In: Finance
Yen has a project that requires an investment of $500 at t=0 and then generates $100, $200, $300, and $400 in the next four years (from t=1 to t=4). What is the payback period in years?
Cash outflow at t0 = - Initial investment = - 500
We get the following cash flows for the project
Year | 0 | 1 | 2 | 3 | 4 |
Cash Flow | -500 | 100 | 200 | 300 | 400 |
To find the payback period, we need to find the cumulative cash flow for the project
Cumulative cash flow in year 0 = Cash flow in year 0 = -500
Cumulative cash flow for a year = Cumulative cash flow for previous year + Cash flow for a year
Cumulative cash for year 1 = Cumulative cash flow for year 0 + Cash flow for year 1 = -500 + 100 = -400
Cumulative cash for year 2 = Cumulative cash flow for year 1 + Cash flow for year 2 = -400 + 200 = -200
Cumulative cash for year 3 = Cumulative cash flow for year 2 + Cash flow for year 3 = -200 + 300 = 100
Cumulative cash for year 4 = Cumulative cash flow for year 3 + Cash flow for year 4 = 100 + 400 = 500
Year | 0 | 1 | 2 | 3 | 4 |
Cash Flow | -500 | 100 | 200 | 300 | 400 |
Cumulative cash flow | -500 | -400 | -200 | 100 | 500 |
Payback of a project is the number of years it takes for a project to recover its initial investment. It is equal to no of years it takes for cumulative cash flow to become equal to zero. Cumulative cash flow change sign from negative to positive in year 3.
Hence payback = 2 + (200/300) = 2 + (2/3) = 2.6666 = 2.67 years (rounded to two places of decimal) = 2 years 8 months
Payback in years = 2.67 years