【正文】 o n r e t a i n e d e a r n i n g s 2 2 . 1 M a i n t e n a n c e o f t a r g e t E PS o r P E r a ti o 14 1 4 . 9 Aswath Damodaran 13 An Alternative to IRR with Capital Rationing ? The problem with the NPV rule, when there is capital rationing, is that it is a dollar value. It measures success in absolute terms. ? The NPV can be converted into a relative measure by dividing by the initial investment. This is called the profitability index. ? Profitability Index (PI) = NPV/Initial Investment ? In the example described, the PI of the two projects would have been: ? PI of Project A = $467,937/1,000,000 = % ? PI of Project B = $1,358,664/10,000,000 = % Project A would have scored higher. Aswath Damodaran 14 Case 3: NPV versus IRR Cash Flow Investment $ 5,000,000 $ 10,000,000 Project A Cash Flow Investment Project B NPV = $1,191,712 IRR=% $ 4,000,000 $ 3,200,000 $ 3,000,000 NPV = $1,358,664 IRR=% $ 10,000,000 $ 3,000,000 $ 3,500,000 $ 4,500,000 $ 5,500,000 Aswath Damodaran 15 Why the difference? These projects are of the same scale. Both the NPV and IRR use timeweighted cash flows. Yet, the rankings are different. Why? Which one would you pick? a) Project A. It gives me the bigger bang for the buck and more margin for error. b) Project B. It creates more dollar value in my business. Aswath Damodaran 16 NPV, IRR and the Reinvestment Rate Assumption ? The NPV rule assumes that intermediate cash flows on the project get reinvested at the hurdle rate (which is based upon what projects of parable risk should earn). ? The IRR rule assumes that intermediate cash flows on the project get reinvested at the IRR. Implicit is the assumption that the firm has an infinite stream of projects yielding similar IRRs. ? Conclusion: When the IRR is high (the project is creating significant surplus value) and the project life is long, the IRR will overstate the true return on the project. Aswath Damodaran 17 Solution to Reinvestment Rate Problem Aswath Damodaran 18 Why NPV and IRR may differ.. Even if projects have the same lives ? A project can have only one NPV, whereas it can have more than one IRR. ? The NPV is a dollar surplus value, whereas the IRR is a percentage measure of return. The NPV is therefore likely to be larger for “l(fā)arge scale” projects, while the IRR is higher for “smallscale” projects. ? The NPV assumes that intermediate cash flows get reinvested at the “hurdle rate”, which is based upon what you can make on investments of parable risk, while the IRR assumes that intermediate cash flows get reinvested at the “IRR”. Aswath Damodaran 19 Comparing projects with different lives.. Project A $1500 $350 $350 $350 $350 $350 $1000 $400 $400 $400 $400 $400 $350 $350 $350 $350 $350 Project B NPV of Project A = $ 442 IRR of Project A = % NPV of Project B = $ 478 IRR for Project B = % Hurdle Rate for Both Projects = 12% Aswath Damodaran 20 Why NPVs cannot be pared.. When projects have different lives. ? The present values of mutually exclusive projects with different lives cannot be pared, since there is a bias towards longerlife projects. To pare the NPV, we have to ? replicate the projects till they have the same life (or) ? convert the present values into annuities ? The IRR is unaffected by project life. We can choose the project with the higher IRR. Aswath Damodaran 21 Solution 1: Project Replication Project A: Replicated $1500 $350 $350 $350 $350 $350 $350 $350 $350 $350 $350 Project B $1000 $400 $400 $400 $400 $400 $400 $400 $400 $400 $400 $1000 (Replication) NPV of Project A replicated = $ 693 NPV of Project B= $ 478 Aswath Damodaran 22 Solution 2: Equivalent Annuities ? Equivalent Annuity for 5year project = $442 * PV(A,12%,5 years) = $ ? Equivalent Annuity for 10year project = $478 * PV(A,12%,10 years) = $ Aswath Damodaran 23 What would you choose as your investment tool? ? Given the advantages/disadvantages outlined for each of the different decision rules, which one would you choose to adopt? a) Return on Investment (ROE, ROC) b) Payback or Discounted Payback c) Net Present Value d) Internal Rate of Return e) Profitability Index ? Do you think your choice has been affected by the events of the last quarter of 2020? If so, why? If not, why not? Aswath Damodaran 24 What firms actually use .. Decision Rule % of Firms using as primary decision rule in 1976 1986 1998 IRR % % % Accounting Return % % % NPV % % % Payback Period % % % Profitability Index % % % Aswath Damodaran 25 II. Side Costs and Benefits ? Most projects considered by any business create side costs and benefits for that business. ? The side costs include the costs created by the use of resources that the business already owns (opportunity costs) and lost revenues for other projects that the firm may have. ? The benefits that may not be captured in the traditional capital budgeting analysis include project synergies (where cash flow benefits may accrue to other projects) and options embedded in projects (including the options to delay, expand or abandon a project). ? The returns on a project should incorporate these costs and benefits. Aswath Damodaran 26 A. Opportunity Cost ? An opportunity cost arises when a project uses a resource that may already have been paid for by the firm. ? When a resource that is already owned by a firm is being considered for use in a project, this resource has to be priced on its next best alternative use, which may be ? a sale of the asset, in which case the opportunity cost is the expected proceeds from the sale, of any capital gains taxes ? renting or leasing the asset out, in which case the opportunity cost is the expected present value of the aftert