CH-8-11 Net Present Value and Other Investment Criteria – Fundamentals of Corporate Finance : Chapter Notes

This Document Contains Chapters 8 to 11 CHAPTER 8 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA CHAPTER IN PERSPECTIVE This chapter continues the valuation theme, but shifts to an internal, managerial focus oriented to the discussion and evaluation of several investment decision criteria. The net present value and internal rate of return decision criteria are consistent with shareholder wealth maximization, for they focus on expected cash flows, when the flow occurs, and the riskiness of the cash flow. The professor must help the student make a transition from the former section and chapters related to valuation in a macroeconomic setting to this microeconomic setting related to making decisions within the business. Managers must assess the expected value added contributions of new investment projects. The net present value measures each project’s expected contribution to shareholder wealth. Help your student to continue the valuation theme from the last chapter into this and future chapters. Tying chapters together with a continuous theme, such as valuation, keep students from getting lost in specific formulas and enables them to see their managerial finance course from an overall perspective and how it relates to other areas of study in their business curriculum. CHAPTER OUTLINE 8.1 NET PRESENT VALUE A Comment on Risk and Present Value Valuing Long-Lived Projects Using the NPV Rule to Choose Among Projects 8.2 OTHER INVESTMENT CRITERIA: Payback Discounted Payback Internal Rate of Return 8-1 This Document Contains Chapters 8 to 11 A Closer Look at the Rate of Return Rule Calculating the Rate of Return for Long-Lived Projects A Word of Caution Some Pitfalls of the IRR Rule 8.3 MORE EXAMPLES OF MUTUALLY EXCLUSIVE PROJECTS Investment Timing Long- versus Short-Lived Equipment Replacing an Old Machine 8.4 CAPITAL RATIONING Soft Rationing Hard Rationing Pitfalls of the Profitability Index 8.5 A Last Look 8.6 Summary TOPIC OUTLINE, KEY LECTURE CONCEPTS, AND TERMS 8.1 NET PRESENT VALUE A. Net present value measures each project’s contribution to shareholder wealth. B. While there are several long-term investment decision criteria, the net present value method is favored because it tends to focus on building shareholder value and has the fewest limiting assumptions. 8-2 A Review of the Basics A. Capital budgeting decisions, the process of choosing investment projects, are important because they usually involve large cash outlays with cash flow return over a long period of time. The four steps in the capital budgeting decision process are: 1. Forecast the future project cash flows, noting when the flow occurs. 2. Estimate the opportunity cost of capital. The opportunity cost of capital is the expected rate of return given up by investing in the project under review. 3. Calculate the present value of the future cash flows discounted at the opportunity cost of capital rate. The present value of the cash flows represents the maximum amount that investors would pay for the investment. 4. NPV Decision Rule: The present value sum of the future cash flows minus the investment outlay is the net present value. If the net present value is positive (greater than zero), make the investment. If the net present value is negative, forgo the investment. If the present value is the maximum amount one would pay for the investment relative to the cost, the NPV represents the added value of the investment. B. The expected net present value of a project is the added shareholders’ wealth provided by the project. A Comment on Risk and Present Value A risky dollar is worth less than a safe one. The appropriate opportunity cost of capital needs to be adjusted for risks. The rate of return of the stock as risky as the project would be the appropriate opportunity cost of capital for the project. Valuing Long-Lived Projects A. Added net present values generated by investments are represented in higher stock prices. B. The net present value method is a proxy for financial market investor, analysis of business investments. C. Projects that are expected to generate negative net present values will reduce shareholders’ wealth by the expected negative NPV. 8-3 Using the NPV Rule to Choose among Projects Where mutually exclusive projects are facing the financial manager, one must be selected and the other deferred or passed by. In cases where competing projects serve the same purpose, select the project with the highest expected NPV. 8.2 OTHER INVESTMENT CRITERIA A. NPV, IRR, and profitability index, with some limitations, are preferred investment decision criteria because they consider three variables: 1. Estimated future cash flows of the investment. 2. The timing of the cash flows—present value analysis. 3. The opportunity rate of return of shareholders, considering the project riskiness relative to other, alternative investor opportunities. B. Another popular decision criterion, payback, is analyzed below, but it has important shortcomings. Payback A. A popular and relatively simple cash flow investment decision criterion is the payback defined as the time until cash flows recover the initial investment of the project. B. The payback rule states that the investment should proceed if the payback period exceeds a specified period. C. While cash flows are considered, the timing of the cash flows and the cash flows beyond the payback period are not considered. The payback method ignores the risk of the project cash flows and the opportunity rate of return of investors. D. The payback method is a popular, simple evaluation method for short-lived projects. Discounted Payback A. Sometimes managers calculate the discounted payback period. This is the 8-4 number of periods before the present value of prospective cash flows equals or exceeds the initial investment. This surmounts the objection that equal weight is given to all cash flows before the cutoff date. However, the discounted payback rule still takes no account of any cash flows after the cutoff date. B. The discounted payback does offer one important advantage over the normal payback criterion. It improves upon the payback period to the extent that equal weight is no longer given to all cash flows before the cutoff date. C. Also, it is useful to know that If a project meets a discounted payback cutoff, it must have a positive NPV, because the cash flows that accrue up to the discounted payback period are (by definition) just sufficient to provide a present value equal to the initial investment. Any cash flows that come after that date tip the balance and ensure positive NPV. D. However, the discounted payback still ignores all cash flows occurring after the arbitrary cut off date and therefore will incorrectly reject some positive NPV opportunities. Also, It is no easier to use than the NPV rule, because it requires determination of both project cash flows and an appropriate discount rate. Internal Rate of Return A. An alternative to the NPV method is the internal rate of return, which is the discount rate that, having discounted the expected cash flows, will produce a present value equal to the cost of the project. In this case, a discount rate that will generate an NPV of zero (Figure 8.2). B. The rate of return decision rule—invest in any project offering a rate of return higher than the opportunity cost of capital. 8-5 A Closer Look at the Rate of Return Rule A. The rate of return, or the internal rate of return, or IRR, or the discounted cash flow (DCF) rate of return, is the discount rate at which NPV equals zero. B. If the rate of return is greater than the opportunity cost of capital, the NPV of the project is greater than zero. C. If the NPV of a project is less than zero (negative) the rate of return is less than the opportunity cost of capital. D. The rate of return rule and the NPV rule are equivalent. Calculating the Rate of Return for Long-Lived Projects A. The IRR of a single future cash flow (PV) or an annuity flow (PV of annuity) may be determined easily and arithmetically as the discount rate that equates the cost of the project with the present value of the future cash flows. B. The IRR of a multiple, uneven cash flow stream involves more than one unknown and is not easily solved arithmetically. One must iterate, often several times, selecting an expected IRR and discounting the cash flows until the NPV of the project is zero. C. The rate of return rule will give the same decision as the NPV rule as long as the NPV of a project declines smoothly as the discount rate increases. A Word of Caution A. Do not confuse the IRR with the opportunity cost of capital. The IRR is the rate of return on the cash flows of the investment. B. The opportunity cost of capital is the minimum IRR acceptable to the firm. The opportunity rate of return is an estimate of the minimum acceptable rate of return demanded by investors in financial markets on similar risk investments. 8-6 Figure 8.3 Pitfalls of the Rate of Return Rule A. While the IRR is easier to understand than the NPV, the NPV should be used as a final decision criterion for an investment. B. The IRR method has a number of theoretical pitfalls that encourages the use of the NPV method: 1. Pitfall 1: mutually exclusive projects. Where mutually exclusive projects are facing the financial manager, one must be selected and the other deferred or passed by. In cases where competing projects serve the same purpose, select the project with the highest expected NPV. The IRR may give a conflicting choice relative to the NPV, which focuses more accurately on shareholder value. Analysis of the IRR on incremental basis will give decisions consistent with the NPV (see Figure 8.5). 8-7 2. Pitfall 1a: mutually exclusive projects involving different outlays, same lives. Small projects may be erroneously selected over larger projects using the IRR. When NPV is higher as the discount rate increases, a project is acceptable only if its internal rate of return is less than the opportunity cost of capital. 3. Pitfall 2: lending or borrowing. The IRR does not distinguish between a lending (investing) or a borrowing (borrow and invest) situation, whereas the NPV clearly points out the negative aspects of the borrowing strategy. 4. Pitfall 3: multiple rates of return. Any change in sign (+,-) in period cash flows produces as many IRR’s as there are changes in the cash flow directions of the investment. Many investments, such as oil or gas wells, entail added outlays after several periods of positive cash flows, producing the arithmetical possibility of multiple IRR’s. Use the NPV, offsetting the discounted negative cash flows against the positive cash flows. 8.3 MORE EXAMPLES OF MUTUALLY EXCLUSIVE PROJECTS The capital budgeting decision analyses, to this point in the chapter, have considered mutually exclusive alternatives. In either Project A or Project B, the proper decision rule was to select the project with the higher NPV. There are other mutually exclusive decision analysis considerations that occur frequently that complicate our simple NPV rule. Three situations are discussed below. Investment Timing A. When to make an investment is a difficult decision in a dynamic world, where new cost-saving technology is always improving and NPV’s are greater if delayed until later. B. The right time to purchase an ever-increasing NPV investment is indicated by the highest present value of future NPV’s, found by discounting the estimated NPV’s of projects made in future periods by the opportunity cost of capital. See Table 8.3. 8-8 Long-Lived versus Short-Lived Equipment A. When comparing mutually exclusive projects that have unequal project lives, one must analyze the costs of the projects, the outlays and the annual costs of the projects. B. Calculate the equivalent annual cost of both machines. Decision Rule: Accept the project with the lowest equivalent annual cost. C. The equivalent annual cost is the annual (annuity or payment) project cost that equates the present value cost of the project (outlay and annual costs) at the opportunity rate of return. The equivalent annual cost is the level annual charge or cost necessary to recover the present value of investment outlays and operating costs. Replacing an Old Machine A. Most equipment is replaced before the end of its useful economic life or its depreciable life. Replacement decisions most often involve replacing old with new with different useful cash-flow lives. B. Calculate the equivalent cost, annuity payment which equates the PV cost at the opportunity rate of return, of the new project’s costs compared to the period cost of the old project. C. If the equivalent period cost of the new project is less than the period cost of the old project, accept the new; if greater, delay the replacement and review later. 8.4 CAPITAL RATIONING A. A business maximizes shareholders’ wealth by accepting every project with a positive NPV. B. The above statement assumes that only negative NPV’s establish a limit on the capital budget of a business and that any financing needed can be raised in financial markets. C. Capital rationing exists if there is a limit on the amount of funds available for investment. There are two forms of capital rationing: soft rationing and hard rationing. Soft Rationing A. Soft rationing exists if businesses themselves, or their senior managers, place limits on the size of the capital budget. 8-9 B. Soft rationing limits can be relaxed if added NPV investments are available; financing is provided easily by financial markets. Hard Rationing A. Hard rationing or limits on the capital budget are set by financial markets (investors). B. With funding constraints, positive NPV projects are forgone. C. With hard rationing, the firm must choose projects, to the limit of its financing ability, from among a list of projects with positive NPV’s. D. Within a hard rationing constraint, choose the projects with the highest profitability index to the limit of the financing budget. The profitability index is the ratio of the sum of present values of the project divided by the initial cost of the investment. It is a relative measure of the value (present value) of a project compared to its cost. The higher profitability index projects have higher PV’s relative to the scarce capital invested. Pitfalls of the Profitability Index A. Using the profitability index decision rule in situations without capital rationing may give erroneous choices, similar to the IRR. B. Using the profitability index without capital rationing wrongly favors small, short- lived projects over large, long-lived projects with higher NPV’s. Further Points Regarding the Investment Criteria Discussed Above: A. NPV, IRR, and profitability index, with some limitations, are preferred investment decision criteria because they consider three variables: 1. Estimated future cash flows of the investment. 2. The timing of the cash flows—present value analysis. 3. The opportunity rate of return of shareholders, considering the project riskiness relative to other, alternative investor opportunities. 4. The Payback and discounted payback period are also popular decision criteria, but each has important shortcomings. 8.5 A LAST LOOK We’ve covered several investment criteria, each with its own nuances. 8-10 A. NPV, IRR, and profitability index, with some limitations, are preferred investment decision criteria because they consider three variables: 1. Estimated future cash flows of the investment. 2. The timing of the cash flows—present value analysis. 3. The opportunity rate of return of shareholders, considering the project riskiness relative to other, alternative investor opportunities. B. NPV is the preferred decision criterion with IRR a distant second. C. NPV only fails to be an effective decision criterion when capital rationing exists; then the profitability ratio is used. Table 8.3 gives an overview and summary of these decision rules. Among the decision rules, NPV is the gold standard. It is the only rule that consistently can be used to rank and choose among mutually exclusive investments. A recent survey of large U.S. and Canadian firms found that for managers in the field, discounted cash- 8-11 flow analysis is in fact the dominant tool for project evaluation. Table 8–4 provides a sample of the results of this survey of CFOs. From the Table, 75 percent of firms either always or almost always use both NPV and IRR to evaluate projects. The dominance of these criteria is even stronger among larger, firms. Firms use other investment criteria as well to evaluate projects. For example, just over half of corporations always or almost always compute a project’s payback period. Profitability index is routinely computed by about 12 percent of firms1 7.6 SUMMARY PEDAGOGICAL IDEAS General Teaching Note - In this chapter, the student is learning various investment decision criteria, but our examples are usually generic “investment projects” that have the excitement of watching paint dry. Consider using a student-oriented investment example and watch their interest in your lecture pick up. A good example is buying an off-campus house for their housing while at the university, or perhaps, becoming a slum landlord by purchasing the place they are now renting while they are in school. It involves an outlay, periodic cash flows, an opportunity rate of return, and a final estimated value when the house is sold. Another project is the expected rate of return on their college education. They must use the incremental cash flow concept, college vs. not college, opportunity cost of not working, an estimated differential in earnings over their working years (they blink when you say to assume a perpetuity), nominal vs. real concept, etc. Before these realistic projects, present the NPV and IRR concepts and decision rules with a very simple example. Establish those mechanical skills, and then show them practical examples to which they can relate. Student Career Planning - Over the next year your students will waste considerable time, and cost, sending resumes to personnel offices of many businesses. Remind them that businesses or corporations or personnel offices do not hire people. People hire people! In the time between now and graduation, they will have the opportunity to meet many people who know people that hire people. Few of those people will come looking for the student. They must go to them and can in a variety of ways. It may start with family members, business associates of their family, speakers who will come to address a class or an organizational meeting, last year’s graduates who have landed good jobs, and so on. Note that as a student in the quest for knowledge (term paper, a class interview assignment or an informational interview), they can walk into every company in the country and, most of the time, talk with whomever they want. Encourage networking, the development of business relationships, keeping in touch with those contacts, and when graduation looms, encourage the student to enlist these contacts in their job search efforts. 1 See J.R. Graham and C.R. Harvey, “The Theory and Practice of Corporate Finance: Evidence from the Field,” Journal of Financial Economics (Vol. 60) May 2001, pp.187- 243. 8-12 People know people, and people hire people! Internet Exercises - Students are bombarded with new terms in a business finance class. There are several good finance glossaries on the Internet that will provide a quick description or explanation of the new term or concept encountered. The International Financial Encyclopedia and the Dictionary of Management and Technology, accessed from the same site, provide extensive coverage of finance terms. InvestorGuide.com provides a site titled Investorwords, which offers an extensive listing of finance terms. http://books.google.ca/books/about/Encyclopedia_of_finance.html?id=I6BH- RKYVG4C&redir_esc=y “Encyclopedia of Finance” (Google e-books) by Cheng.F. Lee and Alice C. Lee is a financial encyclopedia on a wide-range of topics spanning financial management, security analysis, portfolio management, financial markets and instruments, insurance, real estate, options and futures, and international finance. There is also a good coverage of statistical applications in finance, for instance, on topics such as portfolio analysis and option pricing. This e-book could be a good source of reference in the classroom and also for finance professionals. http://www.investorwords.com InvestorWords.com offers an extensive listing of over 5000 “investment and personal finance” oriented terms and 15,000 links between related terms. It is a great site for professors to link from their class home page and useful for beginning finance students. It is recommended that your students bookmark the site. Print a sample copy to distribute in class if you do not have Internet access in the classroom. 8-13 CHAPTER 9 USING DISCOUNTED CASH-FLOW ANALYSIS TO MAKE INVESTMENT DECISIONS CHAPTER IN PERSPECTIVE This chapter builds upon the last chapter and focuses on estimating the expected cash flows of an investment project. There are a number of general concepts and rather detailed procedures that a student must master. One of the more important concepts is that of determining the “incremental” cash-flow impact of a new project. The standard question for the student to ask is, “What changes, given the decision to make the investment?” The Blooper Industries example is a good discussion example that enables one to cover most of the concepts and rules developed in the chapter. When working the cash-flows examples, complete the analysis with an assessment of the NPV and IRR and their corresponding decision rules. This enables the student to tie the last chapter and this one into a continuous process. CHAPTER OUTLINE 9.1 IDENTIFYING CASH FLOWS Discount Cash Flows, Not Profits Discount Incremental Cash Flows Include All Direct Effects Forget Sunk Costs Include Opportunity Costs Recognize the Investment in Working Capital Beware of Allocated Overhead Costs Discount Nominal Cash Flows by the Nominal Cost of Capital Separate Investment and Financing Decisions 9-1 9.2 CALCULATING CASH FLOW Capital Investment Investment in Working Capital Operating Cash Flow 9.3 BUSINESS TAXES IN CANADA AND THE CAPITAL BUDGETING DECISION Depreciation and Capital Cost Allowance The Asset Class System Sale of Assets Termination of Asset Pool Present Values of CCA Tax Shields 9.4 EXAMPLE: BLOOPER INDUSTRIES Calculating Blooper’s Project Cash Flow Calculating the NPV of Blooper’s Project Further Notes and Wrinkles Arising from Blooper’s Project 9.5 SUMMARY Appendix 9A: Deriving the CCA Tax Shield (see Connect) TOPIC OUTLINE, KEY LECTURE CONCEPTS, AND TERMS 9.1 IDENTIFYING CASH FLOWS Discount Cash Flows, Not Profits A. Income statements measure historical performance according to generally accepted accounting principles, not in cash-flow terms. B. Cash flows, when they occur, discounted at the opportunity rate of return is the proper method for net present value. 9-2 Discount Incremental Cash Flows A. Project cash-flow analysis should consider the differential cash flows that occur given the acceptance of the project. B. Incremental cash flows represent the cash-flow changes that the new project creates, or the cash flow with the project less the cash flow without the project. Include All Direct Effects All differential cash-flow implications of the project must be considered, including the impact of the new project on any other aspect of the business cash flows. Forget Sunk Costs A. Cash flows not related to the project are irrelevant in the project cash-flow analysis. B. Cash flows that occur regardless of whether the project investment is made are sunk costs and are not relevant to the current project. Include Opportunity Costs A. Include opportunity cost cash flows, such as the value of land that you could otherwise sell, as a relevant cost of an investment project. B. The opportunity cost, or the best alternative value option of the land owned prior to the investment consideration, is a part of the investment outlay. Recognize the Investment in Working Capital A. The incremental net working capital, added current assets less added current liabilities, represents relevant cash-flow costs of initiating a project and should be part of the NPV analysis. Working capital recovered at the end of the project is a relevant cash flow. B. Ignoring working capital, or the fact that varying levels of incremental net working capital may occur throughout the life of the project, or ignoring the recovery of working capital are three common errors in project cash-flow analysis. 9-3 Beware of Allocated Overhead Costs A. Overhead costs, such as heat and lights, incurred whether the project investment is made or not, are irrelevant to the project cash-flow analysis. B. Include only the additional or incremental cash-flow cost, only when they occur, in the project analysis. Discount Nominal Cash Flows by the Nominal Cost of Capital A. If the discount rate or the opportunity rate of return used in project analysis is in nominal terms, versus inflation adjusted or in real terms, relevant project cash flows should be in nominal terms as well. One may use real, inflation adjusted discount rates and cash flows, but consistency in this matter is what is important. B. Expected cash flows, if inflation is expected during the life of the project, must be adjusted upward to nominal values. The adjustment should reflect the added price changes in the prices of the products, labour costs, etc., rather than a general inflation rate, such as the Consumer Price Index. Separate Investment And Financing Decisions A. When the cash flows of an investment are analyzed, how the investment is financed, or the financing costs of the project, is ignored. B. How the project is financed, and the financing costs, are variables affecting the opportunity rate of return, used to discount the cash flows. Financing the project and its impact is considered when calculating the opportunity rate of return, studied later in the book. C. The value of the investment is considered by itself, independent of financing choice. 9.2CALCULATING CASH FLOW A. Total cash flow from a project includes cash flows from three sources: 1. Cash flows associated with investment in plant and equipment. 2. Cash flows associated with investments in added net working capital. 3. Cash flows from operations. 9-4 B. Net capital investment cash flows often include: 1. Cost of equipment and conditioning for operation. 2. If a replacement project, sale of the old equipment. 3. If a replacement project, the tax effect of selling old equipment. C. Net working capital cash flows include: 1. Incremental changes in working capital investments such as account receivables and inventory, given the decision to invest in the new project. 2. Working capital investments (assets) adjusted for changes in added payables and other spontaneous accruals. D. Incremental cash flows from operations may be calculated three ways: 1. Calculate the annual cash flow from operations using an incremental cash flow statement. Cash flow from operations = cash revenues – cash expenses – cash taxes 2. Calculate the annual net income and add back noncash expenses to determine cash flow from operations. Cash flow from operations = incremental net profit + incremental depreciation 3. Calculate the after-tax amount of each type of cash flow, then sum for the year. 4. The depreciation tax shield, or the net cash flow from reduced taxes from depreciation expenses, is the product of the amount of incremental depreciation times the tax rate. Depreciation tax shield = incremental depreciation x tax rate 9.3 BUSINESS TAXES IN CANADA AND THE CAPITAL BUDGETING DECISION Depreciation and Capital Cost Allowance: A. While calculating profit before tax, or taxable income, the business is allowed to deduct capital cost allowance (or CCA) on its depreciable assets. So, Taxable income = revenues - expenses - CCA 9-5 B. The CCA for each year is calculated by multiplying the balance on the asset, or undepreciated capital cost (UCC), by the appropriate tax rate. Although the CCA itself is a non-cash charge, it affects the cash flow to the extent that it reduces the taxes paid. This tax saving is called the CCA tax shield. The Asset Class System: A. All eligible depreciable assets are grouped into one of over 30 CCA asset classes. Each asset class has been assigned a CCA rate by Canada Customs and Revenue Agency (CCRA). Table 9.1 provides details regarding some of the asset classes. B. For most assets, CCA is calculated by applying the appropriate asset class rate against the declining asset balance (UCC amount). Intangible assets such as leasehold improvements or patents follow the straight line depreciation method for computing CCA. For such assets, CCA essentially represents an annuity series. C. Under the asset class system, all assets within a particular CCA class are depreciated for tax purposes as if they were a single asset. D. The half-year rule allows the firm to include one-half of the purchase cost of the asset in the asset class in the year it is purchased for calculating the year’s CCA. This is the case regardless of when the asset is purchased. The remaining half is added to the asset class in the next year. TTaabbllee 99..11 SSoommee ooff tthhee mmoosstt ccoommmmoonn ccaappiittaall ccoosstt aalllloowwaannccee ((CCCCAA)) ccllaasssseess.. CCllaassss NNuummbbeerr DDeessccrriippttiioonn CCCCAA RRaattee 1 Most buildings bought after 1987 and the cost of certain additions or alterations made after 1987. 4% 3 Most buildings acquired before 1988. Also included is the cost of additions or alterations made after 1987. 5% 7* Canoes, rowboats, and most other vessels, including their motors, furniture, and fittings 15% 8 Property not included in any other class. Also included is data network infrastructure equipment and systems software for that equipment acquired before March 23, 2004. 20% 9* Aircraft, including furniture, fittings, or equipment attached, and their spare parts 25% 10 General-purpose electronic data processing equipment (commonly called computer hardware) and systems 30% 9-6 software for that equipment acquired before March 23, 2004, or after March 22, 2004, and before 2005 if you made an election. Motor vehicles, automobiles, and some passenger vehicles. 12 Chinaware, cutlery, linen, uniforms, dies, jigs, moulds, or lasts, computer software (except systems software), cutting or shaping parts of a machine, certain production costs associated with making a motion picture film, such as apparel or costumes, videotape cassettes, …. 100% 13 Property that is leasehold interest (the maximum CCA rate depends on the type of the leasehold and the terms of the lease) N/A 17 Roads, parking lots, sidewalks, airplane runways, storage areas, or similar surface construction 8% 22* Most power-operated movable equipment bought before 1988 and used for excavating, moving, placing, or compacting earth, rock, concrete, or asphalt 50% 38* Most power-operated movable equipment acquired after 1987 used for moving, excavating, placing, or compacting earth, rock, concrete, or asphalt 30% 45 General-purpose electronic data processing equipment (commonly called computer hardware) and systems software for that equipment acquired after March 22, 2004, and before March 19, 2007. 45% 46 Data network infrastructure equipment acquired after March 22, 2004 30% 50 General-purpose electronic data processing equipment (commonly called computer hardware) and systems software for that equipment, including ancillary data processing equipment acquired after March 18, 2007 55% 52 General-purpose electronic data processing equipment (commonly called computer hardware) and systems software for that equipment, including ancillary data processing equipment acquired after January 27, 2009, and before February 2011. 100% *These asset classes have been extracted from the Income Tax Regulations (C.R.C., c. 945), Department of Justice Canada Web site, laws.justice.gc.ca/eng/C.R.C.- c.945/index.html, accessed October 4, 2010. 9-7 Source: Author’s calculations based on Canada Revenue Agency Web site, www.cra- arc.gc.ca, accessed August 17, 2010. Reproduced with permission of the Canada Revenue Agency and the Minister of Public Works and Government Services Canada, 2011. Sale of Assets: A. A company is entitled to a CCA as long as it owns at least one asset in the asset class. When a depreciable asset is sold, the undepreciated capital cost of its asset class is reduced by the asset’s sale price or its initial cost, whichever is less. The resultant amount is called the adjusted cost of disposal. B. A company may buy new assets and also sell old assets in the same year which may fall within the same asset class. In this case, we would apply the net acquisitions rule, that is, determine the total cost of all additions to an asset class from which we would subtract the adjusted cost of disposal of all assets in that class. If the net acquisition is positive, we would apply the half-year rule and calculate CCA. If, on the other hand, the net acquisition is negative, we do not adjust for the half-year rule. Instead, we subtract the negative net acquisition amount from the beginning UCC balance of the asset class. CCA for the year will be calculated by applying the CCA rate on this net amount. Termination of Asset Pool: A. If the company disposes off its entire pool of assets in an asset class, we determine, once again, the adjusted cost of disposal as the lower of the sale proceeds or initial cost of this pool of assets and subtract this amount from the undepreciated capital cost of the asset class. If this leaves a positive balance in the asset class and there are no other assets remaining in the class, this remaining balance is called a terminal loss and is deducted from taxable income. Also, the undepreciated capital cost then becomes zero, and the asset class ceases to generate CCA tax shields.1 B. If, on the other hand, after deducting the adjusted cost of disposal from the undepreciated capital cost of the asset class, we arrive at a negative balance, this amount is called recaptured depreciation and is added back to taxable income. Once again, the undepreciated capital cost of the asset class becomes zero. C. When an asset is sold for more than its initial cost, the difference between the sale price and initial cost is called a capital gain. Presently capital gains, net of any capital losses, are taxed at 50 percent of the firm’s applicable marginal tax rate. 1We should note that if the asset pool is not completely terminated, that is, there are other assets remaining in the asset class, then a positive balance would simply become the UCC of the class and continue to generate CCA tax shields. 9-8 Present Values of CCA Tax Shields: A. An asset can continue to generate, in perpetuity, CCA tax shields for the firm even after it is sold, provided there are other assets remaining in its class and the total UCC balance for the asset class is positive. Suppose we use the following notation for our subsequent discussion: C d UCCt Tc r S = capital cost of an asset acquired at the beginning of Year 1 = CCA rate for the asset class to which the asset belongs = undepreciated capital cost in year t after deducting CCA for the year = the firm’s tax rate = discount rate = Salvage amount from the sale of the asset at the end of year t B. Equation 1 below can be used to compute the present value of a perpetual tax shield.     + + + r r r d CdTc 1 1 0.5 (1) C. With a residual or salvage value arising from the sale of an asset, we would deduct this salvage value from the UCC of the asset class, and thereby reduce the CCA deductions and CCA tax shields for later years. A general formula for the present value of the CCA tax shield with salvage value: Present value of CCA tax shield = ( )       +     − +    + +     + t c c r d r SdT r r r d CdT 1 1 1 1 0.5 (3) 9.4 EXAMPLE: BLOOPER INDUSTRIES Work carefully through the Blooper Industries example, reinforcing concepts mentioned earlier. See Table 9.5. Calculating Blooper’s Project Cash Flows A. All of the outlay, $10 million, is assumed to be made now or in period zero, with no salvage value expected at the end of the project life. B. Note the changes in net working capital, or net added current assets needed, early in the project. Later, as the project winds down, net current assets are no longer needed and contribute to the positive cash flow. 9-9 C. Revenues are estimated through the periods in which revenues are thought to be generated. Do not arbitrarily cut-off the periods of cash-flow generation. D. Lines four and five are assumed to be cash flow revenue and expenses, with CCA as the only noncash revenue/expense in the analysis. E. Project cash flows are the sum of three components: investment outlay on plant and equipment, investment in project net working capital, and project cash flow from operations. F. Cash flows from operations comprises of (a). operating cash flows excluding CCA and (b). CCA tax shield. Calculating the NPV of Blooper’s Project Cash flows are conservatively assumed to occur at the end of the year. Further Notes and Wrinkles Arising from Blooper’s Project A. Salvage value cash flows will increase the net present value of the project to the extent of the net cash received from the disposal less present value of lost tax shield from the salvage value. B. Nominal annual CCA amounts, given inflation, yield lower real tax shield cash flow. 9.5 SUMMARY PEDAGOGICAL IDEAS General Teaching Note - One of the key concepts developed in this chapter is the process of determining the relevant, incremental cash flows of an investment. From outlay, periodic and final period, this general question applies: “What changes, given our decision to make the investment?” With this concept in mind the after-tax, sunk cost and other concepts are easier to understand, so the suggestion is to start with the “incremental” concept. Student Career Planning - All students are familiar with the business cycle, and most have watched its effect upon their family members. They have studied it in business cases and have seen its effect upon the businesses in the cases they have studied. They now have to watch it with great personal interest. The state of the economy or industry when they graduate will affect the number and variety of entry-level jobs available. Chances are very good that economic conditions have changed, either better or worse, since they declared their major. They need to be reminded to keep up with the economy and 9-10 industries where they have an interest and to read periodicals related to the industry in question on a regular basis and, of course, the business newspapers. Internet Exercises - If your college has a local student chapter of the Financial Management Association, give them a plug this week. Ask the advisor or student officers for a copy of the activity agenda for the term. Pass it around the class with the next meeting highlighted. The FMA national office has a great web site with considerable space devoted to their student chapters. Another great finance and business “career” site for students is WetFeet.com. It provides a full range of information about finance and business careers. Ask your students to check out the site and write a one-page report on a career of interest to them. In the next class spend a few minutes (small group or full class) talking about the career interests in the class and what WetFeet.com provided them. http://www.fma.org The Financial Management Association is an international association of academics, business practitioners, and students, based in Tampa, Florida. Founded in 1970, the FMA sponsors the FMA Honor Society and FMA Student Chapters in colleges and universities around the world. When you promote your local chapter, mention this web site. Under the “For Undergrad/MBA Students” icon from the home page, the services and activities of the Student Chapters are described. The FMA sponsors several student leadership conferences for student members every year and publishes a “Careers in Finance” book for every new member. Students may join the FMA from the web site and gain access to the “member” information available. The Certified in Financial Management Designation, cosponsored by the Institute of Management Accountants with the FMA, is also described. Give your FMA chapter a “plug” in your next class. http://www.wetfeet.com Wetfeet.com is one of the better “exploring careers” sites on the Internet. Your students can explore various business careers in depth, assess salary information, and even chat with a professional in an area of interest. Further, it profiles thousands of companies with product and financial information, links to company home pages, a “discussion board” for each company, and much more. Often when a student is interested in an area of business, we suggest that they look at the companies in the “industry.” Wetfeet.com provides a list of companies in a wide range of industries. This site offers tips on resumes, interviewing, internships, and relocation planning, and so on. Use it for an assignment or just provide an introduction! 9-11 CHAPTER 10 PROJECT ANALYSIS CHAPTER IN PERSPECTIVE The last two chapters focused on the general concepts and specific techniques of the capital budgeting evaluation. This chapter extends those ideas to a more realistic setting within a business. In every business, large and small, the capital budget is prepared and bargained. A small proprietor may assess the value of new equipment by herself over morning coffee. As the business grows, the people dimensions and breadth of competing opportunities grows exponentially! All this is planning, estimating, and setting a course in an uncertain future. A plan should not be a single point in a very uncertain future, but provide a basis for considering alternative results to varying future conditions. “What if” analysis, scenario analysis, break-even analysis (accounting and NPV), etc., are techniques searching for a “feel” for the future. A capital plan should consider several alternative economic situations; a review of new investments should consider the most critical variables that will “make or break” the success of the project. In addition to the useful planning techniques, the chapter offers a good planning perspective for future managers: We do not know what the future holds, but we have a good feel for the results, and are ready, when specific things happen. Consider presenting the chapter within a planning format and overview, rather than looking at a series of specific planning. Offer the student a “forest” perspective, so they will not get lost in the “trees.” CHAPTER OUTLINE 10.1 HOW FIRMS ORGANIZE THE INVESTMENT PROCESS Stage 1: The Capital Budget Stage 2: Project Authorization Problems and Some Solutions 10.2 SOME “WHAT-IF” QUESTIONS Sensitivity Analysis Scenario Analysis 10.3 BREAK-EVEN ANALYSIS 10-1 Accounting Break-Even Analysis Economic Value Added and Break-Even Analysis Operating Leverage 10.4 REAL OPTIONS AND THE VALUE OF FLEXIBILITY The Option to Expand A Second Real Option: The Option to Abandon A Third Real Option: The Timing Option A Fourth Real Option: Flexible Production Facilities 10.5 SUMMARY TOPIC OUTLINE, KEY LECTURE CONCEPTS, AND TERMS 10.1 HOW FIRMS ORGANIZE THE INVESTMENT PROCESS A. There are two important steps in the investment process: the capital budget and project authorization. B. They include the planning and proposals of investment, followed by evaluation and approval. Stage 1: The Capital Budget A. The capital budget is a list of planned investment projects. B. The list may be compiled from the bottom up (divisions and departments) or from the top down (strategic planning). C. Project plans from the bottom up bear the specific knowledge of people close to the customer and other business dimensions; senior management has the perspective of corporate strategy and the big picture of the firm’s operations. 10-2 Stage 2: Project Authorization A. Four different project areas are common in a business: 1. Outlays required by law, such as safety equipment, or projects required under company policy are evaluated to find the lowest cost. 2. Maintenance or cost reduction projects, such as replacement decisions. 3. Projects related to expanding the capacity of existing business activity. 4. Investment projects in new products or services. B. The required outlays, number one above, are mandated and the lowest cost for compliance is the decision rule. The other three types of projects should use the NPV method as a decision criterion. Problems and Some Solutions A. Making sure that assumptions are consistent among competing proposals is important. A top-down set of assumptions, such as an economic forecast, focuses assumptions in a narrow, consistent range. B. Keeping the manager reward system consistent with shareholder returns encourages a long-run focus in investment evaluation, and helps eliminate conflicts of interest. C. Competition for scarce funds may lead to an inflation of estimated project cash- flows or benefits, and an overstatement of the estimated project NPV. D. Capital rationing techniques, which force divisional managers to send only the best projects forward, and intense scrutiny of projects are project-screening techniques that assure only the best projects are accepted for investment. 10.2 SOME “WHAT-IF” QUESTIONS Project cash flows and NPVs may be estimated under different assumptions to improve the decision process. Sensitivity Analysis A. Changing a single, specific variable within a range from most likely to optimistic to pessimistic and evaluating the NPVs is called sensitivity analysis. B. Sensitivity analysis reveals the significant variables, which, if varied or misestimated, would significantly change the NPV and acceptability of the project. 10-3 C. Sensitivity analysis assumes that the individual variables are independent of each other. This is usually not the case. Sales cannot be varied without significantly affecting certain costs. This interrelationship between variables limits the extent that one variable can be changed without altering another, and thus, narrows the range of the sensitivity analysis. Scenario Analysis A. Like sensitivity analysis, scenario analysis involves the same change of variables to see the impact on NPV, but scenario analysis differs from sensitivity analysis in that a particular combination of variables under specific assumptions is compared with another scenario of assumptions. B. Simulation analysis, an extension of scenario analysis, generates many scenarios and, with an estimate of their probability, generates NPV estimates for a wide range of scenarios. 10.3 BREAK-EVEN ANALYSIS A. In any business venture forecast, break-even analysis, or an estimate of the sales point where total revenue equals total expenses is an important focus point for managerial analysis. B. Estimating the accounting break-even point level of sales of a project requires identifying the level of fixed costs involved in the project and the variable cost/sales ratio related to the project. Accounting Break-Even Analysis A. The sales break-even point is estimated to be the fixed costs including depreciation divided by the percentage of sales contribution margin, or the fixed costs including depreciation divided by one minus the variable cost to sales ratio: Break-even Sales = Fixed Costs Inc. Depr. / (1 - Var. Cost / Sales) B. A project that just breaks even in accounting income terms will have a negative NPV. NPV Break-Even Analysis A. Accounting break-even analysis does not consider the cost of capital invested in the project. 10-4 B. The NPV break-even point is the level of sales from a project needed to generate a zero NPV or an internal rate of return that equals the opportunity rate of return of investors. C. With the cost of the project = the present value of cash flows = NPV of zero, the level of sales that generates the periodic cash flows needed to generate the given present value is the unknown. D. The PV of cash flows = annuity factor (periods/opportunity rate) x (depreciation per period) + [(1-tax rate)(sales x contribution margin - fixed cost and depreciation)]. The bracketed quantity represents net income plus depreciation or the after-tax cash flows. Sales higher than the zero NPV sales will produce positive NPV. E. The sales level that produces an NPV of zero is always higher than the sales level for the accounting break-even point. Operating Leverage A. Projects with high proportions of fixed costs generate higher NPVs when sales are high than projects with low proportions of fixed costs (high proportions of variable costs). The contribution to fixed cost, sales less variable costs, contributes to fixed cost until the break-even point and thereafter contributes to profit/cash flows. The high fixed cost project will have a high contribution to profit for each higher level of sales. B.. A project with fixed costs is said to have operating leverage. The extent of operating leverage or the extent of fixed costs versus variable costs/sales is called the degree of operating leverage. C. The degree of operating leverage is the percentage change in profits given a one percent change in sales, or: DOL = percentage change in profits/percentage change in sales D. Arithmetically, the DOL is one plus the fixed costs/profit ratio, measured at a specific level of sales, or: DOL = 1 + fixed costs/profits E. The risk of a project, or the variability of the realizable NPV, is directly related to the degree of operating leverage of the project. The higher the fixed costs, the greater the variation in cash flows given a change from estimated sales. 10-5 10.4 REAL OPTIONS AND THE VALUE OF FLEXIBILITY A. In addition to reviewing all variations of possible cash flows associated with a project, selecting projects with a high degree of flexibility provides managers with the opportunity to adjust to future, unknown, competitive and economic factors associated with the project. B. These flexibility options associated with real assets are called real options. The managers must identify the real options available/needed and estimate their value. C. As with financial options, the value of the option increases with time available and the more uncertain the future. The Option to Expand A. Projects which develop in stages, or are developed with future flexibility in mind, provide managers with options to expand at each stage or to change the nature of the project in the future in response to market forces. B. The cost of the option is the opportunity costs of not doing the entire project now. C. Decision trees assist in measuring the value of management options to vary a future course of action associated with a project with sequential decisions. Decision trees can be very helpful when projects involve future decisions like the diet whiskey project (Figure 10.3) A Second Real Option: The Option to Abandon A. Managers must recognize and evaluate the option to abandon a project at every point after they make the initial investment. A Third Real Option: The Timing Option A. Any project proposal provides the manager the option to invest or accept the project. B. The option to invest can be exercised now or later. C. One must weigh the value of cash flows lost by delaying the project versus the possibility of adding new information about the future cash flows or possible success of the project if it is postponed for a time. 10-6 A Fourth Real Option: Flexible Production Facilities A. Building in an option to change its production or raw material mix provides future flexibility for the manager. B. The cost of the option is the flexibility changes built into the project compared to a single purpose design of the project. 10.5 SUMMARY PEDAGOGICAL IDEAS General Teaching Note - This chapter is best taught with one of the end-of-chapter problems as the basis for introducing concepts and the specific planning techniques. Consider setting up one of the problems and the specific techniques, such as the sales = NPV = zero, in a spread sheet format so that iterating various scenarios and solutions are effected almost immediately. This is a great lecture to take your notebook PC to class and display the problem on the overhead. If not available, work several different alternatives and present, via overheads and/or handouts, the results of varying assumptions. Plotting the relationship between one changing variable and the sales needed, NPV value, etc. is another way to share planning or computer applications with your students. Student Career Planning - Encourage your students to keep up with current events beyond the student newspaper and to read. When they begin to interview for “their job,” recruiters often test the extent to which students have developed an awareness and sense of the value of continuing education, which daily newspapers and current books provide. We both know that this generation is TV focused and are likely to get their news from CBC NewsWorld, CTV or CNN. The “how they do it” is not as important as “that they do it,” for it is but one indicator of increased maturity, a continuous process but one that all recruiters use to make their hiring decisions. Internet Exercises - Two of the most popular professional certifications in finance are the Certified Financial Planner (CFP) and the Chartered Financial Analyst (CFA). The CFP has become the standard for certification in the area of consumer financial planning, and the CFA has long been the professional certification to have in the field of financial markets and security analysis. Introduce your students to these two certifications by referencing the Internet sites of each. http://www.cfp.net/ The Certified Financial Planning Board offers financial planning professionals an opportunity to certify their knowledge and standards for practice by attaining CFP certification. This site offers information to consumers about financial planning, finding a 10-7 CFP certified professional in their area, and fielding complaints about experiences they have had with practitioners. For the student studying in the financial services areas of credit, investment planning, insurance, estate and retirement planning, and the like, the CFP certification will likely be a part of their continuing education after graduation. Is your curriculum CFP certified? If certified, students completing your classes may take the CFP exam while in college. As they work in the field, they gain the added practical experience necessary for the CFP certificate. A review of the CFP Certification link provides students with the scope of financial planning for their career search process. The procedures for gaining certification are also detailed under the Certification link. A look through the site map reveals many links to financial planning, plus a long list of consumer group organizations and colleges/universities offering CFP programs. http://www.cfainstitute.org/ The Association for Investment Management and Research (AIMR) promotes knowledge, professionalism, standards, and ethics in the area of investment management. The Chartered Financial Analyst (CFA) certificate, offered via the AIMR, is the premier professional certification in finance. Through three levels of exams, CFA candidates study a wide range of subjects. Ask your students to explore the scope of the CFA area of study. It will not only provide them with a look at the knowledge areas but give them a taste of the ethical standards associated with the profession. The AIMR also has a number of free books about the CFA that you could order for your office. 10-8 CHAPTER 11 INTRODUCTION TO RISK, RETURN, AND THE OPPORTUNITY COST OF CAPITAL CHAPTER IN PERSPECTIVE While this is the beginning of a new section related to the discussion of risk and return, it is really a “bridging” section between the asset investment orientation of the last section and the financing section which follows this one. The past and prospective investment projects of a business establish a risk profile that determines the opportunity rate of return. There is no cost of capital, required rate of return, or opportunity rate of return independent of where the funds are invested. This connection or bridge of financing and financial markets to the capital budgeting process must be emphasized in order for the students to sense a continuing theme or connection of all the chapters. This chapter introduces risk concepts, historical rates of return, and the concept of the opportunity rate of return. In the next chapter these concepts are inserted in the capital budgeting process. Risk, an important factor in the valuation theme, is focused on financial risk, related to the variability of returns. Most students’ prior experience is with pure risk, the risk of real assets, where the “tail” is single-sided. What is the risk of someone looting their apartment when they are in class? Few students will return to their “digs” to find it cleaned and refurnished, a proxy for the upside return occurrence or second “tail” of possible occurrences. One tail on pure risk and two tails for investment returns! Students often define investment risk as the risk of loss, bringing in their pure risk focus. Show them two tails! CHAPTER OUTLINE 11.1 RATES OF RETURN: A REVIEW 11.2 EIGHTY-FIVE YEARS OF CAPITAL MARKET HISTORY Market Indexes The Historical Record Using Historical Evidence to Estimate Today’s Cost of Capital 11-1 11.3 MEASURING RISK Variance and Standard Deviation A Note on Calculating Variance Measuring the Variation in Stock Returns 11.4 RISK AND DIVERSIFICATION Diversification Asset versus Portfolio Risk Covariance and Correlation Correlation and Portfolio Diversification Market Risk versus Unique Risk 11.5 THINKING ABOUT RISK Message 1: Some Risks Look Big and Dangerous but Really Are Diversifiable Message 2: Market Risks are Macro Risks Message 3: Risk Can be Measured 11.6 SUMMARY TOPIC OUTLINE, KEY LECTURE CONCEPTS, AND TERMS 11.1 RATES OF RETURN: A REVIEW A. Security return, either stock or bonds, are a combination of dividend or interest payments plus any capital gain or loss. B. The annual percentage return on investment is: Percentage Return = capital gain (loss) + dividend or interest initial share or bond price C. The return on a stock can also be calculated as the sum of the dividend yield and 10-2 the capital gains yield. The dividend yield is the annualized dividend/initial investment share price; the capital gains yield is the annualized capital gain/initial investment share price. The annual total return is the sum of annualized dividends and capital gains divided by the initial share price. D. The above return is a nominal return, reflecting how much more money one has at the end of the year. E. The real rate of return is the nominal rate adjusted for the inflation rate in the period or the additional purchasing power one has with the investment return: 1 + real rate of return = 1 + nominal rate of return 1 + inflation rate 11.2 EIGHTY-FIVE YEARS OF CAPITAL MARKET HISTORY A. Managers must estimate current and future required rates of return when evaluating investments. Estimating the required rate begins with a study of historical rates of return on varying risk investments. By looking at the rate of return on other, equivalent risk, investments, managers get a sense of the opportunity rate of return. B. The level of risk and required rate of return are directly related. Investors require higher rates of return for increased risk. Market Indexes A. Market indexes measure the investment performance of the overall market and of different classes of stocks. B. The S&P/TSX Composite Index ("TSX Index") is a value-weighted index of the largest stocks trading on the TSX, the Toronto Stock Exchange. C. The TSX Index replaced the TSE 300 Composite Index in 2002. The key difference between the old TSE 300 and new TSX is the number of stocks in the index. Whereas the TSE 300 always had 300 stocks, the TSX has only those stocks of a minimum size (number of shares × price per share) and liquidity (trade frequently). With the new requirements, about 80 stocks were dropped from the index. As of Janaury 2011 the TSX had 245 stocks in it. D. The TSX, like the TSE 300, is a value-weighted index. The index is calculated by multiplying each stock’s current share price by its corresponding number of shares outstanding and then dividing by the index’s original total value. Thus the weight attached to each stock is its fraction of the total investment in portfolio. A value- weighted index measures the average performance of investors. 10-3 E. Several U.S. stock indexes are widely followed. The Dow Jones Industrial Average is an equal share index of thirty industrial stocks. It is an index of important but few firms, independently of how many shares each company has outstanding. F. Another important U.S. market index is the Standard and Poor’s Composite Index. Like the TSX, it is a market value-weighted index and includes 500 firms, covering about 70 percent of the value of stocks traded. Compared to the Dow, the S&P 500 is a broader index and is adjusted for the relative market value of each company. G. The Nikkei Index 225 (Tokyo), and the Financial Times Index, FTSE 100, (London) are just a few other market performance indices. Morgan Stanley Capital International (MSCI) computes the MSCI World Index and covers 24 countries. The Historical Record A. The historical returns of Treasury bills, long-term Government of Canada bonds, and common stock are compared in Figure 11.1 B. With Treasury bills’ average returns at the low end of the risk scale, a maturity premium is added for long-term Government bond returns. C. The return differentials between risk-free Treasury bills and corporate bonds and common stock returns are risk premiums, or the added return required by investors to invest in risky securities. D. Long-term average returns are a starting point in estimating required rates of return for the future, and the opportunity rate of return used in the capital 10-4 budgeting process. E. The riskier securities had wider fluctuations in their yearly returns over the 85 years studied. See Table 11.1 and Figure 11.2. Using Historical Evidence to Estimate Today’s Cost of Capital A. The opportunity cost of capital is the rate of return given up to invest in the projects of a business rather than in equivalent risk alternatives. B. If the investment’s risk is zero, and the investment is a sure thing, the opportunity cost of capital is the risk-free rate of interest, the Treasury bill rate of return. C. For an investment that has the same risk as the portfolio of stocks in the TSX market index, the opportunity cost of capital is the rate of return that can be expected to be earned on the TSX. We call this portfolio of stocks the market portfolio. D. Estimated stock returns fluctuate yearly (7% average risk premium) above the Treasury bill rate. This assumes that there is a normal, stable risk premium on the market portfolio and that past returns are reliable predictors of future returns. E. Historical returns provide benchmarks for estimating current and future required rates of return. The market portfolio returns, assumed to be stable and similar to historical returns, may serve as proxy for average-risk project opportunity rates of return. F. To calculate the expected return on an investment with risk equal to the risk of the market portfolio, add together the current T-bill rate and the normal market risk premium: expected return = T-bill rate + normal market risk premium 11.3 MEASURING RISK A. Variation around a central tendency or mean may be presented visually by constructing a histogram (Figure 11.3) and studying the dispersion or spread of possible outcomes. B. Another method is calculating a measure of variation used as a proxy for measuring risk, such as the variance or standard deviation. Risk relates to the variability of future returns. 10-5 Variance and Standard Deviation A. The variance of a random variable is the probability-weighted average of squared deviations from the mean. The standard deviation is the square root of the variance. B. The greater the variance or standard deviation, the greater the dispersion, volatility, or variability of returns, and the greater the risk. See Table 11.2 for the calculation of the variance and standard deviation. A Note on Calculating Variance A. In Table 11.3 the use of the probability of each possible outcome is incorporated in the calculation of variance and standard deviation. The results in Table 11.3 are the same as Table 11.2 but have an extract column to incorporate the probability of each of the possible outcomes of the coin-toss game. Measuring the Variation in Stock Returns A. We distinguish between measuring variance when the probability of each possible outcome is known (population variance) and measuring variance based on observed values of the variable (sample variance). B. When all possible outcomes and their probability are known, we can calculate the population variance: population variance = sum of the probability weighted squared deviation from the expected value. C. The variance calculated with observed values is the sample variance. Using the actual observations, the sample mean is calculated. The sample mean is the average of the observations. The deviations between the observed values and the sample means are squared and then summed and divided by the number of observations, less one: sample variance = sum of squared deviations from mean number of observations - 1 D. Table 11.4 is an example of calculating variance and standard deviation using historical stock returns. E. The historical average investment returns and the variability of those returns in Figure 11.3 are in Table 11.5. The comparison of average returns and volatility indicates that historical risk and return are directly related. These are sample variances. 10-6 E. Higher risk is associated with higher average returns. F. One might assume that historical returns and variability (long period) would extend into the future for estimating investor-required or opportunity rates of return. G. Investors will expect a higher rate of return, risk premium over the Treasury bill rate, with higher standard deviation of returns. Review Table 11.1 and Figure 11.3 with the class for a visual presentation of the concepts. 11.4 RISK AND DIVERSIFICATION A. Our measures of variation apply to groupings of securities or portfolios as well as to single securities. B. The variability or risk of a portfolio, or a market portfolio such as the S&P/ TSX Index, is not the simple average of the individual stock variability. The portfolio risk is less than the average risk of the individual securities. Diversification A. The reduced risk of the portfolio is caused by diversification effects of spreading the portfolio across many investments. B. Portfolio diversification works because prices of different stocks do not move exactly together or are not perfectly correlated (+1). Diversification works best, or in other words, the risk-reducing effects of diversification works best, when the stock returns are negatively correlated. Diversification reduces the variability of returns on the portfolio compared to the average variability of the individual stocks. Asset versus Portfolio Risk A. While historical returns on individual securities are good proxies for estimating future returns on individual securities, historical standard deviations of returns are not good risk proxies for stocks held in a portfolio. B. Since stocks and other securities are usually held in portfolios, to take advantage of the diversification effect, the relevant risk of a stock is its impact on the portfolio variability or risk. The incremental risk of a stock added to a portfolio depends on how the stock varies compared to the portfolio variation. If the historical correlation between the stock and portfolio are highly positive (+1), there is no diversification effect of the added stock. If the relationship is negative, zero or low positive, the addition of the stock lowers the portfolio variance or standard deviation or risk. 10-7 C. Incremental risk does not depend upon the added stock’s variability; it depends upon how the stock affects the portfolio’s variability when it is added to the portfolio. Covariance and Correlation A. The correlation coefficient is a statistical measurement of the degree of relatedness of two variables. Its value lies between -1 and +1. B. A correlation coefficient greater than 0 indicates that the variables tend to move together. The variables are positively correlated. If the correlation coefficient is less than 0, the variables are negatively correlated and tend to move in opposite directions. C. Correlation for a sample of date can be measured with the Excel function CORREL. D. Correlation can also be measured using the mathematical definition of correlation: Correlation between x and y = Covariance between x and y standard deviation of x × standard deviation of y E. The covariance of x and y is another measure of co-variation and is similar to variance. The Excel function COVAR can be used to calculate the covariance of a set of observations. We also provide an equation for calculating covariance, 11.11. You can go back to Table 11.8 to see all of the calculations of variance, covariance and correlation. Correlation and Portfolio Diversification A. The standard deviation of a portfolio can be expressed as a combination of the standard deviations of the individual stocks and their correlation. Equation 11.13 shows the factors contributing the standard deviation of the portfolio. By varying the degree of correlation between the stocks, the portfolio’s standard deviation can be changed. The maximum portfolio standard deviation occurs when the stocks’ correlation coefficient is 1, the highest possible. This also equals the average of the stocks’ standard deviations. If the correlation coefficient is less than 1, the portfolio standard deviation is less than the average of the stocks’ standard deviation. See Table 11.10 for an illustration of the effect of different correlation coefficients on the portfolio standard deviation. B. Example 11.2 and Figure 11.5 illustrate the benefits of creating a portfolio consisting of Loblaw and TransCanada stocks. 10-8 Market Risk versus Unique Risk A. The diversification effect or the reduction in portfolio risk takes place with the addition of added securities until about 20 or 30 are included in the portfolio. Beyond that, the diversification effect of added securities is minimal. See Figure 11.7. B. While diversification eliminates the unique risk of individual securities, one cannot eliminate the market risk or systematic risk, the risks that affect the entire stock market. Unique risk can be eliminated because stocks less than perfectly correlated, with correlation coefficients of less than one. The market risk arises because stocks’ correlation coefficients with the market portfolios are greater than zero. C. For a diversified portfolio, only the market risk matters. When one discusses securities investment or investors, it is assumed that the security is held in a diversified portfolio and the relevant risk is market risk. 11.5 THINKING ABOUT RISK Message 1: Some Risks Look Big and Dangerous but Really Are Diversifiable A. Individual project risk may not be as high when the project is part of a portfolio of business investments. As in the discussion above, the relevant risk is the incremental risk effect on the investment portfolio or the impact on the total business performance. Message 2: Market Risks Are Macro Risks A. Investors holding diversified portfolios are concerned with macroeconomic risks, or 10-9 the impact of business cycle, exchange rates, etc., on investor decisions related to investment and disinvestment in financial markets. Specific or unique risk is not relevant. B. Managers must deal with unique risk exposure in addition to market risk, but only market risk affects the opportunity cost of capital (opportunity rate of return) of the firm. Message 3: Risk Can Be Measured A. The risk, measured by the variance or standard deviation, of individual stocks can be easily measured, but when diversification is assumed for investors, only the incremental risk effects of adding a security to a portfolio is relevant. B. In the next chapter this relevant risk, or the individual stock’s relationship with fluctuations in the market portfolio, is discussed and measured. 11.6 SUMMARY PEDAGOGICAL IDEAS General Teaching Note - Just as it was suggested in the first chapter to talk about the differences between financial and pure risks, it is worthwhile to spend a little time reviewing correlation concepts with your students. Most have probably completed their statistical courses by now, but not always. If two courses are offered at your college, variation and standard deviation are likely in the first course with correlation covered later. Some students may not have covered correlation to this point, so a five- minute general coverage or review will enhance their understanding of the beta concept and relative risk. Student Career Planning - The business major has an excellent background for the continued study of law. Many students are nearing their life-long dream of an undergraduate degree and are considering various alternatives, including graduate school. For those considering an MBA, some work experience between degrees is often recommended, but for those considering a law degree, students need to start planning early. Most law schools require the LSAT exam, and early application deadlines are frequent. Who wants to be a lawyer? I want to work in business! Legal studies are excellent preparation for business. Almost all business relationships involve contracts and a “legal perspective.” One’s work as a lawyer may bring him or her close to many business opportunities for investment. Encourage students to consider a variety of alternative careers. While they have eliminated a few to this point, such as science and medicine, there are many left to explore. Remind them to work at their career from a plan. Just like water finds its way downhill, and who knows where, selecting a career without a plan will likely find the student “anywhere” twenty years from now! 10-10 Internet Exercises - Risk is introduced in this chapter. This is probably the first time your students have studied this subject. Most students are familiar with pure risk or the “one-tail” risk of loss. Financial risks often entail “two-tailed” risk of gains/losses. Two other aspects of risk that you might want to share with your students are the following: 1. Risk analysis, measurement, and management are a body of knowledge shared and applied by academics and practitioners alike. Business risk management is an important dimension of corporate financial management. There are professional societies, such as the Society for Risk Analysis that serve to further the knowledge of risk analysis and management. Conclusion: there are careers in risk management! 2. Risk analysis, measurement, and management are easily applied to consumers as well as business. Personal financial planning activities include an assessment and decisions about risks faced by individuals. The two sites reviewed below provide examples of each of the two points above. http://www.sra.org The Society for Risk Analysis (SRA) provides a means for gaining knowledge about risk assessment, risk characterization, risk communication, risk management, and policy related to risk. The scope of the organization goes beyond just business risk to environmental and other risks. This site is an excellent example of the scope of ongoing risk analyses by professionals today. http://urbanext.illinois.edu/risk/ The management of risk may be applied to a consumer or family just as easily as a business. This site, developed by Karen Chan, offers information and application of a personal risk management plan. It follows the same six steps as a corporate risk management process, but the focus is on personal risk management. This site provides an opportunity to expand the concept of risk management and reinforce the concepts and terms of the chapter. 10-11 Instructor Manual for Fundamentals of Corporate Finance Richard A. Brealey, Stewart C. Myers, Alan J. Marcus, Elizabeth Maynes, Devashis Mitra 9780071320573, 9781259272011