# Chapter 5 Net Present Value and Other Investment Rules

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1 University of Science and Technology Beijing Dongling School of Economics and management Chapter 5 Net Present Value and Other Investment Rules Oct Dr. Xiao Ming USTB 1

2 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 Dr. Xiao Ming USTB 2

3 Chapter Outline 5.1 Why Use Net Present Value? 5.2 The Payback Period Method 5.3 The Discounted Payback Period Method 5.4 The Internal Rate of Return 5.5 Problems with the IRR Approach 5.6 The Profitability Index 5.7 The Practice of Capital Budgeting Dr. Xiao Ming USTB 3

4 5.1 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 Dr. Xiao Ming USTB 4

5 The Net Present Value (NPV) Rule 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 Dr. Xiao Ming USTB 5

6 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. Dr. Xiao Ming USTB 6

7 5.2 The Payback Period Method 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 Ranking Criteria: Set by management Dr. Xiao Ming USTB 7

8 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 Dr. Xiao Ming USTB 8

9 5.3 The Discounted Payback Period 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. Dr. Xiao Ming USTB 9

10 5.4 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 Reinvestment assumption: All future cash flows are assumed to be reinvested at the IRR Dr. Xiao Ming USTB 10

11 Internal Rate of Return (IRR) 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 Dr. Xiao Ming USTB 11

12 IRR: Example Consider the following project: \$50 \$100 \$ \$200 The internal rate of return for this project is 19.44% NPV = 0 = \$50 (1 + IRR) + \$100 (1 + IRR) 2 + \$150 (1 + IRR) 3 Dr. Xiao Ming USTB 12

13 NPV Payoff Profile 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 \$ \$ \$50.00 IRR = 19.44% \$0.00-1% (\$50.00) 9% 19% 29% 39% (\$100.00) Discount rate Dr. Xiao Ming USTB 13

14 Calculating IRR with Spreadsheets You start with the same cash flows 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. Dr. Xiao Ming USTB 14

15 5.5 Problems with IRR Multiple IRRs Are We Borrowing or Lending The Scale Problem The Timing Problem Dr. Xiao Ming USTB 15

16 Mutually Exclusive vs. Independent Mutually Exclusive Projects: 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 Dr. Xiao Ming USTB 16

17 Multiple IRRs There are two IRRs for this project: \$200 \$ \$200 - \$800 Which one should we use? NPV \$ \$ % = IRR 2 \$ % 0% 50% 100% 150% 200% (\$50.00) Discount rate (\$100.00) 0% = IRR 1 Dr. Xiao Ming USTB 17

18 Modified IRR 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 for borrowing and reinvestment Dr. Xiao Ming USTB 18

19 The Scale Problem 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? Dr. Xiao Ming USTB 19

20 The Timing Problem Project A Project B \$10,000 \$1,000 \$1, \$10,000 \$1,000 \$1,000 \$12, \$10,000 Dr. Xiao Ming USTB 20

21 The Timing Problem \$5, \$4, \$3, Project A Project B NPV \$2, \$1, \$0.00 (\$1,000.00) 0% 10% 20% 30% 40% 10.55% = crossover rate (\$2,000.00) (\$3,000.00) (\$4,000.00) (\$5,000.00) 12.94% = IRR B Discount rate 16.04% = IRR A Dr. Xiao Ming USTB 21

22 Calculating the Crossover Rate 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, \$1, \$0.00 (\$1,000.00) 0% 5% 10% 15% 20% (\$2,000.00) (\$3,000.00) Discount rate 10.55% = IRR A-B B-A Dr. Xiao Ming USTB 22

23 NPV versus IRR 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 Dr. Xiao Ming USTB 23

24 5.6 The Profitability Index (PI) PI = Total PV of Future Cash Flows Initial Investent Minimum Acceptance Criteria: Accept if PI > 1 Ranking Criteria: Select alternative with highest PI Dr. Xiao Ming USTB 24

25 The Profitability Index 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 Dr. Xiao Ming USTB 25

26 5.7 The Practice of Capital Budgeting Varies by industry: Some firms use payback, others use accounting rate of return. The most frequently used technique for large corporations is either IRR or NPV. Dr. Xiao Ming USTB 26

27 Example of Investment Rules 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 Dr. Xiao Ming USTB 27

28 Example of Investment Rules Project A Project B CF 0 -\$ \$ PV 0 of CF 1-3 \$ \$ NPV = \$41.92 \$90.80 IRR = 0%, 100% 36.19% PI = Dr. Xiao Ming USTB 28

29 Example of Investment Rules Payback Period: Project A Project B Time CF Cum. CF Cum. CF Payback period for project B = 2 years. Payback period for project A = 1 or 3 years? Dr. Xiao Ming USTB 29

30 NPV and IRR Relationship Discount rate NPV for A NPV for B -10% % % % % % % % Dr. Xiao Ming USTB 30

31 NPV Profiles NPV \$400 \$300 IRR 1 (A) IRR (B) IRR 2 (A) \$200 \$100 \$0 (\$100) -15% 0% 15% 30% 45% 70% 100% 130% 160% 190% (\$200) Cross-over Rate Discount rates Project A Project B Dr. Xiao Ming USTB 31

32 Summary Discounted Cash Flow 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 Dr. Xiao Ming USTB 32

33 Summary Payback Criteria Payback period Length of time until initial investment is recovered Take the project if it pays back in some specified period Does not 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 Dr. Xiao Ming USTB 33

34 Quick Quiz Consider an investment that costs \$100,000 and has a cash inflow of \$25,000 every year for 5 years. The required return is 9%, and payback cutoff is 4 years. What is the payback period? What is the discounted payback period? What is the NPV? What is the IRR? Should we accept the project? What method should be the primary decision rule? When is the IRR rule unreliable? Dr. Xiao Ming USTB 34

35 Dr. Xiao Ming USTB 35

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