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 ProjectInvestment ($ Millions) NPV ($ Millions) PI A B C 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? ProjNPV InvestmentPI A230,000200, B141,250125, C194,250175, D162,000150,

Profitability Index Example - continued ProjNPV InvestmentPI A230,000200, B141,250125, C194,250175, D162,000150, Select projects with highest Weighted Avg PI WAPI (BD) = 1.13(125) (150) (25) (300) = 1.01

Profitability Index Example - continued ProjNPV InvestmentPI A230,000200, B141,250125, C194,250175, D162,000150, Select projects with highest Weighted Avg PI WAPI (BC) = 1.13(125) (175) (0) (300) = 1.12

Profitability Index Example - continued ProjNPV InvestmentPI A230,000200, B141,250125, C194,250175, D162,000150, Select projects with highest Weighted Avg PI WAPI (A) = 1.15(200) + 0(0) (0) (300) = 0.77

Profitability Index Example - continued ProjNPV InvestmentPI A230,000200, B141,250125, C194,250175, D162,000150, 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, B –2,000 1,000 1,000 4,000 1,000 1,000 C –3,000 1,000 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, – NPVc = +$39.47

Continue Example 1: Consider the following projects Project C0 C1 C2 C3 C4 C5 A –1,000 1, B –2,000 1,000 1,000 4,000 1,000 1,000 C –3,000 1,000 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, B –2,000 1,000 1,000 4,000 1,000 1,000 C –3,000 1,000 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 – B – – a. Calculate the NPV of each project for discount rates of 0, 10, and 20 percent?

Continue Solution: Discount Rate 0% 10% 20% NPV A NPV B – 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: – C0C1C2C

Continue Discount Rate 0% 10% 20% NPV B-A IRR B-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 – B – – 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 % – 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