# PRY Treehouse Co. is considering a new inventory system that will cost $500,000. The system is... ## Question: PRY Treehouse Co. is considering a new inventory system that will cost$500,000. The system is expected to generate positive cash flows over the next five years in the amounts of $60,000 in year one,$90,000 in year two, $110,000 in year three,$50,000 in year four, and $100,000 in year five. PRY's required rate of return is 12.5%. What is the payback period of this project? ## Payback Period: The payback period is the time period after which the initial cost of a project is repaid by the positive cash flows, expected to be produced by the project. Generally, the shorter the payback period, the more attractive is an investment proposal. ## Answer and Explanation: The formula for the payback period of a project is: {eq}Payback \space period = t + \dfrac{\left | CC_{t} \right |}{C_{t+1}} {/eq} Where: • t = year of the last negative cumulative cash flow • CCt = cumulative cash flow of the year t • Ct+1 = net cash flow of the year following year t The cash flows and cumulative cash flows of the project are shown in the below table: Year Cash Flow ($) Cumulative Cash Flow (\$)
0 -500,000 -500,000
1 60,000 -440,000
2 90,000 -350,000
3 110,000 -240,000
4 50,000 -190,000
5 100,000 -90,000

As calculated in the table, there are no positive cumulative cash flows. It means that the initial cost of the project will never be repaid by the cash flows, and therefore, the project has no payback period.