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Math  /  Data & Statistics

QuestionThe pay back period of an investment that achieves the following cash flow in a row (0,1000,2000,4000)(0,1000,2000,4000) and its initial outlay equals $5000\$ 5000 is:-
Select one: a. 3 years and 5 months b. 3 years and 6 months c. 2 years and 6 months d. 2 years and 5 months

Studdy Solution

STEP 1

1. The payback period is the time it takes for the cumulative cash flows to equal the initial investment.
2. The cash flows are given for each year in the sequence: (0,1000,2000,4000)(0, 1000, 2000, 4000).
3. The initial outlay or investment is $5000\$5000.
4. We need to determine the exact time (in years and months) when the cumulative cash flow equals or exceeds the initial investment.

STEP 2

1. Calculate cumulative cash flows year by year.
2. Determine the year in which the cumulative cash flow first exceeds the initial outlay.
3. Calculate the exact number of additional months required within that year to reach the initial investment.

STEP 3

Calculate the cumulative cash flow at the end of Year 1.
Cumulative Cash Flow at Year 1=0+1000=1000 \text{Cumulative Cash Flow at Year 1} = 0 + 1000 = 1000

STEP 4

Calculate the cumulative cash flow at the end of Year 2.
Cumulative Cash Flow at Year 2=1000+2000=3000 \text{Cumulative Cash Flow at Year 2} = 1000 + 2000 = 3000

STEP 5

Calculate the cumulative cash flow at the end of Year 3.
Cumulative Cash Flow at Year 3=3000+4000=7000 \text{Cumulative Cash Flow at Year 3} = 3000 + 4000 = 7000

STEP 6

Determine the year in which the cumulative cash flow first exceeds the initial outlay of $5000.
Year 3: Cumulative Cash Flow=7000>5000 \text{Year 3: Cumulative Cash Flow} = 7000 > 5000 Thus, the cumulative cash flow exceeds the initial outlay during Year 3.

STEP 7

Calculate the exact number of months required in Year 3 to reach the initial investment of $5000.
The cumulative cash flow at the end of Year 2 is 3000.Theadditionalamountneededtoreach3000. The additional amount needed to reach 5000 is: 5000−3000=2000 5000 - 3000 = 2000
The cash flow in Year 3 is 4000.Thefractionoftheyearneededtoachievetheadditional4000. The fraction of the year needed to achieve the additional 2000 is: \frac{2000}{4000} = 0.5 $ \text{ (half a year)}

STEP 8

Convert the fraction of the year into months.
0.5 years=6 months 0.5 \text{ years} = 6 \text{ months}

STEP 9

Combine the years and months to get the total payback period.
Therefore, the payback period is: 2 years+6 months 2 \text{ years} + 6 \text{ months}
The correct answer is: c. 2 years and 6 months

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