Intro to Finance: Capital Budgeting - Payback Period, Standard vs. Discounted Payback

What This Is

The payback period is a simple, intuitive metric used to evaluate the viability of an investment or project. It measures the time it takes for an investment to generate enough cash flows to recover its initial cost. For example, consider a company investing $100,000 in a new machine that generates $20,000 in annual cash flows. If the machine lasts for 5 years, the payback period would be 5 years, as it takes 5 years for the machine to generate enough cash flows to recover its initial cost.

Key Formulas & Symbols

• Payback Period (Standard): PP = Initial Investment / Annual Cash Flow where PP = payback period, Initial Investment = initial cost of the investment, Annual Cash Flow = annual cash flows generated by the investment.
• Payback Period (Discounted): PPD = Initial Investment / (Annual Cash Flow × (1 - (1 + r)^(-n))) where PPD = discounted payback period, r = periodic discount rate, n = number of periods.
• Discount Rate (r): The rate at which future cash flows are discounted to their present value.
• Annual Cash Flow (CF): The annual cash flows generated by the investment.
• Initial Investment (I): The initial cost of the investment.
• Number of Periods (n): The number of periods over which the investment generates cash flows.

Step-by-Step Calculation

1. Determine the initial investment and annual cash flows generated by the investment.
2. Calculate the payback period using the standard payback period formula: PP = Initial Investment / Annual Cash Flow.
3. If the payback period is not satisfactory, calculate the discounted payback period using the discounted payback period formula: PPD = Initial Investment / (Annual Cash Flow × (1 - (1 + r)^(-n))).
4. Compare the payback period and discounted payback period to determine the viability of the investment.

Common Mistakes

• Mistake: Using the standard payback period formula without considering the time value of money.
• Correction: Use the discounted payback period formula to account for the time value of money.
• Mistake: Failing to consider the opportunity cost of capital.
• Correction: Use a discount rate that reflects the opportunity cost of capital.
• Mistake: Ignoring the risk associated with the investment.
• Correction: Use a risk-adjusted discount rate to account for the risk associated with the investment.

Exam / CFA Tips

• Tip: Be prepared to calculate the payback period and discounted payback period for different scenarios.
• Tip: Understand the assumptions underlying the payback period and discounted payback period formulas.
• Tip: Be able to distinguish between the standard payback period and discounted payback period formulas.

Quick Practice Problem

A company is considering investing $50,000 in a new project that generates $10,000 in annual cash flows. If the discount rate is 10% and the project lasts for 5 years, what is the discounted payback period?

Answer: 4.32 years Explanation: Using the discounted payback period formula, PPD = $50,000 / ($10,000 × (1 - (1 + 0.10)^(-5))) = 4.32 years.

Last-Minute Cram Sheet

• The payback period is a simple metric used to evaluate the viability of an investment.
• The discounted payback period formula accounts for the time value of money.
• The opportunity cost of capital should be reflected in the discount rate.
• The risk associated with an investment should be accounted for using a risk-adjusted discount rate.
• The standard payback period formula is PP = Initial Investment / Annual Cash Flow.
• The discounted payback period formula is PPD = Initial Investment / (Annual Cash Flow × (1 - (1 + r)^(-n))).
• The discount rate (r) should be a positive value.
• The number of periods (n) should be a positive integer.
• The initial investment (I) should be a positive value.
• The annual cash flow (CF) should be a positive value.
• The payback period and discounted payback period formulas assume a constant annual cash flow.