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A 50-year project has a cost of $500,000 and has annual cash flows of $100,000 in...

A 50-year project has a cost of $500,000 and has annual cash flows of $100,000 in years 1-25, and $200,000 in years 26-50. The company's required rate is 8%. Given this information, calculate the payback of the project.

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Answer #1

Computation of Discounted Pay Back Period

Since the required rate is given, the cash flows are to be discounted to find out payback period.

Years Inflow Present value Discount factor @ 8% Present Value
1 100000 0.9259 92590
2 100000 0.8573 85730
3 100000 0.7938 79380
4 100000 0.7350 73500
5 100000 0.6806 68060
6 100000 0.6302 63020
7 100000 0.5835 58350
8 100000 0.5403 54030

Payback Period is the period required to cover the initial investment of the project.

When adding the present value of cash flows till 6th year, it will be near to 500000.

Sum of 6 years inflow = 92590+85730+79380+73500+68060+63020 = 462280

To cover investment of 500000, further amount required = 500000 - 462280 = 37720

This is taken from the 7th year's inflow ie; 37720 / 58350 = 0.646

Therefore Discounted Pay Back Period = 6 years + 0.646 = 6.646 years or 6.65 years

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