The cash payback period for Proposal A is approximately 3.75 years, and for Proposal B, it is approximately 3.38 years.
How do we calculate the cash payback period for each proposal?
We shall estimate the cumulative net cash inflow until it covers the initial investment to determine the cash payback period for each proposal using the formula for the payback period:
Cash Payback Period = Initial Investment / Annual Net Cash Inflow
For Proposal A:
Given:
Initial investment = $1,050,000
Annual net cash inflow = $280,000
The Cash Payback Period = $1,050,000 / $280,000 ≈ 3.75 years
For Proposal B:
Given:
Initial investment = $1,050,000
Annual net cash inflows = $350,000 (Year 1), $315,000 (Year 2), $280,000 (Years 3 and Year 4), $245,000 (Year 5), $210,000 (Year 6)
Since the cash flow for Proposal B is uneven, we will calculate the cumulative net cash inflow for each year:
Year 1: $350,000
Year 2: $350,000 + $315,000 = $665,000
Year 3: $665,000 + $280,000 = $945,000
Year 4: $945,000 + $280,000 = $1,225,000
Year 5: $1,225,000 + $245,000 = $1,470,000
Year 6: $1,470,000 + $210,000 = $1,680,000
Next, we identify the year where the cumulative net cash inflow first exceeds the initial investment of $1,050,000, which is after Year 3.
Then, calculate the remaining portion of the initial investment to be recovered:
$1,050,000 - $945,000 (cumulative inflow in Year 2) = $105,000
Next, divide the remaining investment by the net cash inflow in the year where recovery begins:
$105,000 / $280,000 ≈ 0.375 years
Add the recovered portion of the year to the full year recovered:
0.375 years + 3 years = 3.375 years
Cash Payback Period = 3.38 years.
So, the cash payback period for Proposal A is ≈ 3.75 years, and ≈ 3.38 years for Proposal B.
Question completion:
Project A as well as Project B require an initial investment of $1,050,000, have a 6-year life, and have expected total cash inflows of $1,680,000. Proposal A is expected to provide an annual net cash inflow of $280,000, while the annual net cash inflows for Proposal B are as follows: Year 1 $350,000 Year 2 $315,000 Year 3 $280,000 Year 4 $280,000 Year 5 $245,000 Year 6 $210,000. Determine the cash payback period for each proposal. Round your answers to two decimal places
Cash Payback Period Proposal A years years Proposal B