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Net Present Value and Other Investment Rules
Chapter 6: Net Present Value and Other Investment Rules By Group E (Ursula G. J) (Dayang Halimah)
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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 (IRR)and understand its strengths and weaknesses Be able to compute the net present value (NPV) and understand why it is the best decision criterion
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agenda Capital Budgeting - why we use NPV Value of Money Over Time
Net Present Value (NPV) The payback period method The discounted payback period method The Internal rate of return (IRR) The profitability index (PI)
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Capital budgeting Analysis of potential additions to fixed assets.
Long-term decisions, involve large expenditures NPV is a tool used in capital budgeting, along with IRR. Types of projects: Brand new line of business Expansion of existing line of business Replacement of existing asset Independent vs. Mutually Exclusive
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Good Decision Criteria
We need to ask ourselves the following questions when evaluating capital budgeting decision rules Does the decision rule adjust for the time value of money? Does the decision rule adjust for risk? Does the decision rule provide information on whether we are creating value for the firm?
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Value of money Facts: money wisely invested today will yield a return in the future ( a fact that creates a natural investor desire for cash today) Present value of money is crucial interest for financial people because it provides them with a basis of comparing the profitability of different projects or investments over a period of years.
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Value of money Present value of money is the cash value of future returns or income once a discount (capitalization) rate has been applied to it. Discount or capitalization rate is an interest rate applied to a series of future payments to adjust for risk and uncertainty of the time factor E.g. between 2 future incomes, the one with the longer maturity factor should have a higher risk (means higher discount rate)
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Value of money over time
A different point of view: An investment promises to yield a RM1M one-time profit, one year from now How much of today‘s ringgit am I willing to pay today to have RM1M in a year? p_max = $1M/(1+r) r is the discount rate p_max is the Net Present Value (NPV)
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Net Present Value The difference between the market value of a project and its cost Net present value: a project’s net contribution to wealth – present value minus initial investment. If the present value of a project’s future cash flow is greater than the initial cost, the project is worth undertaking We learn how to estimate the cash flows in chapter 10. We learn how to estimate the required return in chapter 13.
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Why use net present value?
Accepting positive NPV benefits shareholders NPV uses cash flow NPV uses all cash flows of project NPV discount the cash flow properly Reinvestment assumption: the NPV rule assumes that all cash flows can be reinvested at the discounted rate
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Net present value (npv) CONT….
How much value is created from undertaking an investment? The first step is to estimate the expected future cash flows. The second step is to estimate the required return for projects of this risk level. The third step is to find the present value of the cash flows and subtract the initial investment.
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Net present value (npv)
In other words, the present Value in "today's ringgit" of the future net cash flow of a project NPV = PV cash inflows - PV cash outflows ……… n t today C0
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Net Present Value (NPV)
NPV = PV of inflows – PV of Outflows PV = FV N (1 + R) Where PV = present value of future income FV = future income R = interest or discount rate N = number of years or periods
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Project Example Information
You are looking at a new project and you have estimated the following cash flows: Year 0: CF = -165,000 Year 1: CF = 63,120; Year 2: CF = 70,800; Year 3: CF = 91,080; Your required return for assets of this risk is 12%. This example will be used for each of the decision rules so that the students can compare the different rules and see that conflicts can arise. This illustrates the importance of recognizing which decision rules provide the best information for making decisions that will increase owner wealth.
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Computing NPV for the Project
Using the formulas: NPV = 63,120/(1.12) + 70,800/(1.12)2 + 91,080/(1.12)3 – 165,000 = 12,627.42 Using the calculator: CF0 = -165,000; C01 = 63,120; F01 = 1; C02 = 70,800; F02 = 1; C03 = 91,080; F03 = 1; NPV; I = 12; CPT NPV = 12,627.41 Do we accept or reject the project? Again, the calculator used for the illustration is the TI- BA-II plus. The basic procedure is the same; you start with the year 0 cash flow and then enter the cash flows in order. F01, F02, etc. are used to set the frequency of a cash flow occurrence. Many calculators only require you to use that if the frequency is something other than 1. Since we have a positive NPV, we should accept the project.
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NPV – Decision Rule If the NPV is positive, accept the project
A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners. Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal.
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Npv- CONCLUSION NPV rule account for the time value of money
NPV rule account for the risk of the cash flows (the risk of the cash flow is accounted for through the choice of the discount rate) NPV rule provide an indication about the increase in value we should consider the NPV rule for our primary decision rule The answer to all of these questions is yes The risk of the cash flows is accounted for through the choice of the discount rate.
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PAYBACK PERIOD How long does it take the project to “payback” its initial investment Payback Period = number of years to recover the initial costs Minimum acceptable criteria – set by the management Ranking criteria – set by the management
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Payback Period Computation
Estimate the cash flows Subtract the future cash flows from the initial cost until the initial investment has been recovered Decision Rule – Accept if the payback period is less than some preset limit
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Computing Payback for the Project
Assume we will accept the project if it pays back within two years. Year 1: 165,000 – 63,120 = 101,880 still to recover Year 2: 101,880 – 70,800 = 31,080 still to recover Year 3: 31,080 – 91,080 = -60,000 project pays back in year 3 Do we accept or reject the project? The payback period is year 3 if you assume that the cash flows occur at the end of the year, as we do with all of the other decision rules. If we assume that the cash flows occur evenly throughout the year, then the project pays back in 2.34 years. Either way, the payback rule would say to reject the project.
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Decision Criteria Test - Payback
Does the payback rule account for the time value of money? Does the payback rule account for the risk of the cash flows? Does the payback rule provide an indication about the increase in value? Should we consider the payback rule for our primary decision rule? The answer to all of these questions is no.
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PAYBACK METHOD Table: Expected cash flows for Project A through C ($)
YEAR A B C ________________________________________________________________ 0 -$100 -$100 -$100 ,000 PAYBACK PERIOD (YEARS)
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Payback method 3 problems
Timing of cash flow within the payback period is not considered (NPV discounts the cash flows properly) It ignores the cash flows occurring after the payback period (NPV uses all cash flows of the project) Arbitrary standard for payback period
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Advantages and Disadvantages of Payback
Easy to understand Adjusts for uncertainty of later cash flows Biased toward liquidity Disadvantages Ignores the time value of money Requires an arbitrary cutoff point Ignores cash flows beyond the cutoff date (not serve as measure of profitability) Biased against long-term projects, such as research and development, and new projects
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Discounted Payback Period
Compute the present value of each cash flow and then determine how long it takes to pay back on a discounted basis taking the time value of money into account Compare to a specified required period Decision Rule - Accept the project if it pays back on a discounted basis within the specified time
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Computing Discounted Payback for the Project
Assume we will accept the project if it pays back on a discounted basis in 2 years. Compute the PV for each cash flow and determine the payback period using discounted cash flows Year 1: 165,000 – 63,120/1.121 = 108,643 Year 2: 108,643 – 70,800/1.122 = 52,202 Year 3: 52,202 – 91,080/1.123 = -12,627 project pays back in year 3 Do we accept or reject the project? No – it doesn’t pay back on a discounted basis within the required 2-year period
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Decision Criteria Test – Discounted Payback
Does the discounted payback rule account for the time value of money? Does the discounted payback rule account for the risk of the cash flows? Does the discounted payback rule provide an indication about the increase in value? Should we consider the discounted payback rule for our primary decision rule? The answer to the first two questions is yes. The answer to the third question is no because of the arbitrary cut-off date. Since the rule does not indicate whether or not we are creating value for the firm, it should not be the primary decision rule.
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Advantages and Disadvantages of Discounted Payback
Includes time value of money Easy to understand Does not accept negative estimated NPV investments when all future cash flows are positive Biased towards liquidity Disadvantages May reject positive NPV investments Requires an arbitrary cutoff point Ignores cash flows beyond the cutoff point Biased against long-term projects, such as R&D and new products
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Other methods for investment decision
Average Accounting Return Method (AAR) Internal Rate of Return (IRR) Profitability Index (PI) (the above will be presented by Puan Dayang Halimah in the next class) Thank you.
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Average Accounting Return (AAR)
AAR is the average project earnings after taxes and depreciation, divided by the average book value of the investment during its life Average net income / average book value Note that the average book value depends on how the asset is depreciated. Need to have a target cutoff rate Decision Rule: Accept the project if the AAR is greater than a preset rate. The example in the book uses straight line depreciation to a zero salvage; that is why you can take the initial investment and divide by 2. If you use MACRS, you need to compute the BV in each period and take the average in the standard way.
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Computing AAR for the Project
Assume we require an average accounting return of 25% Average Net Income: (13, , ,100) / 3 = 15,340 AAR = 15,340 / 72,000 = .213 = 21.3% Do we accept or reject the project? Students may ask where you came up with the 25%. Point out that this is one of the drawbacks of this rule. There is no good theory for determining what the return should be. We generally just use some rule of thumb. This rule would indicate that we reject the project.
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Decision Criteria Test - AAR
Does the AAR rule account for the time value of money? Does the AAR rule account for the risk of the cash flows? Does the AAR rule provide an indication about the increase in value? Should we consider the AAR rule for our primary decision rule? The answer to all of these questions is no. In fact, this rule is even worse than the payback rule in that it doesn’t even use cash flows for the analysis. It uses net income and book value.
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Advantages and Disadvantages of AAR
Easy to calculate Needed information will usually be available Disadvantages Not a true rate of return; time value of money is ignored Uses an arbitrary benchmark cutoff rate Based on accounting net income and book values, not cash flows and market values
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Internal Rate of Return (IRR)
This is the most important alternative to NPV It is often used in practice and is intuitively appealing It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere The IRR rule is very important. Management, and individuals in general, often have a much better feel for percentage returns and the value that is created, than they do for dollar increases. A dollar increase doesn’t appear to provide as much information if we don’t know what the initial expenditure was. Whether or not the additional information is relevant is another issue.
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IRR – Definition and Decision Rule
Definition: IRR is the discount rate that sets the NPV = 0 Decision Rule: Accept the project if the IRR is greater than the required return Ranking criteria: select alternative with highest IRR Reinvestment assumption: all future cash flow assumed re-invested in at the IRR
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Computing IRR for the Project
If you do not have a financial calculator, then this becomes a trial and error process Calculator Enter the cash flows as you did with NPV Press IRR and then CPT IRR = 16.13% > 12% required return Do we accept or reject the project? Many of the financial calculators will compute the IRR as soon as it is pressed; others require that you press compute.
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IRR: Example Consider the following project:
1 2 3 $50 $100 $150 -$200 The internal rate of return for this project is 19.44%
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NPV Payoff Profile If we graph NPV versus the discount rate, we can see the IRR as the x-axis intercept. IRR = 19.44%
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Calculating IRR with Spreadsheets
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. Click on the Excel icon to go to an embedded spreadsheet so that you can illustrate how to compute IRR on a spreadsheet.
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Decision Criteria Test - IRR
Does the IRR rule account for the time value of money? Does the IRR rule account for the risk of the cash flows? Does the IRR rule provide an indication about the increase in value? Should we consider the IRR rule for our primary decision criteria? The answer to all of these questions is yes, although it is not always as obvious. The IRR rule accounts for time value because it is finding the rate of return that equates all of the cash flows on a time value basis. The IRR rule accounts for the risk of the cash flows because you compare it to the required return, which is determined by the risk of the project. The IRR rule provides an indication of value because we will always increase value if we can earn a return greater than our required return. We should consider the IRR rule as our primary decision criteria, but as we will see, it has some problems that the NPV does not have. That is why we end up choosing the NPV as our ultimate decision rule.
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Advantages of IRR Knowing a return is intuitively appealing
It is a simple way to communicate the value of a project to someone who doesn’t know all the estimation details If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task You should point out, however, that if you get a very large IRR that you should go back and look at your cash flow estimation again. In competitive markets, extremely high IRRs should be rare. Also, since the IRR calculation assumes that you can reinvest future cash flows at the IRR, a high IRR may be unrealistic.
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Summary of Decisions for the Project
Net Present Value Accept Payback Period Reject Discounted Payback Period Average Accounting Return Internal Rate of Return So what should we do – we have two rules that indicate to accept and three that indicate to reject.
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NPV vs. IRR NPV and IRR will generally give us 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
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IRR and Non-conventional Cash Flows
When the cash flows change sign more than once, there is more than one IRR When you solve for IRR you are solving for the root of an equation and when you cross the x-axis more than once, there will be more than one return that solves the equation If you have more than one IRR, which one do you use to make your decision?
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IRR and Mutually Exclusive Projects
If you choose one, you can’t choose the other Example: You can choose to attend graduate school at either Harvard or Stanford, but not both Intuitively you would use the following decision rules: NPV – choose the project with the higher NPV IRR – choose the project with the higher IRR
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Example With Mutually Exclusive Projects
Period Project A Project B -500 -400 1 325 2 200 IRR 19.43% 22.17% NPV 64.05 60.74 The required return for both projects is 10%. Which project should you accept and why? As long as we do not have limited capital, we should choose project A. Students will often argue that you should choose B because then you can invest the additional $100 in another good project, say C. The point is that if we do not have limited capital, we can invest in A and C and still be better off. If we have limited capital, then we will need to examine what combinations of projects with A provide the highest NPV and what combinations of projects with B provide the highest NPV. You then go with the set that will create the most value. If you have limited capital and a large number of mutually exclusive projects, then you will want to set up a computer program to determine the best combination of projects within the budget constraints. The important point is that we DO NOT use IRR to choose between projects regardless of whether or not we have limited capital.
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NPV Profiles IRR for A = 19.43% IRR for B = 22.17%
Crossover Point = 11.8% If the required return is less than the crossover point of 11.8%, then you should choose A If the required return is greater than the crossover point of 11.8%, then you should choose B
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Conflicts Between NPV and IRR
NPV directly measures the increase in value to the firm Whenever there is a conflict between NPV and another decision rule, you should always use NPV IRR is unreliable in the following situations Non-conventional cash flows Mutually exclusive projects
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Modified Internal Rate of Return
Method 1: Discounting Approach Discount all negative cash flows back to the present and add them to the initial investment. There is no rule regarding the discount rate, but the book uses the required rate.
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Modified Internal Rate of Return
Method 2: Reinvestment approach Compound all future cash flows to the end of the project. There is no rule regarding the compounding rate, but the book uses the required rate.
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Profitability Index Measures the benefit per unit cost, based on the time value of money A profitability index of 1.1 implies that for every $1 of investment, we create an additional $0.10 in value This measure can be very useful in situations in which we have limited capital
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Modified Internal Rate of Return
Method 3: Combination Approach Discount negative cash flows back to the present. Compound positive cash flows to the end of the project Different discounting and compounding rates may be used, but the book uses the required rate for both.
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Advantages and Disadvantages of Profitability Index
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
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Summary – Discounted Cash Flow Criteria
Net present value Difference between market value and cost Take 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
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Summary – Payback Criteria
Payback period Length of time until initial investment is recovered Take the project if it pays back within 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
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Summary – Accounting Criterion
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
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End of Chapter Thank you
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