Find the payback for the investment if you are given an investment of $30,000 and an...

Find the payback for the investment if you are given an investment of $30,000 and an annual income of 20,000 in the first year that is increasing 3000/year after that for 6 years. Show work.

Solutions

Expert Solution

Solution :- Initial investment = $ 30,000

Year	Annual income	Cumulative annual income
1	20000	20000
2	23000 (20000 + 3000)	43000 (20000 + 23000)
3	26000 (23000 + 3000)	69000 (20000 + 23000 + 26000)
4	29000 (26000 + 3000)	98000 (20000 + 23000 + 26000 + 29000)
5	32000 (29000 + 3000)	130000 (20000 + 23000 + 26000 + 29000 + 32000)
6	35000 (32000 + 3000)	165000 (20000 + 23000 + 26000 + 29000 + 32000 + 35000)
7	38000 (35000 + 3000)	203000 (20000 + 23000 + 26000 + 29000 + 32000 + 35000 + 38000)

Payback period is the length of time required to recover the initial cost of investment project. In the given question, Pay back period of investment lies between Year 1 and Year 2, accordingly, by interpolation, Payback period is calculated as follows:-

= 1 + (30000 - 20000) / 23000

= 1 + 10000 / 23000

= 1 + 0.43 (approx).

= 1.43 Years.

Conclusion :- Payback period of investment = 1.43 Years.

jeff jeffy answered 1 year ago

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