# Chapter 7. Net Present Value and Other Investment Rules

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1 Chapter 7 Net Present Value and Other Investment Rules Be able to compute payback and discounted payback and understand their shortcomings Understand accounting rates of return and 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 the net present value and understand why it is the best decision criterion 1

2 Four Criteria that a good procedure for evaluating proposed investments should meet. (1) Base the analysis on incremental costs and benefits, and don t arbitrarily exclude any costs or benefits from the analysis. (2) Measure costs and benefits based on cash flows, not earnings. (3) Allow for time value of money and for the risk involved. (4) If forced to choose among proposals, select the one that does shareholders the most good. Net Present Value (NPV) = Total PV of future CF s + Initial Investment Estimating NPV: 1. Estimate future cash flows: how much? and when? 2. Estimate discount rate 3. Estimate initial costs Minimum Acceptance Criteria: Accept if NPV > 0 Ranking Criteria: Choose the highest NPV 2

3 Suppose Big Deal Co. has an opportunity to make an investment of \$100,000 that will return \$33,000 in year 1, \$38,000 in year 2, \$43,000 in year 3, \$48,000 in year 4, and \$53,000 in year 5. If the company s required return is 12% should they make the investment? Cash PV of Year Flow Cash Flow 0 \$ (100,000) \$ (100,000) 1 \$ 33,000 \$ 29,464 2 \$ 38,000 \$ 30,293 3 \$ 43,000 \$ 30,607 4 \$ 48,000 \$ 30,505 5 \$ 53,000 \$ 30,074 Net Present Value \$ 50,943 Answer: YES! The NPV is greater than \$0. Therefore, the investment does return at least the required rate of return. 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 Reinvestment assumption: the NPV rule assumes that all cash flows can be reinvested at the discount rate. 3

4 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. How long does it take the project to pay back its initial investment? Payback Period = number of years to recover initial costs Minimum Acceptance Criteria: Set by management; a predetermined time period Ranking Criteria: Set by management; often the shortest payback period is preferred 4

5 Consider a project with an investment of \$50,000 and cash inflows in years 1,2, & 3 of \$30,000, \$20,000, \$10,000 The timeline above clearly illustrates that payback in this situation is 2 years. The first two years of return = \$50,000 which exactly pays back the initial investment 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 5

6 How long does it take the project to pay back its initial investment, taking the time value of money into account? Decision rule: Accept the project if it pays back on a discounted basis within the specified time. By the time you have discounted the cash flows, you might as well calculate the NPV. Suppose Big Deal Co. has an opportunity to make an investment of \$100,000 that will return \$33,000 in year 1, \$38,000 in year 2, \$43,000 in year 3, \$48,000 in year 4, and \$53,000 in year 5. If the company s required return is 12% and predetermined payback period is 3 years should they make the investment? Cash PV of Cumulative Year Flow Cash Flow PV of Cash Flows 0 \$ (100,000) \$ (100,000) \$ (100,000) 1 \$ 33,000 \$ 29,464 \$ (70,536) 2 \$ 38,000 \$ 30,293 \$ (40,242) 3 \$ 43,000 \$ 30,607 \$ (9,636) 4 \$ 48,000 \$ 30,505 \$ 20,869 5 \$ 53,000 \$ 30,074 \$ 50,943 Answer: NO! At the end of three years the project has still not broken even or paid back. Therefore, it must be rejected. 6

7 Average Net Income AAR Average Book Value of Investment Another attractive, but fatally flawed, approach Ranking Criteria and Minimum Acceptance Criteria set by management 7

8 Disadvantages: Ignores the time value of money Uses an arbitrary benchmark cutoff rate Based on book values, not cash flows and market values Advantages: The accounting information is usually available Easy to calculate 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 Reinvestment assumption: All future cash flows assumed reinvested at the IRR 8

9 Disadvantages: Does not distinguish between investing and borrowing IRR may not exist, or there may be multiple IRRs Problems with mutually exclusive investments Advantages: Easy to understand and communicate Consider the following project: \$50 \$100 \$ \$200 The internal rate of return for this project is 19.44% \$50 \$100 NPV (1 IRR) (1 IRR) 2 \$150 (1 IRR) 3 9

10 If we graph NPV versus the discount rate, we can see the IRR as the x-axis intercept. 0% \$ % \$ % \$ % \$ % \$ % (\$2.08) 24% (\$15.97) 28% (\$28.38) 32% (\$39.51) 36% (\$49.54) 40% (\$58.60) 44% (\$66.82) NPV \$ \$ \$80.00 \$60.00 \$40.00 \$20.00 \$0.00 (\$20.00) -1% 9% 19% 29% 39% (\$40.00) (\$60.00) (\$80.00) Discount rate IRR = 19.44% You start with the cash flows the same as you did for the NPV. You use the IRR function: You first enter your range of cash flows, beginning with the initial cash flow. You can enter a guess, but it is not necessary. The default format is a whole percent you will normally want to increase the decimal places to at least two. 10

11 Multiple IRRs Are We Borrowing or Lending The Scale Problem The Timing Problem There are two IRRs for this project: NPV \$200 \$ \$200 - \$800 \$ Which one should we use? \$ % = IRR 2 \$ % 0% 50% 100% 150% 200% (\$50.00) 0% = IRR 1 Discount rate (\$100.00) 11

12 Calculate the net present value of all cash outflows using the borrowing rate. Calculate the net future value of all cash inflows using the investing rate. Find the rate of return that equates these values. Benefits: single answer and specific rates Would you rather make 100% or 50% on your investments? What if the 100% return is on a \$1 investment, while the 50% return is on a \$1,000 investment? 12

13 Project A Project B \$10,000 \$1,000 \$1, \$10,000 \$1,000 \$1,000 \$12, \$10,000 NPV \$5, \$4, \$3, \$2, \$1, \$0.00 (\$1,000.00) 0% 10% 20% 30% 40% (\$2,000.00) (\$3,000.00) (\$4,000.00) (\$5,000.00) 12.94% = IRR B Project A Project B 10.55% = crossover rate Discount rate 16.04% = IRR A 13

14 Compute the IRR for either project A-B or B-A Year Project A Project B Project A-B Project B-A 0 (\$10,000) (\$10,000) \$0 \$0 1 \$10,000 \$1,000 \$9,000 (\$9,000) 2 \$1,000 \$1,000 \$0 \$0 3 \$1,000 \$12,000 (\$11,000) \$11,000 NPV \$3, \$2, % = IRR \$1, \$0.00 (\$1,000.00) 0% 5% 10% 15% 20% (\$2,000.00) (\$3,000.00) Discount rate A-B B-A NPV and IRR will generally give the same decision. Exceptions: Non-conventional cash flows cash flow signs change more than once Mutually exclusive projects Initial investments are substantially different Timing of cash flows is substantially different 14

15 Mutually Exclusive -- only ONE of several potential projects can be chosen, e.g., acquiring an accounting system. RANK all alternatives, and select the best one. Independent Projects: accepting or rejecting one project does not affect the decision of the other projects. Must exceed a MINIMUM acceptance criteria Total PV of Future Cash Flows PI Initial Investent Minimum Acceptance Criteria: Accept if PI > 1 Ranking Criteria: Select alternative with highest PI 15

16 Disadvantages: Problems with mutually exclusive investments Advantages: May be useful when available investment funds are limited Easy to understand and communicate Correct decision when evaluating independent projects Varies by industry: Some firms use payback, others use accounting rate of return. The most frequently used techniques for large corporations are IRR and NPV. Payback more often used by small firms and firms with CEOs without an MBA 16

17 Compute the IRR, NPV, PI, and payback period for the following two projects. Assume the required return is 10%. Year Project A Project B 0 -\$200 -\$150 1 \$200 \$50 2 \$800 \$ \$800 \$150 Project A Project B CF 0 -\$ \$ PV 0 of CF 1-3 \$ \$ NPV = \$41.92 \$90.80 IRR = 0%, 100% 36.19% PI =

18 Payback Period: Project A Project B CF Time CF Cum. CFCF Cum Payback period for project B = 2 years. Payback period for project A = 1 or 3 years? Discount rate NPV for A NPV for B -10% % % % % % % %

19 NPV \$400 \$300 \$200 IRR 1 (A) IRR (B) IRR 2 (A) \$100 \$0-15% 0% 15% 30% 45% 70% 100% 130% 160% 190% (\$100) (\$200) Cross-over Rate Discount rates Project A Project B Discounted Cash Flow NPV, IRR, Profitability Index Payback Payback period and Discounted Payback period Average Accounting Return 19

20 Net present value Difference between market value and cost Accept the project if the NPV is positive Has no serious problems Preferred decision criterion Internal rate of return Discount rate that makes NPV = 0 Take the project if the IRR is greater than the required return Same decision as NPV with conventional cash flows IRR is unreliable with non-conventional cash flows or mutually exclusive projects Profitability Index Benefit-cost ratio Take investment if PI > 1 Cannot be used to rank mutually exclusive projects May be used to rank projects in the presence of capital rationing Payback period Length of time until initial investment is recovered Take the project if it pays back in some specified period Doesn t account for time value of money, and there is an arbitrary cutoff period Discounted payback period Length of time until initial investment is recovered on a discounted basis Take the project if it pays back in some specified period There is an arbitrary cutoff period Average Accounting Return Measure of accounting profit relative to book value Similar to return on assets measure Take the investment if the AAR exceeds some specified return level Serious problems and should not be used 20

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