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Last Study Topics. Internal Rate of Return Pitfalls of IRR. Today's Study Topics. Profitability Index Numerical What To Discount?. Profitability Index (PI).
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Last Study Topics • Internal Rate of Return • Pitfalls of IRR
Today's Study Topics • Profitability Index • Numerical • What To Discount?
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.
Continue • Example: The opportunity cost of capital is 10 percent, and our company has the following opportunities:
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
Continue For our three projects the profitability index is calculated as follows;
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
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
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
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
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
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?
Continue • Solution: • NPVa = -$90.91 • NPVb = +$4,044.73 • NPVc = +$39.47
Continue • Example 1: Consider the following projects • Project C0 C1 C2 C3 C4 C5 • A –1,000 1,000 0 0 0 0 • B –2,000 1,000 1,000 4,000 1,000 1,000 • C –3,000 1,000 1,000 0 1,000 1,000 • b. Calculate the payback period for each project? • PaybackA = • PaybackB = • PaybackC =
Numericals • Example 1: Consider the following projects • Project C0 C1 C2 C3 C4 C5 • A –1,000 1,000 0 0 0 0 • B –2,000 1,000 1,000 4,000 1,000 1,000 • C –3,000 1,000 1,000 0 1,000 1,000 • c. Which project(s) would a firm using the payback rule accept if the cutoff period were three years? • Solution:
Continue • Example : Consider the following two mutually exclusive projects: • Project C0 C1 C2 C3 • A –100 60 60 0 • B –100 0 0 140 • a. Calculate the NPV of each project for discount rates of 0, 10, and 20 percent?
Continue • Solution: • Discount Rate • 0% 10% 20% • NPVA +20.00 +4.13 -8.33 • NPVB +40.00 +5.18 -18.98 • b. In what circumstances should the company accept project A?
Continue • c- Calculate the NPV of the incremental investment (B – A) for discount rates of 0, 10, and 20 percent. Show that the circumstances in which you would accept A are also those in which the IRR on the incremental investment is less then the opportunity cost of capital. • Solution: The cash flows for (B – A) are: • C0C1C2C3 0 -60 -60 140
Continue • Discount Rate • 0% 10% 20% • NPVB-A +20.00 +1.05 -10.65 • IRRB-A = 10.7% • The company should accept Project A if the discount rate is greater than 10.7%.
Mutually Exclusive Projects • Example: The president of X Enterprises has to make choice between two possible investments; • Cash Flows ($ 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.
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.
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.
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
Summary • Profitability Index • Numerical