Question

A set of cash flows begins at $8000 the first year, with an increase each year...

A set of cash flows begins at $8000 the first year, with an increase each year until n=10 years. If the interest rate is 5%, what is the present value when the annual increase is 15%?

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Answer #1

The annual increase in cash flow is:

The interest is:

Year Cash flow ($) Present value ($)
1 8000 8000/(1.05) = 7619.05
2 8000 × 1.15 = 9200 9200/(1.05)2 = 8344.67
3 9200 × 1.15 = 10580 10580/(1.05)3 = 9139.40
4 10580 × 1.15 = 12167 12167/(1.05)4 = 10009.82
5 12167 × 1.15 = 13992.05 13992.05/(1.05)5 = 10963.14
6 13992.05 × 1.15 = 16090.86 16090.86/(1.05)6 = 12007.25
7 16090.86 × 1.15 = 18504.49 18504.49/(1.05)7 = 13150.79
8 18504.49 × 1.15 = 21280.16 21280.16/(1.05)8 = 14403.25
9 21280.16 × 1.15 = 24472.18 24472.18/(1.05)9 = 15775
10 24472.18 × 1.15 = 28143 28143/(1.05)10 = 17277.36
Net 118689.73

So, the present value will be $118689.73.

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