# Lecture 5 (Chapter 9) Investment Criteria. Some Problems

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1 Lecture 5 (Chapter 9) Investment Criteria Up to now, we have analyzed how to finance a firm (capital structure) Today we switch to analyzing what to do with the money once we ve got it (capital budgeting / investment decisions) Focus on real assets rather than financial assets Continue to use discounted cash flow as primary tool Tasks for today: 1. Calculate the net present value of an investment and apply the NPV decision rule 2. Learn about some rules of thumb, such as the payback rule, accounting return, and the profitability index 3. Calculate the Internal rate of return (IRR) and relate it to the NPV Lecture 5: Investement Criteria 1 Some Problems Consider the following three possible investments, each with a discount rate of 10%: Movie: \$1 million to build a mega-movie-theater. You plan to operate this theater for three years, earning \$200,000 each year, and you believe that you can sell the theater for \$500,000 at the end of the third year. Restaurant: A fast-food restaurant for \$500,000, which will earn you profits of \$75,000 for each of the next 30 years. Mine: A gold mine that will cost \$4 million to construct and will yield profits of \$3 million a year for four years. At the end of the fifth year, a \$9 million charge for environmental cleanup is expected Lecture 5: Investement Criteria 2 1

2 Net Present Value (NPV) Definition: Present value of future cash flows discounted at the opportunity cost of capital minus (net of) the initial investment. Intuitive definitions of NPV: Change in the firm s value from investing in the project Change in shareholders wealth from investing in the project Amount that an outside investor would be willing to pay for the opportunity to carry-out the project Since our job as a manager is to increase the wealth of shareholders, the NPV shows us exactly how well we are doing. It is also a simple application of what we learned about present value, so it is easy to calculate. Lecture 5: Investement Criteria 3 NPV Examples NPV of the movie theater project NPV of the restaurant project NPV of the mine Which projects should we take? Lecture 5: Investement Criteria 4 2

3 Four Steps in Using NPV 1. Forecast the project cash flows. 2. Estimate the opportunity cost of capital (the discount rate). 3. Use the opportunity cost of capital to discount the future cash flows. 4. Apply the NPV decision rule: subtract the initial outlay from the present value of the forecasted cash flows from step 3. If NPV > 0, accept the project. Rationale: if the project s NPV at the opportunity cost of capital is positive, the project adds value to the firm. Lecture 5: Investement Criteria 5 Payback period Payback Rule Length of time before the initial investment in the project is recovered. Payback rule A project should be accepted if its payback period is less than a specified cutoff period. What is the payback period for Movie theater Restaurant Mine Lecture 5: Investement Criteria 6 3

4 Payback Period Rule Advantages Easy to understand; Adjusts for uncertainty of later cash flows; Biased towards liquidity. Disadvantages Ignores time value of money; Requires an arbitrary cutoff point; Ignores cash flows beyond the cut-off date; Biased against long-term project, such as research and development, and new projects. Works only for conventional projects Lecture 5: Investement Criteria 7 Discounted Payback Rule The discounted payback period: The amount of time (i.e. number of years) until discounted net cash flows to exceed the initial investment. Decision rule: An investment is acceptable if its discounted payback is less than some prespecified number of years Example: What is the discounted payback period for the restaurant? Lecture 5: Investement Criteria 8 4

5 Discounted Payback Period Rule Advantages Includes time value of money; Easy to understand; Does not accept negative estimated NPV; Biased towards liquidity. Disadvantages May reject positive NPV investments; Requires an arbitrary cut-off point; Ignores cash flows beyond the cut-off date; Biased against long-term project, such as research and development, and new projects. Works only for conventional projects Lecture 5: Investement Criteria 9 Average Accounting Return Rule Average accounting return (AAR): An investment s average net income divided by it s average book value Decision rule: An investment is acceptable if its average accounting return exceeds a target average accounting return Example What is the AAR for a project that requires an initial investment in machinery of \$15 million? The machinery will be fully depreciated over the project s life of 5 years. The new machinery will generate additional net income of \$2 million the first year, \$5 million the second and third and \$3 million in each of the following years. Lecture 5: Investement Criteria 10 5

6 Average Accounting Return Rule Advantages Easy to calculate; Needed information usually available. Disadvantages Not a true rate of return; time value of money ignored; Uses an arbitrary benchmark cut-off point; Based on accounting (book) values, not cash flows and market values. Lecture 5: Investement Criteria 11 Internal Rate of Return Internal rate of return (IRR): The discount rate that makes the NPV of an investment zero Decision rule: An investment is acceptable if its IRR exceeds the required return. It should be rejected otherwise. Intuition is that when IRR > r, our money grows fasters in this project than in our best alternative (opportunity cost) This looks different from the NPV rule, but it should give the same decisions. IRR > r means that NPV > 0 Remember: IRR is specific to the project and should not be confused with r. r depends on what you have to give up to undertake the project. IRR is the r which makes NPV = 0 Lecture 5: Investement Criteria 12 6

7 IRR Example What is the IRR of the movie theater project? , (1 + IRR) (1 + IRR) (1 + IRR) 1 = As always, when trying to find a rate, we need to either use trial and error, or we need to use a calculator/computer Lecture 5: Investement Criteria 13 Problems with IRR IRR and NPV decision rules will lead to identical decisions if: project cash flows are conventional ; project is independent. Problems when cash flows are non-conventional: The problem is that the NPV graph s slope may change several times, causing it to intersect the NPV = 0 axis in several places. For this to happen, the cashflow must change sign multiple times. (e.g. decommissioning costs, multi-stage project.) Solution: None. Must use NPV rule. Example: Find the IRR of the Mine project. Lecture 5: Investement Criteria 14 7

8 Problems with IRR: Mutually Exclusive Investments Example: Choose one of these two riskless investments: Invest \$1,000 today, get \$4,000 in one year (IRR=300%) Invest \$1,000,000 today, get \$1,500,000 in one year (IRR=50%) IRR ranks the first higher than the second, but fails to take account of size. We d rather make \$500,000 than \$3,000 in profit next year. Example: Given \$1 million to invest and a 7.5% discount rate, which riskless investment would you prefer? one which pays \$2 million after 1 year (IRR=100%) one which pays \$300,000 per year, forever (IRR=30%) We know how to value these two cashflows: The first is worth \$2,000,000 / = \$1,860,465 The second is worth \$300,000 / = \$4,000,000 Lecture 5: Investement Criteria 15 Mutually Exclusive Investments Net present value Project A Project B 0 Discount rate IRR A IRR B Consider projects A and B. for low discount rates, NPV A is higher than NPV B. for high discount rates, NPV B is higher than NPV A. Possible solution: Find IRR of incremental cashflows (change between projects. Better solution: Use NPV Lecture 5: Investement Criteria 16 8

9 IRR Rule Advantages Closely related to NPV, generally leading to identical decisions; Easy to understand and communicate. Disadvantages May result in multiple answers or no answer with nonconventional cash flows; May lead to incorrect decisions in comparisons of mutually exclusive investments. Lecture 5: Investement Criteria 17 Profitability Index (PI) Definition : The PV of an investment s expected cash flows divided by its initial cost. Also referred to as the benefit cost ratio. Decision rule An investment is acceptable if its PI is greater than one. It is unacceptable if its PI is less than one. Investors are indifferent between accepting and rejecting the project if its PI is equal to one. Example PI of Movie theater: PI of Restaurant: PI of Mine: Lecture 5: Investement Criteria 18 9

10 Profitability Index Rule 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. Lecture 5: Investement Criteria 19 Net Present Value (NPV) What we know now Primary investment criteria Shows the increase in stockholder wealth from an investment Requires cashflows and an opportunity cost of capital Other Investment Criteria Payback, Discounted Payback, Average Accounting Return, Profitability Index Understand how to use them and their advantages and disadvantages, but always use NPV when possible Internal Rate of Return Use sparingly, and only for conventional, non-exclusive projects Lecture 5: Investement Criteria 20 10

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