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## Net Present Value and Other Investment Rules

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**Key Concepts and Skills**• Be able to compute payback and discounted payback and understand their shortcomings • Be able to compute the internal rate of return and profitability index, understanding the strengths and weaknesses of both approaches • Be able to compute net present value and understand why it is the best decision criterion**1.Net Present Value**• NPV is the difference between the market value of a project and its cost or how much value is created from undertaking an investment. • The first step is to estimate the expected future cash flows. • The second step is to estimate the required return for projects of this risk level. • The third step is to find the present value of the cash flows and subtract the initial investment, which is the NPV.**Why Use Net Present Value?**• Accepting positive NPV projects benefits shareholders. • NPV uses cash flows • NPV uses all the cash flows of the project • NPV discounts the cash flows properly**n**CFt ∑ PV = (1 + R)t t = 0 Net Present Value Sum of the PVs of all cash flows NOTE: t = 0 Initial cost often is CF0 and is an outflow. n CFt ∑ - CF0 NPV = (1 + R)t t = 1 Initial Outlay**NPV – Decision Rule**If the NPV is positive, accept the project. Reject if negative. • A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners. • Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal.**Calculating NPV with Spreadsheets**• Spreadsheets are an excellent way to compute NPVs, especially when you have to compute the cash flows as well. • Using the NPV function: • The first component is the required return entered as a decimal. • The second component is the range of cash flows beginning with year 1. • Add the initial investment after computing the NPV.**2. Payback Period**• How long does it take to get the initial cost back in a nominal sense? • Computation • Estimate the cash flows • Subtract the future cash flows from the initial cost until the initial investment has been recovered • Decision Rule – Accept if the payback period is less than some preset limit**The Payback Period Method**• Disadvantages: • Ignores the time value of money • Ignores cash flows after the payback period • Biased against long-term projects • Requires an arbitrary acceptance criteria • A project accepted based on the payback criteria may not have a positive NPV**The Payback Period Method**• Disadvantages: • Ignores the time value of money • Ignores cash flows after the payback period • Biased against long-term projects • Requires an arbitrary acceptance criteria • A project accepted based on the payback criteria may not have a positive NPV • Advantages: • Easy to understand • Biased toward liquidity**3.Discounted Payback Period**• Compute the present value of each cash flow and then determine how long it takes to pay back on a discounted basis • Compare to a specified required period • Decision Rule - Accept the project if it pays back on a discounted basis withinthe specified time**4. Profitability Index**• For conventional CF Projects: PV(Cash Inflows) Absolute Value of Initial Investment • PI is essentially a Benefit/Cost Ratio • Minimum Acceptance Criteria: • Accept if PI > 1**Advantages and Disadvantages of the Profitability Index**• Advantages • Closely related to NPV, generally leading to identical decisions • Easy to understand and communicate • May be useful when available investment funds are limited • Disadvantages • May lead to incorrect decisions in comparisons of mutually exclusive investments PI = PV(future CF) | Initial Outlay |**4 Internal Rate of Return**• IRRis the most important alternative to NPV • It is often used in practice and is intuitively appealing • It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere**The Internal Rate of Return**• IRR: the discount rate that sets NPV to zero • Minimum Acceptance Criteria: • Accept if the IRR exceeds the required return • Ranking Criteria: • Select alternative with the highest IRR**Similarity Between NPV & IRR Formulas**NPV: Enter R and solve for NPV IRR: Enter NPV = 0, solve for IRR.**5.5 Problems with IRR**• Multiple IRRs • The Scale Problem • Mutually Exclusive Projects**$200 $800**0 1 2 3 100% = IRR2 - $800 -$200 0% = IRR1 Multiple IRRs There are two IRRs for this project: Which one should we use?**ModifiedInternal Rate of Return (MIRR)**• Controls for some problems with IRR Three Methods: • DiscountingApproach • Reinvestment Approach • 3. Combination Approach • MIRRwill be different number for each method • For this reason, some of us call it the Meaningless IRR rather than the Modified IRR.**Best Method**for MIRR MIRR Method 1DiscountingApproach Step 1: Discount future outflows (negative cash flows) to present and add to CF0 Step 2: Zero out negative cash flows which have been added to CF0. Step 3: Compute IRR normally**MIRR Method 2ReinvestmentApproach**Step 1: Compound ALL cash flows (except CF0) to end of project’s life Step 2: Zero out all cash flows which have been added to the last year of the project’s life. Step 3: Compute IRR normally**MIRR Method 3CombinationApproach**Step 1: Discount all outflows (except CF0) to present and add to CF0. Step 2: Compound all cash inflows to end of project’s life Step 3: Compute IRR normally**The Scale Problem**How to deal with this issue? - Calculate incremental IRR or NPV of incremental cash flows**Dealing with The Scale Problem**How to justify the large budget using the IRR approach?**Dealing with The Scale Problem**• Formula for Calculating the Incremental IRR: • IRR=66.67% • NPV of Incremental Cash Flows:**IRR and Mutually Exclusive Projects**• Mutually exclusive projects • If you choose one, you can’t choose the other • Example: You can choose pursue an MBA at • either the UWM or Marquette, but not both • Intuitively you would use the following decision rules: • NPV – choose the project with the higher NPV • IRR – choose the project with the higher IRR**Example With Mutually Exclusive Projects**The required return for both projects is 10%. Which project should you accept and why?**NPV Profiles**IRR for A = 19.43% IRR for B = 22.17% Crossover Point = 11.8%**With the cross– over in the NPV profiles, we find that the**better project depends critically on the required return. When the required return is low (less than 11.8%), pick project A. When the required return is high (greater than 11.8%), pick project B. Mutually Exclusive**NPV vs. IRR**• NPV and IRR will generally give us the same decision With Two Exceptions: • Non-conventional cash flows – cash flow signs change more than once • There can be multiple IRRs for the same project • Mutually exclusive projects • Initial investments are substantially different • Timing of cash flows is substantially different**5.7 The Practice of Capital Budgeting**• Varies by industry: • Some firms may use payback, while others choose an alternative approach. • The most frequently used technique for large corporations is either IRR or NPV.