Question

The management of Unter Corporation, an architectural design firm, is considering an investment with the following cash flows: Year Investment Cash Inflow 1 $ 54,000 $ 4,000 2 $ 4,000 $ 8,000 3 $ 16,000 4 $ 17,000 5 $ 20,000 6 $ 18,000 7 $ 16,000 8 $ 14,000 9 $ 13,000 10 $ 13,000 Required: 1. Determine the payback period of the investment. 2. Would the payback period be affected if the cash inflow in the last year were several times as large?

Answer 1

The payback period is the time it takes for the cash inflows from an investment to equal the initial investment cost. If the cash inflow in the last year were several times as large, it would affect the payback period.

Step-by-step explanation:

The payback period of an investment is the amount of time it takes for the cash inflows from the investment to equal the initial investment cost. To calculate the payback period, you add up the cash inflows until the total exceeds the initial investment. In this case, the investment has cash inflows of $4,000 in Year 1, $8,000 in Year 2, $16,000 in Year 3, and so on, until Year 10. You would continue adding up the cash inflows until the total exceeds the initial investment of $54,000. Once the total exceeds the initial investment, you would determine the fraction of the final year's cash inflow that is needed to reach the total.

If the cash inflow in the last year were several times as large, it would affect the payback period. This is because a larger cash inflow in the last year would reduce the payback period. Let's say the cash inflow in the last year is 3 times as large, that would mean $39,000 instead of $13,000. Since the cash inflow in the last year is much larger, it would take fewer years to recover the initial investment, resulting in a shorter payback period.

Answer 2

1. 4.65 years

2. No

Step-by-step explanation:

In the payback, we analyze in how many years the invested amount is recovered. The computation is shown below:

In year 0 = $58,000 ($54,000 + $4,000)

In year 1 = $4,000

In year 2 = $8,000

In year 3 = $16,000

In year 4 = $17,000

In year 5 = $20,000

In year 6 = $18,000

And so on

If we sum the first 4 year cash inflows than it would be $45,000

Now we deduct the $45,000 from the $58,000 , so the amount would be $13,000 as if we added the fifth year cash inflow so the total amount exceed to the initial investment. So, we deduct it

And, the next year cash inflow is $20,000

So, the payback period equal to

= 4 years + $13,000 ÷ $20,000

= 4.65 yeas

In 4.65 yeas, the invested amount is recovered.

2. No it does not affected as the initial amount is recovered in less than five year