A proposed project has expected cash flows of $72,000 per year for 5 years. If the project has an initial cost of $400,000, what is the payback period (in years)?

To find the payback period for the proposed project, you need to determine how long it will take for the initial investment to be recovered.

First, let's calculate the annual cash flow. The proposed project has expected cash flows of $72,000 per year for 5 years.

Next, subtract the annual cash flow from the initial cost each year until the total cumulative cash flow becomes positive. The payback period is the number of years it takes to reach this point.

Let's calculate it step by step:

Year 1: Initial cost - Cash Flow = $400,000 - $72,000 = $328,000
Year 2: $328,000 - $72,000 = $256,000
Year 3: $256,000 - $72,000 = $184,000
Year 4: $184,000 - $72,000 = $112,000
Year 5: $112,000 - $72,000 = $40,000

After 5 years, the cumulative cash flow is still negative, and the investment has not been fully recovered.

To find the payback period more precisely, we can calculate the fraction of the last year's cash flow that is needed to reach the positive cumulative cash flow:

Fraction of the last year's cash flow = Cumulative cash flow / Cash flow in the last year

Fraction of the last year's cash flow = $40,000 / $72,000 = 0.5556

Finally, we can calculate the payback period by taking the total number of years (5) and subtracting the fraction of the last year's cash flow:

Payback period = Total number of years - Fraction of the last year's cash flow

Payback period = 5 - 0.5556 = 4.4444 years

Therefore, the payback period for the proposed project is approximately 4.44 years.