1 Chapter 14 Notes Page 1 Capital Budgeting This chapter examines various tools used to evaluate potential projects or investments. Accountants advocate the use of the Simple Rate of Return, which is based upon the accounting concept of Net Income for this purpose. This return is also referred to as the Accounting Rate of Return. Financiers do not like to use Net Income as a basis for evaluating investments because of the discretion that accountants have in determining Net Income (e.g., estimates of various allowances, useful lives, and the choice of depreciation methods). Financiers prefer to use After-Tax Cash Flow as the basis for their analysis. Financiers Capitol Investment? advocate the use of the Payback Period, Net Present Value, and Internal Rate of Return for purposes of evaluating investments. Simple Rate of Return and Payback period are referred to as non-discounting models because they do not utilize the time value of money. Net Present Value and Internal Rate of Return are referred to as discounting models because the time value of money is part of their analysis. All of these tools are used to evaluate the merits of a particular project or investment. The way that the project or investment will be financed is not included in the evaluation (e.g., do not include interest costs). It is assumed that the project or investment is funded with available capital, and the source of that capital is not in issue. Present Value "I'll gladly pay you Tuesday for a hamburger today." Instinctively, you know that a dollar that Wimpy is willing to pay sometime in the future is not as valuable as a dollar in your hand today. This inequality arises because you can put the dollar that you currently have in the bank, earn interest on that deposit, and have more than one dollar (the dollar deposit plus the interest) in the future. The Present Value tells you what you have to put in the bank today in order to have a dollar in the future. While you can use your calculator, Excel or a Present Value table, you should be able to figure out the Present Value of one dollar to be receive at the end of a given period by using the following formula: PVIF = 1 (1+ d) n where d is the discount rate (the interest rate) and n is the number of periods until you receive the one dollar. PVIF is the Present Value Interest Factor (PVIF) or discount factor that is reported on a Present Value table. If you treat n as the number of years
2 Chapter 14 Notes Page 2 and d as the annual interest rate, then your Present Value is based on simple interest. If you change the n to reflect the number of six-month periods, and the d to reflect the amount of interest that is paid in each six-month period, then you have Present Values that reflect semi-annual compounding of interest. By adjusting the d and n to reflect various time periods and interest rates, you can vary the extent of the compounding of interest. For example, if one dollar is to be received at the end of one year, and you can receive interest from your bank at the rate of 10% compounded annually, then you need to deposit the following to have one dollar at the end of the year: You can test this: PVIF = (1/(1.10) 1 ) PVIF = One Year's Interest Is.1 x = Original Principal = We are a little off because of rounding. As another example, assume that one dollar is to be received at the end of a two-year period, and you can receive interest from your bank at the rate of 10% compounded annually, then you need to deposit the following to have one dollar at the end of two years: You can test this: PVIF = (1/(1.10) 2 ) PVIF = One Year's Interest Is.1 x = Original Principal = Amount on Deposit After 1 year: Notice how this is similar to the Present Value of a dollar at the end of one year. The only difference is due to rounding. The Second Year's Interest Is.1 x = Balance At Start of Year = Amount on Deposit After 2 years: If you are to receive a dollar at the end of each year for a given period of time, this is called an annuity. You could figure out the Present Value of that annuity by calculating the Present Value of each dollar you are going to receive using the above formula. This
3 Chapter 14 Notes Page 3 could get cumbersome if the annuity period is long. Alternatively, you could use the formula for calculating the Present Value of an Annuity. Conceptually, the Present Value of an Annuity is that amount that must be invested today at a given interest rate in order to produce sufficient funds to enable annual withdrawals of the annuity amount over the annuity period. PVIF annuity = 1 1/d[ 1 ] (1+d) n For example, if one dollar is to be received at the end of each year for a two-year period, and you can receive interest from your bank at the rate of 10% compounded annually, then you need to deposit the following to be able to withdraw one dollar at the end of each year for two years: The Present Value of one dollar received a year from now is: The Present Value of one dollar received two years from now is: $ Using the Present Value of an Annuity formula: PVIF annuity = [1-(1/(1.10) 2 ]/.1 PVIF annuity = $ Again, the difference is due to rounding. If you deposit $ with a bank at 10% interest, you can withdraw one dollar at the end of each year for two years: Initial Deposit: $ One Year s Interest: Amount On Deposit After One Year: $ Withdrawal of Annuity: -$ Amount On Deposit After Withdrawal of Annuity: Second Year s Interest: Amount On Deposit After Two Years: $ Withdrawal of Annuity: -$ Amount On Deposit After Withdrawal of Annuity: 0 Net Present Value The problem when evaluating a project or investment is that you invest money today, and you get your payoff at some time in the future. As discussed above, we know that comparing a dollar today with a dollar to be received some time in the future is like comparing apples and oranges. Because the investment and the payoff occur at different times you merely cannot say, "I've invested $1,000 and received a payoff of more than $1,000 on that investment". It could be that when you factor in the time value of money (Present Values), you have received a payoff that is less than your original investment.
4 Chapter 14 Notes Page 4 With Net Present Value, you are attempting to compare apples and apples. You convert all of the future dollars of the payoff into present dollars and then compare them to the investment, which is already in present dollars. With Net Present Value you have to take the Present Value of all of the cash to be received from an investment, and subtract out the initial investment. If you have a positive number, then you know that you have received your initial investment along with your minimum required return. The discount (interest rate) is the minimum return that your firm requires on investments. Traditionally, the discount rate is the weighted average cost of capital of your firm. The thought is that you should not invest in a project or investment that will not provide a return at least equal to the cost of the funds that you are investing in that project or investment. A firm, however, is free to set any minimum return that it wishes. The weights used in this calculation are the percentages of the total capital of the firm coming from a particular source of capital (e.g., 20% of our capital comes from equity and 80% of our capital comes from debt). The cost of that capital (debt or equity) is the after-tax cost of that capital (e.g., interest is deductible while dividends are not). Remember that you are considering only After-Tax Cash Flows (not Net Income). Net Present Value is a Finance concept. Typically, the difference between Net Income and After-Tax Cash Flow is the deduction for depreciation and other non-cash expenses from Net Income. Think back to when you learned about the indirect method of preparing a Cash Flow Statement. Under that method, you would start with a firm s Net Income and then add back the depreciation expense (because depreciation expense does not require a current cash outlay in order to get the Cash Flow From Operations. The traditional assumption is that the infusion of funds into an investment or project is made on the first day of the investment or project, and that the payoffs (returns) are received at the end of each year (e.g., the first payoff is received on the last day of the first year). We will be making this assumption in the following discussion. This assumption is not always the case. For example, cash inflows into an investment or project may be made over a number of years, and payoffs can be received during a year or in the year following the year in which it was earned. Depreciation Depreciation is not a cash expense, and therefore is not directly included in the calculation of After-Tax Cash Flow. Depreciation is, however, an income tax deduction. Thus, depreciation is still included in the calculation of the firm s tax expense. The way that depreciation is calculated for financial statement purposes is different than the way that it is calculated for income tax purposes. While firms have many alternatives from which to choose when calculating its depreciation expense, they must follow the rules of the Modified Accelerated Cost Recovery System (MACRS) when preparing their income tax returns. For purposes of this class, we will assume depreciation for both income tax and financial reporting is the straight-line depreciation method, unless otherwise provided.
5 Chapter 14 Notes Page 5 When calculating After-Tax Cash Flow, most books first subtract cash expenses (without considering depreciation) from revenues to get the Before-Tax Cash Flow. They then multiply the Before-Tax Cash Flow by the tax rate to get a preliminary tax expense, which is subtracted from the Before-Tax Cash Flow in order to get a preliminary After-Tax Cash Flow. Because depreciation reduces a firm s tax bill, they then add back the reduction in taxes that the depreciation tax deduction produces (the "Depreciation Tax Shield"). The Depreciation Tax Shield is the tax rate multiplied by the amount of the depreciation tax deduction: A Revenue: $100,000 B Less: Cash Expenses: -40,000 C Before-Tax Cash Flow (A-B): $60,000 $60,000 D Multiplied by Tax Rate: X.4 E Preliminary Taxes (CxD): -$24,000 F Preliminary After-Tax Cash Flow (B-E): $36,000 G Depreciation Deduction: $10,000 H Multiplied by Tax Rate: X,4 I Depreciation Tax Shield (GxH): +$4,000 J After-Tax Cash Flow (F+I): $40,000 An alternate approach to calculating After-Tax Cash Flow, is to use Before-Tax Cash Flow, and then subtract the amount of taxes due (which includes the depreciation deduction in its calculation). A Revenue: $100,000 B Less: Cash Expenses: -40,000 C Before-Tax Cash Flow (A-B): $60,000 $60,000 D Depreciation Deduction: -10,000 E Taxable Income (C-D): $50,000 F Multiplied by Tax Rate: X.4 G Taxes (ExF): -$20,000 H After-Tax Cash Flow (C-G): $40,000 While most books use the Depreciation Tax Shield approach, the calculation of the income tax approach is easier to understand conceptually (and thus involves less memorization). Constant After-Tax Cash Flows When you are dealing with the same savings in each year, remember that you can use the Present Value of an Annuity formula.
6 Chapter 14 Notes Page 6 Salvage Value Remember that if you have a salvage value, then you have to treat it as a cash flow in the last year of the investment or project. If you have an income tax book value (e.g., basis ) that is different than the salvage value, then you will have to take into account the taxes due on the gain from the salvage sale of the asset in your analysis. NPV Example Troy, Inc. operates a theme park centered around the classical ancient world. Troy is considering opening a new attraction simulating a ride in the Trojan Horse. The new attraction would require an investment of $420,000, and would produce the following Before-Tax Cash Flow. Assume no salvage value, and assume that Troy pays taxes at a tax rate of 40%. Also assume that Troy requires a minimum return of 10% from its investments. Assume that depreciation is calculated using the straight-line method with no salvage value: Cash Flow Year 1 $ 100,000 Year 2 200,000 Year 3 250,000 Year 4 150,000 Year 5 100,000 Year 6 100,000 $ 900,000 Most books would calculate the After-Tax Cash Flow using the Depreciation Tax Shield We will assume that the depreciation deduction is $70,000 a year ($420,000/6): Cash Flow -Taxes (CF x.4) +Tax Shield After-Tax Cash Flow [.4(Tx]) Year 1 $ 100,000 - $40,000 + $28,000 88,000 Year 2 200,000 - $80, , ,000 Year 3 250, , , ,000 Year 4 150,000-60, , ,000 Year 5 100,000-40, ,000 88,000 Year 6 100,000-40, ,000 88,000 $ 900,000 $708,000
7 Chapter 14 Notes Page 7 The alternative approach would be to calculate the income tax bill, because taxes are a cash expense. Income for tax purposes include the cash received reduced by the cash expenses, but there is also a deduction for the depreciation. (A) (B) (C=A-B) (D=.4C) Bef-Tx Cash Depreciation Taxable Inc Tax Rate Taxes Year 1 $ 100,000 - $70,000 = $30,000 x.4= 12,000 Year 2 200,000 - $70,000 = 130,000 x.4= 52,000 Year 3 250,000 - $70,000 = 180,000 x.4= 72,000 Year 4 150,000 - $70,000 = 80,000 x.4= 32,000 Year 5 100,000 - $70,000 = 30,000 x.4= 12,000 Year 6 100,000 - $70,000 = 30,000 x.4= 12,000 $ 900,000 $420,000 $480,000 $192,000 Next, subtract the tax bill from the Before-Tax Cash Flow in order to get the After-Tax Cash Flow: (A) (D) (A-D) Before-Tax Cash Flow Less Taxes After-Tax Cash Year 1 $ 100,000 12,000 88,000 Year 2 200,000 52, ,000 Year 3 250,000 72, ,000 Year 4 150,000 32, ,000 Year 5 100,000 12,000 88,000 Year 6 100,000 12,000 88,000 $ 900,000 $708,000 As you can see, you get the same After-Tax Cash Flow with either approach. Now, you need to calculate the Present Value of the After-Tax Cash Flow: Artist s Rendering of Project After Tx Cash x PVIF PV of Cash Flow Year 1 88,000 x $ 80,000 Year 2 148,000 x ,315 Year 3 178,000 x ,733 Year 4 118,000 x ,595 Year 5 88,000 x ,641 Year 6 88,000 x ,673 $708,000 $520,957 Less Original Investment: -420,000 NPV: $100,957 If the NPV is greater than zero, then you know that you are getting at least your minimum required return. Unfortunately, you do not know the actual return that you are
8 Chapter 14 Notes Page 8 getting. It turns out that you are receiving an 18.1% return, but you have no way of knowing that from the NPV calculation. Internal Rate of Return Along with the Net Present Value, financiers also examine whether to make an investment by examining the Cash Payback Period and Internal Rate of Return. Internal Rate of Return represents a modification of the calculation of the Net Present Value that we have discussed above. With these modifications you assume that the Net Present Value is zero, and you solve for the discount (interest) rate. In other words, you are trying to find out the return that the investment produces. You need a computer or calculator to calculate the Internal Rate of Return efficiently. The Internal Rate of Return is very popular in the business world. Among academics, however, its use is discouraged because it has theoretical problems. One complaint is that IRR assumes that cash payoffs that are received are reinvested at the same rate as the IRR, which may not be reasonable for high IRRs. Another objection comes with cash flows from the investment that alternate from positive to negative. In your Finance classes you will be taught to use a modified IRR to counter these objections. On the other hand, NPV is not really used much in the business world. The problem with NPV is that it does not tell you the amount of the return that you are receiving. The NPV approach is, If you tell me what return you want to make, I will tell you if you made it. Using Excel to Calculate IRR and NPV There is a major problem using Excel in calculating NPV. Excel makes the following assumption about the investments and payoffs, which is described in the Excel Help notes: The initial cost [investment] occurs at the end of the first period. Excel also assumes that the first payoff is received at the end of the second year of the investment. These are not traditional assumptions. Excel explains that if you want to assume that the investment occurred on the first day of the investment, you have to add it separately. As the Excel Help notes state: If your first cash flow occurs at the beginning of the first period, the first value must be added to the NPV result, not included in the values arguments.
9 Chapter 14 Notes Page 9 NPV Using Excel s assumptions regarding the date of the investments and payoffs, you would calculate the NPV using Excel by setting up the Investment (a negative number) and the After-Tax Cash Flows as shown below: The Formula is =NPV(Required Rate of Return, Cells Containing Investment and After- Tax Cash Flow. A 10% Required Rate of Return would be written as.1 : If you cannot remember the NPV notation, then select Insert from the Menu Bar, and then select Function. NPV is the name of the function, and it is classified as a Financial function.
10 Chapter 14 Notes Page 10 As noted above, Excel assumes that the investment is made on the last day of the first year, and the first payoff is received on the last day of the second year. Because of this, the answer that Excel returns is not the same as the one that we just calculated. We assumed that the investment was made on the first day of the investment and the first payoff occurs at the end of the first year. Excel will tell you that the NPV is $91,780. It has moved the investment and the each cash flow payoff back one year. If you wish to assume that the investment is made on the first day of the investment, and that the first payoff is received on the last day of the first year, then you should use NPV function to value the payoff (not including the initial investment) and then subtract the initial investment. This is the approach suggested by Excel Help Notes: Rather than using this approach, you could counter the assumption that Excel is making. Excel is pushing everything back one year. If you add one year s interest to each number, then when Excel pushes it back one year, the end result will be the proper value. For example, Excel assumes that the investment is made one year from now, which gives it a present value of $381,818 ($420,000 x.90909). If you increase the $420,000 by one year s interest of 10%, you give increase the investment to $462,000 ($420,000 x 1.1). Now, when Excel pushes the investment back one year, it
11 Chapter 14 Notes Page 11 will give the investment a Present Value of $420,000 ($462,000 x.90909), which is the correct value. Using this approach, gives you the correct NPV: IRR You can calculate the IRR using Excel by setting up the problem the same as with NPV. This time you use the IRR function: =IRR(cells containing investment and cash flow, guess of the IRR). A guess of 10% would be written as.1. If an error appears, it means that your guess was not close, and you should try again.
12 Chapter 14 Notes Page 12 If you cannot remember the formula for IRR, you can select Insert on the Menu Bar. Then select Function. IRR is the name of the function, and it is classified as a financial function: Excel s assumption about the timing of the investment and payoffs does not affect the calculation of the IRR. Whether the investment and payoffs begin now or at end of this year, the return that the payoffs provide on the investment is the same. In other words the return on the investment over the life of the investment (IRR) is the same, whether you make the investment this year or anytime in the future: As you can see, failure to correct for Excel s assumption will provide you with the wrong NPV ($91,780.41), but still provides the correct IRR ( %). The investment and payoffs that are increased by the discount factor (10%) provide you with the correct NPV ($100,958) and IRR ( %) Payback Period A simple tool used to evaluate potential investments is the Payback Period. This method is also referred to as the Cash Payback Period. The Payback Period does not incorporate present value concepts. The Payback Period merely reflects the feeling that if you get your investment back quickly then there is little risk. For example, if you can
13 Chapter 14 Notes Page 13 refinance a loan at a lower interest rate by paying a loan fee of $1,000, and if your interest savings are $100 a month, then you will get your money back in 10 months. After that you will save $100 a month for a number of years. What is the downside to making the investment when you recoup your investment so quickly? So, with Payback Period, you merely state how long it takes to recoup your investment. Besides a rough approximation of risk, the Payback Period is also important to many managers because they are not interested in making investments that provides a longterm return. Such an investment will not help them get their bonus this year and it may be received after they have moved to their next job. If the After-Tax Cash Flow is the same every year, the calculation of the Payback Period is a simple matter: Payback Period = Original Investment Annual After-Tax Cash Flow For example, If the investment is $420,000 and it generates an After-Tax Cash Flow of $100,000 a year, then the Payback Period is 4.2 years: Payback Period = $420,000/$100,000 = 4.2 years If the After-Tax Cash Flow is uneven, then you have to figure it out by examining the cumulative cash received over the life of the investment. Payback Period Example New Attraction We will calculate the Payback Period for the Trojan Horse attraction. You can see that after three years, Troy has not yet recouped its investment, but after the fourth year, Troy has received more than its initial investment. At the beginning of the fourth year, Troy still needs $6,000 to recoup its investment in the Trojan Horse attraction: After-Tax Cash Flow Cumulative After-Tax Cash Flow Cash Flow Needed to Recoup Inv. Year 1 88,000 $ 88,000 $332,000 Year 2 148, , ,000 Year 3 178, ,000 6,000 Year 4 118, ,000 Year 5 88,000 Year 6 88,000 $708,000
14 Chapter 14 Notes Page 14 Troy will receive $118,000 over the entire fourth year, but it only needs part of that year s cash flow in order to recoup its investment, which is calculated: Portion of Year Needed To Recoup Troy s Investment = Cash Needed $6,000_ = Total 4 th Year Cash $118,000 = Troy needs approximately.05 of the fourth year to recoup its investment. The Payback Period is 3.05 years. Simple Rate of Return The Simple Rate of Return is an accounting concept, so it uses Net Income (not After- Tax Cash Flow). This return is also known as the Accounting Rate of Return. There is a different Simple Rate of Return for each year of the investment, but this formula averages them all together, which is why it is also known as the Average Accounting Rate of Return. The definition is: Simple Rate of Return = Average Annual Net Income Original Investment Simple Rate of Return Example We will now calculate the Simple Rate of Return of the investment in the Trojan Horse attraction. We must first calculate the Average Net Income: Yr. (A) (B) (C=A-B) BeforeTax Income (D=.4C) Taxes (40%) (E=C-D) Net Income Cash Flow Deprec. 1 $ 100,000 - $70,000 = $30,000-12,000 = 18, ,000 - $70,000 = 130,000-52,000 = 78, ,000 - $70,000 = 180,000-72,000 = 108, ,000 - $70,000 = 80,000-32,000 = 48, ,000 - $70,000 = 30,000-12,000 = 18, ,000 - $70,000 = 30,000-12,000 = 18,000 $ 900,000 $420,000 $480,000 $192,000 $288,000 Average Annual Net Income = $288,000 / 6 Average Annual Net Income = $48,000 Accounting Rate of Return = Average Net Income / Original Investment Accounting Rate of Return = $48,000/$420,000 Accounting Rate of Return = 11.4%
15 Chapter 14 Notes Page 15 Theme Park Visitors Enjoying New Attraction
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Chapter 20 Lease Financing ANSWERS TO END-OF-CHAPTER QUESTIONS 20-1 a. The lessee is the party leasing the property. The party receiving the payments from the lease (that is, the owner of the property)
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CAPITAL BUDGETING Net Present Value and Other Investment Criteria Net Present Value (NPV) Net present value is the difference between an investment s market value (in today s dollars) and its cost (also
PAPER P9 Management Accounting Financial Strategy The Examiner provides a short study guide, for all candidates revising for this paper, to some first principles of finance and financial management Based
Before you start: Time Value of Money Problems on a Texas Instruments TI-83 1 To calculate problems on a TI-83, you have to go into the applications menu, the blue APPS key on the calculator. Several applications
EXAM 2 OVERVIEW Binay Adhikari FEDERAL RESERVE & MARKET ACTIVITY (BS38) Definition 4.1 Discount Rate The discount rate is the periodic percentage return subtracted from the future cash flow for computing
Chapter 10 The Basics of Capital Budgeting: Evaluating Cash Flows 1 Topics Overview and vocabulary Methods NPV IRR, MIRR Profitability Index Payback, discounted payback Unequal lives Economic life 2 What
CHAPTER 8 INTEREST RATES AND BOND VALUATION Solutions to Questions and Problems 1. The price of a pure discount (zero coupon) bond is the present value of the par value. Remember, even though there are
Understanding Financial Management: A Practical Guide Guideline Answers to the Concept Check Questions Chapter 8 Capital Budgeting Concept Check 8.1 1. What is the difference between independent and mutually
Part 7. Capital Budgeting What is Capital Budgeting? Nancy Garcia and Digital Solutions Digital Solutions, a software development house, is considering a number of new projects, including a joint venture
CHAPTER 12 RISK, COST OF CAPITAL, AND CAPITAL BUDGETING Answers to Concepts Review and Critical Thinking Questions 1. No. The cost of capital depends on the risk of the project, not the source of the money.
Chapter 6 1. Your firm is considering two investment projects with the following patterns of expected future net aftertax cash flows: Year Project A Project B 1 $1 million $5 million 2 2 million 4 million
6 Investment Decisions BASIC CONCEPTS AND FORMULAE 1. Capital Budgeting Capital budgeting is the process of evaluating and selecting long-term investments that are in line with the goal of investor s wealth
Chapter 2 - Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in
The Cost of Capital, and a Note on Capitalization Prepared by Kerry Krutilla 8all rights reserved Introduction Often in class we have presented a diagram like this: Table 1 B B1 B2 B3 C -Co This kind of
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CHAPTER 6 NET PRESENT VALUE AND OTHER INVESTMENT CRITERIA Answers to Concepts Review and Critical Thinking Questions 1. Assuming conventional cash flows, a payback period less than the project s life means
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount
Loan Comparison With this program, the user can compare two loan alternatives or evaluate the potential refinancing of an existing loan. Fast Tools & Resources Loans may differ in their interest rates,
Chapter 5 Capital Budgeting Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Fixed-Income securities. Common stocks. Real assets (capital budgeting). Part C Determination
Chapter 10: Making Capital Investment Decisions Faculty of Business Administration Lakehead University Spring 2003 May 21, 2003 Outline 10.1 Project Cash Flows: A First Look 10.2 Incremental Cash Flows
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Learning Objectives 1-1 Capital Budgeting Cash Flows 1 Corporate Financial Management 3e Emery Finnerty Stowe 1-2 Calculate incremental after-tax cash flows for a capital budgeting project. Explain the
Multiple Choice Questions 1. The financial statement summarizing the value of a firm's equity on a particular date is the: a. income statement. B. balance sheet. c. statement of cash flows. d. cash flow
Chapter 02 How to Calculate Present Values Multiple Choice Questions 1. The present value of $100 expected in two years from today at a discount rate of 6% is: A. $116.64 B. $108.00 C. $100.00 D. $89.00
Chapter 18 Web Extension: Percentage Cost Analysis, Leasing Feedback, and Leveraged Leases Percentage Cost Analysis Anderson s lease-versus-purchase decision from Chapter 18 could also be analyzed using
Cash Flow, Taxes, and Project Evaluation Of the four steps in calculating NPV, the most difficult is the first: Forecasting cash flows. We now focus on this problem, with special attention to What is cash
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C H A P T E R6 The Time Value of Money When plumbers or carpenters tackle a job, they begin by opening their toolboxes, which hold a variety of specialized tools to help them perform their jobs. The financial