Select one of the capital investment evaluation methods described in Chapter 10 of your text. Fully explain the capital evaluation method?s strengths and weaknesses. Take a position and defend the use of your selected method. Be sure to use at least two scholarly sources to support your position. Your initial post should be 200-250 words.

chapter 10 Capital Investment Decisions iStockphoto/Thinkstock Learning Objectives After studying Chapter 10, you will be able to: Explain the nature and importance of capital investment decisions. Identify the relevant cash inflows and outflows in an investment proposal. Format the relevant cash flow data in an investment proposal. Understand how to apply present value evaluation methods to capital investment decisions. Understand how to apply payback period and accounting rate of return methods to capital investment decisions. Compare strengths and weaknesses of capital investment evaluation methods. Comprehend how income taxes impact the cash flows of capital investments. sch80342_10_c10_399-444.indd 399 12/20/12 2:06 PM CHAPTER 10 Chapter Outline Chapter Outline 10.1 The Importance of Capital Investment Decisions 10.2 The Capital Investment Decision Cash Flows Decision Criteria Time Perspectives An Example - Equipment Replacement and Capacity Expansion Formatting the Relevant Data 10.3 The Evaluation Methods Net Present Value Method Internal Rate of Return (IRR) Method The Payback Period Method Accounting Rate of Return Method 10.4 Ethical Issues and Pressures on Management 10.5 Taxes and Depreciation Income Taxes and Capital Investments Depreciation Expense The Tax Shield 10.6 Cost of Capital 10.7 Calculation Issues Inflation and Future Cash Flows Working Capital Uneven Project Lives Evaluation of Projects With Different Initial Investments Gains and Losses on Asset Disposals 10.8 The Time Value of Money Present Value of Money The Present Value of a Series of Future Cash Flows Present Value Analysis Applied Capital Investment Alternatives Rose Stanley, President of Fine Tone Instruments, grabs her briefcase and heads for the airport. After clearing security, running to her gate, and just making her flight, Rose settles into her coach seat, in front of two screaming kids and behind two salespersons who apparently have just made the deal of the century. She opens her briefcase and finds the Capital Spending Proposals file. The deadline for submitting proposals to her was yesterday. She plans to review these on her cross-country flight. The variety surprises her. sch80342_10_c10_399-444.indd 400 12/20/12 2:06 PM Introduction CHAPTER 10 Engineering is pushing to integrate a newly announced semiconductor into an aging product. The new technology will push Fine Tone into new markets with great sales potential but against stiff competition. Adding space to the corporate headquarters will bring three administrative departments together, increase efficiency, and reduce operating expenses. Her production planning manager proposes rearranging several work centers to improve production efficiency for a family of current products. Another project adds capacity to a specialized assembly operation. The plant manager requests funding for an air purification system, which must be installed by year-end to meet new state air quality requirements. An information systems proposal would automate several manual operations, save personnel, and slice inventory by an estimated 10 percent. Her finance manager is negotiating for controlling interest in a firm with technical expertise that Fine Tone needs for new product development. Marketing has proposed a major jump in advertising spending for a product line that has not been meeting sales targets. Rose clearly wants to get the \"biggest bang for the bucks\" from Fine Tone's limited capital investment budget. A quick calculation shows her that this year's investment dollars will fund about half of these proposals. Some proposals are risky, while others have predictable outcomes. Some are straightforward, but many include a host of extraneous issues. Also, financial data are overstated for some proposals and understated for others. Some generate immediate returns; others promise big cash flows years from now. Introduction T his chapter extends the study of incremental analysis begun in Chapter 9 into multiperiod decisions, which are called capital investment decisions. This chapter discusses: 1. Identification of relevant cash flows in capital investments. 2. Techniques and methods for analyzing project data. Capital investment analysis is a planning task and is directly linked to budgeting, as discussed in Chapter 6. Capital budgeting is the process of evaluating specific projects, estimating benefits and costs of the projects, and selecting which projects to fund. Capital budgeting depends on an understanding of the time value of money. For those who are unfamiliar with the time value of money or have not applied present values in financial accounting or other courses, section 10.8 explains the concept. Present value tables necessary for discounting future cash flows are located in section 10.8. sch80342_10_c10_399-444.indd 401 12/20/12 2:06 PM Section 10.2 The Capital Investment Decision CHAPTER 10 Relevant revenues and operating costs for multiperiod decisions are defined as cash inflows and cash outflows, respectively. Since these decisions extend over a period of years, timing of these cash flows are major factors. 10.1 The Importance of Capital Investment Decisions C apital investment is the acquisition of assets with an expected life greater than a year. These decisions attract managers' interest for good reasons: 1. Long-term commitments. Capital decisions often lock the firm into assets for many years. 2. Large amounts of dollars. Capital projects often have big price tags. From Ford Motor Company with an annual investment budget of $7 billion to a small firm buying a $50,000 truck, large relative dollar amounts get attention. 3. Key areas of the firm. New products, new production technology, and research efforts are crucial to a firm's ongoing competitiveness. 4. Source of future earnings. Investing with foresight is the key to the firm's future profits and financial performance. 5. Scarce capital dollars. In most firms, more demands exist for capital funds than the firm can meet. Only the best opportunities should be funded. Excellent analyses and decisions increase the firm's capacity, technology, efficiency, and cash generating power. Poor decisions waste resources, lose opportunities, and impact profits for many years. 10.2 The Capital Investment Decision A capital investment generally includes a cash outflow, which is the investment, and cash inflows, which are the returns on the investment. The decision maker expects cash inflows to exceed cash outflows. The typical investment project has cash outflows at the beginning and cash inflows over the life of the project. Cash Flows Cash flows are the key data inputs in capital investment analyses. Cash has an opportunity cost, since it could be used to buy a productive or financial asset with earning power. Cash is a basic asset. Prices, costs, and values can all be expressed in cash amounts. If the decision impacts several time periods, cash-flow timing becomes a relevant factor. Cash outflows commonly include: 1. 2. 3. 4. The cash cost of the initial investment plus any startup costs. Incremental cash operating costs incurred over the project's life. Incremental working capital such as inventories and accounts receivable. Additional outlays needed to overhaul, expand, or update the asset during the project's life. 5. Additional taxes owed on incremental taxable income. sch80342_10_c10_399-444.indd 402 12/20/12 2:06 PM Section 10.2 The Capital Investment Decision CHAPTER 10 Cash inflows include: 1. Incremental cash revenues received over the project's life. 2. Reduced operating expenses received over the project's life. (A reduction of a cash outflow is treated as a cash inflow.) 3. Cash received from selling old assets being replaced in the new project, net of any tax impacts. 4. Released working capital, perhaps at the project's end. 5. Salvage value (net of taxes) realized from asset disposition at the project's end. These relevant cash flows occur after the \"go\" decision is made to proceed with the project. Therefore, we are estimating future cash flows. Certain cash flows are estimated based on current prices and known technology, whereas others are estimates based on vague facts and unproven methods. Often, cost savings and project benefits are not easily quantified. Much time and expense are spent to develop supporting forecast data. It is important to understand that the same cash-flow estimates are used regardless of the project evaluation method used. Decision Criteria Winning projects generally have the highest rates of return on investment. Decisions are either: Accept or reject or Select A or B or C, etc. (or some combination of these) In the first type, we decide whether the return is acceptable or unacceptable. This is a screening decision. Is the return \"good enough?\" The second type is a preference or ranking decisionselect the best choice from a set of mutually exclusive projects. By picking A, we reject B, C, and any other choices. One possible choice is to do nothing the status quo. Generally, projects are ranked on a scale of high to low returns. The highest ranking projects are selected, until the capital investment budget is spent. Often, funds are limited; many acceptable projects will go unfunded. The firm's goal is to select projects with the highest returns. As in Chapter 9, pertinent nonquantitative factors may sway a decision and cause lower ranked projects to be selected. Time Perspectives In the real world, every conceivable combination of cash-flow timing can exist. However, we assume a simplified timeline. The present point in time is today, Year 0. This is when we assume investments are madenew assets acquired, old assets sold, and any tax consequences of these changes assessed. In real life, several years of cash outflows may precede the start of a project's operation. Generally, annual time periods are used. Using shorter time periods is possible, such as one-month periods for monthly lease payments. Annual flows of cash are assumed to occur at year-end due to the mathematics underlying the construction of the present value tables. sch80342_10_c10_399-444.indd 403 12/20/12 2:06 PM Section 10.2 The Capital Investment Decision CHAPTER 10 An Example - Equipment Replacement and Capacity Expansion As an illustration, Clairmont Timepieces is considering a device costing $100,000 to replace an obsolete production device: 1. The new device's expected life is five years and can probably be sold at the end of Year 5 for $10,000. 2. The vendor recommends an overhaul in Year 3 at a cost of $20,000. 3. Capacity will immediately increase by 1,000 units per year. Each unit sells for $55 and has $30 of variable costs. 4. Additional inventory of $3,000 is needed and will be released at the project's end (i.e., inventory will be returned to the level it was at immediately prior to the purchase of the new production device). 5. Operating costs will be reduced by $15,000 per year. 6. The old device can be sold for $8,000 now, which is its book value. Alternatively, as another option, it could be used for five more years with no salvage or book value at that time. Remember that any cash revenue or cost that does not change is irrelevant and can be ignored. Any cash flow that differs among decision choices is relevant. Additional taxes or tax savings on incremental income or expenses are also relevant cash flows. But, until income tax issues are discussed, taxation implications are ignored. Formatting the Relevant Data As in Chapter 9, adopting a uniform format for analysis of capital investments helps to organize data and to present it in a logical pattern. Using data from the previous example, the timeframe format shown in Figure 10.1 is used throughout our capital investment discussions. Cash outflows are negative numbers, and inflows are positive numbers. Project years begin now (Year 0 or today), and are shown as columns. Specific cash-flow items are shown as rows. The investments of $100,000 in equipment and $3,000 in inventory costs are reduced by the sale of old equipment for $8,000. The net initial investment is $95,000. The additional 1,000 units of sales generate incremental contribution margin of $25,000, using a $55 sales price less a $30 variable cost per unit. Remember that volumes of analytical support may be developed to backup each number in Figure 10.1. The $100,000 device cost would result from evaluations of many devices and negotiations with vendors. Estimates of additional revenues and variable costs come from marketing studies and capacity use. Estimates of cost savings come from production, industrial engineering, and cost accounting analyses. sch80342_10_c10_399-444.indd 404 12/20/12 2:06 PM CHAPTER 10 Section 10.3 The Evaluation Methods Figure 10.1: Format for relevant capital investment data - Clairmont Timepieces Life of the Project Cash Flows: New device Salvage value Sale of old device Added inventory Added contribution savings Operating cost savings Updating costs Net cash investment Net cash inflows Today Year 1 Year 2 Year 3 Year 4 Year 5 $ (100,000) $ 10,000 8,000 (3,000) 3,000 $ 25,000 15,000 $ 25,000 15,000 $ 25,000 15,000 (20,000) $ 25,000 15,000 $ 25,000 15,000 $ 40,000 $ 40,000 $ 20,000 $ 40,000 $ 53,000 $ (95,000) 10.3 The Evaluation Methods T he evaluation methods discussed here are: 1. Present value methods (also called discounted cash-flow methods). (a) Net present value method (NPV). (b) Internal rate of return method (IRR). 2. Payback period method. 3. Accounting rate of return method. Nearly all managerial accountants agree that methods using present value (Methods 1a and 1b) give the best assessment of long-term investments. Methods that do not involve the time value of money (Methods 2 and 3) have serious flaws; however, since they are commonly used for investment evaluation, their strengths and weaknesses are discussed. Net Present Value Method The net present value (NPV) method includes the time value of money by using an interest rate that represents the desired rate of return or, at least, sets a minimum acceptable rate of return. The decision rule is: If the present value of incremental net cash inflows is greater than the incremental investment net cash outflow, approve the project. Using Tables 1 and 2 found at the end of this chapter, the net cash flows for each year are brought back (i.e., discounted) to Year 0 and summed for all years. An interest rate must be specified. This rate is often viewed as the cost of funds needed to finance the project and is the minimum acceptable rate of return. To discount the cash flows, we use the interest rate and the years that the cash flows occur to obtain the appropriate present sch80342_10_c10_399-444.indd 405 12/20/12 2:06 PM CHAPTER 10 Section 10.3 The Evaluation Methods value factors from the present value tables. A portion of Table 1 appears below showing the present value factors (the shaded numbers), corresponding to an interest rate of 12 percent, for each year during the Clairmont Timepieces project's life. Periods (n) 1% 2% 4% 5% 6% 8% 10% 12% 14% 15% 16% 0 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1 0.990 0.980 0.962 0.952 0.943 0.926 0.909 0.893 0.877 0.870 0.862 2 0.980 0.961 0.925 0.907 0.890 0.857 0.826 0.797 0.769 0.756 0.743 3 0.971 0.942 0.889 0.864 0.840 0.794 0.751 0.712 0.675 0.658 0.641 4 0.961 0.924 0.855 0.823 0.792 0.735 0.683 0.636 0.592 0.572 0.552 5 0.951 0.906 0.822 0.784 0.747 0.681 0.621 0.567 0.519 0.497 0.476 6 0.942 0.888 0.790 0.746 0.705 0.630 0.564 0.507 0.456 0.432 0.410 7 0.933 0.871 0.760 0.711 0.665 0.583 0.513 0.452 0.400 0.376 0.354 8 0.923 0.853 0.731 0.677 0.627 0.540 0.467 0.404 0.351 0.327 0.305 9 0.914 0.837 0.703 0.645 0.592 0.500 0.424 0.361 0.308 0.284 0.263 10 0.905 0.820 0.676 0.614 0.558 0.463 0.386 0.322 0.270 0.247 0.227 These present value factors are used in Figure 10.2 to discount the yearly cash flows to their present values. In Figure 10.2, the net cash investment ($95,000) is subtracted from the sum of cash-inflow present values ($137,331). When the residual is positive, the project's rate of return (ROR) is greater than the minimum acceptable ROR. If: Present value of incremental net cash inflows $ Incremental investment cash outflows then: Project's ROR $ Minimum acceptable ROR Net present value is the difference between the present value of the incremental net cash inflows and the incremental investment cash outflows. If net present value is zero or positive, the project is acceptable. When the sum is negative, the project's ROR is less than the discount rate. If: Present value of incremental net cash inflows , Incremental investment cash outflows then: Project's ROR , Minimum acceptable ROR If net present value is negative, the project should be rejected. sch80342_10_c10_399-444.indd 406 12/20/12 2:06 PM CHAPTER 10 Section 10.3 The Evaluation Methods Figure 10.2: Net present value of capital investment cash flows Life of the Project Today Net cash flow (Figure 11.1) $ (95,000) Present value factors at 12% 1.000 Present values at 12% $ (95,000) Sum of PVs for Years 1 to 5 137,331 Net present value $42,331 Year 1 Year 2 Year 3 Year 4 Year 5 $ 40,000 .893 $ 35,720 $ 40,000 .797 $ 31,720 $ 40,000 .712 $ 14,240 $ 40,000 .636 $ 25,440 $ 53,000 .567 $ 30,051 The Interest Rate. What interest rate should be used for discounting the cash flows? This rate has many names that help explain its source and use. Among them are: 1. Cost of capital - a weighted-average cost of long-term funds. Only projects that can earn at least what the firm pays for funds should be accepted. Later, we illustrate a calculation of cost of capital. 2. Minimum acceptable rate of return - a particular rate that is considered to be the lowest ROR that management will accept. 3. Desired rate of return, target rate of return, or required rate of return - a rate that reflects management ROR expectations. 4. Hurdle rate - a threshold that a project's ROR must \"jump over\" or exceed. 5. Cutoff rate - the rate at which projects with a higher ROR are accepted and those with a lower ROR are rejected; often the rate where all available capital investment funds are committed. A firm will use one or more of these terms as its discount rate. While these terms sometimes produce different rates in the business world, we will use these terms interchangeably here. Generally, if a project's ROR is below the chosen discount rate, it is rejected; above this rate, the project is acceptable. Still, whether it is funded depends on the availability of capital funds. In the Clairmont Timepieces example, we assume that management has decided that 12 percent is the minimum acceptable rate of return. Calculations needed to obtain a net present value are shown in Figure 10.2. The net present value is a positive $42,331; therefore, the project earns more than a 12 percent ROR. The net present value method does not provide information about the project's exact ROR; it merely informs whether the project is earning more than, less than, or equal to the minimum acceptable ROR. If other discount rates had been selected, we would find the following net present values: Percentage Present value of net cash inflows 16% $124,328 $95,000 $29,328 20 113,246 95,000 18,246 24 103,713 95,000 8,713 28 95,523 95,000 523 30 91,797 95,000 sch80342_10_c10_399-444.indd 407 2 Investment 5 Net present value (3,203) 12/20/12 2:06 PM CHAPTER 10 Section 10.3 The Evaluation Methods Notice that, as the interest rate increases, the present values of the future cash flows decrease. At 30 percent per year, the project's net present value is negative, and the project is unacceptable. The project's rate of return must be between 28 and 30 percent. Project Ranking. Even though a project has a positive net present value, too many attractive projects may exist, given the investment dollars available. A ranking system is needed. We can rank projects by the amount of net present value each generates, but this ignores the relative size of the initial investments. An extension of the net present value method is the profitability index. It is found by dividing the present value of a project's net cash inflows by its net initial investment. The resulting ratio is cash in to cash out. The higher the ratio is, the more attractive the investment becomes. Notice that an acceptable project should have a profitability index of at least 1. The following projects are ranked by the profitability index. Project Present value of net cash inflows Initial investment Net present value Profitability index A $235,000 $200,000 $35,000 1.18 5 B 170,000 140,000 30,000 1.21 4 C 80,000 60,000 20,000 1.33 1 D 98,000 80,000 18,000 1.23 3 E 52,000 40,000 12,000 1.30 2 Ranking We would typically accept projects with the highest profitability index until we exhaust the capital budget or the list of acceptable projects. Internal Rate of Return (IRR) Method The internal rate of return is the project's ROR and is the rate where the: Net initial investment cash outflow 5 Present value of the incremental net cash inflows Without calculator or computer assistance, the specific ROR is found by trial and error. We search for the rate that yields a zero net present value. In the Clairmont Timepieces example, the internal rate of return was found to be between 28 and 30 percent. The net present value at 28 percent is positive and at 30 percent is negative. By interpolation, we can approximate a \"more accurate\" rate as follows: Rate of return Net present value Calculations 28% $ 523 Base rate 30 (3,202) ($523 4 $3,725) 3 2% 5 0.28% 2% difference $ 3,725 absolute difference Internal rate of return 28.28% 5 28.00% In most cases, however, knowing that the rate is between 28 and 30 percent is adequate. sch80342_10_c10_399-444.indd 408 12/20/12 2:06 PM CHAPTER 10 Section 10.3 The Evaluation Methods Estimating the Internal Rate of Return. By using Table 2 and knowing certain project variables, we can estimate other unknown variables, including a project's internal rate of return. This estimate requires that the annual net cash inflows be an annuity. The variables and a sample set of data are: Variable Example data A 5 Initial investment cash outflow $37,910 B 5 Life of project 5 years C 5 Annual net cash inflow $10,000 per year D 5 Internal rate of return 10 percent E 5 Present value factory at 10 percent (Table 2) 3.791 If we know any three of A, B, C, or D, we can find E and the missing variable. A variety of questions can be answered: 1. What is the internal rate of return of the project? If A, B, and C are known, we can calculate E and find D as follows: E5A4C $37,910 4 $10,000 5 3.791 On Table 2, we go to the 5-period (year) row and move across until we find 3.791 (E) in the 10 percent column (D). At 10 percent, the cash outflow ($37,910) equals the present value of the net cash inflows (3.791 3 $10,000). The internal rate of return is 10 percent. 2. What annual cash inflow will yield a 10 percent IRR from the project? If A, B, and D are known, we can find E and calculate C. E is found in Table 2 by using five years and 10 percent ROR. The annual cash inflow is found as follows: C5A4E $37,910 4 3.791 5 $10,000 per year We need $10,000 per year in cash inflow to earn a 10 percent IRR. 3. What can we afford to invest if the project earns $10,000 each year for five years and we want a 10 percent IRR? If we know B, C, and D, we can find E and then calculate A. The investment is found by using the annual net cash inflow and 3.791 as follows: A5C3E $10,000 3 3.791 5 $37,910 We can pay no more than $37,910 and still earn at least a 10 percent return. 4. How long must the project last to earn at least a 10 percent IRR? If we know A, C, and D, we calculate E and find B as follows: sch80342_10_c10_399-444.indd 409 12/20/12 2:06 PM CHAPTER 10 Section 10.3 The Evaluation Methods E5A4C $37,910 4 $10,000 5 3.791 For a 10 percent IRR, 3.791 is on the 5-period row. The project's life must be at least five years. Most spreadsheet software and business calculators have built-in functions to find the internal rate of return. This simplifies the calculation burden that has limited its use in the past. Project Ranking. Since each project has a specific rate of return, ranking projects under the IRR method is relatively simple. All projects are listed according to their rates of return from high to low. The cost of capital or a cutoff rate can establish a minimum acceptable rate of return. Then, projects are selected by moving down the list until the budget is exhausted or the cutoff rate is reached. Reinvestment Assumption. The internal rate of return method assumes that cash flows are reinvested at the project's internal rate of return. While this assumption may be realistic for cost of capital rates, it may be wishful thinking for projects with high internal rates of return. This issue, however, is best left to finance texts and courses. High Discount Rates. A concern exists about the use of high discount rates in present value methods. A project with significant long-term payoffs may not appear favorable because the long-term payoffs will be discounted so severely. Even huge cash inflows due ten years or more into the future appear to be less valuable than minor cost savings earned in the first year of another project. High discount rates may encourage managers to think only short term, to ignore research, market innovations, and creative product development projects, and to ignore long-term environmental effects. Thus, positive or negative impacts can result from the wise or unwise use of accounting tools and policies. The Payback Period Method The payback period method is a \"quick and dirty\" evaluation of capital investment projects. It is likely that no major firm makes investment decisions based solely on the payback period, but many ask for the payback period as part of their analyses. The payback period method asks: How fast do we get our initial cash investment back? No ROR is given, only a time period. If annual cash flows are equal, the payback period is found as follows: Net initial investment 4 Annual net cash inflow 5 Payback period If the investment is $120,000 and annual net cash inflow is $48,000, the payback period is 2.5 years. We do not know how long the project will last nor what cash flows exist after the 2.5 years. It might last 20 years or 20 days beyond the payback point. sch80342_10_c10_399-444.indd 410 12/20/12 2:06 PM CHAPTER 10 Section 10.3 The Evaluation Methods If annual cash flows are uneven, the payback period is found by recovering the investment cost year by year. In the Clairmont Timepieces example: Year Cash flows Unrecovered investment 0 $(95,000) $95,000 1 40,000 55,000 2 40,000 15,000 3 20,000 0 In Year 3, the cost is totally recovered, using only $15,000 of Year 3's $20,000 (75 percent). The payback period is 2.75 years. The payback method is viewed as a \"bail-out\" risk measure. How long do we need to stick with the project just to get our initial investment money back? It is used frequently in short-term projects where the impact of present values is not great. Such projects as efficiency improvements, cost reductions, and personnel savings are examples. Several major companies set an arbitrary payback period, such as six months, for certain types of cost-saving projects. Using the Payback Reciprocal to Estimate the IRR. The payback period can be used to estimate a project's IRR, assuming a fairly high ROR (over 20 percent) and project life that is more than twice the payback period. For example, if a $40,000 investment earns $10,000 per year for an expected 12 years, the payback period is four years. The reciprocal of the payback period is 1 divided by 4 and gives an IRR estimate of 25 percent. From Table 2 for 12 years, the present value factor (payback period) of 4 indicates a rate of return of between 22 and 24 percent. The payback reciprocal will always overstate the IRR somewhat. If the project's life is very long, say 50 years, the payback reciprocal is an almost perfect estimator. (See the present value factor of 4.000 for 25 percent and 50 periods on Table 2.) Ranking Projects. When the payback period is used to rank projects, the shortest payback period is best. Thus, all projects are listed from low to high. A firm's policy may say that no project with a payback period of over four years will be considered. This acts like a cutoff point. After that, projects would be selected until capital funds are exhausted. The major complaints about the payback period method are that it ignores: 1. The time value of money. 2. The cash flows beyond the payback point. These are serious deficiencies, but the method is easily applied and can be a rough gauge of potential success. sch80342_10_c10_399-444.indd 411 12/20/12 2:06 PM CHAPTER 10 Section 10.3 The Evaluation Methods Accounting Rate of Return Method This method: 1. Ignores the time value of money. 2. Presumes uniform flows of income over the project's life. 3. Includes depreciation expense and other accounting accruals in the calculation of project income, losing the purity of cash flows. In fact, we only discuss this approach because many internal corporate performance reporting systems use accrual accounting data. Many companies use discounted cash flows for investment decisions but report actual results using accrual income and expense measures. The accounting rate of return (ARR) method attempts to measure the return from accrual net income from the project. The ARR subtracts depreciation expense on the incremental investment from the annual net cash inflows. Other accrual adjustments may also be made. The general formula is: Annual net operating cash inflow 2 Annual depreciation expense in incremental investment Average investment 5 Accounting rate of return The average investment, the denominator, is the average of the net initial investment and the ending investment base ($0 if no salvage value exists). This is the average book value of the investment over its life. Some analysts prefer to use the original cost of the investment or replacement cost as the denominator. The numerator is the annual incremental accrual net income from the project. To illustrate, assume the following: Initial investment Salvage value $110,000 $10,000 Annual cash inflow Project life 35,000 5 years Depreciation expense 20,000 ARR calculations are: $35,000 2 $20,000 ($110,000 + $10,000) 2 sch80342_10_c10_399-444.indd 412 5 $15,000 $60,000 5 25 percent 12/20/12 2:06 PM Section 10.4 Ethical Issues and Pressures on Management CHAPTER 10 The 25 percent must be viewed relative to other projects' ARR and cannot be compared to present value rates of return. For ranking purposes, projects are ranked from high to low. An arbitrary percentage may be set as a minimum rate, similar to an accrual return on equity. Another problem with the ARR is the impression it gives of an increasing ROR on an annual basis as an asset grows older. A manager would see this project's performance on annual investment center responsibility report as follows: Average investment (book value) Project net income Year 1 $100,000 $15,000 Year 2 80,000 15,000 18.8 Year 3 60,000 15,000 25.0 Year 4 40,000 15,000 37.5 Year 5 20,000 15,000 75.0 Annual ARR 15.0% The average annual book value declines each year, and net income is assumed to remain constant. As the asset gets older, the ARR increases. It is tempting for managers to reject any proposal that will make their performance reports look less favorable. This is particularly true when their bonuses are tied to accrual accounting performance numbers. Managers will be biased toward sticking with older assets with higher accounting rates of return. They forego new investments that offer new technology, lower operating costs, and greater productivity. 10.4 Ethical Issues and Pressures on Management I n many corporate situations, managers are under pressure to earn high rates of return in the short run. All capital investment analyses depend on the credibility of future cashflow estimates. Unlike past facts which are measured very objectively, future values are based on predictions, opinions, judgments, and perhaps wishful thinking. The quality of decision making rests on a premise that future estimates are made objectively and in good faith. A manager trying to get a needed project approved may develop estimates that are too optimistic because of the manager's enthusiastic support of the idea. Company policies compound the problem by setting very high hurdle or cutoff rates that encourage proposal developers to overestimate future revenues and underestimate investment costs. Managers have been heard to say, \"Show me the hurdle, and I'll make the project jump over it.\" In fact, a vicious cycle may develop: higher hurdles, more bias in estimates; higher hurdles, and so on. To control these problems, many firms have special analysts who evaluate proposals independent of the sponsoring managers. Others perform post-audits to compare actual results to the estimates. Tying responsibility for the project's promises to the manager's future evaluations may help solve some of these problems. sch80342_10_c10_399-444.indd 413 12/20/12 2:06 PM Section 10.5 Taxes and Depreciation CHAPTER 10 The second issue is the severe pressure on managers to show growth in immediate earnings. Key investment analysts and shareholders watch quarterly earnings announcements and other short-term information about the company to make almost daily buy and sell decisions. Capital investment proposals include a mix of short-term and long-term projects. Short-term projects often emphasize cost savings, which may be worthwhile but not strategically important. Long-term projects include research and development and new technology. Unfortunately, these projects often have long payback periods, but they offer significant future potential. If hurdle rates are high, long-term projects will rarely rank as high as short-term projects. The long-run competitiveness and success of a firm may be damaged severely if its managers are biased toward short-term rewards. Japanese firms, for a number of reasons, are said to have a much longer term investment horizon. They are less concerned about the immediate profitability of new products and markets. Market penetration and market share are more important. This allows managers to develop a strategic plan that emphasizes the long-run success of the firm. 10.5 Taxes and Depreciation T he illustrations have thus far ignored income taxes. Also, depreciation expense, being noncash, was used only in the accounting rate of return method. These factors impact capital budgeting significantly. Income Taxes and Capital Investments Except for nonprofit organizations, the real world is a tax-paying world, and capital investment analysis must consider taxes. Taxation rules are complex and impact many cash flows. Taxable income and gains include: 1. Incremental revenues minus incremental expenses. 2. Incremental operating expense savings. 3. Gains on sales of old assets now and of new assets at the project's end. Incremental expenses and losses reduce taxes and include: 1. Incremental operating expenses. 2. Losses on sales of old assets now and of new assets at the end of a project's life. The tax rate should be the expected marginal tax rate for the future year being analyzed. The marginal tax rate is the tax rate applied to any incremental taxable income. For simplicity, we assume that the marginal income tax rate is 40 percent for all income tax-related issues. Clearly, income taxes reduce the ROR on capital projects by reducing net cash inflows. sch80342_10_c10_399-444.indd 414 12/20/12 2:06 PM CHAPTER 10 Section 10.5 Taxes and Depreciation Depreciation Expense The only role that depreciation expense plays in cash-flow-based capital investment analysis is as a deduction in calculating income taxes. If taxes are ignored or are not applicable, as in nonprofit organizations, depreciation expense is also ignored. The Internal Revenue Code uses the terms Accelerated Cost Recovery System (ACRS) and the Modified Accelerated Cost Recovery System (MACRS) to describe the methods used to depreciate tangible assets for tax purposes. To simplify our depreciation expense and taxation discussions, we assume that: (1) straight-line depreciation is used, (2) depreciation expense calculations ignore salvage values, and (3) salvage values are net of tax consequences. To understand the tax and depreciation expense impacts, let us look again at the Clairmont Timepieces example in Figure 10.2 and now apply a tax rate of 40 percent to the incremental operating cash flows. For now, we ignore the effects of depreciation. This is shown in Figure 10.3. Figure 10.3: Net present value analysis with taxes but without depreciation Life of the Project Cash Flows: Net investment cash flows Annual cash inflows (taxable) Taxes on taxable income (40%) Aftertax cash inflows Net annual cash flows Present value factors at 12% Present values at 12% Sum of PVs for Years 1 to 5 Net present value Today Year 1 Year 2 Year 3 Year 4 Year 5 $ 40,000 (16,000) $ 24,000 $ 24,000 .893 $ 21,432 $ 40,000 (16,000) $ 24,000 $ 24,000 .797 $ 19,128 $ 20,000 (8,000) $ 12,000 $ 12,000 .712 $ 8,544 $ 40,000 (16,000) $ 24,000 $ 24,000 .636 $ 15,264 $ 13,000 $ 40,000 (16,000) $ 24,000 $ 37,000 .567 $ 20,979 $ (95,000) $ (95,000) 1.000 $ (95,000) 85,347 $ (9,653) As Figure 10.3 shows, suddenly a very profitable project (just under 30 percent on a no-tax basis) now has a negative net present value using a 12 percent discount rate. We assume that the overhaul in Year 3 is a deductible expense, salvage value is net of taxes, and inventory recovery has no tax effects. The Tax Shield Depreciation expense is a noncash expense, provides a legitimate deduction for tax purposes, and creates a tax shield. By reducing taxable income, cash paid for taxes is reduced. Depreciation saves cash by reducing tax payments. Thus, if depreciation expense increases, tax payments decrease. Cash outflow is reduced. A reduced outflow has the same effect as an increased inflow. sch80342_10_c10_399-444.indd 415 12/20/12 2:06 PM CHAPTER 10 Section 10.5 Taxes and Depreciation The depreciation impact is seen in the Clairmont example. The increase in depreciable assets is $92,000 ($100,000 minus $8,000) and is spread over five years. Currently, salvage value is ignored in most IRS depreciation calculations. Assuming straight-line depreciation, the incremental depreciation expense is $18,400 per year. Aftertax cash flows are: Year 1 Incremental revenues $55,000* 2 Incremental cost of sales 230,000* 15,000* 1 Operating cost savings Incremental cash inflow $40,000 2 Depreciation expense 218,400 Taxable income $21,600 2 Incremental taxes (40 percent) 28,640* Aftertax project net income $12,960 18,400 1 Add back depreciation expense Aftertax cash inflow $31,360 * Cash flows The project's Year 1 aftertax profit, $12,960, and the incremental depreciation expense, $18,400, are summed to find the Year 1 aftertax cash flow. Tax cash outflows for the entire project are included in the Figure 10.4 analysis. The increased tax deduction for depreciation moves the net present value of the project from a negative $9,653 to a positive $16,879, a $26,532 change. This is the present value of the depreciation expense tax savings, as follows (the one dollar difference is due to rounding of present value factors): Depreciation Expense 3 Tax Rate 3 Present Value Factor (for 5 years at 12 percent) 5 Present Value of Tax Shield $18,400 3 0.40 3 3.605 5 $26,533 Figure 10.4: Net present value analysis with depreciation and taxes Life of the Project Cash Flows: Net investment cash flows Annual cash inflows (taxable) Taxes on taxable income (40%) Aftertax cash inflows Net annual cash flows Present value factors at 12% Present values at 12% Sum of PVs for Years 1 to 5 Net present value sch80342_10_c10_399-444.indd 416 Today Year 1 Year 2 Year 3 Year 4 Year 5 $ 40,000 (8,640) $ 31,360 $ 31,360 .893 $ 28,004 $ 40,000 (8,640) $ 31,360 $ 31,360 .797 $ 28,994 $ 20,000 (640) $ 19,360 $ 19,360 .712 $ 13,784 $ 40,000 (8,640) $ 31,360 $ 31,360 .636 $ 19,945 $ 13,000 $ 40,000 (8,610) $ 31,360 $ 44,360 .567 $ 25,152 $ (95,000) $ (95,000) 1.000 $ (95,000) 111,879 $ 16,879 12/20/12 2:06 PM CHAPTER 10 Section 10.7 Calculation Issues Accelerated Depreciation Benefits. The cash saving power of depreciation can be increased by using accelerated depreciation to deduct more depreciation earlier in a project's life. Deferring taxes has a time value of money. By merely changing depreciation methods, the net present value can increase or decrease. This is strictly from speeding up or slowing the depreciation expense deductions and the time value of the tax deferrals. 10.6 Cost of Capital T hroughout our discussions, cost of capital is mentioned frequently. Long-term money has a cost, either real as in interest paid on bonds payable or an opportunity cost as in the use of earnings retained in the business. A basic approach is explained here to show the source of this rate. A weighted-average cost of capital pools a firm's long-term funds and is used because the relative amount of each fund's source affects the average cost. Debt generally is less costly than equity since the creditor assumes less risk and interest is deductible for tax purposes. If a firm has a pretax debt cost of 10 percent and a 40 percent tax rate, the aftertax cost is 6 percent. Dividends, on the other hand, are not deductible for tax purposes and are profit distributions to owners, not a business expense. Assume that a firm has the following long-term funds structure and cost of funds: Book value Mix percentage Pretax cost Aftertax cost Weighted average Bonds payable $10,000,000 25% 10% 6% 1.5% Preferred stock 4,000,000 10 12 12 1.2 Common Stock 14,000,000 35 18 18 6.3 Retained earnings 12,000,000 30 18 18 5.4 Total long-term funds $40,000,000 100% 14.4% The pretax cost percentages come from financial markets calculations. The weightedaverage cost of capital is 14.4 percent. Often financially strong companies have low cost of funds. High risk, financially unstable, or new firms often have high funds costs. 10.7 Calculation Issues T he variety of issues surrounding capital investment decisions are sufficient that entire textbooks have been written about them. Here, we introduce a few of the more significant complexities. Inflation and Future Cash Flows Inflation is a common economic problem. Over the past 40 years in the United States, annual inflation rates have ranged from a high of over 12 percent to a low of under 2 sch80342_10_c10_399-444.indd 417 12/20/12 2:06 PM CHAPTER 10 Section 10.7 Calculation Issues percent. These levels are moderate compared to rates in many other countries. Yet, capital investment decisions should consider inflationary impacts on future cash flows. While several approaches could be used to incorporate inflation into the analysis, the approach we suggest is to build the impacts of inflation into the expected future cash flows. This allows the use of specific inflation rates for each cash-flow component. Also, rates can be changed for each future period. The discount rate will be the noninflated desired rate of return times one plus the expected general inflation rate. To illustrate inflation impacts on estimates of future cash flows, assume that Kazen Motors plans to expand its engine diagnostic business. Equipment will cost about $120,000 and should last about three years. After three years, it is thought that greater on-board computer use will require more powerful testing technology. Annual revenues are expected to be $150,000, personnel costs are $60,000, and other support costs would be about $30,000. Kazen uses a 10 percent desired rate of return. Economic forecasts indicate that inflation will be 6 percent per year for the next few years. But Kazen feels that, at best, prices could be raised no more than 4 percent per year. Personnel costs will probably increase at a 10 percent rate, primarily because of benefits costs. Other costs will increase at an average of 6 percent annually. The equipment, which has no salvage value, will be depreciated on a straight-line basis. Assume a 40 percent tax rate. Cash flows related to the equipment are as follows: Investment Cash flows: Year 1 Year 2 $156,000 $162,240 Personnel costs (60,000) (66,000) (72,600) Other costs (30,000) (31,800) (33,708) ______ (8,000) (7,280) (6,373) $(120,000) $ 52,000 $ 50,920 $ 49,559 Initial investment Revenues Incremental taxes* Net cash flows Year 0 Life of the project Year 3 $(120,000) $150,000 *Taxes in Year 1: ($150,000 2 60,000 2 30,000 2 40,000) 3 0.4 5 $8,000 Taxes in Year 2: ($156,000 2 66,000 2 31,800 2 40,000) 3 0.4 5 $7,280 Taxes in Year 3: ($162,240 2 72,600 2 33,708 2 40,000) 3 0.4 5 $6,373 Notice that depreciation, being based on the historical cost of the investment, is still $40,000 in each year. While all other revenues and costs have inflation built into them, the tax law requires that the depreciation expense is always expressed in historical-cost dollars from the year of acquisition. Using historical cost-based depreciation in tax calculations often leads to higher tax payments since profits grow from inflated revenues. It is dangerous to ignore inflation. To do so assumes that all inflation effects sum to zero, which is rarely the case. Certain cost areas, such as health care, have had unusually high increases in recent years. Forecasting these costs should include estimated inflationary impacts to make cash-flow estimates credible. sch80342_10_c10_399-444.indd 418 12/20/12 2:06 PM CHAPTER 10 Section 10.7 Calculation Issues Working Capital When expansion occurs, inventories and receivables often grow. Financing working capital growth is an integral part of a project's total investment. Unlike depreciable equipment and fixed assets, working capital is committed and can probably be recovered at the end of the project. Often, working capital requirements grow slowly over time as sales increase. Incremental inventories and accounts receivable net of incremental accounts payable can easily be overlooked and omitted from a project's analysis. In contrast, JIT projects often release working capital by reducing inventories, which can help finance the project itself. Assume that Athletic Champs operates a chain of sporting goods stores in shopping malls. Opening a new store requires layout, equipment, and fixtures costing about $450,000. In addition, about $200,000 of inventory is needed to stock a new store. Experience shows that inventory and other working capital needs will grow at about $20,000 per year for the first five years. If Athletic Champs uses an eight-year timeframe for evaluating a store location, assumptions will be needed about the equipment salvage value and the recovery of the working capital investment. The fixed assets' salvage values are estimated to be $50,000 net of taxes, and the entire working capital investment (now $300,000) is thought to be recovered. The cash flows would look like: Life of the project Cash flows: Initial construction Today Year 1 Year 2 Year 5 $(20,000) $(20,000) $(20,000) $(450,000) Working capital needs (200,000) Year 8 $ 50,000 300,000 Working capital recovery is not automatic. Inventory may be obsolete, and receivables might not be collectible. A going-concern assumption can generally be made if the business is expected to continue past the timeframe cutoff. Uneven Project Lives When comparing projects, lives of each project may not match. How can a three-year solution to a problem be compared to a five-year or a eight-year solution? The decision must be viewed from the timeframe of the job to be done. Do we want a solution for three, five, or eight years? How long can the physical asset last? Often, technology changes often make an asset's economic life shorter than its physical life. A three-year solution may be sought, while an asset's physical life might well be twice that long. If the time period is based on the needs of the problem, the task is to find salvage or market values for assets at the end of the defined time period. If the time period is based on the physical lives of the proposed assets, different useful lives of the proposed solutions must be somehow matched. One approach is to use a shorter-lived project as the comparison time period. This requires finding salvage or market values for assets at midpoints in their lives. While no specific rule exists, the investment's timeframe as defined by management seems to be the better choice. Management's intent and common sense, rather than the physical lives of assets, should govern the time period choice. sch80342_10_c10_399-444.indd 419 12/20/12 2:06 PM CHAPTER 10 Section 10.7 Calculation Issues Evaluation of Projects With Different Initial Investments Up to this point, most of the illustrations have assumed that a single investment alternative existed. The firm had to decide whether or not to invest in that project. Actually, a firm may have several alternatives but still have to select only one. In such a case, care must be exercised in using the internal rate of return method, because the project with the highest internal rate of return may not be the most desirable. This can happen in those cases where the dollar investment is not the same. The dollar amount of the return from a larger investment, in many cases, will exceed the dollar return from a smaller investment having a better internal rate of return. Assume that Behar Transit Company must choose between two delivery vans. Each has an estimated life of five years with annual returns as follows: Van I Net investment Net cash inflow for each of 5 years Van II $75,000 $100,000 26,000 33,000 Investments are expected to earn a desired rate of return of at least 12 percent. Van II requires an investment of an additional $25,000 versus Van I. The approximate internal rate of return is computed for each alternative and for the incremental investment as follows: Van I Van II Incremental (II - I) Net investment $(75,000) $(100,000) $(25,000) Annual return 26,000 33,000 7,000 Payback period 2.885 3.030 3.571 Nearest PV factor on Table 2 for 5 periods 2.864 2.991 3.605 22% 20% 12% Nearest IRR given on Table 2 It appears that Van I should be selected because the internal rate of return is higher. The additional $25,000 investment needed by Van II yields a much lower rate of return: 12 percent. But, if the rate of return on the incremental investment is greater than the hurdle rate of return, the larger investment could still be made. In this example, an additional $7,000 per year is returned on an additional investment of $25,000. The rate of return on the incremental investment barely meets the 12 percent desired rate of return. In another situation, Van I could be a Phase I of a pair of sequential jobs and Van II could be Phases I and II combined. Phase I may be executed without Phase II but not vice versa. Advocates of Phase II would clearly argue that both phases be approved at one time. However, as we have seen, Phase II has an IRR of about 12 percent. If the cutoff rate is 15 percent, Phase I and the combined phases are acceptable. But Phase II by itself is unacceptable. Breaking down projects into their subcomponents can give useful insight into the yields on incremental investments. sch80342_10_c10_399-444.indd 420 12/20/12 2:06 PM CHAPTER 10 Section 10.8 The Time Value of Money Gains and Losses on Asset Disposals If assets are sold at more or less than their book values, gains or losses appear with tax implications. The book value is an asset's original cost minus its accumulated depreciation. In the business world, accounting book values and tax cost bases often differ. In our discussions here, unless specifically mentioned, these two amounts are assumed to be the same. If the sale is for more than the book value, a gain occurs; if for less, a loss occurs. Gains and losses on disposals and their impacts on cash flows arise at two points in the capital investment decision: 1. Old assets may be sold as part of investing in a new asset. 2. New assets may be sold at the end of the project's expected life. 10.8 The Time Value of Money D ollars promised in the future are not equal to dollars received now. When given a choice, we all prefer getting $100 today versus $100 two years from now. Dollars due in different time periods should be valued on a uniform scale that recognizes the time value of money. Present value converts future dollars into current dollar equivalents. Future value converts all dollars into equivalent dollars as of some future date. To find these values, we need an interest rate and the number of time periods between today and the future cash flows. Money has earning power. Dollars today grow to larger sums through earning interest on the principal plus earning interest on interest. The investment principal plus compound interest is the future value (FV). The future value of $100 in two years, with interest compounded at the rate of 10 percent annually, is $121. The formula for the future value of $1 is: FV5 (1 + i)n where i 5 interest rate n 5 number of years In the example, the future value is computed as follows: FV of $1 5 (1.10)2 5 $1.21 FV of $100 5 $100 3 $1.21, or $121 An investor who is happy with a 10 percent ROR looks at the receipt of $121 in two years as equivalent to $100 today, assuming certainty. This investor is indifferent between the $100 today or $121 in two years. The interest rate influences the values. If a decision maker has a choice of investments, the preferred choice is the investment with the highest ROR. The reason, of course, is that the investment with the highest ROR will yield the largest future amount or require the sch80342_10_c10_399-444.indd 421 12/20/12 2:06 PM CHAPTER 10 Section 10.8 The Time Value of Money smallest current investment. For example, an alternative investment will earn a 15 percent ROR. Assuming certainty, the future value in two years of the $100 at 15 percent is: $100 3 (1.15)2 5 $100 3 1.3225 5 $132.25 Since $132.25 is larger than $121, the project earning 15 percent is preferred to the 10 percent project. Present Value of Money Because decisions are made today and because future cash flows come in many different patterns and time periods, present values of future dollars are more useful and easier to analyze. It is conventional to use present value analysis. How much money must we invest today to earn a given dollar amount in the future? Or, given an investment, how much will be earned in the future? Or, given an investment and a set of future cash inflows, what is the ROR? Answers to these questions can be found by computing the present value of the future cash flows and comparing it with the amount invested. The present value (PV) of a future value can be computed by multiplying the future value by the present value of $1. The present value of $1 is: PV of $1 5 1 4 (1 1 i)n Assume, for example, that $121 is needed in two years, and the rate of interest is 10 percent. How much must be invested today to have $121 after two years? We first determine the present value of $1 due in two years with interest compounded annually at 10 percent: PV of $1 for 2 years at 10 percent 5 1 4 (1.10)2 5 0.826 Next, we multiply by the future value: PV of $121 for 2 years at 10 percent 5 $121 3 0.826 5 $100 (rounded) The computation can be viewed as: 0 $100 Present Value sch80342_10_c10_399-444.indd 422 Year 1 1 $110 Year 2 2 $121 Future Value 12/20/12 2:06 PM Section 10.8 The Time Value of Money CHAPTER 10 $121 4 1.10 5 $110 is the value at the end of Year 1. $110 4 1.10 5 $100 is the investment at the start of Year 1, or today. This is summarized as follows: $121 4 (1.10)2 or [1 4 (1.10)2] 3 $121 5 $100 The process of reducing a future amount to a present value is called discounting. The present value is sometimes called the discounted value. The rate of interest is the discount rate. The 0.826 is called the present value factor or discount factor. It is seldom necessary to calculate either future values or present values as done here. Calculators and spreadsheet software easily perform these functions. Tables 1 and 2, found at the end of this chapter, give present value factors for various discount (interest) rates for various time periods expressed in years. Table 1 gives the present value of $1 to be received at the end of the various time periods at interest or discount rates shown across the top row of the table. Thus, it is a tabulation of the factor 1 4 (1 1 i)n, where n is the number of years and i is the discount rate. The factor for two years at 10 percent is 0.826, and the present value (PV) of $121 to be received in two years is calculated as follows: PV 5 $121 3 0.826 5 $100 (rounded) The discount factors appearing in Tables 1 and 2 are rounded to the third digit, which is sufficient precision for most capital investment problems. The Present Value of a Series of Future Cash Flows Often, a series of future cash inflows are earned from an investment instead of one cash inflow. As an example, a machine costing $3,500 today is forecast to generate cash inflows of $1,000 each year for five years. The time interval for most decisions is annual, but any time interval (a day, week, month, quarter, etc.) can be used as long as the interest rate (i) is adjusted to correspond to the time period. Calculating present values depends on whether the cash flows series are equal or unequal amounts. An annuity refers to a series of equal cash flows. In either case, however, the underlying concepts are the same. The present value of a series is the sum of the present values of the individual amounts. The present value of these five annual receipts of $1,000 using a 10 percent discount rate is computed as follows: sch80342_10_c10_399-444.indd 423 12/20/12 2:06 PM CHAPTER 10 Section 10.8 The Time Value of Money Year Computation 1 $1,0003 (1 4 1.10)5 2 Explanation $909 PV of $1,000 received at the end of Year 1 1,0003 [1 4 751 PV of $1,000 received at the end of Year 3 (1.10)4]5 683 PV of $1,000 received at the end of Year 4 1,0003 [1 4 5 (1.10)3]5 1,0003 [1 4 4 826 PV of $1,000 received at the end of Year 2 1,0003 [1 4 3 (1.10)2]5 (1.10)5]5 621 PV of $1,000 received at the end of Year 5 $1,000 3 c $3,790 PV of an annuity of $1,000 for 5 years 1 1 1 1 1 1 d 5 $3,790 21 31 411 1 1.10 2 1 1.10 2 1 1.10 2 1.10 1.10 2 5 The present value can also be computed as follows: The decimal equivalents of the fractions can be found in Table 1 and applied to the annual cash inflow: 0.909 1 0.826 1 0.751 1 0.683 1 0.621 5 3.790 $1,000 3 3.790 5 $3,790 Note that the factor, 3.791, can be found on Table 2 using the 10 percent column and the 5-period row. The factors in Table 2 are the sums of the present value factors in Table 1. The difference between 3.790 and 3.791 is due to rounding. The following calculations using interest rates of 8 percent, 10 percent, and 12 percent for five years illustrate this point. 8% 10% Table 2 Table 1 12% Years Table 1 1 0.926 0.909 Table 2 0.893 2 0.857 0.826 0.797 3 0.794 0.751 0.712 4 0.735 0.683 0.636 5 0.681 Total 3.993 0.621 3.993 3.790* Table 1 Table 2 0.567 3.791* 3.605 3.605 * Difference due to rounding. sch80342_10_c10_399-444.indd 424 12/20/12 2:06 PM CHAPTER 10 Section 10.8 The Time Value of Money When calculating, it is easier to add the annual factors and make one computation. Thus, Table 2 is more convenient for evaluating equal cash flows. If the annual cash-flow amounts are not equal, it is necessary to use Table 1. Present Value Analysis Applied Assume that we sell machinery and offer financing to our customers using long-term notes payable. When a contract is signed, the customer makes two promises: 1. To pay the principal amount (the face value of the note) at maturity. 2. To pay interest periodically at the rate stated in the contract. We can either hold the note (earning interest and collecting the principal at the end of the contract) or sell the contract to an investor to get the cash for the sale now. The contract's market value depends on several factors, including the market rate of interest for similar contracts. The sum of the present values of the two promises is the contract's market price. As the market rate of interest rises, the contract's value declines, and vice versa. To illustrate, assume that we sell a $100,000 machine. The buyer signs a ten-year $100,000 contract with an interest rate of 10 percent, paid annually. This contract specifies the following cash payments: Year Interest at 10 percent Payment of principal Total cash outflow 1 $10,000 $10,000 2 10,000 10,000 .... .......... ......... 9 10,000 10,000 10 10,000 $100,000 110,000 Suppose that the current market rate of interest is 12 percent. In this case, investors are not willing to buy the contract at face value, because they could earn 12 percent elsewhere. To sell the contract, we must price the contract below face value. Selling at a price below face allows the investor to increase the rate of return by paying less for the two promises. Promise 1: $100,000 3 0.322 (10 periods at 12 percent from Table 1) Promise 2: $ 10,000 3 5.650 (10 payments at 12 percent from Table 2) $32,200 56,500 Proceeds from sale of the contract Discount sch80342_10_c10_399-444.indd 425 $88,700 $11,300 12/20/12 2:06 PM CHAPTER 10 Chapter Summary The investor that purchases the contract from us at $88,700 (with a discount of $11,300) will earn 12 percent interest on the $88,700 invested. The 12 percent earned is usually called the yield or the effective rate of interest. An effective interest rate or yield to maturity is the rate of interest earned regardless of the compounding period or the stated interest rate. Likewise, if the current market rate of interest is 8 percent, an investor will pay a premium for a contract with a 10 percent interest rate. The selling price and premium are determined as follows: Promise 1: $100,000 3 0.463 (10 periods at 8 percent from Table 1) Promise 2: $ 10,000 3 6.710 (10 payments at 8 percent from Table 2) Proceeds from sale of the contract Premium $46,300 67,100 $113,400 $13,400 Chapter Summary C apital investment decisions are critical to the firm's long-term success. The relevant data for making investment decisions are incremental cash flows, using criteria established in Chapter 9. Capital investments generally have multiperiod cash flows, requiring the use of the time value of money. The opportunity cost of cash to be received in the future can be a significant variable in measuring returns. Four methods are discussed to evaluate the cash flows. Two methods use present values for all cash flows: 1. Net present value, where a rate of return is set and decisions are made based on whether the net present value is positive or negative. 2. Internal rate of return, where the rate of return is found by setting the initial investment equal to the present value of future net cash inflows. Two other methods discussed that do not use the time value of money are the payback period and the accounting rate of return methods. Rarely are funds available to finance all attractive projects. Projects are selected based on rankings of their relative attractiveness. Taxes on profits from capital investments must be calculated and do affect the ROR of projects. The cost of capital is often used to develop a minimum acceptable rate of return. Computational issues such as uneven lives, working capital needs, incremental investment analysis, and inflationary impacts on forecasts are examined. sch80342_10_c10_399-444.indd 426 12/20/12 2:06 PM CHAPTER 10 Problem for Review Problem for Review Pam Williams, owner of a self-storage business, has just received an offer that is worth $600,000 after taxes for the storage buildings. She is interested in another investment opportunity that can probably yield an annual discounted return of 15 percent after taxes. The storage business is expected to continue to yield an annual cash inflow, before taxes, of $170,000 for a period of 15 years. The book value of the storage buildings is $660,000, and straight-line depreciation is used for tax purposes. Zero salvage value is predicted. A 40 percent tax rate applies. Question: Should the offer to sell the storage business be accepted? Explain. Solution: First, solve for the net aftertax cash flow if the business is kept: Cash flow before taxes $170,000 Minus depreciation (44,000) ($660,000 4 15 years) Taxable cash flow $126,000 Taxes (40 percent) (50,400) Aftertax cash flow $ 75,600 Plus depreciation 44