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A 25-year project has a cost of $1,500,000 and has annual cash flows of $400,000 in...

A 25-year project has a cost of $1,500,000 and has annual cash flows of $400,000 in years 1-15, and $200,000 in years 16-25. The company's required rate is 14%. Given this information, calculate the payback of the project.

2.25 years

4.25 years

2.75 years

3.75 years

3.25 years

Solutions

Expert Solution

Payback period is the time period required to cover the initial investment back. It does not take in to account the time value of money. In the payback period, the all cost will be covered and after that the profit will start incurring.

Note : It is assumed that all the cash flows are evenly distributed through out the year.

Initial investment = $ 1,500,000

Cash flows are shown in the below table-

Year Cash flow (in $) Cumulative cash flow (in $)
1 4,00,000 4,00,000
2 4,00,000 8,00,000
3 4,00,000 12,00,000
4 4,00,000 16,00,000
5 4,00,000 20,00,000
6 4,00,000 24,00,000
7 4,00,000 28,00,000
8 4,00,000 32,00,000
9 4,00,000 36,00,000
10 4,00,000 40,00,000
11 4,00,000 44,00,000
12 4,00,000 48,00,000
13 4,00,000 52,00,000
14 4,00,000 56,00,000
15 4,00,000 60,00,000
16 2,00,000 62,00,000
17 2,00,000 64,00,000
18 2,00,000 66,00,000
19 2,00,000 68,00,000
20 2,00,000 70,00,000
21 2,00,000 72,00,000
22 2,00,000 74,00,000
23 2,00,000 76,00,000
24 2,00,000 78,00,000
25 2,00,000 80,00,000

Payback period = 3 + 300,000 / 400,000 = 3 + 0.75

= 3.75 year

( As the initial investment is $1500,000, we need to cover this cost, we will take year corresponding to the cumulative value which is less than or equal to 1500,000, here it is 3 year. In 3 year 1200,000 $ will be covered, we will be needing $300,000 (1500,000 - 1200,000) more to cover full initial cost. As the cash flows are evenly distributed, remaining 300,000 $ will be covered from 4th year inflows of amount 400,000$) . Hence 300,000 / 400,000 is taken.

Hence payback period = 3.75 years.

jeff jeffy answered 1 year ago
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