University:
California State University, Northridge
Course:
FIN 452 | Investment Analysis
Academic year:

2024
Views:

409

Pages:

34
Author:

Skylar Newton

• • • • • Internal Rate of Return Most important alternative to NPV Widely used in practice Intuitively appealing Based entirely on the estimated cash flows Independent of interest rates IRR Definition and Decision Rule • Definition: – IRR = discount rate that makes the NPV = 0 • Decision Rule: – Accept the project if the IRR is greater than the required return NPV vs. IRR NPV: Enter r, solve for NPV n CFt = NPV ∑ t t = 0 (1 + R ) IRR: Enter NPV = 0, solve for IRR. CFt =0 ∑ t t = 0 (1 + IRR ) n Computing IRR For The Project • Without a financial calculator or Excel, this becomes a trial-and-error process • Calculator – Enter the cash flows as for NPV – Press IRR and then CPT – IRR = 16.13% > 12% required return • Do we accept or reject the project? NPV Profile For The Project 70,000 60,000 50,000 NPV 40,000 IRR = 16.13% 30,000 20,000 10,000 0 -10,000 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 -20,000 Discount Rate 0.2 0.22 Decision Criteria Test IRR • Does the IRR rule: – – – – Account for the time value of money? Account for the risk of the cash flows? Provide an indication about the increase in value? Permit project ranking? • Should we consider the IRR rule for our primary decision criteria? IRR - Advantages • Preferred by executives – Intuitively appealing – Easy to communicate the value of a project • If the IRR is high enough, may not need to estimate a required return • Considers all cash flows • Considers time value of money • Provides indication of risk IRR - Disadvantages • Can produce multiple answers • Cannot rank mutually exclusive projects • Reinvestment assumption flawed Summary of Decisions for the Project Summary Net Present Value Accept Payback Period ??? Average Accounting Return ??? Internal Rate of Return Accept NPV vs. IRR • NPV and IRR will generally give the same decision • Exceptions – Non-conventional cash flows • Cash flow sign changes more than once – Mutually exclusive projects • Initial investments are substantially different • Timing of cash flows is substantially different • Will not reliably rank projects IRR & Non-Conventional Cash Flows • “Non-conventional” – Cash flows change sign more than once – Most common: • Initial cost (negative CF) • A stream of positive CFs • Negative cash flow to close project. • For example, nuclear power plant or strip mine. – More than one IRR …. – Which one do you use to make your decision? Multiple IRRs • Descartes Rule of Signs CFt =0 ∑ t t = 0 (1 + IRR ) n • Polynomial of degree n→n roots – When you solve for IRR you are solving for the root of an equation – 1 real root per sign change – Rest = imaginary (i2 = -1) Non-Conventional Cash Flows • Suppose an investment will cost $90,000 initially and will generate the following cash flows: – Year 1: 132,000 – Year 2: 100,000 – Year 3: -150,000 • The required return is 15%. • Should we accept or reject the project? Non-Conventional Cash Flows Summary of Decision Rules • NPV > 0 at 15% required return, so you should Accept • IRR =10.11% (using a financial calculator), which would tell you to Reject • Recognize the non-conventional cash flows and look at the NPV profile I= YR 0 1 2 3 NPV IRR-1 IRR-2 15% CF -$90,000 $132,000 $100,000 -$150,000 $1,769.54 10.11% 42.66% >0 < 15% > 15% NPV Profile IRR = 10.11% and 42.66% $4,000.00 $2,000.00 NPV $0.00 ($2,000.00) 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 ($4,000.00) ($6,000.00) ($8,000.00) When you cross the x-axis more than once, there will be more than one return that solves the equation ($10,000.00) Discount Rate Independent versus Mutually Exclusive Projects • Independent – The cash flows of one project are unaffected by the acceptance of the other. • Mutually Exclusive – The acceptance of one project precludes accepting the other. Reinvestment Rate Assumption • IRR assumes reinvestment at IRR • NPV assumes reinvestment at the firm’s weighted average cost of capital(opportunity cost of capital) – More realistic – NPV method is best • NPV should be used to choose between mutually exclusive projects Example of Mutually Exclusive Projects Period Project A Project B 0 -500 -400 1 325 325 2 325 200 IRR 19.43% 22.17% NPV 64.05 60.74 The required return for both projects is 10%. Which project should you accept and why? NPV Profiles IRR for A = 19.43% $160.00 $140.00 IRR for B = 22.17% $120.00 Crossover Point = 11.8% NPV $100.00 $80.00 A B $60.00 $40.00 $20.00 $0.00 ($20.00) 0 0.05 0.1 0.15 ($40.00) Discount Rate 0.2 0.25 0.3 Two Reasons NPV Profiles Cross • Size (scale) differences. – Smaller project frees up funds sooner for investment. – The higher the opportunity cost, the more valuable these funds, so high discount rate favors small projects. • Timing differences. – Project with faster payback provides more CF in early years for reinvestment. – If discount rate is high, early CF especially good Conflicts Between NPV and IRR • NPV directly measures the increase in value to the firm • Whenever there is a conflict between NPV and another decision rule, always use NPV • IRR is unreliable in the following situations: – Non-conventional cash flows – Mutually exclusive projects Modified Internal Rate of Return (MIRR) • Controls for some problems with IRR • Method 1.Discounting Approach = Discount future outflows to present and add to CF0 MIRR will be unique number for each method – Discount (finance) / compound (reinvestment) rate externally supplied MIRR Method 1 Discounting Approach 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 Method 1: Discounting Approach R= 20% Yr CF ADJ MCF 0 -60 -69.444 -129.44444 1 155 155 2 -100 0 IRR= 19.74% MIRR versus IRR • MIRR correctly assumes reinvestment at opportunity cost = WACC • MIRR avoids the multiple IRR problem • Managers like rate of return comparisons, and MIRR is better for this than IRR Profitability Index • Measures the benefit per unit cost, based on the time value of money – A profitability index of 1.1 implies that for every $1 of investment, we create an additional $0.10 in value • Can be very useful in situations of capital rationing • Decision Rule: If PI > 1.0 → Accept Profitability Index • For conventional CF Projects: CFt ∑ t t =1 (1 + r ) PI = CF0 n PV(Cash Inflows) Absolute Value of Initial Investment Advantages and Disadvantages of Profitability Index • Advantages – Closely related to NPV, generally leading to identical decisions • Considers all CFs • Considers TVM – Easy to understand and communicate – Useful in capital rationing • Disadvantages – May lead to incorrect decisions in comparisons of mutually exclusive investments (can conflict with NPV) Profitability Index Example of Conflict with NPV CF(0) PV(CIF) PI NPV A (10,000.00) 15,000.00 1.50 5,000.00 B (100,000.00) 125,000.00 1.25 25,000.00 Capital Budgeting In Practice • Consider all investment criteria when making decisions • NPV and IRR are the most commonly used primary investment criteria • Payback is a commonly used secondary investment criteria • All provide valuable information Summary Calculate ALL -- each has value Method What it measures NPV Payback IRR → $ increase in VF → Liquidity → E(R), risk Metric $$ Years % NPV Summary Net present value = – Difference between market value (PV of inflows) and cost – Accept if NPV > 0 – No serious flaws – Preferred decision criterion IRR Summary Internal rate of return = – Discount rate that makes NPV = 0 – Accept if IRR > required return – Same decision as NPV with conventional cash flows – Unreliable with: • Non-conventional cash flows • Mutually exclusive projects – MIRR = better alternative Payback Summary Payback period = – Length of time until initial investment is recovered – Accept if payback < some specified target – Doesn’t account for time value of money – Ignores cash flows after payback – Arbitrary cutoff period – Asks the wrong question

Net Present Value and Other Investment Criteria, Part 2

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