The payback period is a crucial financial metric used by businesses to assess the time it takes to recover their initial investment in a particular project or asset. In the case of Vandezande Inc.’s potential acquisition of a new machine, the payback period can be calculated based on the incremental net cash flows provided for each year.
The initial investment for the new machine is $458,000, and the incremental net cash flows for each of the five years are as follows:
To calculate the cumulative cash flows over time, we can sum up the cash flows for each year until we reach or exceed the initial investment. Let’s calculate the cumulative cash flows:
At the end of Year 3, the cumulative cash flows have exceeded the initial investment of $458,000. This means that the payback period for this investment falls between Year 2 and Year 3. To determine the exact payback period, we can calculate the fraction of the initial investment that is recovered in Year 3:
Recovery fraction in Year 3 = (Cumulative cash flow at the end of Year 3 – Initial investment) / Cash flow in Year 3
Recovery fraction in Year 3 = ($467,000 – $458,000) / $165,000 = $9,000 / $165,000 ≈ 0.0545
Now, we can calculate the payback period:
Payback period = Year 3 + (Recovery fraction in Year 3)
Payback period = 3 + 0.0545 ≈ 3.0545 years
Rounded to the nearest tenth, the payback period for Vandezande Inc.’s investment in the new machine is approximately 3.1 years. Therefore, the answer closest to the calculated payback period is:
B. 3.1
In conclusion, Vandezande Inc. can expect to recover its initial investment in the new machine in approximately 3.1 years based on the provided incremental net cash flows. This metric is valuable for assessing the project’s risk and liquidity as it indicates how long it will take to recoup the investment from the cash generated by the asset.
The payback period is a crucial financial metric used by businesses to assess the time it takes to recover their initial investment in a particular project or asset. In the case of Vandezande Inc.’s potential acquisition of a new machine, the payback period can be calculated based on the incremental net cash flowsnet cash flows provided for each year.The initial investment for the new machine is $458,000, and the incremental net cash flows for each of the five years are as follows:
– Year 1: $150,000
– Year 2: $152,000
– Year 3: $165,000
– Year 4: $148,000
– Year 5: $150,000
To calculate the cumulative cash flows over time, we can sum up the cash flows for each year until we reach or exceed the initial investment. Let’s calculate the cumulative cash flows:
– Year 1: $150,000
– Year 2: $150,000 + $152,000 = $302,000
– Year 3: $302,000 + $165,000 = $467,000
At the end of Year 3, the cumulative cash flows have exceeded the initial investment of $458,000. This means that the payback period for this investment falls between Year 2 and Year 3. To determine the exact payback period, we can calculate the fraction of the initial investment that is recovered in Year 3:
Recovery fraction in Year 3 = (Cumulative cash flow at the end of Year 3 – Initial investment) / Cash flow in Year 3
Recovery fraction in Year 3 = ($467,000 – $458,000) / $165,000 = $9,000 / $165,000 ≈ 0.0545
Now, we can calculate the payback period:
Payback period = Year 3 + (Recovery fraction in Year 3)
Payback period = 3 + 0.0545 ≈ 3.0545 years
Rounded to the nearest tenth, the payback period for Vandezande Inc.’s investment in the new machine is approximately 3.1 years. Therefore, the answer closest to the calculated payback period is:
B. 3.1
In conclusion, Vandezande Inc. can expect to recover its initial investment in the new machine in approximately 3.1 years based on the provided incremental net cash flows. This metric is valuable for assessing the project’s risk and liquidity as it indicates how long it will take to recoup the investment from the cash generated by the asset.
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