### Learning Outcomes

- Calculate the payback period on a steady flow of cash

South Side Brewery is building a stage for musicians. The company expects revenue to increase by $6,000 per month as a result of increased alcohol sales and expenses (cost of the bands) to increase by $4,000 per month. The cost to build the stage with a lighting and sound system is $120,000. It will be good for at least eight years.

Management wants to know how long it will take for the stage to pay for itself.

The formula for payback period on a steady flow of cash is: cost/annual cash flows

Annual net cash inflows will be $2,000/month * 12 months = $24,000.

$120,000 / $24,000 = 5 years.

Here is a table of net cash inflows:

Net cash inflows (additional cash revenues – additional cash expenses)

New stage | |
---|---|

Year 1 | $ 24,000 |

Year 2 | $ 24,000 |

Year 3 | $ 24,000 |

Year 4 | $ 24,000 |

Year 5 | $ 24,000 |

Year 6 | $ 24,000 |

Year 7 | $ 24,000 |

Year 8 | $ 24,000 |

And here is a table that shows how the cost is recaptured over time:

Description | Amount |
---|---|

Cost | $ 120,000 |

Recaptured YR 1 | $ (24,000) |

Left to recapture | Single Line$ 96,000 |

Recaptured YR 2 | $ (24,000) |

Left to recapture | Single Line$ 72,000 |

Recaptured YR 3 | $ (24,000) |

Left to recapture | Single Line$ 48,000 |

Recaptured YR 4 | $ (24,000) |

Left to recapture | Single Line$ 24,000 |

Recaptured YR 5 | $ (24,000) |

Left to recapture | Single Line$ – |

Let’s look at a slightly more complicated example.

JuxtaPos makes interlocking wooden puzzles. One of the machines is old, and management is considering either replacing it or refurbishing it. Replacing it will cost $80,000. The new machine would last 10 years and have a residual value of $10,000. Refurbishing the old machine for $56,000 will keep it in service for another eight years, and it will have no residual value at the end of that time.

You have estimated production under both scenarios, and you used those numbers to compute revenue. You have also estimated operating costs and created the following table of net cash inflows:

Net cash inflows (additional cash revenues – additional cash expenses)

Refurbish | Purchase New | |
---|---|---|

Year 1 | $ 18,000 | $ 20,000 |

Year 2 | 16,000 | 19,000 |

Year 3 | 14,000 | 18,000 |

Year 4 | 12,000 | 17,000 |

Year 5 | 10,000 | 15,000 |

Year 6 | 8,000 | 13,000 |

Year 7 | 6,000 | 10,000 |

Year 8 | 4,000 | 7,000 |

Year 9 | 5,000 | |

Year 10 (includes proceeds from sale of machine) | 12,000 | |

Single Line$ 88,000Double line | Single Line$ 136,000Double line |

What is the payback period for each option?

The cash flows aren’t even, so the simple formula won’t work. However, an Excel spreadsheet could quickly give you an answer (you could also do this on a piece of paper easily enough).

Refurbish

Description | Amount | % of cash flows | months | years |
---|---|---|---|---|

Cost to refurbish | $ 56,000 | |||

Recaptured YR 1 | $ (18,000) | 100% | 12.0 | 1.00 |

Left to recapture | Single Line$ 38,000 | |||

Recaptured YR 2 | $ (16,000) | 100% | 12.0 | 1.00 |

Left to recapture | Single Line$ 22,000 | |||

Recaptured YR 3 | $ (14,000) | 100% | 12.0 | 1.00 |

Left to recapture | Single Line$ 8,000 | |||

Recaptured YR 4 | $ (8,000) | 67% | 8.0 | 0.67 |

Left to recapture | Single Line$ – |

Notice that cash flows in Year 4 are $12,000, but we only had $8,000 left to recapture, so we estimate that it will take 3.67 years, or three years and eight months, to recapture the entire cost of refurbishing the existing machine.

If we purchase a new machine, it will take 4.46 years (roughly four years, five and a half months) to recapture the cost.

Purchase

Description | Amount | % of cash flows | months | years |
---|---|---|---|---|

Cost to purchase | $ 80,000 | |||

Recaptured YR 1 | $ (20,000) | 100% | 12.0 | 1.00 |

Left to recapture | Single Line$ 60,000 | |||

Recaptured YR 2 | $ (19,000) | 100% | 12.0 | 1.00 |

Left to recapture | Single Line$ 41,000 | |||

Recaptured YR 3 | $ (18,000) | 100% | 12.0 | 1.00 |

Left to recapture | Single Line$ 23,000 | |||

Recaptured YR 4 | $ (17,000) | 100% | 12.0 | 1.00 |

Left to recapture | Single Line$ 6,000 | |||

Recaptured YR 5 | $ (6,000) | 46% | 5.5 | 0.46 |

Left to recapture | Single Line$ – |

Year 5 net cash inflows were $15,000, but we only had $6,000 of the original cost of the machine left to recapture, which is 46% of the $15,000, which equates to roughly five and a half months. You could round this final partial year to six months since this calculation is based on estimation and is not a precision measurement, so the payback period is four and a half years.

The payback method is quick and easy to apply, but it has several drawbacks. As you might have noticed, it doesn’t take the overall investment into account. Purchasing a new machine resulted in $136,000 in total cash inflows over the next 10 years, while refurbishing (because of higher maintenance costs and lower outputs) resulted in only $88,000 in net cash inflows. However, the refurbishing option pays for itself more quickly (three years, eight months as opposed to four years, six months for the replacement).

In addition, this analysis does not take into account the time value of money.

Here is another example of how to calculate the payback of a project:

You can view the transcript for “The Payback Method” here (opens in new window).

Before we address these two issues, check your understanding of the basic idea of the payback method.