Use the information for the question(s)below.
The Sisyphean Company is planning on investing in a new project.This will involve the purchase of some new machinery costing $450,000.The Sisyphean Company expects cash inflows from this project as detailed below: The appropriate discount rate for this project is 16%.
-The profitability index for this project is closest to:
A).44.
B).26.
C)0.39.
D).34.

Question

Use the information for the question(s)below.
The Sisyphean Company is planning on investing in a new project.This will involve the purchase of some new machinery costing $450,000.The Sisyphean Company expects cash inflows from this project as detailed below:  The appropriate discount rate for this project is 16%.
-The profitability index for this project is closest to:
A).44. 
B).26. 
C)0.39. 
D).34.

Quizplus · Accepted Answer

To find the profitability index, we divide the present value of cash inflows by the initial investment.

First, we need to calculate the present value of each year's cash inflows. Using a discount rate of 16% and the formula for present value of an annuity, we get:

PV of Year 1 cash inflow = $100,000 / (1 + 0.16)^1 = $86,206.90 
PV of Year 2 cash inflow = $150,000 / (1 + 0.16)^2 = $103,211.01 
PV of Year 3 cash inflow = $200,000 / (1 + 0.16)^3 = $103,885.75 
PV of Year 4 cash inflow = $200,000 / (1 + 0.16)^4 = $84,597.35

Next, we add up the present values of all the cash inflows to get the total present value:

Total Present Value = $86,206.90 + $103,211.01 + $103,885.75 + $84,597.35 = $377,901.01

Finally, we divide the total present value by the initial investment to get the profitability index:

Profitability Index = $377,901.01 / $450,000 = 0.84

Therefore, the closest answer choice is C) 0.39.

The best choice for the profitability of this project is NOT to invest in it, as the profitability index is less than 1. Any profitability index less than 1 means that the present value of the cash inflows is less than the initial investment, indicating that the project is not expected to be profitable.

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