Question

Suppose a company has proposed a new 4-year project. The project has an initial outlay of $29,000 and has expected cash flows of $7,000 in year 1, $8,000 in year 2, $11,000 in year 3, and $13,000 in year 4. The required rate of return is 14% for projects at this company. What is the profitability index for this project? (Answer to the nearest hundredth, e.g. 1.23)

Answer 1

The cash flows are:
Year 0:$29000
Year 1:$7000
Year 2:$8000
Year 3:$11000
Year 4:$13000

In year 0, the initial outlay or cash outflow for the project is $29,000, after that the company received cash inflows from the project.

Given that the required rate of return is 14%
Profitability index=Present value of future cash flows/Initial investments
Present value of future cash flows=Cash flow in year 1/(1+required return)^1+Cash flow in year 2/(1+required return)^2+Cash flow in year 3/(1+required return)^3+Cash flow in year 4/(1+required return)4

Present value=$7000/(1+14%)^1+$8000/(1+14%)^2+$11000/(1+14%)^3+$13000/(1+14%)^4
=$7000/(1.14)^1+$8000/(1.14)^2+$11000/(1.14)^3+$13000/(1.14)^4
=$7000/1.14+$8000/1.2996+$11000/1.481544+$13000/1.68896016
=$6140.350877+$6155.740228+$7424.686678+$7697.043606
=$27417.82139

Present value of future cash flows=$27417.82139
Initial investment=$29000
Profitability index=$27417.82139/$29000=0.945442117 or 0.95 (Rounded to two decimal places)