Hospitality management accounting phần 9 pdf

CAPITAL BUDGETING AND THE INVESTMENT DECISION INTRODUCTION CHAPTER 12 This chapter begins by discussing some of the problems associated with capital asset decisions, such as the long life of the assets, the initial high cost, and the unknown future costs and benefits. Two fairly simple methods of measuring proposed investments—the accounting rate of return and the payback period—are then illustrated and explained. The concept of the time value of money is then discussed, and discounted cash flow is illustrated in conjunction with time value. Discounted cash flow is then used in conjunction with two other investment measurement methods: net present value and internal rate of return. Net present value and internal rate of return are then contrasted, and capital investment control is discussed. The chapter concludes by demonstrating how discounted cash flow can be used to help make leasing versus buying decisions. CHAPTER OBJECTIVES After studying this chapter, the reader should be able to 1 Discuss the ways in which long-term asset management differs from day- to-day budgeting. 2 Explain how the accounting rate of return is calculated, use the equation, and explain the major disadvantage of this method. 4259_Jagels_12.qxd 4/14/03 11:10 AM Page 491 3 Give the equation for the payback period, use the equation, and state the pros and cons of this method. 4 Discuss the concept of the time value of money and explain the term discounted cash flows. 5 Use discounted cash flow tables in conjunction with the net present value method to make investment decisions. 6 Use discounted cash flow tables in conjunction with the internal rate of return method to make investment decisions. 7 Contrast the net present value and internal rate of return methods and explain how they can give conflicting rankings of investment proposals. 8 Solve problems relating to the purchase versus the leasing of fixed assets. THE INVESTMENT DECISION This chapter concerns methods of evaluating which long-term asset to se- lect. This is frequently referred to as capital budgeting. We are not so much concerned with the budgeting process as we are with the decision about whether to make a specific investment, or which of two or more investments would be best. The largest investment that a hotel or food service business has to make is in its land and buildings, which is an infrequent investment decision for each separate property. This chapter is primarily about more frequent investment decisions, for items such as equipment, furniture purchases, and replacements. In- vestment decision making, or capital budgeting, differs from day-to-day decision making and ongoing budgeting for a number of reasons. Some of these will be discussed. LONG LIFE OF ASSETS Capital investment decisions concern assets that have a relatively long life. Day- to-day decisions concerning current assets are decisions about items (such as inventories) that are turning over frequently. A wrong decision about the purchase of a food item does not have a long-term effect. But a wrong decision about a piece of equipment (a long-term asset) can involve a time span stretch- ing over many years. This long life of a capital asset creates another problem— that of estimating the life span of an asset to determine how far into the future the benefits of its purchase are going to be spread. Life span can be affected by both physical wear and tear on the equipment and by obsolescence—invention of a newer, better, and possibly more profitable piece of equipment. 492 CHAPTER 12 CAPITAL BUDGETING AND THE INVESTMENT DECISION 4259_Jagels_12.qxd 4/14/03 11:10 AM Page 492 COSTS OF ASSETS Day-to-day purchasing decisions do not usually involve large amounts of money for any individual purchase. But the purchase of a capital asset or assets normally requires the outlay of large sums of money, and one has to be sure that the initial investment outlay can be recovered over time by the net income gen- erated by the investment. FUTURE COSTS AND BENEFITS As will be demonstrated, analysis techniques to aid in investment decision making involve future costs and benefits. On one hand, the future is always uncer- tain; on the other hand, if we make a decision based solely on historic costs and net income, we may be no better off, since they might not be representative of future costs and net income. For example, one factor considered is the recovery (scrap) value of the asset at the end of its economic life. If two comparable items of equipment were being evaluated and the only difference from all points of view was that one was estimated to have a higher scrap value than the other at the end of their equal economic lives, the decision would probably be made in favor of the item with the highest future trade-in value. However, because of technological change, that decision could eventually be the wrong one in five or more years. TOOLS TO GUIDE INVESTMENT DECISIONS These, then, are some of the hazards of making decisions about capital investments. The hazards can seldom be eliminated, but there are techniques available that will allow the manager to reduce some of the guesswork. Although a variety of techniques are available, only four will be discussed in this chapter: 1. Accounting rate of return 2. Payback period 3. Net present value 4. Internal rate of return To set the scene for the accounting rate of return and the payback period methods, consider a restaurant that is using an inefficient dishwasher. The part- time wages of the employee who runs the dishwasher are $4,000 a year. The restaurant is investigating the value of installing a new dishwasher that will elim- inate the need for the part-time employee, since the servers can operate the machine. Two machines are being considered, and we have information about them, as shown in Exhibit 12.1. TOOLS TO GUIDE INVESTMENT DECISIONS 493 4259_Jagels_12.qxd 4/14/03 11:10 AM Page 493 ACCOUNTING RATE OF RETURN The accounting rate of return (ARR) is sometimes called the average rate of return. It compares the average annual net income (after taxes) resulting from the investment with the average investment. The formula for the ARR is Using the information from Exhibit 12.1, the ARR for each machine is Machine A ؍؍5 ᎏ ᎏ 1 ᎏ ᎏ . ᎏ ᎏ 3 ᎏ ᎏ % ᎏ ᎏ Machine B ؍؍5 ᎏ ᎏ 1 ᎏ ᎏ . ᎏ ᎏ 4 ᎏ ᎏ % ᎏ ᎏ Note that average investment is the initial investment plus the trade-in value divided by 2. The average investment is (Initial investment ؉ Trade-in value) ᎏᎏᎏᎏᎏ 2 $1,260 ᎏ $2,450 $1,260 ᎏᎏᎏ [($4,700 ؉ $200) / 2] $1,540 ᎏ $3,000 $1,540 ᎏᎏᎏ [($5,000 ؉ $1,000) / 2] Net annual saving ᎏᎏᎏ Average investment 494 CHAPTER 12 CAPITAL BUDGETING AND THE INVESTMENT DECISION Machine A Machine B Cash cost, including Installation $5,000 $4,700 Economic life 5 years 5 years Trade in (residual) value $1,000 $200 Depreciation ϭ $800 per year ϭ $900 per year Saving, wages of cashier $ ᎏ ᎏ 4 ᎏ ᎏ , ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 4 ᎏ ᎏ , ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ Expenses Maintenance $ 350 $ 300 Supplies 650 1,000 Depreciation ᎏᎏ ᎏ 8 ᎏ 0 ᎏ 0 ᎏᎏᎏ ᎏ 9 ᎏ 0 ᎏ 0 ᎏ Total expenses $ ᎏ ᎏ 1 ᎏ ᎏ , ᎏ ᎏ 8 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 2 ᎏ ᎏ , ᎏ ᎏ 2 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ Net saving (before income tax) $2,200 $1,800 Tax (30%) ( ᎏ ᎏ ᎏ 6 ᎏ 6 ᎏ 0 ᎏ )( ᎏ ᎏ ᎏ 5 ᎏ 4 ᎏ 0 ᎏ ) Net Annual Saving $ ᎏ ᎏ 1 ᎏ ᎏ , ᎏ ᎏ 5 ᎏ ᎏ 4 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 1 ᎏ ᎏ , ᎏ ᎏ 2 ᎏ ᎏ 6 ᎏ ᎏ 0 ᎏ ᎏ $4,700 Ϫ $200 ᎏᎏ 5 $5,000 Ϫ $1,000 ᎏᎏ 5 EXHIBIT 12.1 Data Concerning Two Alternative Machines 4259_Jagels_12.qxd 4/14/03 11:10 AM Page 494 In the example given, the assumption was made that net annual saving is the same for each of the five years. In reality, this might not always be the case. For example, there might be expenses in year 0001 (or in any of the other years) that are nonrecurring—for example, training costs or a major overhaul. Alter- natively, the amount of an expense might change over the period—for example, depreciation computed using double-declining balance. To take care of this, we project total savings and total costs for each year for the entire period under re- view. We add up the annual net savings to give us the net saving figure for the entire period. This net saving figure for the entire period can then be divided by the number of years of the project to give an average annual net savings figure to be used in the equation. Let us illustrate this for Machine A only. Savings and expenses are as in Exhibit 12.1, except that in year 0003 there will be a special overhaul cost of $1,000, and the double-declining balance method of depreciation (rather than straight line) will be used. Since the asset has a five-year life, the depreciation rate is 40 percent. Exhibit 12.2 shows the results. Total net saving over the five-year period will be the sum of the individual years’ savings. This amounts to $7,000. The average annual net saving will be $7,000 divided by 5 equals $1,400. ARR ؍؍4 ᎏ ᎏ 6 ᎏ ᎏ . ᎏ ᎏ 7 ᎏ ᎏ % ᎏ ᎏ The same approach should be carried out for Machine B, and then a com- parison can be made. Note that in Exhibit 12.2 the change in the method of $1,400 ᎏ $3,000 TOOLS TO GUIDE INVESTMENT DECISIONS 495 Machine A Year 1 Year 2 Year 3 Year 4 Year 5 Wage saving $ ᎏ ᎏ 4 ᎏ ᎏ , ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 4 ᎏ ᎏ , ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 4 ᎏ ᎏ , ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 4 ᎏ ᎏ , ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 4 ᎏ ᎏ , ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ Maintenance 350 350 350 350 350 Supplies 650 650 650 650 650 Depreciation 2,000 1,200 720 80 0 Overall ᎏᎏ ᎏ ᎏᎏᎏ ᎏᎏ ᎏ ᎏᎏᎏ ᎏ 1 ᎏ , ᎏ 0 ᎏ 0 ᎏ 0 ᎏᎏᎏ ᎏ ᎏᎏᎏ ᎏᎏ ᎏ ᎏᎏᎏ Total expenses $ ᎏ ᎏ 3 ᎏ ᎏ , ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 2 ᎏ ᎏ , ᎏ ᎏ 2 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 2 ᎏ ᎏ , ᎏ ᎏ 7 ᎏ ᎏ 2 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 1 ᎏ ᎏ , ᎏ ᎏ 0 ᎏ ᎏ 8 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 1 ᎏ ᎏ , ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ Net saving (before income tax) $1,000 $1,800 $1,280 $2,920 $3,000 Income tax ( ᎏᎏ ᎏ 3 ᎏ 0 ᎏ 0 ᎏ )( ᎏ ᎏ ᎏ 5 ᎏ 4 ᎏ 0 ᎏ )( ᎏᎏ ᎏ 3 ᎏ 8 ᎏ 4 ᎏ )( ᎏᎏ ᎏ 8 ᎏ 7 ᎏ 6 ᎏ )( ᎏ ᎏ ᎏ 9 ᎏ 0 ᎏ 0 ᎏ ) Net Saving $ ᎏ ᎏ ᎏ ᎏ ᎏ ᎏ 7 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 1 ᎏ ᎏ , ᎏ ᎏ 2 ᎏ ᎏ 6 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ ᎏ ᎏ ᎏ ᎏ 8 ᎏ ᎏ 9 ᎏ ᎏ 6 ᎏ ᎏ $ ᎏ ᎏ 2 ᎏ ᎏ , ᎏ ᎏ 0 ᎏ ᎏ 4 ᎏ ᎏ 4 ᎏ ᎏ $ ᎏ ᎏ 2 ᎏ ᎏ , ᎏ ᎏ 1 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ EXHIBIT 12.2 Net Savings for Machine A after Special Overhaul and Double-Declining Balance Depreciation 4259_Jagels_12.qxd 4/14/03 11:10 AM Page 495 depreciation, by itself, did not affect the change in the ARR since average depreciation is still $800 per year, and average tax and average net saving are the same. In this particular case, the only factor that caused our ARR to decrease from 51.3 percent to 46.7 percent for Machine A was the $1,000 overhaul expense. The advantage of the accounting rate of return method is its simplicity. It is used to compare the anticipated return from a proposal with a minimum desired return. If the proposal’s return is less than desired, it is rejected. If the proposal’s ARR is greater than the desired rate of return, a more in-depth analysis using other investment techniques might then be used. The major disadvantage of the accounting rate of return method is that it is based on net income or net savings rather than on cash flow. PAYBACK PERIOD The payback period method overcomes the cash flow shortcoming of the accounting rate of return method. The payback method compares the initial investment with the annual cash inflows: Payback period (years) ؍ Since Exhibit 12.1 only gives us net annual saving and not net annual cash saving, we must first convert the figures to a cash basis. This is accomplished by adding back the depreciation (an expense that does not require an outlay of cash). Machine A Machine B Net annual saving $1,540 $1,260 Add depreciation ᎏᎏ ᎏ 8 ᎏ 0 ᎏ 0 ᎏᎏᎏ ᎏ 9 ᎏ 0 ᎏ 0 ᎏ Net annual cash saving $ ᎏ ᎏ 2 ᎏ ᎏ , ᎏ ᎏ 3 ᎏ ᎏ 4 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 2 ᎏ ᎏ , ᎏ ᎏ 1 ᎏ ᎏ 6 ᎏ ᎏ 0 ᎏ ᎏ Therefore, our payback period for each machine is Machine A Machine B ᎏ $ $ 5 2 , , 0 3 0 4 0 0 ᎏ ϭ 2 ᎏ ᎏ . ᎏ ᎏ 1 ᎏ ᎏ 4 ᎏ ᎏ years ᎏ $ $ 4 2 , , 7 1 0 6 0 0 ᎏ ϭ 2 ᎏ ᎏ . ᎏ ᎏ 1 ᎏ ᎏ 8 ᎏ ᎏ years Despite its higher initial cost, Machine A recovers its initial investment in a slightly shorter period than does Machine B. This confirms the results of the accounting rate of return calculation made earlier. The payback method only Initial investment ᎏᎏᎏ Net annual cash saving 496 CHAPTER 12 CAPITAL BUDGETING AND THE INVESTMENT DECISION 4259_Jagels_12.qxd 4/14/03 11:10 AM Page 496 considers the cash flows until the cost of the asset has been recovered. Since the ARR calculation takes into account all of the benefit flows from an investment and not just those during the payback period, the ARR method could be considered more realistic. However, the payback method considers cash flows while the ARR method only considers net savings. Note that in this illustration, straight-line depreciation was used and it was assumed the net annual cash saving figure was the same for each year. This might not be the case in reality. For example, the use of an accelerated method of depreciation (such as double declining balance) will increase the depreciation expense in the early years. This, in turn, will reduce income taxes and increase cash flow in those years, making the calculation of the payback period a little more difficult. To illustrate, consider an initial $6,000 investment and the following annual cash flows resulting from that investment: Year 1 $2,500 Year 2 1,800 Year 3 1,400 Year 4 900 Year 5 700 By the end of year three, $5,700 ($2,500 ϩ $1,800 ϩ $1,400) will have been recovered, with the remaining $300 to be recovered in year four. This remaining amount will be recovered in one-third of a year 4 ($300 divided by $900). Total payback time will, therefore, be 3.33 years. The payback period analysis method, although simple, does not really mea- sure the merits of investments, but only the speed with which the investment might be recovered. It has a use in evaluating a number of proposals so that only those that fall within a predetermined payback period will be considered for fur- ther evaluation using other investment techniques. However, both the payback period and the ARR methods still suffer from a common fault: They ignore the time value of cash flows, or the concept that money now is worth more than the same amount of money at some time in the future. This concept will be discussed in the next section, after which we will explore the use of the net present value and internal rate of return methods. DISCOUNTED CASH FLOW The concept of discounted cash flow can probably best be understood by look- ing first at an example of compound interest. Exhibit 12.3 shows, year by year, what happens to $200 invested at a 10 percent compound interest rate; at the end of four years, the investment would be worth $292.82. TOOLS TO GUIDE INVESTMENT DECISIONS 497 4259_Jagels_12.qxd 4/14/03 11:10 AM Page 497 Although a calculation can be made for any amount, any interest rate, and for any number of years into the future with this formula, it is much easier to use a table of discount factors. Exhibit 12.4 illustrates such a table. If we go to the number (called a factor) that is opposite year 4 and under the 10 percent column, we will see that it is 0.6830. This factor tells us that $1.00 received at the end of Year 4 is worth only $1.00 ϫ $0.683, or $0.683 right now. In fact, this factor tells us that any 498 CHAPTER 12 CAPITAL BUDGETING AND THE INVESTMENT DECISION Discounting is simply the reverse of compounding interest. In other words, at a 10 percent interest rate, what is $292.82 four years from now worth to me today? The solution could be worked out manually using the following equation: P ϭ F ϫ where P ϭ present value F ϭ future amount I ϭ interest rate used as a decimal n ϭ number of years ahead for the future amount For example, using the already illustrated figures, we have P ϭ $292.82 ϫ ϭ $292.82 ϫ ᎏ 1.4 1 641 ᎏ ϭ $292.82 ϫ 0.683 ϭ $ ᎏ ᎏ 2 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ 1 ᎏᎏ (1 ϩ 0.10) 4 1 ᎏ (1 ϩ i) n Jan. 1 Dec. 31 Dec. 31 Dec. 31 Dec. 31 0001 0001 0002 0003 0004 Balance forward $200.00 $200.00 $220.00 $242.00 $266.20 Interest 10% ᎏᎏ 2 ᎏ 0 ᎏ . ᎏ 0 ᎏ 0 ᎏᎏᎏ 2 ᎏ 2 ᎏ . ᎏ 0 ᎏ 0 ᎏᎏᎏ 2 ᎏ 4 ᎏ . ᎏ 2 ᎏ 0 ᎏᎏᎏ 2 ᎏ 6 ᎏ . ᎏ 6 ᎏ 2 ᎏ Investment value, end of year $ ᎏ ᎏ 2 ᎏ ᎏ 2 ᎏ ᎏ 0 ᎏ ᎏ . ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 2 ᎏ ᎏ 4 ᎏ ᎏ 2 ᎏ ᎏ . ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 2 ᎏ ᎏ 6 ᎏ ᎏ 6 ᎏ ᎏ . ᎏ ᎏ 2 ᎏ ᎏ 0 ᎏ ᎏ $ ᎏ ᎏ 2 ᎏ ᎏ 9 ᎏ ᎏ 2 ᎏ ᎏ . ᎏ ᎏ 8 ᎏ ᎏ 2 ᎏ ᎏ EXHIBIT 12.3 Compound Interest, $200 @ 10% 4259_Jagels_12.qxd 4/14/03 11:10 AM Page 498 Period 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 25% 30% 1 0.9524 0.9434 0.9546 0.9259 0.9174 0.9091 0.9009 0.8929 0.8850 0.8772 0.8696 0.8621 0.8547 0.8475 0.8403 0.8333 0.8000 0.7692 2 0.9070 0.8900 0.8734 0.8573 0.8417 0.8264 0.8116 0.7972 0.7831 0.7695 0.7561 0.7432 0.7305 0.7182 0.7062 0.6944 0.6400 0.5917 3 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 0.7312 0.7118 0.6951 0.6750 0.6575 0.6407 0.6244 0.6086 0.5934 0.5787 0.5120 0.4552 4 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830 0.6587 0.6355 0.6133 0.5921 0.5718 0.5523 0.5337 0.5158 0.4987 0.4823 0.4096 0.3501 5 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209 0.5935 0.5674 0.5428 0.5194 0.4972 0.4761 0.4561 0.4371 0.4191 0.4019 0.3277 0.2693 6 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645 0.5346 0.5066 0.4803 0.4556 0.4323 0.4104 0.3898 0.3704 0.3521 0.3349 0.2621 0.2072 7 0.7107 0.6651 0.6228 0.5835 0.5470 0.5132 0.4817 0.4524 0.4251 0.3996 0.3759 0.3538 0.3332 0.3139 0.2959 0.2791 0.2097 0.1594 8 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 0.4339 0.4039 0.3762 0.3506 0.3269 0.3050 0.2848 0.2660 0.2487 0.2326 0.1678 0.1226 9 0.6446 0.5919 0.5439 0.5003 0.4604 0.4241 0.3909 0.3606 0.3329 0.3075 0.2843 0.2630 0.2434 0.2255 0.2090 0.1938 0.1342 0.0943 10 0.6139 0.5584 0.5084 0.4632 0.4224 0.3855 0.3522 0.3220 0.2946 0.2697 0.2472 0.2267 0.2080 0.1911 0.1756 0.1615 0.1074 0.0725 11 0.5847 0.5298 0.4751 0.4289 0.3875 0.3505 0.3173 0.2875 0.2607 0.2366 0.2149 0.1954 0.1778 0.1619 0.1476 0.1346 0.0859 0.0558 12 0.5568 0.4970 0.4440 0.3971 0.3555 0.3186 0.2858 0.2567 0.2307 0.2076 0.1869 0.1685 0.1520 0.1372 0.1240 0.1122 0.0687 0.0429 13 0.5303 0.4688 0.4150 0.3677 0.3262 0.2897 0.2575 0.2292 0.2042 0.1821 0.1625 0.1452 0.1299 0.1163 0.1042 0.0935 0.0550 0.0330 14 0.5051 0.4423 0.3878 0.3405 0.2993 0.2633 0.2320 0.2046 0.1807 0.1597 0.1413 0.1252 0.1110 0.0986 0.0876 0.0779 0.0440 0.0254 15 0.4810 0.4173 0.3625 0.3152 0.2745 0.2394 0.2090 0.1827 0.1599 0.1401 0.1229 0.1079 0.0949 0.0835 0.0736 0.0649 0.0352 0.0195 16 0.4581 0.3937 0.3387 0.2919 0.2519 0.2176 0.1883 0.1631 0.1415 0.1229 0.1069 0.0930 0.0811 0.0708 0.0618 0.0541 0.0281 0.0150 17 0.4363 0.3714 0.3166 0.2703 0.2311 0.1978 0.1696 0.1456 0.1252 0.1078 0.0929 0.0802 0.0693 0.0600 0.0520 0.0451 0.0225 0.0116 18 0.4155 0.3503 0.2959 0.2503 0.2120 0.1799 0.1528 0.1300 0.1108 0.0946 0.0808 0.0691 0.0592 0.0508 0.0437 0.0376 0.0180 0.0089 19 0.3957 0.3305 0.2765 0.2317 0.1945 0.1635 0.1377 0.1161 0.0981 0.0829 0.0703 0.0596 0.0506 0.0431 0.0367 0.0313 0.0144 0.0068 20 0.3769 0.3118 0.2584 0.2146 0.1784 0.1486 0.1240 0.1037 0.0868 0.0728 0.0611 0.0514 0.0433 0.0365 0.0308 0.0261 0.0115 0.0053 EXHIBIT 12.4 Table of Discontinued Cash Flows 4259_Jagels_12.qxd 4/14/03 11:10 AM Page 499 amount of money at the end of four years from now at a 10 percent interest (discount) rate is worth only 68.3 percent of that amount right now. Let us prove this by taking our $292.84 amount at the end of year 0004 from Exhibit 12.3 and discounting it back to the present: $292.82 ؋ 0.683 ؍ $ ᎏ ᎏ 2 ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ . ᎏ ᎏ 0 ᎏ ᎏ 0 ᎏ ᎏ We know $200 is the right answer because it is the amount we started with in our illustration of compounding interest in Exhibit 12.3. To illustrate with another example, assume we have a piece of equipment that a supplier suggests will probably have a trade-in value of $1,200 five years from now. At a 12 percent interest rate, what is the present value of $1,200? $1,200 ؋ 0.5674 ؍ $ ᎏ ᎏ 6 ᎏ ᎏ 8 ᎏ ᎏ 0 ᎏ ᎏ . ᎏ ᎏ 8 ᎏ ᎏ 8 ᎏ ᎏ The factor (multiplier) of 0.5674 was obtained from Exhibit 12.4 on the year-5 line under the 12 percent column. The factors in Exhibit 12.4 are based on the assumption that the money is all received in a lump sum on the last day of the year. This is not normally the case in reality, since outflows of cash for expenses (e.g., wages, supplies, and maintenance) occur continuously or peri- odically throughout its life and not just at the end of each year. Although continuous discounting is feasible, for most practical purposes the year-end assumption, using the factors from Exhibit 12.4, will give us solutions that are ac- ceptable for decision making. For a series of annual cash flows, one simply applies the related annual discount factor for that year to the cash inflow for that year. For example, a cash inflow of $1,000 a year for each of three years using a 10 percent factor will give us the following total discounted cash flow: Year Factor Amount Total 1 0.9091 $1,000 $ 909.10 2 0.8264 1,000 826.40 3 0.7513 1,000 ᎏᎏ ᎏ 7 ᎏ 5 ᎏ 1 ᎏ . ᎏ 3 ᎏ 0 ᎏ $ ᎏ ᎏ 2 ᎏ ᎏ , ᎏ ᎏ 4 ᎏ ᎏ 8 ᎏ ᎏ 6 ᎏ ᎏ . ᎏ ᎏ 8 ᎏ ᎏ 0 ᎏ ᎏ In this illustration, the cash flows are the same each year. Alternatively, in the case of equal annual cash flows, one can total the individual discount factors (in our case, this would be 0.9091 ϩ 0.8264 ϩ 0.7513 ϭ 2.4868) and mul- tiply this total by the annual cash flow: 2.4868 ؋ $1,000 ؍ $ ᎏ ᎏ 2 ᎏ ᎏ , ᎏ ᎏ 4 ᎏ ᎏ 8 ᎏ ᎏ 6 ᎏ ᎏ . ᎏ ᎏ 8 ᎏ ᎏ 0 ᎏ ᎏ Special tables have been developed from which one can directly read the combined discount factor to be used in the case of equal annual cash flows, but 500 CHAPTER 12 CAPITAL BUDGETING AND THE INVESTMENT DECISION 4259_Jagels_12.qxd 4/14/03 11:10 AM Page 500 [...]... 0 .92 59 0.8573 0. 793 8 0.7350 0.6806 Present Value ϭ ϭ ϭ ϭ ϭ $21 ,99 0 19, 2 89 16,868 14,700 ( 8,508) ᎏᎏᎏᎏᎏᎏᎏ $64,3 39 ᎏᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏᎏ Annual Cash Outflow Discount Factor 8% $15,000 ϫ 15,000 ϫ 15,000 ϫ 15,000 ϫ 15,000 ϫ Total present value 0 .92 59 0.8573 0. 793 8 0.7350 0.6806 EXHIBIT 12.13 Total Present Values Converted from Exhibits 12.11 and 12.12 Present Value ϭ ϭ ϭ ϭ ϭ $13,888 12,860 11 ,90 7 11,025 10,2 09. .. Flow Discount Factor 10% $ 3,000 3,000 3,000 10,000 0 .90 91 0.8264 0.7513 0.6830 Annual Cash Flow Discount Factor 25% $ 3,000 3,000 3,000 10,000 0.8000 0.6400 0.5120 0.4 096 Initial cost Alternative B Present Value $ 2,727 2,4 79 2,254 6,830 ᎏᎏᎏᎏᎏᎏᎏ $14, 290 ( 10,000) ᎏᎏᎏᎏᎏᎏᎏ $ 4, 290 ᎏᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏᎏ Present Value $ 2,400 1 ,92 0 1,536 4, 096 ᎏᎏᎏᎏᎏᎏᎏ $ 9, 952 ᎏᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏᎏ $10,000 ᎏᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏᎏ Annual Cash... Discount Factor 10% $7,000 4,000 3,000 3,000 0 .90 91 0.8264 0.7513 0.6830 Annual Cash Flow Discount Factor 31% $7,000 4,000 3,000 3,000 0.7634 0.5827 0.4448 0.3 396 Present Value $ 6,364 3,306 2,254 2,0 49 ᎏᎏᎏᎏᎏᎏᎏ $13 ,97 3 ( 10,000) ᎏᎏᎏᎏᎏᎏᎏ $ 3 ,97 3 ᎏᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏᎏ Present Value $ 5,344 2,331 1,334 1,0 19 ᎏᎏᎏᎏᎏᎏᎏ $10,028 ᎏᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏᎏ $10,000 ᎏᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏᎏ EXHIBIT 12 .9 Two Investment Alternatives and Their... equipment and furniture Total present value Annual Cash Flow ؋ Discount Factor 7% ‫؍‬ Present Value $18,000 20,000 22,000 25,000 30,000 ϫ ϫ ϫ ϫ ϫ 0 .93 46 0.8734 0.8163 0.76 29 0.7130 ϭ ϭ ϭ ϭ ϭ $16,823 17,468 17 ,95 9 19, 073 21, 390 10,000 ϫ 0.7130 ϭ 7,130 ᎏᎏᎏᎏᎏᎏᎏ $99 ,843 ᎏᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏᎏ EXHIBIT 12.8 Discount Factor Arrived at by Trial and Error 505 506 CHAPTER 12 CAPITAL BUDGETING AND THE INVESTMENT DECISION... present value Machine B ‫ ؍‬Present Value ϭ $ 1 ,95 5 ϭ 3,801 ϭ 3,062 ϭ 3,142 ϭ 3,477 ᎏᎏᎏᎏᎏᎏᎏ $15,437 ( 10,000) ᎏᎏᎏᎏᎏᎏᎏ $ 5,437 ᎏᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏᎏ Net Cash Flow $2,267 4,367 4,017 4,367 4,567 ؋ Discount Factor ‫ ؍‬Present Value ϫ ϫ ϫ ϫ ϫ ϭ $ 2,061 ϭ 3,6 09 ϭ 3,018 ϭ 2 ,98 3 ϭ 2,836 ᎏᎏᎏᎏᎏᎏᎏ $14,507 ( 9, 400) ᎏᎏᎏᎏᎏᎏᎏ $ 5,107 ᎏᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏᎏ 0 .90 91 0.8264 0.7513 0.6830 0.62 09 EXHIBIT 12.6 Conversion of Annual Cash Flows... ᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏ $8,000 ᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏ $8,000 ᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏ $8,000 ᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏ $3,500 90 0 $ 90 0 $ 90 0 $ 90 0 1,300 1,800 ᎏᎏᎏᎏᎏᎏ $7,500 ᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏ $ 500 ( 150) ᎏᎏᎏᎏᎏᎏ $ 350 1,800 ᎏᎏᎏᎏᎏᎏ 1,300 1,800 ᎏᎏᎏᎏᎏᎏ $4,000 ᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏ $4,000 ( 1,200) ᎏᎏᎏᎏᎏᎏ $2,800 1,800 ᎏᎏᎏᎏᎏᎏ $ 90 0 750 1,300 1,800 ᎏᎏᎏᎏᎏᎏ $4,750 ᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏ $3,250 ( 97 5) ᎏᎏᎏᎏᎏᎏ $2,275 1,800 ᎏᎏᎏᎏᎏᎏ 1,300 1,800 ᎏᎏᎏᎏᎏᎏ $4,000 ᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏ $4,000... (%) Demand 1 2 3 4 5 898 97 0 1,048 1,132 1,223 108 108 108 108 108 97 0 1,048 1,132 1,223 1,321 In year 1 the current average nightly demand for rooms figure of 898 (calculated in step 1) is multiplied by the composite growth rate figure of 108 percent (100% ϩ 8% composite growth rate figure calculated in step 2) to arrive at the future demand figure of 97 0 rooms in the year 1 The 97 0 figure is carried... each machine is calculated as follows: Machine A Initial cost Residual (trade-in, scrap) value Depreciation, straight line Machine B $10,000 ( 1,000) ᎏᎏᎏᎏᎏᎏᎏ $ 9, 000 ᎏᎏᎏᎏᎏᎏᎏ $9, 400 ( 200) ᎏᎏᎏᎏᎏᎏ $9, 200 ᎏᎏᎏᎏᎏᎏ $9, 000 ᎏᎏ ϭ $1,800 per yr ᎏᎏᎏᎏᎏᎏ 5 $9, 200 ᎏᎏ ϭ $1,840 per yr ᎏᎏᎏᎏᎏᎏ 5 The trade-in, or scrap, value is a partial recovery of our initial investment and is, therefore, added in as a positive cash... Average Nightly Demand 224 81 2 09 1 19 2 65 ᎏᎏᎏ 898 ᎏᎏᎏ For each hotel, the number of rooms has been multiplied by that hotel’s average occupancy percentage to arrive at average nightly demand We use these figures to calculate the total average nightly demand of 898 rooms The average annual occupancy of the most competitive hotels is then calculated using the following equation: 898 Average nightly demand... ᎏᎏᎏᎏᎏᎏ $8,000 ᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏ $3,000 850 $ 850 $ 850 $ 850 1,700 1,840 ᎏᎏᎏᎏᎏᎏ $7, 390 ᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏ $ 610 ( 183) ᎏᎏᎏᎏᎏᎏ $ 427 1,840 ᎏᎏᎏᎏᎏᎏ 1,700 1,840 ᎏᎏᎏᎏᎏᎏ $4, 390 ᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏ $3,610 ( 1,083) ᎏᎏᎏᎏᎏᎏ $2,527 1,840 ᎏᎏᎏᎏᎏᎏ $ 850 500 1,700 1,840 ᎏᎏᎏᎏᎏᎏ $4, 890 ᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏ $3,110 ( 93 3) ᎏᎏᎏᎏᎏᎏ $2,177 1,840 ᎏᎏᎏᎏᎏᎏ 1,700 1,840 ᎏᎏᎏᎏᎏᎏ $4, 390 ᎏᎏᎏᎏᎏᎏ ᎏᎏᎏᎏᎏᎏ $3,610 ( 1,083) ᎏᎏᎏᎏᎏᎏ $2,527 1,840 ᎏᎏᎏᎏᎏᎏ $2,267 ᎏᎏᎏᎏᎏᎏ . 30% 1 0 .95 24 0 .94 34 0 .95 46 0 .92 59 0 .91 74 0 .90 91 0 .90 09 0. 892 9 0.8850 0.8772 0.8 696 0.8621 0.8547 0.8475 0.8403 0.8333 0.8000 0.7 692 2 0 .90 70 0. 890 0 0.8734 0.8573 0.8417 0.8264 0.8116 0. 797 2 0.7831. 0. 399 6 0.37 59 0.3538 0.3332 0.31 39 0. 295 9 0.2 791 0.2 097 0.1 594 8 0.6768 0.6274 0.5820 0.5403 0.50 19 0.4665 0.43 39 0.40 39 0.3762 0.3506 0.32 69 0.3050 0.2848 0.2660 0.2487 0.2326 0.1678 0.1226 9. 0. 299 3 0.2633 0.2320 0.2046 0.1807 0.1 597 0.1413 0.1252 0.1110 0. 098 6 0.0876 0.07 79 0.0440 0.0254 15 0.4810 0.4173 0.3625 0.3152 0.2745 0.2 394 0.2 090 0.1827 0.1 599 0.1401 0.12 29 0.10 79 0. 094 9

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