Many decisions in operations management involve large

SUPPLEMENT Financial Analysis J LEARNING GOALS After reading this supplement, you should be able to: 1. Explain the time value of money concept. 2. Demonstrate the use of the net present value, internal rate of return, and payback methods of financial analysis. 3. Discuss the importance of combining managerial judgment with quantitative techniques when making investment decisions. Many decisions in operations management involve large capital investments. Automation, vertical integration, capacity expansion, layout revisions, and installing a new ERP system are but some examples. In fact, most of a firm s assets are tied up in the operations function. Therefore, the operations manager should seek high-yield capital projects and then assess their costs, benefits, and risks. Such projects require strong cross-functional coordination, particularly with finance and accounting. The projects must fit in with the organization s financial plans and capabilities. If a firm plans to open a new production facility in 2010, it must begin lining up financing in 2006. The projects must also be subjected to one or more types of financial analysis to assess their attractiveness relative to other investment opportunities. This supplement presents a brief overview of basic financial analyses and the types of computer support available for making such decisions. See your finance textbook for a more comprehensive treatment of the subject. J.1

J.2 SUPPLEMENT J > FINANCIAL ANALYSIS < time value of money The concept that a dollar in hand can be invested to earn a return, so that more than one dollar will be available in the future. compounding interest The process by which interest on an investment accumulates, and then earns interest itself for the remainder of the investment period. future value of an investment The value of an investment at the end of the period over which interest is compounded. present value of an investment The amount that must be invested now to accumulate to a certain amount in the future at a specific interest rate. discounting The process of finding the present value of an investment, when the future value and the interest rate are known. discount rate The interest rate used in discounting the future value to its present value. > TIME VALUE OF MONEY < An important concept underlying many financial analysis techniques is that a dollar in hand today is worth more than a dollar to be received in the future. A dollar in hand can be invested to earn a return, so that more than one dollar will be available in the future. This concept is known as the time value of money. FUTURE VALUE OF AN INVESTMENT If $5,000 is invested at 10 percent interest for one year, at the end of the year the $5,000 will have earned $500 in interest and the total amount available will be $5,500. If the interest earned is allowed to accumulate, it also earns interest and the original investment will grow to $12,970 in 10 years. The process by which interest on an investment accumulates, and then earns interest itself for the remainder of the investment period, is known as compounding interest. The value of an investment at the end of the period over which interest is compounded is called the future value of an investment. To calculate the future value of an investment, you first express the interest rate and the time period in the same units of time as the interval at which compounding occurs. Let us assume that interest is compounded annually, express all time periods in years, and use annual interest rates. To find the value of an investment one year in the future, multiply the amount invested by the sum of 1 plus the interest rate (expressed as a decimal). The value of a $5,000 investment at 12 percent per year one year from now is $5,000(1.12) = $5,600 If the entire amount remains invested, at the end of two years you would have In general, $5,600(1.12) = $5,000(1.12) 2 = $6,272 F = P(1 + r) n where F = future value of the investment at the end of n periods P = amount invested at the beginning, called the principal r = periodic interest rate n = number of time periods for which the interest compounds PRESENT VALUE OF A FUTURE AMOUNT Let us look at the converse problem. Suppose that you want to make an investment now that will be worth $10,000 in one year. If the interest rate is 12 percent and P represents the amount invested now, the relation becomes Solving for P gives F = $10,000 = P(1 + 0.12) F P = ( 1+ ) r n The amount that must be invested now to accumulate to a certain amount in the future at a specific interest rate is called the present value of an investment. The process of finding the present value of an investment, when the future value and the interest rate are known, is called discounting the future value to its present value. If the number of time periods n for which discounting is desired is greater than 1, the present value is determined by dividing the future value by the nth power of the sum of 1 plus the interest rate. The general formula for determining the present value is F P = ( 1+ ) The interest rate is also called the discount rate. 10, 000 = = $ 8, 929 1 ( 1+ 0. 12) r n

> TECHNIQUES OF ANALYSIS < J.3 PRESENT VALUE FACTORS Although you can calculate P from its formula in a few steps with most pocket calculators, you also can use a table. To do so, write the present value formula another way: Let [1/(1 + r) n ] be the present value factor, which is called pf and which you can find in Table J.1. This table gives you the present value of a future amount of $1 for various time periods and interest rates. To use the table, locate the column for the appropriate interest rate and the row for the appropriate period. The number in the body of the table where this row and column intersect is the pf value. Multiply it by F to get P. For example, suppose that an investment will generate $15,000 in 10 years. If the interest rate is 12 percent, Table J.1 shows that pf = 0.3220. Multiplying it by $15,000 gives the present value, or P = F(pf) = $15,000(0.3220) = $4,830 ANNUITIES An annuity is a series of payments of a fixed amount for a specified number of years. All such payments are treated as happening at the end of a year. Suppose that you want to invest an amount at an interest rate of 10 percent so that you may draw out $5,000 per year for each of the next four years. You could determine the present value of this $5,000 four-year annuity by treating the four payments as single future payments. The present value of an investment needed now, in order for you to receive these payments for the next four years, is the sum of the present values of each of the four payments. That is, A much easier way to calculate this amount is to use Table J.2. Look for the factor in the table at the intersection of the 10 percent column and the fourth-period row. It is 3.1699. For annuities, this present value factor is called af, to distinguish it from the present value factor for a single payment. To determine the present value of an annuity, multiply its amount by af, to get P = A(af) = $5,000(3.1699) = $15,849 where P = present value of an investment A = amount of the annuity received each year af = present value factor for an annuity > TECHNIQUES OF ANALYSIS < You can now apply these concepts to the financial analysis of proposed investments. Three basic financial analysis techniques are 1. the net present value method 2. the internal rate of return method 3. the payback method F 1 P = = F n n ( 1+ r) ( 1+ r) $ 5, 000 $ 5, 000 $ 5, 000 $ 5, 000 P = + + + 1 + 0. 10 ( 1 + 2 0. 10) ( 1 + 0. 10) ( 1 + 0. 10) = $ 4, 545+ $ 4, 132+ $ 3, 757+ $ 3, 415 = $ 15, 849 3 4 These methods work with cash flows. Cash flow is the cash that will flow into and out of the organization because of the project, including revenues, costs, and changes in assets and liabilities. Be sure to remember two points when determining cash flows for any project: 1. Consider only the amounts of cash flows that will change if the project is undertaken. These amounts are called incremental cash flows and are the difference between the cash flows with the project and without it. TUTOR J.1 annuity A series of payments on a fixed amount for a specified number of years. TUTOR J.2 cash flow The cash that will flow into and out of the organization because of the project, including revenues, costs, and changes in assets and liabilities.

TABLE J.1 Present Value Factors for a Single Payment Interest Rate (r) Number of Periods (n) 0.01 0.02 0.03 0.04 0.05 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9259 0.9091 0.8929 0.8772 0.8621 0.8475 0.8333 0.8197 0.8065 0.7937 0.7812 0.7692 2 0.9803 0.9612 0.9426 0.9246 0.9070 0.8900 0.8573 0.8264 0.7972 0.7695 0.7432 0.7182 0.6944 0.6719 0.6504 0.6299 0.6104 0.5917 3 0.9706 0.9423 0.9151 0.8890 0.8638 0.8396 0.7938 0.7513 0.7118 0.6750 0.6407 0.6086 0.5787 0.5507 0.5245 0.4999 0.4768 0.4552 4 0.9610 0.9238 0.8885 0.8548 0.8227 0.7921 0.7350 0.6830 0.6355 0.5921 0.5523 0.5158 0.4823 0.4514 0.4230 0.3968 0.3725 0.3501 5 0.9515 0.9057 0.8626 0.8219 0.7835 0.7473 0.6806 0.6209 0.5674 0.5194 0.4761 0.4371 0.4019 0.3700 0.3411 0.3149 0.2910 0.2693 6 0.9420 0.8880 0.8375 0.7903 0.7462 0.7050 0.6302 0.5645 0.5066 0.4556 0.4104 0.3704 0.3349 0.3033 0.2751 0.2499 0.2274 0.2072 7 0.9327 0.8706 0.8131 0.7599 0.7107 0.6651 0.5835 0.5132 0.4523 0.3996 0.3538 0.3139 0.2791 0.2486 0.2218 0.1983 0.1776 0.1594 8 0.9235 0.8535 0.7894 0.7307 0.6768 0.6274 0.5403 0.4665 0.4039 0.3506 0.3050 0.2660 0.2326 0.2038 0.1789 0.1574 0.1388 0.1226 9 0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5002 0.4241 0.3606 0.3075 0.2630 0.2255 0.1938 0.1670 0.1443 0.1249 0.1084 0.0943 10 0.9053 0.8203 0.7441 0.6756 0.6139 0.5584 0.4632 0.3855 0.3220 0.2697 0.2267 0.1911 0.1615 0.1369 0.1164 0.0922 0.0847 0.0725 11 0.8963 0.8043 0.7224 0.6496 0.5847 0.5268 0.4289 0.3505 0.2875 0.2366 0.1954 0.1619 0.1346 0.1122 0.0938 0.0787 0.0662 0.0558 12 0.8874 0.7885 0.7014 0.6246 0.5568 0.4970 0.3971 0.3186 0.2567 0.2076 0.1685 0.1372 0.1122 0.0920 0.0757 0.0625 0.0517 0.0429 13 0.8787 0.7730 0.6810 0.6006 0.5303 0.4688 0.3677 0.2897 0.2292 0.1821 0.1452 0.1163 0.0935 0.0754 0.0610 0.0496 0.0404 0.0330 14 0.8700 0.7579 0.6611 0.5775 0.5051 0.4423 0.3405 0.2633 0.2046 0.1597 0.1252 0.0985 0.0779 0.0618 0.0492 0.0393 0.0316 0.0254 15 0.8613 0.7430 0.6419 0.5553 0.4810 0.4173 0.3152 0.2394 0.1827 0.1401 0.1079 0.0835 0.0649 0.0507 0.0397 0.0312 0.0247 0.0195 16 0.8528 0.7284 0.6232 0.5339 0.4581 0.3936 0.2919 0.2176 0.1631 0.1229 0.0930 0.0708 0.0541 0.0415 0.0320 0.0248 0.0193 0.0150 17 0.8444 0.7142 0.6050 0.5134 0.4363 0.3714 0.2703 0.1978 0.1456 0.1078 0.0802 0.0600 0.0451 0.0340 0.0258 0.0197 0.0150 0.0116 18 0.8360 0.7002 0.5874 0.4936 0.4155 0.3503 0.2502 0.1799 0.1300 0.0946 0.0691 0.0508 0.0376 0.0279 0.0208 0.0156 0.0118 0.0089 19 0.8277 0.6864 0.5703 0.4746 0.3957 0.3305 0.2317 0.1635 0.1161 0.0829 0.0596 0.0431 0.0313 0.0229 0.0168 0.0124 0.0092 0.0068 20 0.8195 0.6730 0.5537 0.4564 0.3769 0.3118 0.2145 0.1486 0.1037 0.0728 0.0514 0.0365 0.0261 0.0187 0.0135 0.0098 0.0072 0.0053 21 0.8114 0.6598 0.5375 0.4388 0.3589 0.2942 0.1987 0.1351 0.0926 0.0638 0.0443 0.0309 0.0217 0.0154 0.0109 0.0078 0.0056 0.0040 22 0.8034 0.6468 0.5219 0.4220 0.3418 0.2775 0.1839 0.1228 0.0826 0.0560 0.0382 0.0262 0.0181 0.0126 0.0088 0.0062 0.0044 0.0031 23 0.7954 0.6342 0.5067 0.4057 0.3256 0.2618 0.1703 0.1117 0.0738 0.0491 0.0329 0.0222 0.0151 0.0103 0.0071 0.0049 0.0034 0.0024 24 0.7876 0.6217 0.4919 0.3901 0.3101 0.2470 0.1577 0.1015 0.0659 0.0431 0.0284 0.0188 0.0126 0.0085 0.0057 0.0039 0.0027 0.0018 25 0.7798 0.6095 0.4776 0.3751 0.2953 0.2330 0.1460 0.0923 0.0588 0.0378 0.0245 0.0160 0.0105 0.0069 0.0046 0.0031 0.0021 0.0014 26 0.7720 0.5976 0.4637 0.3607 0.2812 0.2198 0.1352 0.0839 0.0525 0.0331 0.0211 0.0135 0.0087 0.0057 0.0037 0.0025 0.0016 0.0011 27 0.7644 0.5859 0.4502 0.3468 0.2678 0.2074 0.1252 0.0763 0.0469 0.0291 0.0182 0.0115 0.0073 0.0047 0.0030 0.0019 0.0013 0.0008 28 0.7568 0.5744 0.4371 0.3335 0.2551 0.1956 0.1159 0.0693 0.0419 0.0255 0.0157 0.0097 0.0061 0.0038 0.0024 0.0015 0.0010 0.0006 29 0.7493 0.5631 0.4243 0.3207 0.2429 0.1846 0.1073 0.0630 0.0374 0.0224 0.0135 0.0082 0.0051 0.0031 0.0020 0.0012 0.0008 0.0005 30 0.7419 0.5521 0.4120 0.3083 0.2314 0.1741 0.0994 0.0573 0.0334 0.0196 0.0116 0.0070 0.0042 0.0026 0.0016 0.0010 0.0006 0.0004 35 0.7059 0.5000 0.3554 0.2534 0.1813 0.1301 0.0676 0.0356 0.0189 0.0102 0.0055 0.0030 0.0017 0.0009 0.0005 0.0003 0.0002 0.0001 40 0.6717 0.4529 0.3066 0.2083 0.1420 0.0972 0.0460 0.0221 0.0107 0.0053 0.0026 0.0013 0.0007 0.0004 0.0002 0.0001 0.0001 0.0000 P F = = + n ( 1 r ) F ( pf ) where P = present value of a single investment F = future value of a single payment n = number of periods for which P is to be invested r = periodic interest rate pf = present value factor for $1 = 1/(1 + r) n J.4

TABLE J.2 Present Value Factors of an Annuity Interest Rate (r) Number of Periods (n) 0.01 0.02 0.03 0.04 0.05 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 0.30 1 0.9901 0.9804 0.9709 0.9615 0.9524 0.9434 0.9259 0.9091 0.8929 0.8772 0.8621 0.8475 0.8333 0.8197 0.8065 0.7937 0.7812 0.7692 2 1.9704 1.9416 1.9135 1.8861 1.8594 1.8334 1.7833 1.7355 1.6901 1.6467 1.6052 1.5656 1.5278 1.4915 1.4568 1.4235 1.3916 1.3609 3 2.9410 2.8839 2.8286 2.7751 2.7232 2.6730 2.5771 2.4869 2.4018 2.3216 2.2459 2.1743 2.1065 2.0422 1.9813 1.9234 1.8684 1.8161 4 3.9020 3.8077 3.7171 3.6299 3.5460 3.4651 3.3121 3.1699 3.0373 2.9137 2.7982 2.6901 2.5887 2.4936 2.4043 2.3202 2.2410 2.1662 5 4.8534 4.7135 4.5797 4.4518 4.3295 4.2124 3.9927 3.7908 3.6048 3.4331 3.2743 3.1272 2.9906 2.8636 2.7454 2.6351 2.5320 2.4356 6 5.7955 5.6014 5.4172 5.2421 5.0757 4.9173 4.6229 4.3553 4.1114 3.8887 3.6847 3.4976 3.3255 3.1669 3.0205 2.8850 2.7594 2.6427 7 6.7282 6.4720 6.2303 6.0021 5.7864 5.5824 5.2064 4.8684 4.5638 4.2883 4.0386 3.8115 3.6046 3.4155 3.2423 3.0833 2.9370 2.8021 8 7.6517 7.3255 7.0197 6.7327 6.4632 6.2098 5.7466 5.3349 4.9676 4.6389 4.3436 4.0776 3.8372 3.6193 3.4212 3.2407 3.0758 2.9247 9 8.5660 8.1622 7.7861 7.4353 7.1078 6.8017 6.2469 5.7590 5.3282 4.9464 4.6065 4.3030 4.0310 3.7863 3.5655 3.3657 3.1842 3.0190 10 9.4713 8.9826 8.5302 8.1109 7.7217 7.3601 6.7101 6.1446 5.6502 5.2161 4.8332 4.4941 4.1925 3.9232 3.6819 3.4648 3.2689 3.0915 11 10.3676 9.7868 9.2526 8.7605 8.3064 7.8869 7.1390 6.4951 5.9377 5.4527 5.0286 4.6560 4.3271 4.0354 3.7757 3.5435 3.3351 3.1473 12 11.2551 10.5753 9.9540 9.3851 8.8633 8.3838 7.5361 6.8137 6.1944 5.6603 5.1971 4.7932 4.4392 4.1274 3.8514 3.6059 3.3868 3.1903 13 12.1337 11.3484 10.6350 9.9856 9.3936 8.8527 7.9038 7.1034 6.4235 5.8424 5.3423 4.9095 4.5327 4.2028 3.9124 3.6555 3.4272 3.2233 14 13.0034 12.1062 11.2961 10.5631 9.8986 9.2950 8.2442 7.3667 6.6282 6.0021 5.4675 5.0081 4.6106 4.2646 3.9616 3.6949 3.4587 3.2487 15 13.8651 12.8493 11.9379 11.1184 10.3797 9.7122 8.5595 7.6061 6.8109 6.1422 5.5755 5.0916 4.6755 4.3152 4.0013 3.7261 3.4834 3.2682 16 14.7179 13.5777 12.5611 11.65423 10.8378 10.1059 8.8514 7.8237 6.9740 6.2651 5.6685 5.1624 4.7296 4.3567 4.0333 3.7509 3.5026 3.2832 17 15.5623 14.2919 13.1661 12.1657 11.2741 10.4773 9.1216 8.0216 7.1196 6.3729 5.7487 5.2223 4.7746 4.3908 4.0591 3.7705 3.5177 3.2948 18 16.3983 14.9920 13.7535 12.6593 11.6896 10.8276 9.3719 8.2014 7.2497 6.4674 5.8178 5.2732 4.8122 4.4187 4.0799 3.7861 3.5294 3.3037 19 17.2260 15.6785 14.3238 13.1339 12.0853 11.1581 9.6036 8.3649 7.3658 6.5504 5.8775 5.3162 4.8435 4.4415 4.0967 3.7985 3.5386 3.3105 20 18.0456 16.3514 14.8775 13.5903 12.4622 11.4699 9.8181 8.5136 7.4694 6.6231 5.9288 5.3527 4.8696 4.4603 4.1103 3.8083 3.5458 3.3158 21 18.8570 17.0112 15.4150 14.0292 12.8212 11.7641 10.0168 8.6487 7.5620 6.6870 5.9731 5.3837 4.8913 4.4756 4.1212 3.8161 3.5514 3.3198 22 19.6604 17.6580 15.9369 14.4511 13.1630 12.0416 10.2007 8.7715 7.6446 6.7429 6.0113 5.4099 4.9094 4.4882 4.1300 3.8223 3.5558 3.3230 23 20.4558 18.2922 16.4436 14.8568 13.4886 12.3034 10.3711 8.8832 7.7184 6.7921 6.0442 5.4321 4.9245 4.4985 4.1371 3.8273 3.5592 3.3254 24 21.2434 18.9139 16.9355 15.2470 13.7986 12.5504 10.5288 8.9847 7.7843 6.8351 6.0726 5.4509 4.9371 4.5070 4.1428 3.8312 3.5619 3.3272 25 22.0232 19.5235 17.4131 15.6221 14.0939 12.7834 10.6748 9.0770 7.8431 6.8729 6.0971 5.4669 4.9476 4.5139 4.1474 3.8342 3.5640 3.3286 26 22.7952 20.1210 17.8768 15.9828 14.3752 13.0032 10.8100 9.1609 7.8957 6.9061 6.1182 5.4804 4.9563 4.5196 4.1511 3.8367 3.5656 3.3297 27 23.5596 20.7069 18.3270 16.3296 14.6430 13.2105 10.9352 9.2372 7.9426 6.9352 6.1364 5.4919 4.9636 4.5243 4.1542 3.8387 3.5669 3.3305 28 24.3164 21.2813 18.7641 19.6631 14.8981 13.4062 11.0511 9.3066 7.9844 6.9607 6.1520 5.5016 4.9697 4.5281 4.1566 3.8402 3.5679 3.3312 29 25.0658 21.8444 19.1885 16.9837 15.1411 13.5907 11.1584 9.3696 8.0218 6.9830 6.1656 5.5098 4.9747 4.5312 4.1585 3.8414 3.5687 3.3317 30 25.8077 22.3965 19.6004 17.2920 15.3725 13.7648 11.2578 9.4269 8.0552 7.0027 6.1772 5.5168 4.9789 4.5338 4.1601 3.8424 3.5693 3.3321 35 29.4086 24.9986 21.4872 18.6646 16.3742 14.4982 11.6546 9.6442 8.1755 7.0700 6.2153 5.5386 4.9915 4.5411 4.1644 3.8450 3.5708 3.3330 40 32.8347 27.3555 23.1148 19.7929 17.1591 15.0463 11.9246 9.7791 8.2438 7.1050 6.2335 5.5482 4.9966 4.5439 4.1659 3.8458 3.5712 3.3332 P = A A A + + + = A ( 1 + r ) + 2 n ( 1 r ) ( 1 + r ) 1/( 1+ r) = A( af ) = 1 n where P = present value of a single investment A = amount of annuity to be received at the end of each period n = number of periods for which the annuity is received r = periodic interest rate af = annuity factor for an annuity of $ 1= 1/( 1+ r ) j n = 1 j j j J.5

J.6 SUPPLEMENT J > FINANCIAL ANALYSIS < 2. Convert cash flows to after-tax amounts before applying the net present value, payback, or internal rate of return method to them. This step introduces taxes and depreciation into the calculations. DEPRECIATION AND TAXES straight-line method The simplest method of calculating annual depreciation; found by subtracting the estimated salvage value from the amount of investment required at the beginning of the project, and then dividing by the asset s expected economic life. salvage value The cash flow from the sale or disposal of plant and equipment at the end of a project s life. TUTOR J.3 Modified Accelerated Cost Recovery System (MACRS) The only acceptable depreciation method for tax purposes that shortens the lives of investments, giving firms larger early tax deductions. Depreciation is an allowance for the consumption of capital. In this type of analysis, depreciation is relevant for only one reason: It acts as a tax shield. Depreciation is not a legitimate cash flow because it is not cash that is actually paid out each year. However, depreciation does affect how an accountant calculates net income, against which the income-tax rate is applied. Therefore, depreciation enters into the calculation, as a tax shield, only when tax liability is figured. Taxes must be paid on pretax cash inflows minus the depreciation that is associated with the proposed investment. United States tax laws allow either straight-line or accelerated depreciation. Straight-Line Depreciation The straight-line method of calculating annual depreciation is the simplest and usually is adequate for internal planning purposes. First, subtract the estimated salvage value from the amount of investment required at the beginning of the project and then divide by the number of years in the asset s expected economic life. Salvage value is the cash flow from the sale or disposal of plant and equipment at the end of a project s life. 1 The general expression for annual depreciation is where D = annual depreciation I = amount of the investment S = salvage value n = number of years of project life D = I S n Accelerated Depreciation If the tax shields come earlier, they are worth more. Tax laws allow just that, with what is called accelerated depreciation. Since 1986, the only acceptable accelerated depreciation method is the Modified Accelerated Cost Recovery System (MACRS). MACRS shortens the lives of investments, giving firms larger tax deductions. It creates six classes of investments, each of which has a recovery period or class life. Depreciation for each year is calculated by multiplying the asset s cost by the fixed percentage in Table J.3. 2 The following are examples of the first four classes. 3-year class: specially designed tools and equipment used in research 5-year class: autos, copiers, and computers 7-year class: most industrial equipment and office furniture 10-year class: some longer-life equipment Table J.3 does not show the 27.5- and 31.5-year classes, which are reserved for real estate. MACRS depreciation calculations ignore salvage value and the actual expected economic life. If there is salvage value after the asset has been fully depreciated, it is treated as taxable income. Taxes The income-tax rate varies from one state or country to another. Calculation of the tax total should include all relevant federal, state, and local income taxes. When doing a financial analysis, you may want to use an average income-tax rate based on the firm s tax rate over the past several years, or you may want to base the tax rate on the highest tax 1 Disposal of property often results in an accounting gain or loss that can increase or decrease income tax and affect cash flows. These tax effects should be considered in determining the actual cash inflow or outflow from disposal of property. 2 The table can be confusing because it allows a depreciation deduction for one more year than would seem appropriate for a given class. The reason is that MACRS assumes that assets are in service for only 6 months of the first year and 6 months of the last year. An asset in the second class still has a 5-year life, but it spans 6 calendar years.

> TECHNIQUES OF ANALYSIS < J.7 TABLE J.3 MACRS Depreciation Allowances Class of Investment Year 3-Year 5-Year 7-Year 10-Year 1 33.33 20.00 14.29 10.00 2 44.45 32.00 24.49 18.00 3 14.81 19.20 17.49 14.40 4 7.41 11.52 12.49 11.52 5 11.52 8.93 9.22 6 5.76 8.93 7.37 7 8.93 6.55 8 4.45 6.55 9 6.55 10 6.55 11 3.29 100.0% 100.0% 100.0% 100.0% bracket that applies to the taxpaying unit. The one thing you should never do is ignore taxes in making a financial analysis. ANALYSIS OF CASH FLOWS You now are ready to determine the after-tax cash flow for each year of the project s life. Use the following four steps to calculate the flow year by year. 1. Subtract the new expenses attributed to the project from new revenues. If revenues are unaffected, begin with the project s cost savings. 2. Next subtract the depreciation (D), to get pretax income. 3. Subtract taxes, which constitute the pretax income multiplied by the tax rate. The difference is called the net operating income (NOI). 4. Compute the total after-tax cash flow as NOI + D, adding back the depreciation that was deducted temporarily to compute the tax. Calculating After-Tax Cash Flows EXAMPLE J.1 A local restaurant is considering adding a salad bar. The investment required to remodel the dining area and add the salad bar will be $16,000. Other information about the project is as follows. 1. The price and variable cost per salad are $3.50 and $2.00, respectively. 2. Annual demand should be about 11,000 salads. 3. Fixed costs, other than depreciation, will be $8,000, which cover the energy to operate the refrigerated unit and wages for another part-time employee to stock the salad bar during peak business hours. 4. The assets go into the MACRS 5-year class for depreciation purposes, with no salvage value. 5. The tax rate is 40 percent. 6. Management wants to earn a return of at least 14 percent on the project. Determine the after-tax cash flows for the life of this project.

J.8 SUPPLEMENT J > FINANCIAL ANALYSIS < SOLUTION The cash flow projections are shown in the following table. Depreciation is based on Table J.3. For example, depreciation in 2009 is $3,200 (or $16,000 0.20). The cash flow in 2014 comes from depreciation s tax shield in the first half of the year. Year Item 2008 2009 2010 2011 2012 2013 2014 Initial Information Annual demand (salads) 11,000 11,000 11,000 11,000 11,000 Investment $16,000 Interest (discount) rate 0.14 Cash Flows Revenue $38,500 $38,500 $38,500 $38,500 $38,500 Expenses: Variable costs 22,000 22,000 22,000 22,000 22,000 Expenses: Fixed costs 8,000 8,000 8,000 8,000 8,000 Depreciation (D) 3,200 5,120 3,072 1,843 1,843 922 Pretax income $ 5,300 $ 3,380 $ 5,428 $ 6,657 $ 6,657 $922 Taxes (40%) 2,120 1,352 2,171 2,663 2,663 369 Net operating Income (NOI) $ 3,180 $ 2,208 $ 3,257 $ 3,994 $ 3,994 $553 Total cash flow (NOI + D) $ 6,380 $ 7,148 $ 6,329 $ 5,837 $ 5,837 $ 369 net present value (NPV) method The method that evaluates an investment by calculating the present values of all after-tax total cash flows and then subtracting the initial investment amount for their total. hurdle rate The interest rate that is the lowest desired return on an investment; the hurdle over which the investment must pass. internal rate of return (IRR) The discount rate that makes the NPV of a project zero. payback method A method for evaluating projects that determines how much time will elapse before the total of after-tax flows will equal, or pay back, the initial investment. NET PRESENT VALUE METHOD The net present value (NPV) method is used to evaluate an investment by calculating the present values of all after-tax total cash flows and then subtracting the original investment amount (which is already a present value) from their total. The difference is the project s net present value. If it is positive for the discount rate used, the investment earns a rate of return higher than the discount rate. If the net present value is negative, the investment earns a rate of return lower than the discount rate. Most firms set the discount rate equal to the overall weighted average cost of capital, which becomes the lowest desired return on investment. If a negative net present value results, the project is not approved. The discount rate that represents the lowest desired return on investment is thought of as a hurdle over which the investment must pass and is often referred to as the hurdle rate. INTERNAL RATE OF RETURN METHOD A related technique involves calculating the internal rate of return (IRR), which is the discount rate that makes the NPV of a project zero. It is internal because it depends only on the cash flows of the investment, not on rates offered elsewhere. With this method, a project is acceptable only if the IRR exceeds the hurdle rate. The IRR is a single number that summarizes the merits of the investment. It can be used to rank multiple projects from best to worst, so it is particularly useful when the budget limits new investments in any year. You can find the IRR by trial and error. Start with a low discount rate and calculate the NPV. If it exceeds 0, increase the discount rate and try again. The NPV will eventually go to 0 and later to a negative value. When the NPV is near 0, you have found the IRR. PAYBACK METHOD The other commonly used method of evaluating projects is the payback method, which determines how much time will elapse before the total of after-tax cash flows will equal, or pay back, the initial investment.

> TECHNIQUES OF ANALYSIS < J.9 Even though it is scorned by many academics, the payback method continues to be widely used, particularly at lower management levels. It can be quickly and easily applied and gives decision makers some idea of how long recovery of invested funds will take. Uncertainty surrounds every investment project. The costs and revenues on which analyses are based are best estimates, not actual values. An investment project with a quick payback is not considered as risky as one with a long payback. The payback method also has drawbacks. A major criticism is that it encourages managers to focus on the short run. A project that takes a long time to develop but generates excellent cash flows later in its life usually is rejected under the payback method. The payback method also has been criticized for its failure to consider the time value of money. For these reasons, we recommend that payback analysis be combined with a more sophisticated method such as NPV or IRR in analyzing the financial implications of a project. Calculating NPV, IRR, and Payback Period EXAMPLE J.2 What are the NPV, IRR, and payback period for the salad bar project in Example J.1? SOLUTION Management wants to earn a return of at least 14 percent on its investment, so we use that rate to find the pf values in Table J.1. The present value of each year s total cash flow and the NPV of the project are as follows. TUTOR J.4 2009: $6,380(0.8772) = $5,597 2010: $7,148(0.7695) = $5,500 2011: $6,329(0.6750) = $4,272 2012: $5,837(0.5921) = $3,456 2013: $5,837(0.5194) = $3,032 2014: $ 369(0.4556) = $ 168 NPV of project = ($5,597 + $5,500 + $4,272 + $3,456 + $3,032 + $168) $16,000 = $6,024 Because the NPV is positive, the recommendation would be to approve the project. To find the IRR, let us begin with the 14 percent discount rate, which produced a positive NPV. Incrementing at 4 percent with each step, we reach a negative NPV with a 30 percent discount rate. If we back up to 28 percent to fine tune our estimate, the NPV is $322. Therefore, the IRR is about 29 percent. The computer can provide a more precise answer with much less computation. Discount Rate NPV 14% $6,025 18% $4,092 22% $2,425 26% $ 977 30% $ 199 To determine the payback period, we add the after-tax cash flows at the bottom of the table in Example J.1 for each year until we get as close as possible to $16,000 without exceeding it. For 2009 and 2010, cash flows are $6,380 + $7,148 = $13,528. The payback method is based on the assumption that cash flows are evenly distributed throughout the year, so in 2011 only $2,472 must be received before the payback point is reached. As $2,472/$6,329 is 0.39, the payback period is 2.39 years.

J.10 SUPPLEMENT J > FINANCIAL ANALYSIS < COMPUTER SUPPORT The proliferation of microcomputers and the corresponding use of computer spreadsheets make it easy to evaluate projected cash flows with NPV, IRR, and payback period methods. The following computer output shows spreadsheet analysis for the salad bar in Example J.1. The analyst inputs the investment expenditure, depreciation method, discount rate, and pretax cash flows. If only cost savings are involved, the revenue row would be replaced by them and there would be no separate rows for variable costs and fixed costs. The computer then calculates the depreciation, taxes, after-tax cash flows, NPV, IRR, and payback period. OM Explorer makes it easy to evaluate projected cash flows with NPV, IRR, and payback period methods. Figure J.1 shows the output using the Financial Analysis Solver for the salad bar in Example J.1. With such spreadsheets, the analyst no longer performs present value calculations by using formulas or tables but instead focuses on data collection and the evaluation of many different scenarios relating to a project. They are referred to as what-if analyses and allow an analyst to look at what would happen to financial performance if certain events or combinations of events were to occur. MANAGING BY THE NUMBERS The precision and analytical detachment that come from using the NPV, IRR, or payback method can be deceiving. In fact, U.S. business has been accused of managing by the numbers, with a preference for short-term results from low-risk projects. Part of the problem lies with managers who are on the fast track to the top of their organizations. They occupy a rung on the ladder for a short time and then move up, and so they perceive it to be in their career interests to favor investments that give quick results. They establish short paybacks and high hurdle rates. They ignore or forgo long-term benefits from technological advances, innovative product plans, and strategic capacity additions. Over the long run, this narrow vision jeopardizes the firm s competitive advantage and even its survival. Managing by the numbers has a second cause. Projects with the greatest strategic impact are likely to be riskier and have qualitative benefits that cannot be easily quantified. Consider an investment in some of the newer types of flexible automation. Benefits can include better quality, quicker delivery times, higher sales, and lower inventory. The equipment might be reprogrammed to handle new products not yet conceived of by the firm. Enough might be learned with the new technology that subsequent investments will pay off FIGURE J.1 OM Explorer Output for Salad Bar

> SELECTED REFERENCES < J.11 at an even higher rate of return. The mistake is to ignore these benefits simply because they cannot be easily quantified. Including risks and qualitative factors as part of the analysis is far better than ignoring them. Using a preference matrix also may help an analyst recognize qualitative factors more explicitly. The message is clear. Financial analysis is a valuable tool for evaluating investment projects. However, it can never replace the insight that comes from hands-on experience. Managers must use their judgment, taking into account not only NPV, IRR, or payback data but also how the project fits operations and corporate strategy. > SELECTED REFERENCES < Brealey, Richard A., Stewart C. Meyers, and Alan J. Marcus. Fundamentals of Corporate Finance. New York: McGraw- Hill, 1995. Brigham, Eugene F., and Louis C. Gapenski. Financial Management: Theory and Practice, 7th ed. Orlando: Dryden, 1994. Hayes, Robert H., and William J. Abernathy. Managing Our Way to Economic Decline. Harvard Business Review (July August 1980), pp. 67 77. Hodder, James E., and Henry E. Riggs. Pitfalls in Evaluating Risky Projects. Harvard Business Review (January February 1985), pp. 128 135. Kieso, Donald E., and Jerry J. Weygandt. Intermediate Accounting, 4th ed. New York: John Wiley & Sons, 1983. Luehrman, Timothy A. What s It Worth? A General Manager s Guide to Valuation. Harvard Business Review (May June 1997), pp. 132 142. Ross, Stephen A., Randolph W. Westerfield, and Bradford D. Jordon. Fundamentals of Corporate Finance, 2d ed. Homewood, Ill.: Irwin Professional Publication, 1993.