This is “Payback Period”, section 13.2 from the book Finance for Managers (v. 0.1).
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Our first decision making technique is very intuitive and very easy to calculate. Payback periodThe amount of time until our initial investment is recovered. is the amount of time until the initial investment is recovered. For example, a project costs $100 and we earn $20 (after tax) a year. We will have our $100 back in five years. Simple enough!
Cash flows may be uneven, but this barely adds to the complexity. Consider the same project that cost $100, but earns $40 the first year (all after-tax), $30 the second year, $25 the third year, $20 the fourth year and $20 the fifth year? What is our payback period now? We receive our $100th investment during the 4th year, so our payback period is between 3 and 4 full years. Some companies will always round up to the next higher year (“Our investment will be fully paid back in four years…”). Others will add some “precision” by attempting to figure out what fraction of the year has passed. The result is comprised of two parts: the number of full years and the partial year. The number of full years is our initial result, rounded down (in our example, three). If a balance remains then the partial year is the remaining cost at the beginning of the year divided by the cash flow that year. That gives us a portion of the year that it takes to get the balance of the project paid off.
Equation 13.1 Payback Period
Payback Period = Number of Full Years + Partial YearEquation 13.2 Partial Year
$$\text{PartialYear}=\text{}\frac{\text{UnrecoveredCostBeginningofYear}}{\text{CashFlowthatYear}}$$In our example, $95 has been recovered in the first three years, leaving $100 − $95 = $5. Since we will receive $25 dollars in the fourth year, our partial year is $5 / $20 = 0.25. Our total payback period is then 3 + 0.25 = 3.25 years.
Companies that utilize payback period will set a maximum threshold that all accepted projects must remain under. If projects are mutually exclusive, then typically the one with the shortest payback period is chosen.
Gator Lover’s Ice Cream is a small ice cream manufacturer. Gator Lover’s Ice Cream wants to either open a new store (Project A) or buy a new machine to mass produce ice cream to sell to supermarkets (Project B). The relevant cash flows are shown in Table 13.1 "Gator Lover’s Ice Cream Project Analysis".
Table 13.1 Gator Lover’s Ice Cream Project Analysis
Project A | Project B | |
---|---|---|
Initial Investment | ($48,000) | ($52,000) |
Year | Operating Cash Inflows (after-tax) | |
1 | $15,000 | $18,000 |
2 | $15,000 | $20,000 |
3 | $15,000 | $15,000 |
4 | $15,000 | $12,000 |
5 | $15,000 | $10,000 |
Total Years 1–5 | $75,000 | $75,000 |
Figure 13.1 Timeline for Project A
Figure 13.2 Timeline for Project B
Let’s calculate the payback period for both projects. Project A cost $48,000 and earns $15,000 every year. So after three years we have earned $45,000, leaving only $3,000 remaining of the initial $48,000 investment. The cash flow in year four is $15,000. The $3,000 divided by $15,000 gives us 0.2.
$$\text{PaybackPeriodProjectA}=3+\text{}\frac{\mathrm{3,000}}{\mathrm{15,000}}=3.2\text{years}$$Project B cost $52,000 and earns back uneven cash flows. In year one the project earns $18,000, in year two it earns $20,000 and it earns $15,000 in the third year. At the end of the second year it has earned back $18,000 + $20,000 = $38,000, leaving $52,000 − $38,000 = $14,000. In the third year the project earns $15,000. The balance of $14,000 will be paid off by the $15,000 earned that year. The $14,000 is divided by the $15,000 to give us 0.93.
$$\text{PaybackPeriodProjectB}=2+\text{}\frac{\mathrm{14,000}}{\mathrm{15,000}}=2.93\text{years}$$If our threshold is 4 years, then both projects would be viable. If the projects are independent, then both should be undertaken. If the projects are mutually exclusive, then we would pick Project B, as the payback period is shorter.
Payback period may not tell the whole story. Consider a project such as researching a new drug? Development can take over a decade before positive cash flows are seen, but the potential upside could be huge! What about the cash flows that happen after the end of the payback period? Payback period is a popular tool because it’s quick to calculate and easy to explain, but it is not always appropriate, and can lead to the rejection of long-term projects that add value. Often, companies will use payback period on only projects requiring smaller investments where the risk is small, and use a more complex method, such as NPV or IRR, for more involved projects.
Payback period is a quick and easy way to determine how long until we get our money back.
Calculate the payback period for the following:
Project A: Initial Cost $80,000 earns $19,000 per year.
Project B: Initial Cost $100,000 earns $25,000 per year.