Problem 24-2A Analysis and computation of payback period, accounting rate of return, and net present value LO P1, P2, P3 [The following information applies to the questions displayed below.] Most Company has an opportunity to invest in one of two new projects. Project Y requires a $305,000 investment for new machinery with a five-year life and no salvage value. Project Z requires a $305,000 investment for new machinery with a four-year life and no salvage value. The two projects yield the following predicted annual results. The company uses straight-line depreciation, and cash flows occur evenly throughout each year. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.) Project Y Project Z $350,000 $280,000 Sales Expenses Direct materials Direct labor Overhead including depreciation Selling and administrative expenses Total expenses Pretax income Income taxes (38%) Net income 49,000 70,000 126,000 25,000 270,000 80,000 30,400 $ 49,600 35,000 42,000 126,000 25,000 228,000 52,000 19,760 $ 32, 240 Required: 1. Compute each project's annual expected net cash flows. Net income Depreciation expense Project Y Project Z $ 49,600 $ 32,240 61,000 76,250 Expected net cash flows $ 110,600 $ 108,490 2. Determine each project's payback period. Payback Period Payback Period Choose Numerator: I Choose Denominator: Cost of investment 1 Annual net cash flow $ 305,000/ $ 110,600 $ 305,000 1$ 108,490 = Project Y Project Z Payback period 2.76 years 2.81 years = 3. Compute each project's accounting rate of return. Accounting Rate of Return Choose Numerator: Choose Denominator: Project Y Project Z Annual after-tax net income $ 49,600 / $ 32,2401 Accounting Rate of Return Accounting rate of return 32.5 % Annual average investment $ 152,500 $ 152,500 = 21.1 % Project Y Chart values are based on: n = Select Chart Amount II x PV Factor Present Value 0 $ Net present value Project z Chart values are based on: n = Select Chart Amount X PV Factor Present Value 0 = $ Net present value TABLE B.1* Present Value of 1 p=1/(1 + i)" Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 0.9901 0.9803 0.9706 0.96 10 0.9515 0.9420 0.9327 0.9235 0.9143 0.9053 0.8963 0.8874 0.8787 0.8700 0.8613 0.8528 0.8444 0.8360 0.8277 0.8195 0.7798 0.7419 0.7059 0.6717 0.9804 0.9612 0.9423 0.9238 0.9057 0.8880 0.8706 0.8535 0.8368 0.8203 0.8043 0.7885 0.7730 0.7579 0.7430 0.7284 0.7142 0.7002 0.6864 0.6730 0.6095 0.5521 0.5000 0.4529 0.9709 0.9426 0.9151 0.8885 0.8626 0.8375 0.8131 0.7894 0.7664 0.7441 0.7224 0.7014 0.6810 0.6611 0.6419 0.6232 0.6050 0.5874 0.5703 0.5537 0.4776 0.4120 0.3554 0.3066 0.9615 0.9246 0.8890 0.8548 0.8219 0.7903 0.7599 0.7307 0.7026 0.6756 0.6496 0.6246 0.6006 0.5775 0.5553 0.5339 0.5134 0.4936 0.4746 0.4564 0.3751 0.3083 0.2534 0.2083 0.9524 0.9070 0.8638 0.8227 0.7835 0.7462 0.7107 0.6768 0.6446 0.6139 0.5847 0.5568 0.5303 0.5051 0.4810 0.4581 0.4363 0.4155 0.3957 0.3769 0.2953 0.2314 0.1813 0.1420 0.9434 0.8900 0.8396 0.7921 0.7473 0.7050 0.6651 0.6274 0.5919 0.5584 0.5268 0.4970 0.4688 0.4423 0.4173 0.3936 0.3714 0.3503 0.3305 0.3118 0.2330 0.1741 0.1301 0.0972 0.9346 0.8734 0.8163 0.7629 0.7130 0.6663 0.6227 0.5820 0.5439 0.5083 0.4751 0.4440 0.4150 0.3878 0.3624 0.3387 0.3166 0.2959 0.2765 0.2584 0.1842 0.1314 0.0937 0.0668 0.9259 0.8573 0.7938 0.7350 0.6806 0.6302 0.5835 0.5403 0.5002 0.4632 0.4289 0.3971 0.3677 0.3405 0.3152 0.2919 0.2703 0.2502 0.2317 0.2145 0.1460 0.0994 0.0676 0.0460 0.9174 0.8417 0.7722 0.7084 0.6499 0.5963 0.5470 0.5019 0.4604 0.4224 0.3875 0.3555 0.3262 0.2992 0.2745 0.2519 0.2311 0.2120 0.1945 0.1784 0.1160 0.0754 0.0490 0.0318 0.9091 0.8264 0.7513 0.6830 0.6209 0.5645 0.5132 0.4665 0.4241 0.3855 0.3505 0.3186 0.2897 0.2633 0.2394 0.2176 0.1978 0.1799 0.1635 0.1486 0.0923 0.0573 0.0356 0.0221 0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523 0.4039 0.3606 0.3220 0.2875 0.2567 0.2292 0.2046 0.1827 0.1631 0.1456 0.1300 0.1161 0.1037 0.0588 0.0334 0.0189 0.0107 0.8696 0.7561 0.6575 0.5718 0.4972 0.4323 0.3759 0.3269 0.2843 0.2472 0.2149 0.1869 0.1625 0.1413 0.1229 0.1069 0.0929 0.0808 0.0703 0.0611 0.0304 0.0151 0.0075 0.0037 * Used to compute the present value of a known future amount. For example: How much would you need to invest today at 10% compounded semiannually to accumulate $5,000 in 6 years from today? Using the factors of n = 12 and i = 5% (12 semiannual periods and a semiannual rate of 5%), the factor is 0.5568. You would need to invest $2,784 today ($5,000 x 0.5568). TABLE B.2 Future Value of 1 f= (1 + i)" Rate Perlods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 1.0000 1.0100 1.0201 1.0303 1.0406 1.0510 1.0615 1.0721 1.0829 1.0937 1.1046 1.1157 1.1268 1.1381 1.1495 1.1610 1.1726 1.1843 1.1961 1.2081 1.2202 1.2824 1.3478 1.4166 1.4889 1.0000 1.0200 1.0404 1.0612 1.0824 1.1041 1.1262 1.1487 1.1717 1.1951 1.2190 1.2434 1.2682 1.2936 1.3195 1.3459 1.3728 1.4002 1.4282 1.4568 1.4859 1.6406 1.8114 1.9999 2.2080 1.0000 1.0300 1.0609 1.0927 1.1255 1.1593 1.1941 1.2299 1.2668 1.3048 1.3439 1.3842 1.4258 1.4685 1.5126 1.5580 1.6047 1.6528 1.7024 1.7535 1.8061 2.0938 2.4273 2.8139 3.2620 1.0000 1.0400 1.0816 1.1249 1.1699 1.2167 1.2653 1.3159 1.3686 1.4233 1.4802 1.5395 1.6010 1.6651 1.7317 1.8009 1.8730 1.9479 2.0258 2.1068 2.1911 2.6658 3.2434 3.9461 4.8010 1.0000 1.0500 1.1025 1.1576 1.2155 1.2763 1.3401 1.4071 1.4775 1.5513 1.6289 1.7103 1.7959 1.8856 1.9799 2.0789 2.1829 2.2920 2.4066 2.5270 2.6533 3.3864 4.3219 5.5160 7.0400 1.0000 1.0600 1.1236 1.1910 1.2625 1.3382 1.4185 1.5036 1.5938 1.6895 1.7908 1.8983 2.0122 2.1329 2.2609 2.3966 2.5404 2.6928 2.8543 3.0256 3.2071 4.2919 5.7435 7.6861 10.2857 1.0000 1.0700 1.1449 1.2250 1.3108 1.4026 1.5007 1.6058 1.7182 1.8385 1.9672 2.1049 2.2522 2.4098 2.5785 2.7590 2.9522 3.1588 3.3799 3.6165 3.8697 5.4274 7.6123 10.6766 14.9745 1.0000 1.0800 1.1664 1.2597 1.3605 1.4693 1.5869 1.7138 1.8509 1.9990 2.1589 2.3316 2.5182 2.7196 2.9372 3.1722 3.4259 3.7000 3.9960 4.3157 4.6610 6.8485 10.0627 14.7853 21.7245 1.0000 1.0900 1.1881 1.2950 1.4116 1.5386 1.6771 1.8280 1.9926 2.1719 2.3674 2.5804 2.8127 3.0658 3.3417 3.6425 3.9703 4.3276 4.7171 5.1417 5.6044 8.6231 13.2677 20.4140 31.4094 1.0000 1.1000 1.2100 1.3310 1.4641 1.6 105 1.7716 1.9487 2.1436 2.3579 2.5937 2.8531 3.1384 3.4523 3.7975 4.1772 4.5950 5.0545 5.5599 6.1159 6.7275 10.8347 17.4494 28.1024 45.2593 1.0000 1.1200 1.2544 1.4049 1.5735 1.7623 1.9738 2.2107 2.4760 2.7731 3.1058 3.4785 3.8960 4.3635 4.8871 5.4736 6.1304 6.8660 7.6900 8.6128 9.6463 17.0001 29.9599 52.7996 93.0510 1.0000 1.1500 1.3225 1.5209 1.7490 2.0114 2.3131 2.6600 3.0590 3.5179 4.0456 4.6524 5.3503 6.1528 7.0757 8.1371 9.3576 10.7613 12.3755 14.2318 16.3665 32.9190 66.2118 133.1755 267.8635 Used to compute the future value of a known present amount. For example: What is the accumulated value of $3,000 invested today at 8% compounded quarterly for 5 years? Using the factors of n = 20 and i = 2% (20 quarterly periods and a quarterly interest rate of 2%), the factor is 1.4859. The accumulated value is $4,457.70 ($3,000 x 1.4859). (1 + i)" TABLE B.3 Present Value of an Annuity of 1 Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 0.9901 1.9704 2.9410 3.9020 4.8534 5.7955 6.7282 7.6517 8.5660 9.4713 10.3676 11.2551 12.1337 13.0037 13.8651 14.7179 15.5623 16.3983 17.2260 18.0456 22.0232 25.8077 29.4086 32.8347 0.9804 1.9416 2.8839 3.8077 4.7135 5.6014 6.4720 7.3255 8.1622 8.9826 9.7868 10.5753 11.3484 12.1062 12.8493 13.5777 14.2919 14.9920 15.6785 16.3514 19.5235 22.3965 24.9986 27.3555 0.9709 1.9135 2.8286 3.7171 4.5797 5.4172 6.2303 7.0197 7.7861 8.5302 9.2526 9.9540 10.6350 11.2961 11.9379 12.5611 13.1661 13.7535 14.3238 14.8775 17.4131 19.6004 21.4872 23.1148 0.9615 1.8861 2.7751 3.6299 4.4518 5.2421 6.0021 6.7327 7.4353 8.1109 8.7605 9.3851 9.9856 10.5631 11.1184 11.6523 12.1657 12.6593 13.1339 13.5903 15.6221 17.2920 18.6646 19.7928 0.9524 1.8594 2.7232 3.5460 4.3295 5.0757 5.7864 6.4632 7.1078 7.7217 8.3064 8.8633 9.3936 9.8986 10.3797 10.8378 11.2741 11.6896 12.0853 12.4622 14.0939 15.3725 16.3742 17.1591 0.9434 1.8334 2.6730 3.4651 4.2124 4.9173 5.5824 6.2098 6.8017 7.3601 7.8869 8.3838 8.8527 9.2950 9.7122 10.1059 10.4773 10.8276 11.1581 11.4699 12.7834 13.7648 14.4982 15.0463 0.9346 1.8080 2.6243 3.3872 4.1002 4.7665 5.3893 5.9713 6.5152 7.0236 7.4987 7.9427 8.3577 8.7455 9.1079 9.4466 9.7632 10.0591 10.3356 10.5940 11.6536 12.4090 12.9477 13.3317 0.9259 1.7833 2.5771 3.3121 3.9927 4.6229 5.2064 5.7466 6.2469 6.7101 7.1390 7.5361 7.9038 8.2442 8.5595 8.8514 9.1216 9.3719 9.6036 9.8181 10.6748 11.2578 11.6546 11.9246 0.9174 1.7591 2.5313 3.2397 3.8897 4.4859 5.0330 5.5348 5.9952 6.4177 6.8052 7.1607 7.4869 7.7862 8.0607 8.3126 8.5436 8.7556 8.9501 9.1285 9.8226 10.2737 10.5668 10.7574 0.9091 1.7355 2.4869 3.1699 3.7908 4.3553 4.8684 5.3349 5.7590 6.1446 6.4951 6.8137 7.1034 7.3667 7.6061 7.8237 8.0216 8.2014 8.3649 8.5136 9.0770 9.4269 9.6442 9.7791 0.8929 1.6901 2.4018 3.0373 3.6048 4.1114 4.5638 4.9676 5.3282 5.6502 5.9377 6.1944 6.4235 6.6282 6.8109 6.9740 7.1196 7.2497 7.3658 7.4694 7.8431 8.0552 8.1755 8.2438 0.8696 1.6257 2.2832 2.8550 3.3522 3.7845 4.1604 4.4873 4.7716 5.0188 5.2337 5.4206 5.5831 5.7245 5.8474 5.9542 6.0472 6.1280 6.1982 6.2593 6.4641 6.5660 6.6166 6.6418 * Used to calculate the present value of a series of equal payments made at the end of each period. For example: What is the present value of $2,000 per year for 10 years assuming an annual interest rate of 9%. For (n= 10,i=9%), the PV factor is 6.4177. $2,000 per year for 10 years is the equivalent of $12,835 today ($2,000 X 6.4177). f=[(1 + i)" 1 Vi TABLE B.43 Future Value of an Annuity of 1 Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 1.0000 2.0100 3.0301 4.0604 5.1010 6.1520 7.2135 8.2857 9.3685 10.4622 11.5668 12.6825 13.8093 14.9474 16.0969 17.2579 18.4304 19.6147 20.8109 22.0190 28.2432 34.7849 41.6603 48.8864 1.0000 1.0000 2.0200 2.0300 3.0604 3.0909 4.1216 4.1836 5.2040 5.3091 6.3081 6.4684 7.4343 7.6625 8.5830 8.8923 9.7546 10.1591 10.9497 11.4639 12.1687 12.8078 13.4121 14.1920 14.6803 15.6178 15.9739 17.0863 17.2934 18.5989 18.6393 20.1569 20.0121 21.7616 21.4123 23.4144 22.8406 25.1169 24.2974 26.8704 32.0303 36.4593 40.5681 47.5754 49.9945 60.4621 60.4020 75.4013 1.0000 2.0400 3.1216 4.2465 5.4163 6.6330 7.8983 9.2142 10.5828 12.0061 13.4864 15.0258 16.6268 18.2919 20.0236 21.8245 23.6975 25.6454 27.6712 29.7781 41.6459 56.0849 73.6522 95.0255 1.0000 1.0000 2.0500 2.0600 3.1525 3.1836 4.3101 4.3746 5.5256 5.6371 6.8019 6.9753 8.1420 8.3938 9.5491 9.8975 11.0266 11.4913 12.5779 13.1808 14.2068 14.9716 15.9171 16.8699 17.7130 18.8821 19.5986 21.0151 21.5786 23.2760 23.6575 25.6725 25.8404 28.2129 28.1324 30.9057 30.5390 33.7600 33.0660 36.7856 47.7271 54.8645 66.4388 79.0582 90.3203 111.4348 120.7998 154.7620 1.0000 2.0700 3.2149 4.4399 5.7507 7.1533 8.6540 10.2598 11.9780 13.8164 15.7836 17.8885 20.1406 22.5505 25.1290 27.8881 30.8402 33.9990 37.3790 40.9955 63.2490 94.4608 138.2369 199.6351 1.0000 2.0800 3.2464 4.5061 5.8666 7.3359 8.9228 10.6366 12.4876 14.4866 16.6455 18.9771 21.4953 24.2149 27.1521 30.3243 33.7502 37.4502 41.4463 45.7620 73.1059 113.2832 172.3168 259.0565 1.0000 1.0000 2.0900 2.1000 3.2781 3.3100 4.5731 4.6410 5.9847 6.1051 7.5233 7.7156 9.2004 9.4872 11.0285 11.4359 13.0210 13.5795 15.1929 15.9374 17.5603 18.5312 20.1407 21.3843 22.9534 24.5227 26.0192 27.9750 29.3609 31.7725 33.0034 35.9497 36.9737 40.5447 41.3013 45.5992 46.0185 51.1591 51.1601 57.2750 84.7009 98.3471 136.3075 164.4940 215.7108 271.0244 337.8824 442.5926 1.0000 2.1200 3.3744 4.7793 6.3528 8.1152 10.0890 12.2997 14.7757 17.5487 20.6546 24.1331 28.0291 32.3926 37.2797 42.7533 48.8837 55.7497 63.4397 72.0524 133.3339 241.3327 431.6635 767.0914 1.0000 2.1500 3.4725 4.9934 6.7424 8.7537 11.0668 13.7268 16.7858 20.3037 24.3493 29.0017 34.3519 40.5047 47.5804 55.7175 65.0751 75.8364 88.2118 102.4436 212.7930 434.7451 881.1702 1,779.0903 Used to calculate the future value of a series of equal payments made at the end of each period. For example: What is the future value of $4,000 per year for 6 years assuming an annual interest rate of 8%. For (n = 6, i = 8%), the FV factor is 7.3359. $4,000 per year for 6 years accumulates to $29,343.60 ($4,000 x 7.3359). Problem 24-2A Analysis and computation of payback period, accounting rate of return, and net present value LO P1, P2, P3 [The following information applies to the questions displayed below.] Most Company has an opportunity to invest in one of two new projects. Project Y requires a $305,000 investment for new machinery with a five-year life and no salvage value. Project Z requires a $305,000 investment for new machinery with a four-year life and no salvage value. The two projects yield the following predicted annual results. The company uses straight-line depreciation, and cash flows occur evenly throughout each year. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.) Project Y Project Z $350,000 $280,000 Sales Expenses Direct materials Direct labor Overhead including depreciation Selling and administrative expenses Total expenses Pretax income Income taxes (38%) Net income 49,000 70,000 126,000 25,000 270,000 80,000 30,400 $ 49,600 35,000 42,000 126,000 25,000 228,000 52,000 19,760 $ 32, 240 Required: 1. Compute each project's annual expected net cash flows. Net income Depreciation expense Project Y Project Z $ 49,600 $ 32,240 61,000 76,250 Expected net cash flows $ 110,600 $ 108,490 2. Determine each project's payback period. Payback Period Payback Period Choose Numerator: I Choose Denominator: Cost of investment 1 Annual net cash flow $ 305,000/ $ 110,600 $ 305,000 1$ 108,490 = Project Y Project Z Payback period 2.76 years 2.81 years = 3. Compute each project's accounting rate of return. Accounting Rate of Return Choose Numerator: Choose Denominator: Project Y Project Z Annual after-tax net income $ 49,600 / $ 32,2401 Accounting Rate of Return Accounting rate of return 32.5 % Annual average investment $ 152,500 $ 152,500 = 21.1 % Project Y Chart values are based on: n = Select Chart Amount II x PV Factor Present Value 0 $ Net present value Project z Chart values are based on: n = Select Chart Amount X PV Factor Present Value 0 = $ Net present value TABLE B.1* Present Value of 1 p=1/(1 + i)" Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 0.9901 0.9803 0.9706 0.96 10 0.9515 0.9420 0.9327 0.9235 0.9143 0.9053 0.8963 0.8874 0.8787 0.8700 0.8613 0.8528 0.8444 0.8360 0.8277 0.8195 0.7798 0.7419 0.7059 0.6717 0.9804 0.9612 0.9423 0.9238 0.9057 0.8880 0.8706 0.8535 0.8368 0.8203 0.8043 0.7885 0.7730 0.7579 0.7430 0.7284 0.7142 0.7002 0.6864 0.6730 0.6095 0.5521 0.5000 0.4529 0.9709 0.9426 0.9151 0.8885 0.8626 0.8375 0.8131 0.7894 0.7664 0.7441 0.7224 0.7014 0.6810 0.6611 0.6419 0.6232 0.6050 0.5874 0.5703 0.5537 0.4776 0.4120 0.3554 0.3066 0.9615 0.9246 0.8890 0.8548 0.8219 0.7903 0.7599 0.7307 0.7026 0.6756 0.6496 0.6246 0.6006 0.5775 0.5553 0.5339 0.5134 0.4936 0.4746 0.4564 0.3751 0.3083 0.2534 0.2083 0.9524 0.9070 0.8638 0.8227 0.7835 0.7462 0.7107 0.6768 0.6446 0.6139 0.5847 0.5568 0.5303 0.5051 0.4810 0.4581 0.4363 0.4155 0.3957 0.3769 0.2953 0.2314 0.1813 0.1420 0.9434 0.8900 0.8396 0.7921 0.7473 0.7050 0.6651 0.6274 0.5919 0.5584 0.5268 0.4970 0.4688 0.4423 0.4173 0.3936 0.3714 0.3503 0.3305 0.3118 0.2330 0.1741 0.1301 0.0972 0.9346 0.8734 0.8163 0.7629 0.7130 0.6663 0.6227 0.5820 0.5439 0.5083 0.4751 0.4440 0.4150 0.3878 0.3624 0.3387 0.3166 0.2959 0.2765 0.2584 0.1842 0.1314 0.0937 0.0668 0.9259 0.8573 0.7938 0.7350 0.6806 0.6302 0.5835 0.5403 0.5002 0.4632 0.4289 0.3971 0.3677 0.3405 0.3152 0.2919 0.2703 0.2502 0.2317 0.2145 0.1460 0.0994 0.0676 0.0460 0.9174 0.8417 0.7722 0.7084 0.6499 0.5963 0.5470 0.5019 0.4604 0.4224 0.3875 0.3555 0.3262 0.2992 0.2745 0.2519 0.2311 0.2120 0.1945 0.1784 0.1160 0.0754 0.0490 0.0318 0.9091 0.8264 0.7513 0.6830 0.6209 0.5645 0.5132 0.4665 0.4241 0.3855 0.3505 0.3186 0.2897 0.2633 0.2394 0.2176 0.1978 0.1799 0.1635 0.1486 0.0923 0.0573 0.0356 0.0221 0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523 0.4039 0.3606 0.3220 0.2875 0.2567 0.2292 0.2046 0.1827 0.1631 0.1456 0.1300 0.1161 0.1037 0.0588 0.0334 0.0189 0.0107 0.8696 0.7561 0.6575 0.5718 0.4972 0.4323 0.3759 0.3269 0.2843 0.2472 0.2149 0.1869 0.1625 0.1413 0.1229 0.1069 0.0929 0.0808 0.0703 0.0611 0.0304 0.0151 0.0075 0.0037 * Used to compute the present value of a known future amount. For example: How much would you need to invest today at 10% compounded semiannually to accumulate $5,000 in 6 years from today? Using the factors of n = 12 and i = 5% (12 semiannual periods and a semiannual rate of 5%), the factor is 0.5568. You would need to invest $2,784 today ($5,000 x 0.5568). TABLE B.2 Future Value of 1 f= (1 + i)" Rate Perlods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 1.0000 1.0100 1.0201 1.0303 1.0406 1.0510 1.0615 1.0721 1.0829 1.0937 1.1046 1.1157 1.1268 1.1381 1.1495 1.1610 1.1726 1.1843 1.1961 1.2081 1.2202 1.2824 1.3478 1.4166 1.4889 1.0000 1.0200 1.0404 1.0612 1.0824 1.1041 1.1262 1.1487 1.1717 1.1951 1.2190 1.2434 1.2682 1.2936 1.3195 1.3459 1.3728 1.4002 1.4282 1.4568 1.4859 1.6406 1.8114 1.9999 2.2080 1.0000 1.0300 1.0609 1.0927 1.1255 1.1593 1.1941 1.2299 1.2668 1.3048 1.3439 1.3842 1.4258 1.4685 1.5126 1.5580 1.6047 1.6528 1.7024 1.7535 1.8061 2.0938 2.4273 2.8139 3.2620 1.0000 1.0400 1.0816 1.1249 1.1699 1.2167 1.2653 1.3159 1.3686 1.4233 1.4802 1.5395 1.6010 1.6651 1.7317 1.8009 1.8730 1.9479 2.0258 2.1068 2.1911 2.6658 3.2434 3.9461 4.8010 1.0000 1.0500 1.1025 1.1576 1.2155 1.2763 1.3401 1.4071 1.4775 1.5513 1.6289 1.7103 1.7959 1.8856 1.9799 2.0789 2.1829 2.2920 2.4066 2.5270 2.6533 3.3864 4.3219 5.5160 7.0400 1.0000 1.0600 1.1236 1.1910 1.2625 1.3382 1.4185 1.5036 1.5938 1.6895 1.7908 1.8983 2.0122 2.1329 2.2609 2.3966 2.5404 2.6928 2.8543 3.0256 3.2071 4.2919 5.7435 7.6861 10.2857 1.0000 1.0700 1.1449 1.2250 1.3108 1.4026 1.5007 1.6058 1.7182 1.8385 1.9672 2.1049 2.2522 2.4098 2.5785 2.7590 2.9522 3.1588 3.3799 3.6165 3.8697 5.4274 7.6123 10.6766 14.9745 1.0000 1.0800 1.1664 1.2597 1.3605 1.4693 1.5869 1.7138 1.8509 1.9990 2.1589 2.3316 2.5182 2.7196 2.9372 3.1722 3.4259 3.7000 3.9960 4.3157 4.6610 6.8485 10.0627 14.7853 21.7245 1.0000 1.0900 1.1881 1.2950 1.4116 1.5386 1.6771 1.8280 1.9926 2.1719 2.3674 2.5804 2.8127 3.0658 3.3417 3.6425 3.9703 4.3276 4.7171 5.1417 5.6044 8.6231 13.2677 20.4140 31.4094 1.0000 1.1000 1.2100 1.3310 1.4641 1.6 105 1.7716 1.9487 2.1436 2.3579 2.5937 2.8531 3.1384 3.4523 3.7975 4.1772 4.5950 5.0545 5.5599 6.1159 6.7275 10.8347 17.4494 28.1024 45.2593 1.0000 1.1200 1.2544 1.4049 1.5735 1.7623 1.9738 2.2107 2.4760 2.7731 3.1058 3.4785 3.8960 4.3635 4.8871 5.4736 6.1304 6.8660 7.6900 8.6128 9.6463 17.0001 29.9599 52.7996 93.0510 1.0000 1.1500 1.3225 1.5209 1.7490 2.0114 2.3131 2.6600 3.0590 3.5179 4.0456 4.6524 5.3503 6.1528 7.0757 8.1371 9.3576 10.7613 12.3755 14.2318 16.3665 32.9190 66.2118 133.1755 267.8635 Used to compute the future value of a known present amount. For example: What is the accumulated value of $3,000 invested today at 8% compounded quarterly for 5 years? Using the factors of n = 20 and i = 2% (20 quarterly periods and a quarterly interest rate of 2%), the factor is 1.4859. The accumulated value is $4,457.70 ($3,000 x 1.4859). (1 + i)" TABLE B.3 Present Value of an Annuity of 1 Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 0.9901 1.9704 2.9410 3.9020 4.8534 5.7955 6.7282 7.6517 8.5660 9.4713 10.3676 11.2551 12.1337 13.0037 13.8651 14.7179 15.5623 16.3983 17.2260 18.0456 22.0232 25.8077 29.4086 32.8347 0.9804 1.9416 2.8839 3.8077 4.7135 5.6014 6.4720 7.3255 8.1622 8.9826 9.7868 10.5753 11.3484 12.1062 12.8493 13.5777 14.2919 14.9920 15.6785 16.3514 19.5235 22.3965 24.9986 27.3555 0.9709 1.9135 2.8286 3.7171 4.5797 5.4172 6.2303 7.0197 7.7861 8.5302 9.2526 9.9540 10.6350 11.2961 11.9379 12.5611 13.1661 13.7535 14.3238 14.8775 17.4131 19.6004 21.4872 23.1148 0.9615 1.8861 2.7751 3.6299 4.4518 5.2421 6.0021 6.7327 7.4353 8.1109 8.7605 9.3851 9.9856 10.5631 11.1184 11.6523 12.1657 12.6593 13.1339 13.5903 15.6221 17.2920 18.6646 19.7928 0.9524 1.8594 2.7232 3.5460 4.3295 5.0757 5.7864 6.4632 7.1078 7.7217 8.3064 8.8633 9.3936 9.8986 10.3797 10.8378 11.2741 11.6896 12.0853 12.4622 14.0939 15.3725 16.3742 17.1591 0.9434 1.8334 2.6730 3.4651 4.2124 4.9173 5.5824 6.2098 6.8017 7.3601 7.8869 8.3838 8.8527 9.2950 9.7122 10.1059 10.4773 10.8276 11.1581 11.4699 12.7834 13.7648 14.4982 15.0463 0.9346 1.8080 2.6243 3.3872 4.1002 4.7665 5.3893 5.9713 6.5152 7.0236 7.4987 7.9427 8.3577 8.7455 9.1079 9.4466 9.7632 10.0591 10.3356 10.5940 11.6536 12.4090 12.9477 13.3317 0.9259 1.7833 2.5771 3.3121 3.9927 4.6229 5.2064 5.7466 6.2469 6.7101 7.1390 7.5361 7.9038 8.2442 8.5595 8.8514 9.1216 9.3719 9.6036 9.8181 10.6748 11.2578 11.6546 11.9246 0.9174 1.7591 2.5313 3.2397 3.8897 4.4859 5.0330 5.5348 5.9952 6.4177 6.8052 7.1607 7.4869 7.7862 8.0607 8.3126 8.5436 8.7556 8.9501 9.1285 9.8226 10.2737 10.5668 10.7574 0.9091 1.7355 2.4869 3.1699 3.7908 4.3553 4.8684 5.3349 5.7590 6.1446 6.4951 6.8137 7.1034 7.3667 7.6061 7.8237 8.0216 8.2014 8.3649 8.5136 9.0770 9.4269 9.6442 9.7791 0.8929 1.6901 2.4018 3.0373 3.6048 4.1114 4.5638 4.9676 5.3282 5.6502 5.9377 6.1944 6.4235 6.6282 6.8109 6.9740 7.1196 7.2497 7.3658 7.4694 7.8431 8.0552 8.1755 8.2438 0.8696 1.6257 2.2832 2.8550 3.3522 3.7845 4.1604 4.4873 4.7716 5.0188 5.2337 5.4206 5.5831 5.7245 5.8474 5.9542 6.0472 6.1280 6.1982 6.2593 6.4641 6.5660 6.6166 6.6418 * Used to calculate the present value of a series of equal payments made at the end of each period. For example: What is the present value of $2,000 per year for 10 years assuming an annual interest rate of 9%. For (n= 10,i=9%), the PV factor is 6.4177. $2,000 per year for 10 years is the equivalent of $12,835 today ($2,000 X 6.4177). f=[(1 + i)" 1 Vi TABLE B.43 Future Value of an Annuity of 1 Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 30 35 40 1.0000 2.0100 3.0301 4.0604 5.1010 6.1520 7.2135 8.2857 9.3685 10.4622 11.5668 12.6825 13.8093 14.9474 16.0969 17.2579 18.4304 19.6147 20.8109 22.0190 28.2432 34.7849 41.6603 48.8864 1.0000 1.0000 2.0200 2.0300 3.0604 3.0909 4.1216 4.1836 5.2040 5.3091 6.3081 6.4684 7.4343 7.6625 8.5830 8.8923 9.7546 10.1591 10.9497 11.4639 12.1687 12.8078 13.4121 14.1920 14.6803 15.6178 15.9739 17.0863 17.2934 18.5989 18.6393 20.1569 20.0121 21.7616 21.4123 23.4144 22.8406 25.1169 24.2974 26.8704 32.0303 36.4593 40.5681 47.5754 49.9945 60.4621 60.4020 75.4013 1.0000 2.0400 3.1216 4.2465 5.4163 6.6330 7.8983 9.2142 10.5828 12.0061 13.4864 15.0258 16.6268 18.2919 20.0236 21.8245 23.6975 25.6454 27.6712 29.7781 41.6459 56.0849 73.6522 95.0255 1.0000 1.0000 2.0500 2.0600 3.1525 3.1836 4.3101 4.3746 5.5256 5.6371 6.8019 6.9753 8.1420 8.3938 9.5491 9.8975 11.0266 11.4913 12.5779 13.1808 14.2068 14.9716 15.9171 16.8699 17.7130 18.8821 19.5986 21.0151 21.5786 23.2760 23.6575 25.6725 25.8404 28.2129 28.1324 30.9057 30.5390 33.7600 33.0660 36.7856 47.7271 54.8645 66.4388 79.0582 90.3203 111.4348 120.7998 154.7620 1.0000 2.0700 3.2149 4.4399 5.7507 7.1533 8.6540 10.2598 11.9780 13.8164 15.7836 17.8885 20.1406 22.5505 25.1290 27.8881 30.8402 33.9990 37.3790 40.9955 63.2490 94.4608 138.2369 199.6351 1.0000 2.0800 3.2464 4.5061 5.8666 7.3359 8.9228 10.6366 12.4876 14.4866 16.6455 18.9771 21.4953 24.2149 27.1521 30.3243 33.7502 37.4502 41.4463 45.7620 73.1059 113.2832 172.3168 259.0565 1.0000 1.0000 2.0900 2.1000 3.2781 3.3100 4.5731 4.6410 5.9847 6.1051 7.5233 7.7156 9.2004 9.4872 11.0285 11.4359 13.0210 13.5795 15.1929 15.9374 17.5603 18.5312 20.1407 21.3843 22.9534 24.5227 26.0192 27.9750 29.3609 31.7725 33.0034 35.9497 36.9737 40.5447 41.3013 45.5992 46.0185 51.1591 51.1601 57.2750 84.7009 98.3471 136.3075 164.4940 215.7108 271.0244 337.8824 442.5926 1.0000 2.1200 3.3744 4.7793 6.3528 8.1152 10.0890 12.2997 14.7757 17.5487 20.6546 24.1331 28.0291 32.3926 37.2797 42.7533 48.8837 55.7497 63.4397 72.0524 133.3339 241.3327 431.6635 767.0914 1.0000 2.1500 3.4725 4.9934 6.7424 8.7537 11.0668 13.7268 16.7858 20.3037 24.3493 29.0017 34.3519 40.5047 47.5804 55.7175 65.0751 75.8364 88.2118 102.4436 212.7930 434.7451 881.1702 1,779.0903 Used to calculate the future value of a series of equal payments made at the end of each period. For example: What is the future value of $4,000 per year for 6 years assuming an annual interest rate of 8%. For (n = 6, i = 8%), the FV factor is 7.3359. $4,000 per year for 6 years accumulates to $29,343.60 ($4,000 x 7.3359)