FI 305 Morosan - Chapters 9 & 10

ASKING THE RIGHT QUESTION - You should always ask your yourself ... 1. If the answer is "yes," it should ... 2. If the answer is "no," it should ... 3. If the answer is "part of it," then we should ...

- "Will this cash flow occur ONLY if we accept the project?" 1. be included in the analysis because it is incremental. 2. not be included in the analysis because it will occur anyway. 3. include the part that occurs because of the project.

COMPUTING DEPRECIATION Straight-line depreciation - D = - Few or many assets are depreciated straight-line for tax purposes. MACRS - Need to know which asset class is appropriate for ... - Multiply ... - Depreciate to ... - Mid-year ...

- (initial cost - salvage) / number of years - Few - tax purposes - the percentage given in table by the initial cost. - zero - convention

SUMMARY - DCF CRITIERIA IRR - Discount rate that makes NPV = ? - Take the prokject if the IRR is ... - Same decision as NPV with ... - IRR is ... with nonconventional cash flows or mutually exclusive projects.

- 0 - greater than the required return. - conventional cash flows - unreliable

Accept or Reject - NPV - Payback Period - Discounted Payback Period - AAR - IRR

- Accept - Reject - Reject - Reject - Accept

SUMMARY OF DECISION RULES - The NPV is positive at a required retuen of 15%, so you should ... - If you use the financial calculator, you would get an IRR of 10.11%, which would tell you to ... - You need to recognize that there are ... and look at the ...

- Accept - Reject - non-conventional cash flows, NPV profile.

A project's average net income divided by its average book value is referred to as the project's average: - IRR - NPV - Profitability Index - Accounting Return - Payback Period

- Accounting return

AVERAGE ACCOUNTING RETURN (AAR) - ? / ? - Note that average book value depends on - Need to have a - Decision Rule:

- Average net income / average book value - how the asset is depreciated - target cutoff rate - Accept the project if the AAR is greater than a preset rate.

SUMMARY - DCF CRITERIA Profitability Index - ... ratio - Take investment if PI > ? - Cannot be used to rank ... - May be used to rank ...

- Benfit-cost - 1 - mutually exclusive projects - projects in the presence of capital ratioining

DISCOUNTED PAYBACK PERIOD - Compute the ... and then determine ... - Compare to a ... - Decision Rule:

- Compute the present value of each cash flow and then determine how long it takes to pay back on a discounted basis. - Compare to a specified required period. - Accept the project if it pays back on a discounted basis within the specified time.

Example: Depreciation and After-tax Salvage - You purchase equipment for $100,000, and it costs $10,000 to have it delivered and installed. - Based on past information, you believe that you can sell the equipment for $17,000 when you are done with it in 6 years. - The company's marginal tax rate is 21%. - What is the depreciation expense each year and the after-tax salvage in year 6 for each of the following situations? - Suppose the appropriate depreciation schedule is straight-line.

- D = (110,000 - 17,000) / 6 = 15,500 every year for 6 years - BV in year 6 = 110,000 - 6(15,500) = 17,000 - After-tax salvage = 17,000 - .21(17,000 - 17,000) = 17,000

MORE ON NWC Why do we have to consider changes in NWC separately? - GAAP requires that sales be recored on the ... - GAAP also requires that we record cost of good sold when ... - Finally, we have to buy ...

- GAAP requires that sales be recorded on the income statement when made, not when cash is received. - GAAP also requires that we record cost of goods sold when the corresponding sales are made, whether we have actually paid our suppliers yet. - Finally, we have to buy inventory to support sales, although we haven't collected cash yet.

IRR - DEFINITION AND DECISON RULE - Definition: - Decision Rule:

- IRR is the return that makes the NPV = 0 - Accept the project if the IRR is greater than the required return.

PROFTIABILITY INDEX - Measures the ..., based on the ... - A profitability index of 1.1 implies that ... - This measure can be very useful in situations in which we have ...

- Measures the benefit per unit cost, based on the time value of money. - for every $1 of investment, we create an additional $0.10 in value. - This measure can be very usefyl in situations in which we have limited capital.

INTERNAL RATE OF RETURN (IRR) - This is the most impotant alternative to - It is often used in ... and is ... - It is based entirely on the ...

- NPV. - It is often used in practice and is intuitively appealing. - estimated cash flows and is independent of interest rates found elsewhere.

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?

- No - No - No - No

DECISION CRITERA 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?

- No - No - No - 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. Thus, it is not surprising that most surveys indicate that few large firms employ the payback and/or AAR methods exclusively.

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?

- Yes - Yes - 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. Therefore, it is the discounted payback rule we consider.

DECISION CRITERIA TEST - NPV - Does the NPV rule account for the time value of money? - Does the NPV rule account for the risk of the cash flows? - Does the NPV rule provide an indication about the increase in value? - Should we consider the NPV rule for our primary decision rule?

- Yes - Yes (The risk of the cash flows is accounted for through the choice of the discount rate.) - Yes - Yes

OTHER METHODS OF COMPUTING OCF 1. Bottom-Up Approach - OCF = - Works only when there is 2. Top-Down Approach - OCF = - Do not subtract ... 3. Tax Shield Approach - OCF =

1. - NI + depreciation - no interest expense 2. - Sales - Costs - Taxes - non-cash deductions 3. - (Sales - Costs)(1 - T) + Depreciation x T

ADVANTAGES OF PROFITABILITY INDEX 1. 2. 3.

1. Closely related to NPV, generally leading to identical decisions 2. Easy to understand and communicate. 3. May be useful when available investment funds are limited.

GOOD DECISION CRITERIA We need to ask ourselves the following 3 questions when evaluating capital budgeting decision rules:

1. Does the decision rule adjust for the time value of money? 2. Does the decision rule adjust for risk? 3. Does the decision rule provide the information on whether we are creating value for the firm?

Advantages of AAR 1. 2.

1. Easy to calculate 2. Needed information will usually be available

ADVANTAGES OF PAYBACK 1. 2. 3.

1. Easy to understand 2. Adjusts for uncertainty of later cash flows 3. Biased toward liquidity

COMPUTING IRR - Calculator 1. 2. 3.

1. Enter the cash flows as you did with NPV. 2. Press IRR and then CPT. 3. IRR = 16.13% > 12% required return Accept

DISADVANTAGES OF PAYBACK 1. 2. 3. 4.

1. Ignores the TVM 2. Requires an arbitrary cutoff point 3. Ignores cash flows beyond the cutoff date 4. Biased against long-term projects, such as research and development, and new projects

Advantages of Discounted Payback 1. 2. 3. 4.

1. Includes TVM 2. Easy to understand 3. Does not accept negative estimated NPV investments when all future cash flows are positive 4. Biased towards liquidty

ADVANTAGES OF IRR 1. 2. 3.

1. Knowing a return is intuitively appealing 2. It is a simple way to communicate the value of a project to someone who does not know all the estimation details. 3. If the IRR is high enough, you may not need to estimate a required return, which is often a difficult task.

Disadvantages of Discounted Payback 1. 2. 3. 4.

1. May reject positive NPV investments 2. Requires an arbitrary cutoff point 3. Ignores cash flows beyond the cutoff point 4. Biased against long-term projects, such as R&D and new products

Disadvantages of AAR 1. 2. 3.

1. Not a true rate of return; time value of money is ignored 2. Uses an arbitrary benchmark cutoff rate 3. Based on accounting net income and book values, not cash flows and market values

NET PRESENT VALUE (NPV) - How much value is created from undertaking an investment? (3 steps)

1. The first step is to estimate the expected future cash flows. 2. The second step is to estimate the required return for projects of this risk level. 3. The third step is to find the present value of the cash flows and subtract the initial investment.

Which one of the following methods of project analysis is defined as computing the value of a project based on the present value of the project's anticipated cash flows? - Expected earnings model - Constant dividend growth model - Internal rate of return - Discounted cash flow valuation - Average accounting return

Discounted cash flow valuation

PROJECT EXAMPLE INFORMATION You are reviewing a new project and have estimated the following cash flows: Year 0: CF = -165,000 Year 1: CF = 63,120; NI = 13,620 Year 2: CF = 70,800; NI = 3,300 Year 3: CF = 91,080; NI = 29,100 Average Book Value = 72,000 Your required return for assets of this risk level is 12%. Do we accept or reject the project? (Compute NPV)

Formula: NPV = -165,000 + 63,120/(1.12) + 70,800/(1.12)^2 + 91,080/(1.12)^3 = 12,627.41 Calculator: CF(0) = -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 ACCEPT the project due to positive NPV.

Based on the IRR rule, an investment is acceptable if the

IRR exceeds the required return. It should be rejected otherwise.

NPV - DECISION RULE

If the NPV is positive, accept the project.

Which of the following are advantages of the payback method of project analysis? - Ignores time value of money, ease of use - Ease of use, arbitrary cutoff point - Considers time value of money, liquidity bias - Liquidity bias, arbitrary cutoff point - Liquidity bias, ease of use

Liquidity bias, ease of use

DISADVANTAGES OF PROFITBAILITY INDEX 1.

May lead to incorrect decisions in comparisons of mutually exclusive investments

Southern Chicken is considering two projects. Project A consists of creating an outdoor eating area on the unused portion of the restaurant's property. Project B would use that outdoor space for creating a drive-thru service window. When trying to decide which project to accept, the firm should rely most heavily on which one of the following analytical methods? - IRR - NPV - Accounting Rate of Return - Profitability Index - Payback

NPV

ANOTHER EXAMPLE: NONCONVENTIONAL CASH FLOWS Suppose an investment will cost $90,000 initially and will generate the following cash flows: - Year 1: 132,000 - Year 2: 100,000 - Year 3: -150,000 - The required return is 15%/ Should we accept or reject this project>

NPV = - 90,000 + 132,000 / 1.15 + 100,000 / (1.15)^2 - 150,000 / (1.15)^3 = 1,769.54 If you compute the IRR on the calculator, you get 10.11% because it is the first one that you come to. So, if you just blindly use the calculator without recognizing the uneven cash flows, NPV would say to accept and IRR would say to reject.

The incremental cash flows for project evaluation consist of any and all changes in

the firm's future cash flows that are a direct consequence of taking the project.

Equivalent Annual Cost (EAC)

the present value of a project's costs calculated on an annual basis

Discounted Cash Flow (DCF) valuation

the process of valuing an investment by discounting its future cash flows

If a project has a net present value equal to zero, then: - the project's PI must also be equal to zero. - the project earns a return exactly equal to the discount rate. - the total of the cash inflows must equal the initial cost of the project. - a decrease in the project's initial cost will cause the project to have a negative NPV. - any delay in receiving the projected cash inflows will cause the project to have a positive NPV.

the project earns a return exactly equal to the discount rate.

Depreciation Tax Shield

the tax saving that results from the depreciation deduction, calculated as depreciation multiplied by the corporate tax rate

Which one of the following statements related to the internal rate of return (IRR) is correct? - The IRR yields the same accept and reject decisions as the net present value method given mutually exclusive projects. - Financing type projects should be accepted if the IRR exceeds the required return. - The average accounting return is a better method of analysis than the IRR from a financial point of view. - A project with an IRR equal to the required return would reduce the value of a firm if accepted. - The IRR is equal to the required return when the net present value is equal to zero.

The IRR is equal to the required return when the net present value is equal to zero.

The internal rate of return is: - a better methodology than net present value when dealing with unconventional cash flows. - equivalent to the discount rate that makes the net present value equal to one. - the discount rate that makes the net present value of a project equal to the initial cash outlay. - tedious to compute without the use of either a financial calculator or a computer. - highly dependent upon the current interest rates offered in the marketplace.

tedious to compute without the use of either a financial calculator or a computer.

The net present value of a project will increase if: - the aftertax salvage value of the fixed assets increases. - the final cash inflow decreases. - the initial capital requirement increases. - the required rate of return increases. - some of the cash inflows are deferred until a later year.

the aftertax salvage value of the fixed assets increases.

Payback Period

the amount of time required for an investment to generate cash flows sufficient to recover its initial cost

Stand-Alone Principle

the assumption that evaluation of a project may be based on the project's incremental cash flows

Erosion

the cash flows of a new project that come of a firm's existing projects

Incremental Cash Flows

the difference between a firm's future cash flows with a project and those without the project

Net Present Value (NPV)

the difference between an investment's market value and its cost

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?

- Yes 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. - Yes 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. - Yes 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. - Yes We could 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.

SUMMARY - ACCOUNTING CRITERION Average Accounting Return - Measure of ... - Similar to return on ... - Take the investment if the ... - Serious problems and should ...

- accounting profit relative to book value - assets measure - AAR exceeds some speicific return level. - not be used

AFTER-TAX SALVAGE - If the salvage value is different from the ... - Book value = - After-tax salvage =

- book value of the asset, then there is a tax effect. - initial cost - accumulated depreciaition - salvage - T x (salvage - book value)

MODIFIED IRR - Calculate the NPV of all cash outlfows using the ... - Calculate the NFV of all cash inflows using the ... - Find the ... that equates ... - Benefits:

- borrowing rate - investing rate - Find the rate of return that equates these values. - single answer and specific rates for borrowing and reinvestment

IRR AND MUTUALLY EXCLUSIVE PROJECTS Mutually exclusive projects - If you chose one, you ... - Example: ? Intuitively, which of the following decision rules would you use?

- can't chose the other. - You can choose to attend graduate school at either Harvard or Stanford, but not both. NPV and IRR

NPV vs. IRR Exceptions - Nonconventional cash flows (definition) - Mutually exclusive projects 1. Initial investments are 2. Timing of cash flows is

- cash flow signs change more than once 1. substantially different (issue of scale) 2. susbtantially different

DEPRECIATION - The depreciation expense used for capital budgeting should be the ... - Depreciation itself is a ... - Depreciation tax shield =

- depreciation schedule required by the IRS for tax purposes. - non-cash expense; consequently, it is only relevant because it affects taxes. - D (depreciation expense) x T (marginal tax rate)

CONFLICTS BETWEEN NPV AND IRR - NPV directly measures the ... - Whenever there is a conflict between NPV and another decision rule, you should ... - IRR is unreliable in the following situations: 1. 2.

- increase in value to the firm. - ALWAYS use NPV. - 1. Nonconventional cash flows 2. Mutually exclusive projects

REPLACEMENT PROBLEM - COMPUTING CASH FLOWS - Remember that we are interested in ... - If we buy the new machine, then we will ...

- incremental cash flows - sell the old machine

SUMMARY - DCF CRITERIA NPV - Difference between ... - Take the project if the NPV is ... - Has many or no serious problems - Preferrred or Deferred decision crtierion.

- market value and cost. - positive. - no - preferred

IRR AND NONCONVENTIONAL CASH FLOWS - When the cash flows change sign more than once, there is ... IRR. - When you solve for IRR you are solving for ..., and when you cross the ... more than once, there will be ... that solves the equation. - If you have more than one ..., which one do you ...

- more than one - 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?

PRO FORMA STATEMENTS AND CASH FLOW - Capital budgeting relies heavily on ... - Computing cash flows - refresher 1. Operating Cash Flow (OCF) = 2. OCF = 3. Cash Flow From Assets (CFFA) =

- pro forma accounting statements, particularly income statements. - Computing cash flows - refresher 1. OCF = EBIT + depreciation - taxes 2. OCF = net income + depreciation (when there is no interest expense) 3. CFFA = OCF - net capital spending (NCS) - changes in NWC

SUMMARY - PAYBACK CRITERIA Payback Period - Length of time until initial investment is ... - Take the project if it ... - Doesn't account for ..., and there is ...

- recovered - pays back within some specified period - TVM, arbitrary cutoff period

SUMMARY - PAYBACK CRITERIA Discounted Payback Period - Length of time until initial investment is ... - Take the project if it ... - There is an ...

- recovered on a discounted basis. - pays back in some specified period. - arbitrary cutoff period.

CAPITAL BUDGETING IN PRACTICE - We should consider ... when making decisions. - NPV and IRR are the most commonly used ... - Payback is a commonly used ....

- several investment criteria - primary investment criteria - secondary investment criteria

NET PRESENT VALUE (NPV) - The difference between

- the market value of a project and its cost

NPV vs. IRR - NPV and IRR will generally give us ...

- the same decision

RELEVANT CASH FLOWS - The cash flows that should be included in a capital budgeting analysis are those that ... - These cash flows are called ... - The stand-alone principle allows us to ...

- will only occur (or not occur) if the project is accepted. - incremental cash flows. - analyze each project in isolation from the firm simply by focusing on incremental cash flows.

Exmaple of Projected Capital Requirements

-----------------------Year------------------------------- ---------------0---------1----------2----------3---------4 NWC NFA Total

Example of Projected Total Cash Flows

-----------------------Year------------------------------- ---------------0---------1----------2----------3---------4 OCF Change in NWC NCS CFFA

Mutually Exclusive Investment Decisions

A situation in which taking one investment prevents the taking of another.

COMPREHENSIVE PROBLEM - A $1,000,000 investment is depreciated using a seven-year MACRS class life. - It requires $150,000 in additional inventory and will increase accounts payable by $50,000. - It will generate $400,000 in revenue and $150,000 in cash expenses annually, and the tax rate is 21%. - What is the incremental cash flow in years 0, 1, 7, and 8?

Annual depreciation expense: Year 1: .1429 × $1million = $142,900 Year 7: .0893 × $1million = $89,300 Year 8: .0446 × $1million = $44,600 Time 0 cash flow = -$1million investment - ($150,000 - $50,000) = -$1,100,000 Time 1 cash flow = ($400,000 - $150,000) × (1 - .21) + (.21 × $89,300) = $227,509 Time 7 cash flow = ($400,000 - $150,000) × (1 - .21) + (.21 × $142,900) = $216,253 Time 8 cash flow = ($400,000 - $150,000) x (1 - .21) + (.21 × $44,600) + $100,000 NWC = $306,866 (assumes zero salvage value)

EXAMPLE WITH MUTUALLY EXCLUSIVE PROJECTS Period ------- Project A -------- Project B 0 ---------------- -500 ------------- -400 1 ----------------- +325 ------------ +325 2 ----------------- +325 ------------ +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. Embedded in the analysis, we may want to calculate the NPV of the incremental project, i.e., the additional CF represented by project A above project B. The IRR of this CF stream is the crossover point and provides the return on the incremental investment.

PAYBACK PERIOD How long does it take to get the initial cost back in a nominal sense? Computation Decision Rule

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 thna some preset limit.

COMPREHENSIVE PROBLEM An investment project has the following cash flows: CF0 = -1,000,000; C01 - C08 = 200,000 each - If the required rate of return is 12%, what decision should be made using NPV? - How would the IRR decision rule be used for this project, and what decision would be reached? - How are the above two decisions related?

NPV = -$6,472; reject the project since it would lower the value of the firm. IRR = 11.81%, so reject the project since it would tie up investable funds in a project that will provide insufficient return. The NPV and IRR decision rules will provide the same decision for all independent projects with conventional/normal cash flow patterns. If a project adds value to the firm (i.e., has a positive NPV), then it must be expected to provide a return above that which is required. Both of those justifications are good for shareholders.

The final decision on which one of two mutually exclusive projects to accept ultimately depends upon which one of the following? - Timing of the cash inflows - Total cash inflows of each project - Initial cost of each project - Length of each project's life - Net present value

Net present value

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 required payback 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 decision rule should be the primary decision method? - When is the IRR rule unreliable?

Payback period = 4 years The project does not pay back on a discounted basis. NPV = -2,758.72 IRR = 7.93%

USING THE NPV RULE Suppose we are asked to decide whether a new consumer product should be launched. Based on projected sales and costs, we expect that the cash flows over the five-year life of the project will be $2,000 in the first two years, $4,000 in the next two, and $5,000 in the last year. It will cost about $10,000 to begin production. We use a 10 percent discount rate to evaluate new products. What should we do here?

Present value = ($2,000/1.1)+(2,000/1.1^2)+(4,000/1.1^3) +(4,000/1.1^4)+(5,000/1.1^5) =$1,818+1,653+3,005+2,732+3,105 =$12,313 The present value of the expected cash flows is $12,313, but the cost of getting those cash flows is only $10,000, so the NPV is $12,313 − 10,000 = $2,313. This is positive; so, based on the net present value rule, we should take on the project.

Samuelson Electronics has a required payback period of three years for all of its projects. Currently, the firm is analyzing two independent projects. Project A has an expected payback period of 2.9 years and a net present value of $4,200. Project B has an expected payback period of 3.1 years with a net present value of $26,400. Which project(s) should be accepted based on the payback decision rule? - Project A only - Project B only - Both A and B - Neither A nor B - Either, but not both projects

Project A only

Example of Pro Forma Income Statement

Sales VC Gross Profit FC Depreciation EBIT Taxes (x%) Net Income

CALCULATING DISCOUNTED PAYABCK Consider an investment that costs $400 and pays $100 per year forever. We use a 20 percent discount rate on this type of investment. What is the ordinary payback? What is the discounted payback? What is the NPV?

The NPV and ordinary payback are easy to calculate in this case because the investment is a perpetuity. The present value of the cash flows is $100/.2 = $500, so the NPV is $500 − 400 = $100. The ordinary payback is obviously four years. To get the discounted payback, we need to find the number of years such that a $100 annuity has a present value of $400 at 20 percent. In other words, the present value annuity factor is $400/$100 = 4, and the interest rate is 20 percent per period; so what's the number of periods? If we solve for the number of periods, we find that the answer is a little less than nine years, so this is the discounted payback.

CALCULATING PAYBACK Here are the projected cash flows from a proposed investment: Year --------- Cash Flow 1 ---------------- $100 2 ---------------- 200 3 ---------------- 500 This project costs $500. What is the payback period for this investment?

The initial cost is $500. After the first two years, the cash flows total $300. After the third year, the total cash flow is $800, so the project pays back sometime between the end of Year 2 and the end of Year 3. Because the accumulated cash flows for the first two years are $300, we need to recover $200 in the third year. The third-year cash flow is $500, so we will have to wait $200/$500 = .4 years to do this. The payback period is thus 2.4 years, or about two years and five months.

COMPUTING PAYBACK 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 acccept 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.

Profitability Index (PI)

The present value of an investment's future cash flows divided by its initial cost. Also called the benefit-cost ratio.

A project has a net present value of zero. Which one of the following best describes this project? - The summation of all of the project's cash flows is zero. - The project's cash inflows equal its cash outflows in current dollar terms. - The project requires no initial cash investment. - The project has no cash flows. - The project has a zero percent rate of return.

The project's cash inflows equal its cash outflows in current dollar terms.

WHAT'S THE IRR? You are looking at an investment that requires you to invest $51 today. You'll get $100 in one year, but you must pay out $50 in two years. What is the IRR on this investment?

You're on the alert now for the nonconventional cash flow problem, so you probably wouldn't be surprised to see more than one IRR. If you start looking for an IRR by trial and error, it will take you a long time. The reason is that there is no IRR. The NPV is negative at every discount rate, so we shouldn't take this investment under any circumstances. What's the return on this investment? Your guess is as good as ours.

Accelerated Cost Recovery System (ACRS)

a depreciation method under U.S. tax law allowing for the accelerated write-off of property under various classifications

Net Present Value Profile

a graphical representation of the relationship between an investment's NPVs and various discount rates

A project's average net income divided by its average book value is referred to as the project's average: - accounting return - IRR - NPV - payback period - profitability index

accounting return.

You are comparing two mutually exclusive projects. The crossover point is 12.3 percent. You have determined that you should accept project A if the required return is 13.1 percent. This implies you should: - always accept Project A. - always accept Project A if the required return exceeds the crossover rate. - accept Project B only when the required return is equal to the crossover rate. - be indifferent to the projects at any discount rate above 13.1 percent. - accept Project B if the required return is less than 13.1 percent.

always accept Project A if the required return exceeds the crossover rate.

Average Accounting Return (AAR)

an investment's average net income divided by its average book value

The PV of a perpetuity is: PV =

annual cash flow / R. This illustrates the inverse relationship between the payback period cutoff and the discount rate.

Based on the average accounting return rule, a project is acceptable if its

average accounting return exceeds a target average accounting return.

The length of time a firm must wait to recoup the money it has invested in a project is called the: - profitability period - valuation period - interal return period - discounted cash period - payback period

payback period

The IRR on an investment is the

required return that results in a zero NPV when it is used as the discount rate.

Mutually exclusive projects are best defined as competing projects that: - both require the total use of the same limited resource. - both have negative cash outflows at time zero. - have the same life span. - have the same initial start-up costs. - would need to commence on the same day.

both require the total use of the same limited resource.

Based on the payback rule, an investment is acceptable if its

calculated payback period is less than some prespecified number of years.

Payback Period Cutoff =

cost/annual cash flow

COMMON TYPES OF CASH FLOWS Sunk Costs - Opportunity Costs Side Effects 1. Positive side effects - 2. Negative side effects - Changes in ... ... costs - Taxes

costs that have accrued in the past costs of lost options 1. benefits to other projects 2. costs to other projects net working capital Financing - Taxes

The IRR that causes the net present value of the differences between two project's cash flows to equal zero is called the: - required return. - crossover rate. - present value rate. - break-even rate. - zero-sum rate.

crossover rate

If a firm accepts Project A it will not be feasible to also accept Project B because both projects would require the simultaneous and exclusive use of the same piece of machinery. These projects are considered to be: - mutually exclusive - independent - operationally distinct - economically scaled - interdependent

mutually exclusive

NPV - DECISION RULE A positive NPV means that the project is

expected to add value to the firm and will therefore increase the weatlh of the owners.

Pro Forma Financial Statements

financial statements projecting future years' operations

NPV - DECISION RULE Since our goal is to increase owner wealth, NPV is a direct measure of

how well this project will meet our goal.

Net present value: - is very similar in its methodology to the average accounting return. - is the best method of analyzing mutually exclusive projects. - cannot be applied when comparing mutually exclusive projects. - is the easiest method of evaluation for nonfinancial managers. - is less useful than the internal rate of return when comparing different-sized projects.

is the best method of analyzing mutually exclusive projects.