Question

In: Finance

Yen has a project that requires an investment of $500 at t=0 and then generates $100,...

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?

Solutions

Expert Solution

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


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