Payback Method

Introduction

The payback period is the time that the net accumulated cash flow takes to equal the initial investment in the project. It is the first of the three methods in Economic Analysis.

How it works

If the net annual cash flow is the same each year:

$$n=\frac{IC}{NACF}\text{or}0=-IC+n\times NACF$$

where:

• $n$ is the payback period in years
• $IC$ is the investment cost
• $NACF$ is the net annual cash flow, which is annual revenue minus annual cost, $R-C$

If the cash flow is different each year, find $n$ so that the sum of the cash flows equals the investment:

$$0=-IC+\sum _{i=1}^{n}NAC{F}_i$$

Rules for the signs and the result:

• costs are negative values, and revenues or savings are positive values
• $NACF$ is positive, because the revenue from the robot is more than its operating cost
• most companies want a payback of 2 to 3 years or less
• a payback of less than 1 year is excellent

Example 1

A robot project has these values:

• total investment cost IC=\100{,}000$
• annual operating cost C=\20{,}000$
• annual revenue R=\65{,}000$
• service life of 5 years

Net annual cash flow:

$$NACF=65,000-20,000=\$45,000$$

Payback period:

$$n=\frac{100,000}{45,000}=2.22\text{ years}$$

Limitation

The payback method ignores the time value of money. It also ignores the effect of the salvage value of the robot (see Example 5 in Differences in Production Rates).