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Last Study Topics

Learn about the key concepts of Profitability Index (PI) and how it aids in project selection when resources are limited. Follow examples and calculations to understand how PI can optimize investment decisions efficiently.

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Last Study Topics

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  1. Last Study Topics • Internal Rate of Return • Pitfalls of IRR

  2. Today's Study Topics • Profitability Index • Numerical • What To Discount?

  3. Profitability Index (PI) • When resources are limited, the profitability index (PI) provides a tool for selecting among various project combinations and alternatives • A set of limited resources and projects can yield various combinations. • The highest weighted average PI can indicate which projects to select.

  4. Continue • Example: The opportunity cost of capital is 10 percent, and our company has the following opportunities:

  5. Continue • We must pick the projects that offer the highest net present value (NPV) per dollar of initial outlay. • This ratio is known as the profitability index. • PI = NPV / INV

  6. Continue For our three projects the profitability index is calculated as follows;

  7. Profitability Index Example We only have $300,000 to invest. Which do we select? Proj NPV Investment PI A 230,000 200,000 1.15 B 141,250 125,000 1.13 C 194,250 175,000 1.11 D 162,000 150,000 1.08

  8. Profitability Index Example - continued Proj NPV Investment PI A 230,000 200,000 1.15 B 141,250 125,000 1.13 C 194,250 175,000 1.11 D 162,000 150,000 1.08 Select projects with highest Weighted Avg PI WAPI (BD) = 1.13(125) + 1.08(150) + 0.0 (25) (300) = 1.01

  9. Profitability Index Example - continued Proj NPV Investment PI A 230,000 200,000 1.15 B 141,250 125,000 1.13 C 194,250 175,000 1.11 D 162,000 150,000 1.08 Select projects with highest Weighted Avg PI WAPI (BC) = 1.13(125) + 1.11(175) + 0.0 (0) (300) = 1.12

  10. Profitability Index Example - continued Proj NPV Investment PI A 230,000 200,000 1.15 B 141,250 125,000 1.13 C 194,250 175,000 1.11 D 162,000 150,000 1.08 Select projects with highest Weighted Avg PI WAPI (A) = 1.15(200) + 0(0) + 0.0 (0) (300) = 0.77

  11. Profitability Index Example - continued Proj NPV Investment PI A 230,000 200,000 1.15 B 141,250 125,000 1.13 C 194,250 175,000 1.11 D 162,000 150,000 1.08 Select projects with highest Weighted Avg PI WAPI (BD) = 1.01 WAPI (A) = 0.77 WAPI (BC) = 1.12

  12. Numericals • Example 1: Consider the following projects • Project C0 C1 C2 C3 C4 C5 • A –1,000 1,000 0 0 0 0 • B –2,000 1,000 1,000 4,000 1,000 1,000 • C –3,000 1,000 1,000 0 1,000 1,000 • a. If the opportunity cost of capital is 10 percent, which projects have a positive NPV?

  13. Continue • Solution: • NPVa = -$90.91 • NPVb = +$4,044.73 • NPVc = +$39.47

  14. Continue • Example 1: Consider the following projects • Project C0 C1 C2 C3 C4 C5 • A –1,000 1,000 0 0 0 0 • B –2,000 1,000 1,000 4,000 1,000 1,000 • C –3,000 1,000 1,000 0 1,000 1,000 • b. Calculate the payback period for each project? • PaybackA = • PaybackB = • PaybackC =

  15. Numericals • Example 1: Consider the following projects • Project C0 C1 C2 C3 C4 C5 • A –1,000 1,000 0 0 0 0 • B –2,000 1,000 1,000 4,000 1,000 1,000 • C –3,000 1,000 1,000 0 1,000 1,000 • c. Which project(s) would a firm using the payback rule accept if the cutoff period were three years? • Solution:

  16. Continue • Example : Consider the following two mutually exclusive projects: • Project C0 C1 C2 C3 • A –100 60 60 0 • B –100 0 0 140 • a. Calculate the NPV of each project for discount rates of 0, 10, and 20 percent?

  17. Continue • Solution: • Discount Rate • 0% 10% 20% • NPVA +20.00 +4.13 -8.33 • NPVB +40.00 +5.18 -18.98 • b. In what circumstances should the company accept project A?

  18. Continue • c- Calculate the NPV of the incremental investment (B – A) for discount rates of 0, 10, and 20 percent. Show that the circumstances in which you would accept A are also those in which the IRR on the incremental investment is less then the opportunity cost of capital. • Solution: The cash flows for (B – A) are: • C0C1C2C3 0 -60 -60 140

  19. Continue • Discount Rate • 0% 10% 20% • NPVB-A +20.00 +1.05 -10.65 • IRRB-A = 10.7% • The company should accept Project A if the discount rate is greater than 10.7%.

  20. Mutually Exclusive Projects • Example: The president of X Enterprises has to make choice between two possible investments; • Cash Flows ($ thousands) • Project C0 C1 C2 IRR (%) • A –400 250 300 23 • B –200 140 179 36 • The opportunity cost of capital is 9 percent. Mr. Clops is tempted to take B, which has the higher IRR.

  21. Continue • a. Explain to Mr. Clops why this is not the correct procedure. • Solution: Because Project A requires a larger capital outlay, it is possible that Project A has both a lower IRR and a higher NPV than Project B. (In fact, NPVA is greater than NPVB for all discount rates less than 10 percent.) • Because the goal is to maximize shareholder wealth, NPV is the correct criterion.

  22. Continue • b. Show him how to adapt the IRR rule to choose the best project. • Solution: To use the IRR criterion for mutually exclusive projects, calculate the IRR for the incremental cash flows: • C0 C1 C2 IRR • A - B -200 +110 +121 10% • Because the IRR for the incremental cash flows exceeds the cost of capital, the additional investment in A is worthwhile.

  23. Continue • c. Show him that this project also has the higher NPV. • Solution: Calculate the Respective NPV’s of Project A & B; • NPVA = $81.86 • NPVB = $79.10

  24. Summary • Profitability Index • Numerical

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