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The Optimality of the NPV Rule In this chapter, we will introduce alternative investment rules such as … IRR: Internal Rate of Return The Payback Rule Accounting-Based Rules … and see why NPV is preferable to all 0 The Net Present Value (NPV) Rule Net Present Value (NPV) = Total PV of future CF’s + Initial Investment CF Estimating NPV: 1. Estimate future cash flows: how much? and when? 2. Estimate discount rate 3. Estimate initial costs Acceptance Criteria: Accept if NPV > 0 Ranking Criteria: If mutually exclusive projects, choose the highest NPV 1 Good Attributes of the NPV Rule 1. Uses cash flows 2. Uses ALL cash flows of the project 3. Discounts ALL cash flows properly In recent years, the NPV rule has become the dominant investment rule. Today, we will see why other rules are inferior. 2 The Payback Period Rule 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 3 The Payback Period Rule 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 4 The Discounted Payback Period Rule How long does it take the project to “pay back” its initial investment taking the time value of money into account? By the time you have discounted the cash flows, you might as well calculate the NPV. You are still ignoring cash flows far in the future (as in strategic investments). 5 Average Accounting Return Rule Average Net Income AAR Average Book Value of Investent Ranking Criteria and Minimum Acceptance Criteria set by management Disadvantages: Ignores the time value of money Uses an arbitrary benchmark cutoff rate Most seriously: Based on book values, not cash flows and market values Advantages: The accounting information is readily available Easy to calculate 6 Internal Rate of Return (IRR) IRR: the discount that sets NPV to zero Minimum Acceptance Criteria: Accept if the IRR exceeds the required return. Ranking Criteria: Select alternative with the highest IRR Disadvantages: Does not distinguish between investing and borrowing. IRR may not exist or there may be multiple IRR Problems with mutually exclusive investments Advantages: Easy to understand and communicate 7 The Internal Rate of Return: Example Consider the following project: $50 $100 $150 0 1 2 3 -$200 The internal rate of return for this project is 19.44% $50 $100 $150 NPV 0 (1 IRR ) (1 IRR ) (1 IRR )3 2 8 The NPV Payoff Profile for This Example If we graph NPV versus discount rate, we can see the IRR as the x-axis intercept. Discount Rate NPV $120.00 0% $100.00 $100.00 4% $71.04 $80.00 8% $47.32 $60.00 12% $27.79 $40.00 NPV 16% $11.65 20% ($1.74) IRR = 19.44% $20.00 24% ($12.88) $0.00 28% ($22.17) 32% ($29.93) -1% ($20.00) 9% 19% 29% 39% 36% ($36.43) ($40.00) 40% ($41.86) ($60.00) Discount rate 9 Problems with the IRR Approach • Multiple IRRs are possible. • Are We Borrowing or Lending? • The Scale Problem. • The Timing Problem. 10 Multiple IRRs $200 $800 There are two IRRs for this project. 0 1 2 3 Which one to use? -$200 - $800 100% = IRR2 NPV $100.00 $50.00 $0.00 -50% 0% ($50.00) 50% 0% = IRR1100% 150% 200% Discount rate ($100.00) ($150.00) 11 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? 12 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 1 2 3 -$10,000 The preferred project in this case depends on the discount rate, not the IRR. 13 The Timing Problem: Projects A and B $5,000.00 $4,000.00 Project A $3,000.00 Project B $2,000.00 10.55% = “crossover rate” NPV $1,000.00 $0.00 ($1,000.00) 0% 10% 20% 30% 40% ($2,000.00) ($3,000.00) 12.94% = IRRB 16.04% = IRRA ($4,000.00) 14 Discount rate 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 $3,000.00 10.55% = IRR $2,000.00 $1,000.00 NPV A-B $0.00 B-A ($1,000.00) 0% 5% 10% 15% 20% ($2,000.00) ($3,000.00) Discount rate 15 Mutually Exclusive vs. Independent Projects 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. 16 Profitability Index (PI) Rule Total PV of Future Cash Flows PI Initial Investent Minimum Acceptance Criteria: Accept if PI > 1 Ranking Criteria: Select alternative with highest PI Disadvantages: Problems with mutually exclusive investments Advantages: May be useful when available investment funds are limited Correct decision when evaluating independent projects; simple rule 17 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 18 Example of Investment Rules Project A Project B CF0 -$200.00 -$150.00 PV0 of CF1-3 $241.92 $240.80 NPV = $41.92 $90.80 IRR = 0%, 100% 36.19% PI = 1.2096 1.6053 19 Example of Investment Rules Payback Period: Project A Project B Time CF Cum. CF CF Cum. CF 0 -200 -200 -150 -150 1 200 0 50 -100 2 800 800 100 0 3 -800 0 150 150 Payback period for project B = 2 years. Payback period for project A = 1 or 3 years? 20 Relationship Between NPV and IRR Discount rate NPV for A NPV for B -10% -87.52 234.77 0% 0.00 150.00 20% 59.26 47.92 40% 59.48 -8.60 60% 42.19 -43.07 80% 20.85 -65.64 100% 0.00 -81.25 120% -18.93 -92.52 21 NPV Profiles $400 NPV $300 IRR 1(A) IRR (B) IRR 2(A) $200 $100 $0 -15% 0% 15% 30% 45% 70% 100% 130% 160% 190% ($100) ($200) Project A Discount rates Cross-over Rate Project B 22 A Real World Capital Budgeting Puzzle: Poterba and Summers (1982) showed empirically that firms use much higher hurdle rates than what finance theory would predict, i.e. they compute NPV at discount rates way above the cost of capital. Why would they do that? 23 Capital Budgeting in the Real World (advanced) Some firms face financial constraints (e.g. right now, it is difficult to tap into equity markets). Division managers have more detailed knowledge than headquarters. They often overstate their situation to get funding. However, there are limits to overstatements (post-audits of forecasts, divisions have to meet their own projections) 24 Capital Budgeting in the Real World (advanced) Thus, NPV rule cannot be applied directly. However, applying NPV-rule with higher cost of capital can account for some of the overstatements. It is important to design incentive schemes that lead to • Efficient capital allocation and investments. • High managerial effort in the interest of shareholders. 25 Summary and Conclusions This chapter evaluates the most popular alternatives to NPV: Payback period Accounting rate of return Internal rate of return Profitability index We see how all other investment rules in existence are inferior to NPV. 26

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posted: | 9/29/2011 |

language: | English |

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