment with inflows of$4,000, $3,000, and$5,000)
• Discounted payback period accounts for the time value of money by discounting future cash flows at the project's discount rate before calculating the payback period

Decision Rules and Project Ranking

• Under the payback period decision rule, a project is accepted if its payback period is less than some specified cutoff period (2 years) and rejected if it exceeds the cutoff period
• Shorter payback periods are preferred as they indicate less risk and quicker recovery of invested funds
• When ranking mutually exclusive projects, the project with the shortest payback period is preferred
• Payback period ignores cash flows beyond the cutoff date, does not measure profitability, and is biased towards short-term projects

Profitability Metrics

Calculating Profitability Index and Benefit-Cost Ratio

• Profitability index (PI) measures the ratio of the present value of a project's future cash inflows to the initial cash outflow $\text{PI} = \frac{\text{PV of Future Cash Inflows}}{\text{Initial Cash Outflow}}$
• A PI greater than 1 indicates the project has a positive net present value (NPV) as the present value of cash inflows exceeds the initial outflow
• Benefit-cost ratio is similar to PI but includes the present value of cash outflows in the denominator $\text{Benefit-Cost Ratio} = \frac{\text{PV of Cash Inflows}}{\text{PV of Cash Outflows}}$
• A benefit-cost ratio exceeding 1 signals the project's benefits outweigh its costs on a present value basis

Decision Rules and Project Ranking

• Using the PI decision rule, a project is accepted if its PI exceeds 1 and rejected if the PI is less than 1
• For the benefit-cost ratio, projects with a ratio greater than 1 are accepted and ratios below 1 are rejected
• When ranking mutually exclusive projects, the project with the highest PI or benefit-cost ratio is preferred (Project A with a PI of 1.3 is preferred over Project B with a PI of 1.1)
• Unlike the payback period, PI and benefit-cost ratio consider all of a project's cash flows, account for the time value of money, and measure a project's relative profitability