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Project A as well as project B require an initial investment of $1,050,000, have a six-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

User Joran
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1 Answer

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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

User Renato Mefi
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