A firm is considering a new inventory system that will cost $120,000. The system

Question

A firm is considering a new inventory system that will cost $120,000. The system is expected to generate positive cash flows over the next four years in the amounts of $35,000 in year 1, $55,000 in year 2, $65,000 in year 3, and $40,000 in year 4. The firm's required rate of return is 9%. 1) What is the payback period of this project? 2) What is the net present value (NPV)
of the project? _____ 3) Based on the information , what is the internal rate of return
(IRR) of this project? 4) what is the profitability index (PI) of
this project?

Explanation / Answer

amount payed back after 2years = 90000

payback period = 2 + 30000/65000

= 2.46 years

discount payback method

amount to be payed after 2 years = 120000 - 35000/1.09 + 55000/1.09^2

= 41597.5086272

discounted payback period

= 2 + 41597.5086272/65000/1.09^3

= 2.83 years

NPV = -120000 + 35000/1.09 + 55000/1.09^2 + 65000/1.09^3 + 40000/1.09^4

= 36931.43

3)
0 = -120000 + 35000/(1+IRR) + 55000/(1+IRR)^2 + 65000/(1+IRR)^3 + 40000/(1+IRR)^4

IRR = 21.78%

4)

PV of cash flows = 156931.426019

Profitability index PI = 156931.426019/120000 = 1.31

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