Capital Budgeting (Including Leasing)

Transcription

1 Chapter 8 Capital Budgeting (Including Leasing) 8. CAPITAL BUDGETING DECISIONS DEFINED Capital budgeting is the process of making long-term planning decisions for investments. There are typically two types of investment decisions: () selection decisions concerning proposed projects (for example, investments in long-term assets such as property, plant, and equipment, or resource commitments in the form of new product development, market research, re-funding of long-term debt, introduction of a computer, etc.) and () replacement decisions (for example, replacement of existing facilities with new facilities). 8. MEASURING CASH FLOWS The incremental (or relevant) after-tax cash flows that occur with an investment project are the ones that are measured. In general the cash flows of a project fall into the following three categories: () the initial investment; () the incremental (relevant) cash inflows over the life of the project; and () the terminal cash flow. Initial Investment The initial investment (I) is the initial cash outlay necessary to purchase the asset and put it in operating order. It is determined as follows: Initial investmentcost of assetþinstallation cost þworking capital investmentsproceeds fromsale of old assettaxes on saleof old asset The proceeds from the sale of old assets are subject to some type of tax. There are three possibilities:. The asset is sold for more than its book value.. The asset is sold for its book value.. The asset is sold for less than its book value. Additional working capital (in the form of increased inventory, cash, and receivables) is usually required to support a new investment project. This should be included in the project s initial outlay. At the end of the project s life, it should be recaptured as part of the project s terminal cash flow. EXAMPLE 8. Assume that an asset has a book value of $6, and initially cost $,. Assume further that the firm s ordinary marginal tax rate is percent. Consider each of the three possible tax situations dealing with the sale of the old asset.. The old asset is sold for $8,. In this case, the total gain is simply recapture of depreciation and taxed at the ordinary rate. Therefore, ð $ 8, $6, Þð: Þ ¼ $6,8. The old asset is sold for $6,. In this case, no taxes result since there is neither a gain nor a loss on the sale.. The old asset is sold for $5,. In this case there is a loss, which results in tax savings. The tax savings are as follows: ð $ 6, $5, Þð: Þ ¼ $, Copyright 7, 998, 986 by The McGraw-Hill Companies, Inc. Click here for terms of use. 5

2 6 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8 Taxes on the gain from the sale of an old asset or the tax savings on a loss must be considered when determining the amount of the initial investment of a new asset. EXAMPLE 8. XYZ Corporation is considering the purchase of a new machine for $5,, which will be depreciated on a straight-line basis over 5 years with no salvage value. In order to put this machine in operating order, it is necessary to pay installation charges of $5,. The new machine will replace an existing machine, purchased years ago at a cost of $,, that is depreciated on a straight-line basis (with no salvage value) over its 8-year life (i.e., $, per year depreciation). The old machine can be sold for $55, to a scrap dealer. The company is in the percent tax bracket. The machine will require an increase investment in inventory of $5,. The key calculation of the initial investment is the taxes on the sale of the old machine. The total gain, which is the difference between the selling price and the book value, is $5, ($55, $5,). The tax on this $5, total gain is $5,7 (% $5,). Therefore, the amount of initial investment is: Purchase price of the machine + Installation cost + Increased investment in inventory Proceeds from sales of old machine + Taxes on sale of old machine Initial investment $5, 5, 5, 55, 5,7 $ 85,7 Incremental (Relevant) Cash Inflows The relevant cash inflows over a project s expected life involve the incremental after-tax cash flows resulting from increased revenues and/or savings in cash operating costs. Cash flows are not the same as accounting income, which is not usually available for paying the firms bills. The differences between accounting income and cash flows are such noncash charges as depreciation expense and amortization expense. The computation of relevant or incremental cash inflows after taxes involves the following two steps:. Compute the after-tax cash flows of each proposal by adding back any noncash charges, which are deducted as expenses on the firm s income statement, to net profits (earnings) after taxes; that is: After-tax cash inflows ¼ net profits ð or earnings Þ after taxes þ depreciation. Subtract the cash inflows after taxes resulting from use of the old asset from the cash inflows generated by the new asset to obtain the relevant (incremental) cash inflows after taxes. EXAMPLE 8. XYZ Corporation has provided its revenues and cash operating costs (excluding depreciation) for the old and the new machine, as follows: Revenue Annual Cash Operating Costs Net Profits before Depreciation and Taxes Old machine New machine $5, $8, $7, $6, $ 8, $, Recall from Example 8. that the annual depreciation of the old machine and the new machine will be $, and $5,, respectively.

3 CHAP. 8] CAPITAL BUDGETING (INCLUDING LEASING) 7 To arrive at net profits after taxes, we first have to deduct depreciation expenses from the net profits before depreciation and taxes, as follows: Net Profits after Taxes Add Depreciation After-Tax Cash Inflows Old machine New machine ($8, $,)(.6) = $7, ($, $5,)(.6) = $7,8 $, $5, $57, $87,8 Subtracting the after-tax cash inflows of the old machine from the cash inflows of the new machine results in the relevant, or incremental, cash inflows for each year. Therefore, in this example, the relevant or incremental cash inflows for each year are $87,8 $57, = $,8. Alternatively, the incremental cash inflows after taxes can be computed, using the following simple formula: After-tax incremental cash inflows ¼ ð increase in revenues Þð ðincrease in cash changes Þð tax rate Þ tax rate Þ þ ðincrease in depreciation expenses Þð tax rate Þ EXAMPLE 8. Using the data in Example 8., after-tax incremental cash inflows for each year are: Increase in revenue ( tax rate): ($8, $5,)(.6) Increase in cash charges ( tax rate): ($6, $7,)(.6) + Increase in depreciation expense tax rate: ($5, $,)(.6) $6, ( 5,) 9, $,8 Terminal Cash Flow Cash flows associated with a project s termination generally include the disposal value of the project plus or minus any taxable gains or losses associated with its sale. The way in which to compute these gains or losses is very similar to the method for computing the taxes on the sale of an old asset. In most cases, the disposal value at the end of the project s useful life results in a taxable gain since its book value (or undepreciated value) is usually zero. The terminal cash flow must include the recapture of working capital investments required in the initial outlay. 8. CAPITAL BUDGETING TECHNIQUES Several methods of evaluating investment projects are as follows:. Payback period. Discounted payback period. Accounting rate of return (ARR). Net present value (NPV) 5. Internal rate of return (IRR) 6. Profitability index (or benefit/cost ratio) The NPV method and the IRR method are called discounted cash flow (DCF) methods. Each of these methods is discussed below.

4 8 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8 Payback Period The payback period measures the length of time required to recover the amount of initial investment. It is computed by dividing the initial investment by the cash inflows through increased revenues or cost savings. EXAMPLE 8.5 Assume: Cost of investment Annual after-tax cash savings $8, $, Then, the payback period is: initial investment cost Payback period ¼ increased revenues or lost savings ¼ $, ¼ $8, 6 years Decision rule: Choose the project with the shorter payback period. The rationale behind this choice is: The shorter the payback period, the less risky the project, and the greater the liquidity. EXAMPLE 8.6 Consider two projects whose after-tax cash inflows are not even. Assume each project costs $,. Cash Inflow Year 5 6 A ($) 5 6 B ($) 5 When cash inflows are not even, the payback period has to be found by trial and error. The payback period of project A is ($, = $ + $ + $ + $) years. The payback period of project B is ($, = $5 + $ + $): $ years þ $ ¼ years Project B is the project of choice in this case, since it has the shorter payback period. The advantages of using the payback period method of evaluating an investment project are that () it is simple to compute and easy to understand, and () it handles investment risk effectively. The shortcomings of this method are that () it does not recognize the time value of money, and () it ignores the impact of cash inflows received after the payback period; essentially, cash flows after the payback period determine profitability of an investment. Discounted Payback Period You can take into account the time value of money by using the discounted payback period. The payback period will be longer using the discounted method since money is worth less over time. Discounted payback is computed by adding the present value of each year s cash inflows until they equal the initial investment. initial cash outlays Discounted payback ¼ discounted annual cash inflows

5 CHAP. 8] CAPITAL BUDGETING (INCLUDING LEASING) 9 EXAMPLE 8.7 Year You invest $, and receive the following cash inflows. Cash Inflow $5,, 8, PV Factor Present Value $,65 6,5,8 Accumulated Present Value $,65,55 5,8 The discounted payback period is calculated as follows: $, $,55 $,55 þ $5,8 $, ¼ years þ :7 years ¼ :7 years Accounting Rate of Return Accounting rate of return (ARR) measures profitability from the conventional accounting standpoint by relating the required investment or sometimes the average investment to the future annual net income. Decision rule: Under the ARR method, choose the project with the higher rate of return. EXAMPLE 8.8 Consider the following investment: Initial investment Estimated life Cash inflows per year Depreciated per year (using straight line) $6,5 years $, $5 The accounting rate of return for this project is: net income $, $5 ARR ¼ investment ¼ :% $6,5 ¼ If average investment (usually assumed to be one-half of the original investment) is used, then: $, $5 ARR ¼ $,5 ¼ : 8% The advantages of this method are that it is easily understandable, simple to compute, and recognizes the profitability factor. The shortcomings of this method are that it fails to recognize the time value of money, and its uses accounting data instead of cash flow data. Net Present Value Net present value (NPV) is the excess of the present value (PV) of cash inflows generated by the project over the amount of the initial investment (I): NPV ¼ PV I The present value of future cash flows is computed using the so-called cost of capital (or minimum required rate of return) as the discount rate. In the case of an annuity, the present value would be PV ¼ A PVIFA where A is the amount of the annuity. The value of PVIFA is found in Appendix D. Decision rule: If NPV is positive, accept the project. Otherwise, reject it.

6 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8 EXAMPLE 8.9 Consider the following investment: Initial investment Estimated life Annual cash inflows Cost of capital (minimum required rate of return) $,95 years $, % Present value of the cash inflows is PV = A PVIFA = $, = $, (5.65) Initial investment (I) PVIFA%, Net present value (NPV = PV I) $6,95.6,95. $,.6 Since the NPV of the investment is positive, the investment should be accepted. The advantages of the NPV method are that it obviously recognizes the time value of money and it is easy to compute whether the cash flows form an annuity or vary from period to period. Internal Rate of Return Internal rate of return (IRR) is defined as the rate of interest that equates I with the PV of future cash inflows. In other words, at IRR, or I ¼ PV NPV ¼ Decision rule: Accept the project if the IRR exceeds the cost of capital. Otherwise, reject it. EXAMPLE 8. Assume the same data given in Example 8.8, and set the following equality (I = PV): $,95 ¼ $, PVIFA $,95 PVIFA ¼ $, ¼ : 7 which stands somewhere between 8 percent and percent in the -year line of Appendix D. The interpolation follows: Therefore, 8% IRR % PV Factor Difference.77. :77 IRR ¼ 8% þ : ð % 8% Þ ¼ 8% þ :586 ð % Þ ¼ 8% þ :7% ¼ 9:7% Since the IRR of the investment is greater than the cost of capital ( percent) accept the project. The advantage of using the IRR method is that it does consider the time value of money and, therefore, is more exact and realistic than the ARR method.

7 CHAP. 8] CAPITAL BUDGETING (INCLUDING LEASING) The shortcomings of this method are that () it is time-consuming to compute, especially when the cash inflows are not even, although most business calculators and spreadsheet software have a program to calculate IRR, and () it fails to recognize the varying sizes of investment in competing projects and their respective dollar profitabilities. Use of Spreadsheet Software Spreadsheet programs can be used in making IRR calculations. For example, Excel has a function IRR (values, guess). Excel considers negative numbers as cash outflows such as the initial investment, and positive numbers as cash inflows. Many financial calculators have similar features. As in Example 8.8, suppose you want to calculate the IRR of a $,95 investment (the value 95 entered in year is followed by monthly cash inflows of $,). Using a guess of % (the value of.), which is in effect the cost of capital, your formula would (values,.), and Excel would return 9.5%, as shown below. Year $ (,95),,,,,,,,,, IRR =9.5% NPV = $,.67 Note: The Excel formula for NPV is NPV (discount rate, cash inflow values) + I, where I is given as a negative number. Summary of Decision Rules Using Both IRR and NPV Methods International Rate of Return (IRR) Using the present-value tables, financial calculator, or Excel, compute the IRR. If the IRR exceeds the cost of capital, accept the project; if not, reject the project. Net Present Value (NPV) Calculate the NPV using the cost of capital as the discount rate. If the NPV is positive, accept the project; otherwise, reject the project. Multiple Internal Rates of Return In nonconventional (mixed) projects that have one or more periods of cash outflows (inflows) with periods of cash inflows (outflows), there may be multiple internal rates of return. EXAMPLE 8. Consider a strip-mining project with the following cash flows: ð $ 6, Þ 55, ð, Þ This project yields two IRRs = 5% and.%. Unfortunately, financial calculators and spreadsheet software are not aware of this problem and just report the first IRR. Descartes rule of signs states that in a capital-budgeting context, the number of IRRs is equal to the number of variations in the sign of the cash flow series or is less than that number by an even integer. According to the rule, for example, if the series of cash flows has three variations in sign, this series must have either three or one value of IRR.

8 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8 Profitability Index (Benefit/Cost Ratio) The profitability index is the ratio of the total PV of future cash inflows to the initial investment, that is, PV/I. This index is used as a means of ranking projects in descending order of attractiveness. If the profitability index is greater than, then accept the project. Decision rule: If the profitability index is greater than, then accept the project. EXAMPLE 8. Using the data in Example 8.8, the profitability index is PV $6,95 I ¼ $,95 ¼ : Since this project generates $. for each dollar invested (i.e., its profitability index is greater than ), accept the project. 8. MUTUALLY EXCLUSIVE INVESTMENTS A project is said to be mutually exclusive if the acceptance of one project automatically excludes the acceptance of one or more other projects. In the case where one must choose between mutually exclusive investments, the NPV and IRR methods may result in contradictory indications. The conditions under which contradictory rankings can occur are:. Projects that have different life expectancies.. Projects that have different sizes of investment.. Projects whose cash flows differ over time. For example, the cash flows of one project increase over time, while those of another decrease. The contradictions result from different assumptions with respect to the reinvestment rate on cash flows from the projects.. The NPV method discounts all cash flows at the cost of capital, thus implicitly assuming that these cash flows can be reinvested at this rate.. The IRR method implies a reinvestment rate at IRR. Thus, the implied reinvestment rate will differ from project to project. The NPV method generally gives correct ranking, since the cost of capital is a more realistic reinvestment rate. EXAMPLE 8. Assume the following: Cash Flows A B () () 5. Computing IRR and NPV at percent gives the following different rankings: A B IRR % 5% NPV at % The NPVs plotted against the appropriate discount rates form a graph called a NPV profile (Fig. 8-).

9 CHAP. 8] CAPITAL BUDGETING (INCLUDING LEASING) Fig. 8- NPV profile At a discount rate larger than percent, A has a higher NPV than B. Therefore, A should be selected. At a discount rate less than percent, B has the higher NPV than A, and thus should be selected. The correct decision is to select the project with the higher NPV, since the NPV method assumes a more realistic reinvestment rate, that is, the cost of capital. 8.5 THE MODIFIED INTERNAL RATE OF RETURN (MIRR) When the IRR and NPV methods produce a contradictory ranking for mutual exclusive projects, the modified IRR, or MIRR, overcomes the disadvantage of IRR. The MIRR is defined as the discount rate which forces I ¼ PV of terminal ð future Þ value compounded at the cost of capital The MIRR forces cash flow reinvestment at the cost of capital rather than the project s own IRR, which was the problem with the IRR.. MIRR avoids the problem of multiple IRRs.. Conflicts can still occur in ranking mutually exclusive projects with differing sizes. NPV should again be used in such a case. EXAMPLE 8. In Example 8., Project A s MIRR is: First, compute the project s terminal value at a % cost of capital. Next, find the IRR by setting: FVIF, ¼ :6 ¼ 75:69 ¼ 75:69 PVIFMIRR,5 PVIF ¼ =75:69 ¼ :569, which gives MIRR ¼ about % Now we see the consistent ranking from both the NPV and MIRR methods.

10 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8 MIRR NPV at % A % $ 9.8 B 5 $ COMPARING PROJECTS WITH UNEQUAL LIVES A replacement decision typically involving two mutually exclusive projects. When these two mutually exclusive projects have significantly different lives, an adjustment would be necessary. We discuss two approaches: () the replacement chain (common life) approach and () the equivalent annual annuity approach. The Replacement Chain (Common Life) Approach This procedure extends one, or both, projects until an equal life is achieved. For example, Project A has a 6-year life, while Project B has a -year life. Under this approach, the projects would be extended to a common life of 6 years. Project B would have an adjusted NPV equal to the NPV Bplus the NPV B discounted for years at the project s cost of capital. Then the project with the higher NPV would be chosen. EXAMPLE 8.5 Sims Industries, Inc. is considering two machines to replace an old machine. Machine A has a life of years, will cost $,5, and will produce net cash savings of $,8 per year. Machine B has an expected life of 5 years, will cost $,, and will produce net cash savings in operating costs of $6, per year. The company s cost of capital is percent. Project A s NPV is NPV A¼ PV I ¼ $,8 PVIFA, $,5 ¼ $ 57:8 Project B s extended time line can be set up as follows: ¼ $,8 ð 5:6 Þ $,5 ¼ $5,7:8 $, (in hundredths) Or, alternatively, Adjusted NPV B¼ PV I ¼ $6, PVIFA, $, PVIF5, $, ¼ $ 6, ð 5:6 Þ $, ð :59 Þ $, ¼ $,96:6 $,88: $, ¼ $ 98:6 NPV B¼ PV I ¼ $6, PVIFA5, $, ¼ $ 6, ð : Þ $, ¼ $,598:6 $, ¼ $ 598:6 Adjusted NPV B¼ NPV Bþ NPV Bdiscounted for 5 years ¼ $ 598:6 þ $598:6 PVIF5, ¼ $ 598:6 þ $598:6 ð :59 Þ ¼ $ 598:6 þ $:9 ¼ $ 99:5 ð due to rounding errors Þ

11 CHAP. 8] CAPITAL BUDGETING (INCLUDING LEASING) 5 The Equivalent Annual Annuity (EAA) Approach It is often cumbersome to compare projects with different lives. For example, one project might have a -year life versus a -year life for the other. This would require a replacement chain analysis over years, the lowest common denominator of the two lives. In such a case, it is often simpler to use an alternative approach, the equivalent annual annuity method. This procedure involves three steps:. Determine each project s NPV over its original life.. Find the constant annuity cash flow or EAA, using NPV of each project PVIFA n,i. Assuming infinite replacement, find the infinite horizon (or perpetuity) NPV of each project, using EAA of each cost of capital EXAMPLE 8.6 From Example 8., NPVA= $57.8 and NPVB= $ To obtain the constant annuity cash flow or EAA, we do the following: EAA A¼ $57:8=PVIFA, ¼ $57:8=5:6 ¼ $: EAA B¼ $598:6=PVIFA5, ¼ $598:6=: ¼ $7:6 Thus, the infinite horizon NPVs are as follows: 8.7 REAL OPTIONS Infinite horizon NPV A¼ $:=: ¼ $75:7 Infinite horizon NPV B¼ $7:6=: ¼ $,5: Almost all capital budgeting proposals can be viewed as real options. Also, projects and operations contain implicit options, such as the option as to when to take a project, the option to expand, the option to abandon, and the option to suspend or contract operations. Deciding when to take a project is called the investment timing option. Example 8.7 A project costs $ and has a single future cash flow. If we take it today, the cash flow will be $ in year. If we wait year, the project will still cost $, but the cash flow the following year (i.e., years from now) will be $ because the potential market is bigger. If these are only two options, and the relevant discount rate is percent, what should we do? To answer this question, we need to compute the two NPVs. If we take it today, the NPV = $ + /. = $9.9. If we wait year from now, the NPV at that time would be: NPV = $ + /. = $8.8. Here, $8.8 is the NPV year from now. We need the value today, so we discount back $8.8/. = $6.5. If we wait, the NPV is $6.5 today compared to $9.9 if we start immediately, so the optimal time to begin the project is year from now. The fact that we do not have to take a project immediately is often called the option to wait. In this example, the value of the option to wait is the difference in NPVs, $ = $7.. This $7. is the extra value created by deferring the start of the act as opposed to taking it today. Example 8.8 A project costs $ and has a future cash flow of $ per year forever. If we wait year, the project will cost $ because of inflation, but the cash flows will be $8 per year forever. If these are the only two options, and the relevant discount rate is percent, what should we do? What is the value of the option to wait? In this case, the project is a simple perpetuity. If we take it today, the NPV is: NPV ¼ $ þ =: ¼ $5 If we wait year, the NFV at that time would be: NPV ¼ $ þ 8=: ¼ $6

12 6 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8 So, $6 is the NPV year from now, but we need to know the value today. Discounting back one period, we get: NPV ¼ $6=: ¼ $:86 If we wait, the NPV is $.86 today compared to $5 if we start immediately, so the optimal time to begin the project is now. What is the value of the option to wait? It is not $.86 $5 = $7.. Because an option can never have a negative value, the option to wait has a zero value. 8.8 THE CONCEPT OF ABANDONMENT VALUE The notion of abandonment value recognizes that abandonment of a project before the end of its physical life can have a significant impact on the project s return and risk. This distinguishes between the project s economic life and physical life. Two types of abandonment can occur:. Abandonment of an asset since it is being unprofitable.. Sale of the asset to some other party who can extract more value than the original owner. EXAMPLE 8.9 ABC Company is considering a project with an initial cost of $5, and net cash flows of $, for next three years. The expected abandonment cash flows for years,,, and are $5,, $,, $,5, and $. The firm s cost of capital is percent. We will compute NPVs in three cases. Case. NPV of the project if kept for years NPV ¼ PV I ¼ $, PVIFA, ¼ $, ð :869 Þ $5, ¼ $ 6: Case. NPV of the project if abandoned after year NPV ¼ PV I ¼ $, PVIF, þ $,5 PVIF, $ 5, ¼ $, ð :99 Þ þ $, ð :99 Þ $5, ¼ $,88: þ $,77: $5, ¼ $5:5 Case. NPV of the project if abandoned after year NPV ¼ PV I ¼ $, PVIF, þ $, PVIF, þ $,5 PVIF, $ 5, ¼ $, ð :99 Þ þ $, ð :86 Þ þ $,5 ð :86 Þ $5, ¼ $,88: þ $,65:8 þ $,66: $5, ¼ $57 The company should abandon the project after year. 8.9 CAPITAL RATIONING Many firms specify a limit on the overall budget for capital spending. Capital rationing is concerned with the problem of selecting the mix of acceptable projects that provides the highest overall NPV. The profitability index is used widely in ranking projects competing for limited funds. EXAMPLE 8. following: A company with a fixed budget of $5, needs to select a mix of acceptable projects from the Projects A B C D E F I ($) 7,,, 6,, 8, PV ($), 5, 6,5 79, 8, 95, NPV ($), 5, 6,5 9,, 5, Profitability Index Ranking 5 6

13 CHAP. 8] CAPITAL BUDGETING (INCLUDING LEASING) 7 The ranking resulting from the profitability index shows that the company should select projects A, B, and D: A B D I $ 7,, 6, $, PV $, 5, 79, $6, Therefore, NPV ¼ $6, $, ¼ $6, Unfortunately, the profitability index method has some limitations. One of the more serious is that it breaks down whenever more than one resource is rationed. A more general approach to solving capital rationing problems is the use of mathematical (or zero-one) programming. Here the objective is to select the mix of projects that maximizes the NPV subject to a budget constraint. EXAMPLE 8. Using the data given in Example 8. set up the problem as a mathematical programming problem. First label project A as X, B as X, and so on; the problem can be stated as follows: Maximize subject to NPV ¼ $,X þ $ 5,X þ $ 6,5X þ $ 9,X $,X 5þ $ 5,X 6 $7,X þ $,X þ $,X þ $ 6,X þ $,X5 þ $ 8,X6 % $5, X t¼, ð i ¼,,...,6 Þ Using the mathematical program solution routine, the solution to this problem is: X ¼, X ¼, X ¼ and the NPV is $6,. Thus, projects A, B, and D should be accepted. 8. HOW DOES INCOME TAXES AFFECT INVESTMENT DECISIONS? Income taxes make a difference in many capital budgeting decisions. In other words, the project that is attractive on a before-tax basis may have to be rejected on an after-tax basis. Income taxes typically affect both the amount and the timing of cash flows. Since net income, not cash inflows, is subject to tax, after-tax cash inflows are not usually the same as after-tax net income. Let us define: S = Sales E = Cash operating expenses d = Depreciation t = Tax rate Then, before-tax cash inflows (or before-tax cash savings) = S E and net income = S E d. By definition, After-tax cash inflows ¼ before-tax cash inflows taxes ¼ ðs E Þ ðs E d Þ ðt Þ A Comprehensive treatment of the problem appears in H. Martin Weingartner, Capital Budgeting of Interrelated Projects Survey and Synthesis, Management Science, vol., March 966, pp

14 8 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8 Rearranging gives the short-cut formula: After-tax cash inflows ¼ ð S E Þ ð t Þ þ ðd Þð t Þ As can be seen, the deductibility of depreciation from sales in arriving at net income subject to taxes reduces income tax payments and thus serves as a tax shield: Tax shield ¼ tax saving on depreciation ¼ ð d Þð t Þ Example 8. Then, Assume: S = $, E = $, d = $5 per year using the straight line method t = % After-tax cash inflow ¼ ð $, $, Þ ð :Þ þ ð $ 5 Þð: Þ ¼ ð $, Þð:7Þ þ ð $ 5 Þð: Þ ¼ $, þ $5 ¼ $,55 Note that a tax shield ¼ tax savings on depreciation ¼ ð d Þðt Þ ¼ ($5)(: Þ ¼ $5 Since the tax shield is dt, the higher the depreciation deduction, the higher the tax savings on depreciation. Therefore, an accelerated depreciation method (such as double-declining balance) produces higher tax savings than the straight-line method. Accelerated methods produce higher present values for the tax savings, which may make a given investment more attractive. 8. CAPITAL BUDGETING DECISIONS AND THE MODIFIED ACCELERATED COST RECOVERY SYSTEM (MACRS) Although the traditional depreciation methods still can be used for computing depreciation for book purposes, 98 saw a new way of computing depreciation deductions for tax purposes. The current rule is called the Modified Accelerated Cost Recovery System (MACRS) rule, as enacted by Congress in 98 and then modified somewhat in 986 under the Tax Reform Act of 986. This rule is characterized as follows:. It abandons the concept of useful life and accelerates depreciation deductions by placing all depreciable assets into one of eight age property classes. It calculates deductions, based on an allowable percentage of the asset s original cost (see Tables 8- and 8-). With a shorter asset tax life than useful life, the company would be able to deduct depreciation more quickly and save more in income taxes in the earlier years, thereby making an investment more attractive. The rationale behind the system is that this way the government encourages the company to invest in facilities and increase its productive capacity and efficiency. (Remember that the higher d, the larger the tax shield (d )(t).). Since the allowable percentages in Table 8- add up to %, there is no need to consider the salvage value of an asset in computing depreciation.. The company may elect the straight-line method. The straight-line convention must follow what is called the half-year convention. This means that the company can deduct only half of the regular straight-line depreciation amount in the first year. The reason for electing to use the MACRS optional straight-line method is that some firms may prefer to stretch out depreciation deductions using the straight-line method rather than to accelerate them. Those firms are the

15 CHAP. 8] CAPITAL BUDGETING (INCLUDING LEASING) 9 Table 8-. Modified accelerated cost recovery system classification of assets Property class Year -year 5-year 7-year -year 5-year -year Total.%.5.8 a 7. %.% a %.% a %.% a % 5.% a %.8% a % a Denotes the year of changeover to straight-line depreciation. ones that just start out or have little or no income and wish to show more income on their income statements.. If an asset is disposed of before the end of its class life, the half-year convention allows half the depreciation for that year (early disposal rule). EXAMPLE 8. Assume that a machine falls under a -year property class costs $, initially. The straight-line option under MACRS differs from the traditional straight-line method in that under this method the company would deduct only $5 depreciation in the first year and the fourth year ($,/ years = $,; $,/ = $5). The table below compares the straight-line with half-year convention with the MACRS. Year Straight-line (half-year) Depreciation $ 5,, 5 $, Cost $,,,, MACRS (%) MACRS Deduction $ 999,5 $,

16 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8 Table 8.. MACRS tables by property class MACRS Property Class Useful Life Examples of Assets & Depreciation Method (ADR Midpoint Life) a -year property % years or less Most small tools are declining balance included; the law specifically excludes autos and light trucks from this property class. 5-year property % More than years to Autos and light trucks, declining balance less than years computers, typewriters, copiers, duplicating equipment, heavy general-purpose trucks, and research and experimentation equipment are included. 7-year property % years or more to less Office furniture and declining balance than 6 years fixtures and most items of machinery and equipment used in production are included. -year property % 6 years or more to less Various machinery and declining balance than years equipment, such as that used in petroleum distilling and refining and in the milling of grain, are included. 5-year property 5% years or more to less Sewage treatment plants, declining balance than 5 years telephone and electrical distribution facilities, and land improvements are included. -year property 5% 5 years or more Service stations and declining balance other real property with an ADR midpoint life of less than 7.5 years are included. 7.5-year property Not applicable All residential rental straight-line property is included..5-year property Not applicable All nonresidential real straight-line property is included. a The term ADR midpoint life means the useful life of an asset in a business sense; the appropriate ADR midpoint lives for assets are designated in the Tax Regulations.

17 CHAP. 8] CAPITAL BUDGETING (INCLUDING LEASING) EXAMPLE 8. A machine costs $,. Annual cash inflows are expected to be $5,. The machine will be depreciated using the MACRS rule and will fall under the -year property class. The cost of capital after taxes is %. The estimated life of the machine is 5 years. The salvage value of the machine at the end of the fifth year is expected to be $,. The tax rate is %. Should you buy the machine? The formula for computation of after-tax cash inflows (S E )( t) + (d )(t) needs to be computed separately. The NPV analysis can be performed as follows: Present value % Present value (S E)( t): $5, $5, (.) = $,5 For 5 years for 5 years (d )(t): Year Cost MACRS(%) d $,5 (d)(t).79 a $,68.5 $,. $, $ b 98.9 $,.5,5,5.86 b,.7 $,.8,8.75 b. $, b 5.6 Salvage value: $, $,(.) = $8 c $8.6 b 5.6 in year 5: in year 5 Present value (PV) $6,86. a T (%, years) =.7 (from Table ). b T values (year,,,, 5) obtained from Table. c Any salvage value received under the MACRS rules is a taxable gain (the excess of the selling price over book value, $, in this example), since the book value will be zero at the end of the life of the machine. Since NPV = PV I = $6,86. $, = $6,86. is positive, the machine should be bought. 8. LEASING Leasing provides an alternative to purchasing an asset in order to acquire its services without directly incurring any fixed debt obligation. There are two basic types of leases available to the business firm:. An operating lease is basically a short-term lease. It is cancelable at the option of the firm leasing the asset (the lessee). Such leases are commonly used for leasing such items as computer hardware, cash registers, vehicles, and equipment.. A financial (capital) lease is a longer-term lease than an operating lease. It constitutes a noncancelable contractual commitment on the part of the lessee to make a series of payments to the firm that actually owns the asset (the lessor) for the use of the asset. Accounting for Leases Prior to 977, most financial (capital) leases were not included in the balance sheets of the lessee. Instead, they were reported in the footnotes of the balance sheet. However, in November 976, the Financial Accounting Standards Board (FASB), which is a part of the American Institute of Certified Public Accountants, issued a statement that requires any lease meeting one or more of the following criteria to be included in the body of the balance sheet of the lessor. Financial Accounting Standards Board, Statement of Accounting Standards No., Accounting for Leases, November 976, Stamford, CN.

18 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8. The lease transfers ownership of the property to the lessee by the end of the lease term.. The lease contains a bargain repurchase option.. The lease term is equal to 75 percent or more of the estimated economic life of the leased property.. The present value of the minimum lease payments equals or exceeds 9 percent of the excess of the fair value of the property over any related investment tax credit retained by the lessor. The Lease-Purchase Decision The lease-purchase decision is a decision that commonly confronts firms considering the acquisition of new assets. It is a hybrid capital budgeting decision which forces a company to compare the leasing and purchasing alternatives. To make an intelligent decision, an after-tax, cash outflow, present value comparison is needed. There are special steps to take when making this comparison. When considering a lease, take the following steps:. Find the annual lease payment. Since the annual lease payment is typically made in advance, the formula to be used is: amount of lease Amount of lease ¼ A þ A ð PVIFA i,n Þ or A ¼ Notice we use n rather than n.. Find the after-tax cash outflows.. Find the present value of the after-tax cash outflows. þ PVIFA i,n When considering a purchase, take the following steps:. Find the annual loan amortization by using: amount of loan for the purchase A ¼ PVIFA i,n This step may not be necessary since this amount is usually available.. Calculate the interest. The interest is segregated from the principal in each of the annual loan payments because only the interest is tax-deductible.. Find the cash outflows by adding interest and depreciation (plus and maintenance costs), and then compute the after-tax outflows.. Find the present value of the after-tax cash outflows, using Appendix C. EXAMPLE 8.5 A firm has decided to acquire an asset costing $, that has an expected life of 5 years, after which the asset is not expected to have any residual value. The asset can be purchased by borrowing or it can be leased. If leasing is used, the lessor requires a percent return. As is customary, lease payments are to be made in advance, that is, at the end of the year prior to each of the years. The tax rate is 5 percent and the firm s cost of capital, or after-tax cost of borrowing, is 8 percent. First compute the present value of the after-tax cash outflows associated with the leasing alternative.. Find the annual lease payment: amount of lease A ¼ þ PVIFAi,n $, $, $, ¼ þ PVIFA %, years ¼ þ :7 ¼ :7 ¼ $ :6 ð rounded Þ Steps and can be done in the same schedule, as follows:

19 CHAP. 8] CAPITAL BUDGETING (INCLUDING LEASING) Year 5 () Lease Payment ($),6,6 () Tax Savings ($),68 a,68 () = () () After-Tax Cash Outflow ($),6,68 (,68) () PV at 8%.. b.686 c (5) = () () PV of Cash Outflow ($, Rounded),6 8,7 (7,9) 5,76 a $,6 5% b From Appendix D. c From Appendix C. If the asset is purchased, the firm is assumed to finance it entirely with a percent unsecured term loan. Straight-line depreciation is used with no salvage value. Therefore, the annual depreciation is $, ($,/5 years). In this alternative, first find the annual loan payment by using: amount of loan A ¼ PVIFA i,n $, $, 6:8 ð rounded Þ $ ¼ PVIFA %,5 years ¼ :796 ¼. Calculate the interest by setting up a loan amortization schedule. Year 5 () () (5) = () () Loan Beginning-of-Year () = ()(%) () = () () End-of-Year Payment ($) Principal ($) Interest ($) Principal ($) Principal ($) 6,8,, 6,8 8,69 6,8 8,69 8,6 8,9 65,6 6,8 6,8 6,8 65,6 5,779,976 a 6,56,578,98 9,8,8,98 a 5,779,976 a Because of rounding errors, there is a slight difference between () and (). Steps (cash outflows) and (present values of those outflows) can be done as follows: () () () () = () + () (5) = ()(5%) (6) = () (5) (8) = (6) (7) Loan Interest Depreciation Total Tax Cash (7) PV of cash Year Payment ($) ($) ($) Deductions ($) Savings ($) Outflow ($) PV at 8% Outflow ($) 6,8,,, 5,,8.959,58 5 6,8 6,8 6,8 6,8 8,6, 6,56,,578,,98, 8,6 6,56,578,98,8,8,89,99,,,9 5, ,59,,58, 5,88 The sum of the present values of the cash outflows for leasing and purchasing by borrowing shows that purchasing is preferable because the PV of borrowing is less than the PV of leasing ($5,88 versus $5,76). The incremental savings would be $,675 ($5,76 $5,88). 8. CAPITAL BUDGETING AND INFLATION The accuracy of capital budgeting decisions depends on the accuracy of the data regarding cash inflows and outflows. For example, failure to incorporate price-level changes due to inflation in capital budgeting situations can result in errors in the predicting of cash flows and thus is incorrect decisions.

20 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8 Typically, an analyst has two options dealing with a capital budgeting situation with inflation: Either restate the cash flows in nominal terms and discount them at a nominal cost of capital (minimum required rate of return) or restate both the cash flows and cost of capital in constant terms and discount the constant cash flows at a constant cost of capital. The two methods are basically equivalent. EXAMPLE 8.6 A company has the following projected cash flows estimated in real terms: Period Real Cash Flows (s) 5 5 The nominal cost of capital is 5 percent. Assume that inflation is projected at percent a year. Then the first cash flows for year, which is $5, in current dollars, will be 5,. = $8,5 in year- dollars. Similarly the cash flow for year will be 5, (.) = $6,5 in year- dollars, so on. If we discount these nominal cash flows at the 5 percent nominal cost of capital, we have the following net present value (NPV): Period Cash Flows PVIF (Appendix C) Present Values NPV = 5.9 or $5,9 Instead of converting the cash-flow forecasts into nominal terms, we could convert the cost of capital into real terms by using the following formula: In the example, this gives Real cost of capital ¼ þ nominal cost of capital þ inflation rate Real cost of capital ¼ ð þ :5 Þ =ð þ : Þ ¼ :5=: ¼ :5 ¼ :5 or :5% We will obtain the same answer except for rounding errors ($5,9 versus $5,58). Cash Period Flows PVIF = /( +.5) n Present Values 5 5. /( +.5) =.957 /(.5) =.96 /(.5) = NPV = 5.58 or $5,58

21 CHAP. 8] CAPITAL BUDGETING (INCLUDING LEASING) 5 Review Questions. The initial investment is minus. plus installation cost minus plus or. The total gain is split into subject to tax rates. and. These breakdowns are. After-tax cash inflows equal net profits after taxes plus. The NPV method and the IRR method are called. methods. 5. is the process of making decisions. 6. is the or cash savings in operating expenses. divided by the cash inflow through increased revenues 7. The shorter the, the less risky the project and the greater the. 8. Accounting rate of return does not recognize the. 9. Internal rate of return is the rate at which equals.. Accept the investment if its IRR exceeds.. IRR is difficult to compute when the cash flows are.. In, the NPV and the IRR methods may produce.. is used widely in ranking the investments competing for limited funds.. The method discounts all cash flows at the, thus implicitly assuming that these cash flows can be reinvested at this rate. 5. MACRS rules abandon the concept of. 6. is taken in the year in which an asset is first placed into service. 7. The straight-line depreciation method with only half of the regular straight-line deduction amount in the 8. Immediate disposal of an old machine usually results in tible from current income for tax purposes. allows the company to deduct year. that is fully deduc- 9. The FASB requires firms to their. certain financial (capital) leases and to restate. Lease payments represent a desired rate of return to the.. If two mutually exclusive projects have unequal lives, either of the two methods may be used for the analysis: the and the.

22 6 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8. The overcomes many of the IRR s disadvantages.. Real options involve the right to buy or sell, not. Answers: () cost (purchase price) of the asset, the proceeds from sale of the old asset, taxes on the sale of old asset; () a capital gain, recapture of depreciation, different; () depreciation; () discounted cash flow (DCF); (5) Capital budgeting, long-term investment; (6) Payback period, initial amount of investment; (7) payback period, liquidity; (8) time value of money; (9) present value of cash inflows, the initial investment; () the cost of capital; () not even; () mutually exclusive investments, conflicting rankings; () Profitability index (or benefit/cost ratio); () NPV, cost of capital; (5) useful life; (6) Investment tax credit (ITC); (7) the half-year convention, first; (8) a loss; (9) capitalize, balance sheets; () lessor; () replacement chain (common life) approach, equivalent annual annuity (EAA); () modified internal rate of return (MIRR); () real assets, financial assets. Solved Problems 8. Capital Gain (Loss) and Recapture of Depreciation. For each of the following cases, compute the total taxes resulting from the sale of the asset. Assume a percent ordinary tax rate. The asset was purchased for $75, years ago and has a book value (undepreciated value) of $,. (a) The asset is sold for $8,. (b) The asset is sold for $7,. (c) The asset is sold for $,. (d ) The asset is sold for $8,. (a) Total gain ¼ selling price book value ¼ $ 8, $, ¼ $, Total taxes are: $,6 (% $,) (b) Gain: $7, $, ¼ $, Tax: $, : (c) No Tax: ¼ $, (d ) Loss: $8, $, ¼ $, Tax saving: $, : ¼ $68 8. Calculation of Initial Investment. A firm is considering replacing an old machine with another. The new machine costs $9, plus $, to install. For each of the four cases given in Problem 8., calculate the initial investment of the replacement. Cost of new machine + Installation cost Proceeds from sale of old machine + Taxes on sale of old machine Invalid investment (a) $9,, 8, 7,5 $7,5 (b) $9,, 7,,8 $,8 (c) $9,,, $6, 8. Incremental Cash Inflows. National Bottles Corporation is contemplating the replacement of one of its bottling machines with a new one that will increase revenue from $5, to $, per year and reduce cash operating costs from $, to $, per year. The new machine will cost $8, and have an estimated life of years with no salvage value. The firm uses straight-line depreciation and is subject to a 6 percent tax rate. The old machine has been fully depreciated (d ) $9,, 8, (9) $6,8

23 CHAP. 8] CAPITAL BUDGETING (INCLUDING LEASING) 7 and has no salvage value. What is the incremental (relevant) cash inflows generated by the replacement? cost Annual depreciation of the new machine ¼ expected life Revenue Annual Cash Operating Costs $8,,8 per year ¼ ¼ $ Net Profits before Depreciation and Taxes Old New $5, $, $, $, $, $, Net profits after taxes and after-tax cash inflows for both machines are computed as follows: Old New Net Profits after Taxes ($, )(.6) = $7, ($, $,8)(.6) = $8,78 Add Depreciation $ $,8 After-Tax Cash Inflows $ 7, $,58 Therefore, the relevant incremental cash inflows for each year are: $,58 $7, ¼ $6,58 Alternatively, use the shortcut formula, as follows: Increase in revenue ( tax rate): ($, $5,)(.6) Increase in cash charges ( tax rate): ($, $,)(.6) + Increase in depreciation tax rate: ($,8 )(.6) After-tax cash inflows $, (,8),8 $6,58 8. Basic Evaluation Methods. The following data are given for the Alright Aluminum Company: Initial cost of proposed equipment Estimated useful life Estimated annual savings in cash operating expenses Predicted residual value at the end of the useful life Cost of capital $75, 7 years $8, $, % Compute the: (a) payback period; (b) present value of estimated annual savings; (c) present value of estimated residual value; (d ) total present value of estimated cash inflows; (e) net present value (NPV); and ( f ) internal rate of return (IRR). (a) (b) Payback period ¼ initial investment $75, annual savings ¼ $8, ¼ : 67 years PV ¼ A PVIFA%,7 years ¼ $8, :568 ¼ $8,8 ð rounded Þ

24 8 CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8 (c) (d ) (e) ( f ) At IRR, I = PV. Thus, PV ¼ $, PVIF%,7 years ¼ $, :5 ¼ $,57 ð rounded Þ Total PV ¼ $8,8 þ $,57 ¼ $8,55 NPV ¼ PV I ¼ $8,55 $75, ¼ $8,55 $75, ¼ $8, PVIFA r,7 $75, PVIFA r,7 ¼ $ 8, ¼ :667 which is somewhere between percent and 5 percent in the 7-year line. Using interpolation, % True rate 5% Difference PVIFA :88 :667 5 IRR ¼ % þ :88 :6 ð % % Þ :6 ¼ % þ :79 ð % Þ ¼ % þ :95% ¼ :95% 8.5 Payback Period and ARR. The John-in-the-Box Store is a fast food restaurant chain. Potential franchisees are given the following revenue and cost information: Building and equipment Annual revenue Annual cash operating costs $9, $5, $8, The building and equipment have a useful life of years. The straight-line method for depreciation is used. The income tax is percent. Given these facts: (a) What is the payback period? (b) What is the accounting rate of return? Therefore, Net profits before depreciation and taxes ¼ $5, $8, ¼ $, $9, Annual depreciation ¼ years ¼ $,5 Net profit after taxes ¼ ð $, $,5 Þð : Þ ¼ $69, After-tax cash inflows ¼ $69, þ $,5 ¼ $9,8 (a) Initial investment $9, 5 (b) Payback period ¼ annual cash flow ¼ $9,8 ¼ : years net income $69, Accounting rate of return ¼ investment ¼ $9, ¼ or using average investment in the denominator gives: $69, ARR ¼ $9,= ¼ 8 : 8% 8.6 Basic Evaluation Methods. The Rango Company is considering a capital investment for which the initial outlay is $,. Net annual cash inflows (before taxes) are predicted to be $, :%

25 CHAP. 8] CAPITAL BUDGETING (INCLUDING LEASING) 9 for years. Straight-line depreciation is to be used, with an estimated salvage value of zero. Ignore income taxes. Compute the: (a) payback period; (b) accounting rate of return (ARR); (c) net present value (NPV), assuming a cost of capital (before tax) of percent; and (d ) internal rate of return (IRR). (a) (b) initial investment $, 5 years Payback period ¼ annual cash flow ¼ $,=year ¼ net income Accounting rate of return ð ARR Þ ¼ initial investment $, Depreciation ¼ years ¼ $, =year Accounting rate of return ¼ ð $, $, Þ =year ¼ : $, ¼ % (c) Net present value ð NPV Þ ¼ PV of cash inflows ½discounted at the cost of capital ð % Þ initial investment $, ðpvifa %,Þ $, ¼ $, ð 5:65 Þ $, ¼ $,6:8 (d ) Internal rate of return (IRR) is the rate which equates the amount invested with the present value of cash inflows generated by the project. $, ¼ $, ð PVIFA r,þ $, 5 PVIFA r, ¼ $, ¼ which is between 5 percent and 6 percent in Appendix D. Using interpolation, 5% True rate 6% Difference PVIFA :88 5: :88 IRR ¼ 5% þ 6 % 5% Þ ¼ 5% þ :856 ð % Þ 5:88 :8 ð ¼ 5% þ :% ¼ 5:% 8.7 Basic Capital Budgeting Decisions. Consider an investment which has the following cash flows: Year 5 Cash Flow ($) (,),,,, 5, (a) (b) Compute the: () payback period; () net present value (NPV) at percent cost of capital; and () internal rate of return (IRR). Based on () and () in part (a), make a decision about the investment. Should it be accepted