Question

Profitability Index A project has an initial cost of $44,600, expected net cash inflows of $14,000 per year for 12 years, and a cost of capital of 14%. What is the project's PI? Do not round your intermediate calculations. Round your answer to two decimal places.

Answer 1

The cash flows are as follows:

Year 0:   -$44600
Year 1:   $14,000
Year 2:   $14,000
Year 3:   $14,000
Year 4:   $14,000
Year 5:   $14,000
Year 6:   $14,000
Year 7:   $14,000
Year 8:   $14,000
Year 9:   $14,000
Year 10: $14,000
Year 11: $14,000
Year 12: $14,000

Profitability index=(Present value of future cash flows)/(Initial cash outflow)
Present value of future cash flows= Summation of (cash flow in year n)/(1+Cost of capital)^n
Given that the cost of capital=14%
Present value of future cash flows=$14000/(1+14%)^1+$14000/(1+14%)^2+$14000/(1+14%)^3+$14000/(1+14%)^4+$14000/(1+14%)^5+$14000/(1+14%)^6+$14000/(1+14%)^7+$14000/(1+14%)^8+$14000/(1+14%)^9+$14000/(1+14%)^10+$14000/(1+14%)^11+$14000/(1+14%)^12
=$14000/(1.14)^1+$14000/(1.14)^2+$14000/(1.14)^3+$14000/(1.14)^4+$14000/(1.14)^5+$14000/(1.14)^6+$14000/(1.14)^7+$14000/(1.14)^8+$14000/(1.14)^9+$14000/(1.14)^10+$14000/(1.14)^11+$14000/(1.14)^12
=$14000/1.14+$14000/1.2996+$14000/1.481544+$14000/1.68896016+$14000/1.925414582+$14000/2.194972624+$14000/2.502268791+$14000/2.852586422+$14000/3.251948521+$14000/3.707221314+$14000/4.226232298+$14000/4.81790482

=$12280.70175+$10772.5454+$9449.60123+$8289.12388+$7271.161303+$6378.211667+$5594.922516+$4907.82677+$4305.175+$3776.413333+$3312.643275+$2905.827434

=$79244.15356 or $79244.15 (Rounded to two decimal places)

Initial investment=$44600
Profitability index=$79244.15/$44600=1.776774664 or 1.78 (Rounded to two decimal places)