. Preference Decisions: NPV vs. IRR vs. Profitability Index

Stephens Industries is contemplating four projects: Project P, Project Q, Project R, and Project S. The capital costs and estimated after- tax net cash flows of each project are shown in the table that follows. Stephens’s after- tax cost of capital is 12 percent. Excess funds can-not be reinvested at greater than 12 percent.
Initial cost $ 200,000 $ 235,000 $ 190,000 $ 210,000
Annual cash flows:
Year 1 93,000 90,000 45,000 40,000
Year 2 93,000 85,000 55,000 50,000
Year 3 93,000 75,000 65,000 60,000
Year 4 0 55,000 70,000 65,000
Year 5 0 50,000 75,000 75,000
Net present value $ 23,370 $ 29,827 $ 27,233 $( 7,854)
Internal rate of 18.7% 17.6% 17.2% 10.6%
return Profitability index 1.12 1.13 1.14 0.95

Required
A. Which of the four projects are acceptable ­options? Why?

Project R, which has a minimal initial cost but have a higher profitability index

To determine which of the four projects are acceptable options, we can use three different criteria: Net Present Value (NPV), Internal Rate of Return (IRR), and Profitability Index. Let's analyze each criterion:

1. Net Present Value (NPV):
NPV measures the profitability of a project by calculating the present value of its expected cash flows, taking into account the company's cost of capital. A positive NPV indicates that the project is expected to generate more cash inflows than the initial investment.

- Project P: NPV = $23,370. Since it has a positive NPV, it is an acceptable option.
- Project Q: NPV = $29,827. Also, since it has a positive NPV, it is an acceptable option.
- Project R: NPV = $27,233. With a positive NPV, it is an acceptable option.
- Project S: NPV = $(7,854). It has a negative NPV, so it is not an acceptable option.

Based on NPV, Projects P, Q, and R are acceptable options, while Project S is not.

2. Internal Rate of Return (IRR):
IRR is the discount rate that makes the NPV of a project equal to zero. It represents the project's rate of return, and a higher IRR is generally preferred.

- Project P: IRR = 18.7%. Since it is greater than the cost of capital, it is an acceptable option.
- Project Q: IRR = 17.6%. It is also greater than the cost of capital, making it an acceptable option.
- Project R: IRR = 17.2%. With an IRR higher than the cost of capital, it is an acceptable option.
- Project S: IRR = 10.6%. Although it is still higher than the cost of capital, it has the lowest IRR among the projects.

Based on IRR, Projects P, Q, and R are acceptable options, while Project S has a relatively lower IRR.

3. Profitability Index:
The profitability index is calculated by dividing the present value of cash inflows by the initial investment. A profitability index greater than 1 indicates that the project is expected to generate positive returns.

- Project P: Profitability Index = 1.12. With a profitability index greater than 1, it is an acceptable option.
- Project Q: Profitability Index = 1.13. It also has a profitability index greater than 1, making it an acceptable option.
- Project R: Profitability Index = 1.14. With a profitability index greater than 1, it is an acceptable option.
- Project S: Profitability Index = 0.95. It has a profitability index below 1, indicating it may not generate positive returns.

Based on the profitability index, Projects P, Q, and R are acceptable options, while Project S has a lower profitability index.

In summary, based on the analysis of NPV, IRR, and Profitability Index, Projects P, Q, and R are acceptable options, while Project S is not.