Chap5
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  • Like everything else, capital budgeting is a cost-benefit exercise! At the margin, the benefits from the decision making process should exceed the costs of capital budgeting efforts!!!
  • Note that although we add the initial investment, this value is a negative number!!!
  • Click on the Excel icon to go to an embedded Excel worksheet that has example cash flows, along with the correct and incorrect ways to compute NPV. Click on the cell with the solution to see the difference in the formulas.
    Again, note that when we add the initial investment, this is a negative number.
  • Note that the NPV recognizes the magnitude, risk, and timing of cash flows, which was an important description of why stock price maximization should be the primary corporate goal.
  • While the payback period is widely used in practice, it is rarely the primary decision criterion. As William Baumol pointed out in the early 1960s, the payback rule serves as a crude “risk screening” device – the longer cash is tied up, the greater the likelihood that it will not be returned. The payback period may be helpful when mutually exclusive projects are compared. Given two similar projects with different paybacks, the project with the shorter payback is often, but not always, the better project.
  • Cash flows prior to the cutoff are implicitly discounted at a rate of zero, and cash flows after the cutoff are discounted using an infinite discount rate.
  • Similar advantages and disadvantages as standard payback method, with the exception that cash flows prior to the cutoff are not discounted at zero.
    The discounted payback period is the length of time until accumulated discounted cash flows equal or exceed the initial investment. Use of this technique entails all the work of NPV, but its decision rule is arbitrary. Redeeming features of this approach are that (1) the time value of money is accounted for and (2) if the project pays back on a discounted basis, it has a positive NPV (assuming no large negative cash flows after the cut-off period).
  • Solving this type of problem with the formula is almost impossible (a long process of trial and error would be involved). However, you can use your IRR function together with your CF buttons to solve a problem like this.
  • Click on the Excel icon to go to an embedded spreadsheet so that you can illustrate how to compute IRR on a spreadsheet.
  • It is good to mention that the number of IRRs is equivalent to the number of sign changes in the cash flows.
  • The preferred project in this case depends on the discount rate, not the IRR.
  • The cross-over rate is the IRR of project A-B
  • PI basically indicates the value you are receiving in exchange for one unit of currency invested. This type of information is extremely useful for situations with capital rationing.
  • Careful, when projects are of different scale, the PI measure can be misleading – here it agrees with the NPV, but sometimes it will give you a different decision – Remember, PI considers the “bang for the buck” but not the initial scale of the investment!!!!
  • Payback period = 4 years
    The project does not pay back on a discounted basis.
    NPV = -2758.72
    IRR = 7.93%

Transcript

  • 1. CHAPTER 5 Net Present Value and Other Investment Rules
  • 2. Slide 2 Outline 1. The Capital Budgeting Process 2. Investment Decision Criteria       Net Present Value The Payback Period Method The Discounted Payback Period Method The Internal Rate of Return Problems with the IRR Approach The Profitability Index 1. The Practice of Capital Budgeting
  • 3. Slide 3 1. The Capital Budgeting Process • Decision making on capital projects – projects with a life of a year or more • Steps Involved: – Generating Ideas – Analyzing individual projects • Forecast cash flows, evaluate profitability – Plan the capital budgets • Consider timing, prioritize and see the big picture – Monitoring and postauditing
  • 4. Slide 4 2. Investment Decision Criteria 1) 2) 3) 4) 5) Net Present Value The Payback Period Method The Discounted Payback Period Method The Internal Rate of Return The Profitability Index
  • 5. Slide 5 1) Net Present Value (NPV) • Net Present Value (NPV) n CFt = ∑(1 + r ) t + Outlay (neg ) t =1 Total PV of future CF’s + Initial Investment (Outlay) • 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
  • 6. Calculating NPV with Spreadsheets Slide 6 • 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.
  • 7. Slide 7 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 • Reinvestment assumption: the NPV rule assumes that all cash flows can be reinvested at the discount rate.
  • 8. Slide 8 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
  • 9. Slide 9 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
  • 10. 3) The Discounted Payback Period Slide 10 • 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.
  • 11. Slide 11 4) The Internal Rate of Return • IRR:the discount rate that sets NPV to zero n CFt ∑(1 + IRR ) t + Outlay (neg ) = 0 t =1 • 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
  • 12. Slide 12 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
  • 13. Slide 13 IRR: Example Consider the following project: $50 0 -$200 $100 $150 1 2 3 The internal rate of return for this project is 19.44% $50 $100 $150 NPV = 0 = −200 + + + 2 3 (1 + IRR) (1 + IRR) (1 + IRR)
  • 14. Slide 14 NPV Payoff Profile If we graph NPV versus the discount rate, we can see the IRR as the x-axis intercept. $100.00 $73.88 $51.11 $31.13 $13.52 ($2.08) ($15.97) ($28.38) ($39.51) ($49.54) ($58.60) ($66.82) NPV 0% 4% 8% 12% 16% 20% 24% 28% 32% 36% 40% 44% $120.00 $100.00 $80.00 $60.00 $40.00 $20.00 $0.00 ($20.00) -1% ($40.00) ($60.00) ($80.00) IRR = 19.44% 9% 19% Discount rate 29% 39%
  • 15. Calculating IRR with Spreadsheets Slide 15 • 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.
  • 16. Slide 16 Problems with IRR  Multiple IRRs  Are We Borrowing or Lending  The Scale Problem  The Timing Problem
  • 17. Slide 17 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
  • 18. Multiple IRRs Slide 18 There are two IRRs for this project: $200 NPV 0 -$200 $800 1 2 3 - $800 Which one should we use? $100.00 100% = IRR2 $50.00 $0.00 -50% 0% ($50.00) ($100.00) 50% 0% = IRR1 100% 150% 200% Discount rate
  • 19. Slide 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?
  • 20. Slide 20 The Timing Problem $10,000 $1,000 $1,000 Project A 0 1 2 3 -$10,000 $1,000 $1,000 $12,000 Project B 0 -$10,000 1 2 3
  • 21. Slide 21 The Timing Problem $5,000.00 Project A $4,000.00 Project B $3,000.00 NPV $2,000.00 $1,000.00 10.55% = crossover rate $0.00 ($1,000.00) 0% 10% 20% 30% ($2,000.00) ($3,000.00) ($4,000.00) ($5,000.00) 12.94% = IRRB 16.04% = IRRA Discount rate 40%
  • 22. Slide 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 $3,000.00 $2,000.00 $1,000.00 $0.00 ($1,000.00) 0% 10.55% = IRR 5% 10% 15% ($2,000.00) ($3,000.00) Discount rate 20% A-B B-A
  • 23. Slide 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
  • 24. Slide 24 5) The Profitability Index (PI) Total PV of Future Cash Flows PI = Initial Investent • Minimum Acceptance Criteria: – Accept if PI > 1 • Ranking Criteria: – Select alternative with highest PI
  • 25. Slide 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
  • 26. Slide 26 3. 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 IRR or NPV.
  • 27. Slide 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 $100 3 -$800 $150
  • 28. Slide 28 Example of Investment Rules CF0 PV0 of CF1-3 NPV = IRR = PI = Project A -$200.00 Project B -$150.00 $241.92 $240.80 $41.92 $90.80 0%, 100% 36.19% 1.2096 1.6053
  • 29. Slide 29 Example of Investment Rules Payback Period: Time 0 1 2 3 Project A Project B CF Cum. CF CF Cum. CF -200 -200 -150 -150 200 0 50 -100 800 800 100 0 -800 0 150 150 Payback period for project B = 2 years. Payback period for project A = 1 or 3 years?
  • 30. Slide 30 NPV and IRR Relationship Discount rate -10% 0% 20% 40% 60% 80% 100% 120% NPV for A -87.52 0.00 59.26 59.48 42.19 20.85 0.00 -18.93 NPV for B 234.77 150.00 47.92 -8.60 -43.07 -65.64 -81.25 -92.52
  • 31. Slide 31 NPV NPV Profiles $400 $300 IRR 1(A) IRR (B) IRR 2(A) $200 $100 $0 -15% 0% 15% 30% 45% 70% 100% 130% 160% 190% ($100) ($200) Cross-over Rate Discount rates Project A Project B
  • 32. Slide 32 Summary – Discounted Cash Flow • Net present value – – – – • Internal rate of return – – – – • Difference between market value and cost Accept the project if the NPV is positive Has no serious problems Preferred decision criterion 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
  • 33. Slide 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
  • 34. Slide 34 Key Concepts and Skills • 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
  • 35. Slide 35 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?