Required information Problem 25-2A 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 $350,000 investment for new machinery with a four-year life and no salvage value. Project Z requires a $350,000 investment for new machinery with a three-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 Sales $280,000 Expenses Direct materials 49,000 70,000 35,000 42,000 Direct labor Overhead including depreciation Selling and administrative expenses Total expenses 126,000 25,000 228,000 52,000 15,600 $ 36,400 126,000 25,000 270,000 Pretax income 80,000 Income taxes (30 % ) 24,000 $ 56,000 Net income Problem 25-2A Part 3 3. Compute each project's accounting rate of return. Answer is complete but not entirely correct. Accounting Rate of Return Accounting Rate of Return Choose Numerator: Choose Denominator: Annual average Annual pre-tax income Accounting rate of return investment Project Y 56,000 167,500 33.4 % = Project Z 167,500x 36,928 22.0 % = 4. Determine each project's net present value using 8% as the discount rate. Assume that cash flows occur at each year-end. (Round your intermediate calculations.) Project Y Chart values are based on: n = 8% Select Chart PV Factor = Present Value Amount X Net present value Project Z Chart values are based on: n = Present Value Select Chart Amount PV Factor X 0 Net present value TABLE B.1 p = 1/(1 i Present Value of 1 Rate Perlods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 0.9804 0.9346 1 0.9901 0.9709 0.9615 0.9524 0.9434 0.9259 0.9174 0.9091 0.8929 0.8696 0.7972 2 0.9803 0.9612 0.9426 0.9246 0.9070 0.8900 0.8734 0.8573 0.8417 0.8264 0.7561 0.9151 0.8890 0.8638 0.7938 3 0.9706 0.9423 0.8396 0.8163 0.7722 0.7513 0.7118 0.6575 0.7350 0.5718 4 0.9610 0.9238 0.8885 0.8548 0.8227 0.7921 0.7629 0.7084 0.6830 0.6355 0.8626 0.8219 0.9515 0.9057 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209 0.5674 0.4972 0.6663 6 0.9420 0.8880 0.8375 0.7903 0.7462 0.7050 0.6302 0.5963 0.5645 0.5066 0.4323 0.7599 0.5470 0.4523 7 0.9327 0.8706 0.8131 0.7107 0.6651 0.6227 0.5835 0.5132 0.3759 0.7307 8 0.9235 0.8535 0.7894 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 0.4039 0.3269 0.9143 0.8368 0.7664 0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3606 0.2843 0.4632 0.4224 0.3855 10 0.9053 0.8203 0.7441 0.6756 0.6139 0.5584 0.5083 0.3220 0.2472 0.5268 11 0.8963 0.8043 0.7224 0.6496 0.5847 0.4751 0.4289 0.3875 0.3505 0.2875 0.2149 0.3971 0.2567 12 0.8874 0.7885 0.7014 0.6246 0.5568 0.4970 0.4440 0.3555 0.3186 0.1869 13 0.8787 0.7730 0.6810 0.6006 0.5303 0.4688 0.4150 0.3677 0.3262 0.2897 0.2292 0.1625 0.505 14 0.8700 0.7579 0.6611 0.5775 0.4423 0.3878 0.3405 0.2992 0.2633 0.2046 0.1413 0.6419 0.1229 15 0.8613 0.7430 0.5553 0.4810 0.4173 0.3624 0.3152 0.2745 0.2394 0.1827 0.8528 0.7284 0.3936 0.3387 16 0.6232 0.5339 0.4581 0.2919 0.2519 0.2176 0.1631 0.1069 17 0.8444 0.7142 0.4363 0.1978 0.6050 0.5134 0.3714 0.3166 0.2959 0.2703 0.2311 0.1456 0.0929 18 0.4936 0.0808 0.8360 0.7002 0.5874 0.4155 0.3503 0.2502 0.2120 0.1799 0.1300 0.1945 19 0.8277 0.6864 0.5703 0.4746 0.3957 0.3305 0.2765 0.2317 0.1635 0.1161 0.0703 0.1037 20 0.8195 0.6730 0.5537 0.4564 0.3769 0.3118 0.2584 0.2145 0.1784 0.1486 0.0611 25 0.7798 0.6095 0.4776 0.3751 0.2953 0.2330 0.1842 0.1460 0.1160 0.0923 0.0588 0.0304 0.1314 0.0151 30 0.7419 0.5521 0.4120 0.3083 0.2314 0.1741 0.0994 0.0754 0.0573 0,0334 35 0.0075 0.7059 0.5000 0.3554 0.2534 0.1813 0.130 0.0937 0.0676 0.0490 0.0356 0.0189 40 0.3066 0.2083 0.0668 0.0037 0.6717 0.4529 0.1420 0.0972 0.0460 0.0318 0.0221 0.0107 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 ($5,000x0.5568). TABLE B.3 /i 1 (1i)" Present Value of an Annuity of 1 Rate Perlods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 0.9804 0.8929 1 0.9901 0.9709 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 0.8696 2 1.9704 1.9416 1.9135 1.8861 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355 1.6901 1.6257 2.2832 2.9410 2.8839 2.8286 2.7751 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 2.4018 3,8077 3.3872 3.2397 2.8550 4 3.9020 3.7171 3.6299 3.5460 3.4651 3.3121 3.1699 3.0373 4.8534 4.2124 3.8897 3,7908 5 4.7135 4,5797 4.4518 4.3295 4.1002 3.9927 3.6048 4.1114 3.3522 4.6229 4.4859 5.7955 5.6014 5.4172 5.2421 5.0757 4.9173 4.7665 4.3553 3.7845 7 6.7282 6,4720 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4,5638 4.1604 8 7.6517 7.3255 7,0197 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 4.9676 4.4873 8.5660 8.1622 7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7590 5.3282 4.7716 7.3601 5.0188 10 9.4713 8.9826 8.5302 8.1109 7.7217 7.0236 6.7101 6.4177 6.1446 5.6502 9.7868 9.2526 5.2337 11 10.3676 8.7605 8.3064 7.8869 7.4987 7.1390 7.5361 6.8052 6.4951 5.9377 12 11.2551 10.5753 9.9540 9.3851 8.8633 8.3838 7.9427 7.1607 6.8137 6.1944 5.4206 9.9856 7.4869 13 12.1337 11.3484 10.6350 9.3936 8.8527 8.3577 7.9038 7.1034 6.4235 5.5831 7.3667 14 13.0037 12.1062 11.2961 10.5631 9.8986 9.2950 8.7455 8.2442 7.7862 6.6282 5.7245 8.5595 8.0607 15 13.8651 12.8493 11.9379 11.1184 10.3797 9.7122 9.1079 7,6061 6.8109 5.8474 14.7179 16 13.5777 12.5611 11.6523 10.8378 10.1059 9.4466 8.8514 8.3126 7.8237 6,9740 5.9542 14.2919 6,0472 17 15.5623 13.1661 12.1657 11.2741 10.4773 9.7632 9.1216 8.5436 8.0216 7.1196 18 16.3983 14.9920 13.7535 12.6593 11.6896 10.8276 10.0591 9.3719 8.7556 8.2014 7.2497 6.1280 13.1339 8.3649 6.1982 19 17.2260 15.6785 14.3238 12.0853 11.1581 10.3356 9.6036 8.9501 7.3658 18.0456 12.4622 9.1285 20 16.3514 14.8775 13.5903 11.4699 10.5940 9.8181 8.5136 7.4694 6.2593 19.5235 11.6536 9,0770 6.4641 25 22.0232 17.4131 15.6221 14.0939 12.7834 10.6748 9.8226 7.8431 10.2737 30 25.8077 22.3965 19.6004 17.2920 15.3725 13.7648 12.4090 11.2578 9.4269 8.0552 6.5660 29,4086 12.9477 35 24.9986 21.4872 18.6646 16.3742 14.4982 11.6546 10.5668 9,6442 8.1755 6.6166 13.3317 40 32,8347 27.3555 23.1148 19.7928 17.1591 15.0463 11.9246 10.7574 9.7791 8.2438 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 ($2,0000 x 6.4177) TABLE B.4 f-[(1i" 1Vi Future Value of an Annuity of 1 Rate Perlods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 1.0000 1 1.0000 1,0000 1,0000 1.0000 1.0000 1,0000 1,0000 1.0000 1.0000 1.0000 1.0000 2.1200 2,0100 2,0200 2,0300 2.0400 2.0500 2,0600 2.0700 2.0800 2.0900 2.1000 2.1500 3.4725 3 3.0301 3.0604 3.0909 3.1216 3.1525 4.3101 3.1836 3.2149 3.2464 3.2781 3.3100 3.3744 4.2465 4,9934 4 4.0604 4.1216 4.1836 4.3746 4.4399 4.5061 4.5731 4,6410 4.7793 5.4163 5.1010 5.2040 5.3091 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051 6.3528 6.7424 6.1520 6,4684 6.9753 7.3359 8.1152 6 6.3081 6.6330 6.8019 7.1533 7.5233 7.7156 8.7537 7.4343 7.8983 7 7.2135 7.6625 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872 10.0890 11.0668 9.5491 10.2598 13.7268 8 8.2857 8,5830 8.8923 9.2142 9.8975 10.6366 11.0285 11.4359 12.2997 10.1591 11.4913 12.4876 16.7858 9.3685 9.7546 10.5828 11.0266 11.9780 13.0210 13,5795 14.7757 12,5779 10 10.4622 10.9497 11.4639 12.0061 13.1808 13.8164 14.4866 15.1929 15.9374 17.5487 20.3037 11 11.5668 12.1687 12.8078 13.4864 14.2068 14,9716 15.7836 16.6455 17.5603 18.5312 20,6546 24.3493 20.1407 12 12.6825 13.4121 14.1920 15.0258 15.9171 16.8699 17.8885 18.9771 21.3843 24.1331 29.0017 13.8093 24,5227 34,3519 13 14.6803 15.6178 16.6268 17.7130 18.8821 20.1406 21.4953 22,9534 28.0291 14 14.9474 15.9739 17.0863 18.2919 19.5986 21.0151 22.5505 24.2149 26,0192 27.9750 32.3926 40.5047 25.1290 15 16.0969 17.2934 18.5989 20.0236 21.5786 23.2760 27.1521 29.3609 31.7725 37.2797 47.5804 17.2579 27.8881 35.9497 16 18.6393 20.1569 21.8245 23.6575 25.6725 30.3243 33.0034 42.7533 55.7175 17 18.4304 20.0121 21.7616 23.6975 25.8404 28.2129 30.8402 33.7502 36.9737 40,5447 48.8837 65.0751 19.6147 75.8364 18 21.4123 23.4144 25.6454 28.1324 30.9057 33.9990 37.4502 41.3013 45.5992 55.7497 20.8109 33.7600 41.4463 63.4397 19 22.8406 25.1169 27.6712 30,5390 37.3790 46.0185 51.1591 88.2118 57.2750 20 22.0190 24.2974 26.8704 29.7781 33.0660 36.7856 40.9955 45.7620 51.1601 72.0524 102.4436 84.7009 25 28.2432 32.0303 36.4593 41.6459 47.7271 54.8645 63.2490 73.1059 98.3471 133.3339 212.7930 34,7849 30 40.5681 47.5754 56.0849 66.4388 79.0582 94.4608 113.2832 136.3075 164.4940 241.3327 434.7451 49.9945 73.6522 111.4348 138.2369 215.7108 271,0244 35 41.6603 60.4621 90.3203 172.3168 431.6635 881.1702 40 337.8824 48.8864 60.4020 75.4013 95.0255 120.7998 154.7620 199.6351 259,0565 442.5926 767.0914 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) mst TABLE B.2 f (1i" Future Value of 1 Rate 8% Perlods 1% 2% 3% 4% 5% 6% 7% 9% 10% 12% 15% 1.0000 1,0000 0 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0300 1 1.0100 1,0200 1.0400 1.0500 1.0600 1.0700 1,0800 1.0900 1.1000 1.1200 1.1500 1.0201 1.1449 2 1.0404 1.0609 1.0816 1.1025 1.1236 1.1664 1.1881 1.2100 1.2544 1,3225 1.2597 1.2950 1.0303 1.0612 1.0927 1.1249 1.1576 1.1910 1.2250 1.3310 1.4049 1.5209 1.1255 1.2625 1.4116 1.5735 4 1.0406 1.0824 1.1699 1.2155 1.3108 1.3605 1.4641 1,7490 1.3382 1.5386 5 1.0510 1.1041 1.1593 1.2167 1.2763 1.4026 1.4693 1.6105 1.7623 2.0114 1.5007 1.6771 1.0615 1.1262 1.1941 1.2653 1.3401 1.4185 1.5869 1.7716 1.9738 2.3131 1.2299 1.2668 1.1487 1.3159 1.9487 7 1.0721 1.4071 1.5036 1.6058 1.7138 1.8280 2.2107 2.6600 1.1717 1.3686 1.4775 1.9926 2.1436 8 1.0829 1.5938 1.7182 1.8509 2.4760 3.0590 1.1951 1.3048 1.5513 2.1719 3.5179 1.0937 1.4233 1.6895 1.8385 1.9990 2.3579 2.7731 1.9672 10 1.1046 1.2190 1.3439 1.4802 1.6289 1.7908 2.1589 2.3674 2.5937 3.1058 4.0456 1.8983 4.6524 11 1.1157 1.2434 1,3842 1.5395 1.7103 2.1049 2.3316 2,5804 2.8531 3.4785 2.0122 12 1.1268 1.2682 1.4258 1.6010 1.7959 2.2522 2.5182 2.8127 3.1384 3.8960 5.3503 3.0658 13 1.1381 1.2936 1.4685 1.6651 1.8856 2.1329 2.4098 2.7196 3.4523 4.3635 6.1528 14 1.1495 1.3195 1,5126 1.7317 1.9799 2.2609 2.5785 2.9372 3.3417 3.7975 4.8871 7.0757 1.5580 15 1.1610 1.3459 1.8009 2.0789 2.3966 2.7590 3.1722 3.6425 4.1772 5.4736 8.1371 1.1726 1.3728 1.6047 2.5404 16 18730 2.1829 2.9522 3.4259 3.9703 4.5950 6.1304 9.3576 1.4002 2.2920 4.3276 10.7613 17 1.1843 1.6528 1.7024 1.9479 2.6928 2.8543 3.1588 3.7000 5.0545 5.5599 6.8660 2.0258 4.7171 18 1.1961 1.4282 2.4066 3.3799 3.9960 7.6900 12.3755 1.4568 3.6165 19 1.2081 1.7535 2.1068 2,5270 3.0256 4.3157 5.1417 6.1159 8.6128 14.2318 20 1.2202 1.4859 1.8061 2.1911 2.6533 3.2071 3.8697 4,6610 5.6044 6.7275 9.6463 16.3665 25 1.2824 1.6406 2,0938 2.6658 3.3864 4.2919 5.4274 6.8485 8.6231 10.8347 17.0001 32.9190 1.3478 30 1.8114 2,4273 3.2434 4,3219 5.7435 7.6123 10.0627 13.2677 17.4494 29.9599 66.2118 1.9999 35 1.4166 2.8139 3.9461 5,5160 7.6861 10.6766 14.7853 20.4140 28.1024 52,7996 133.1755 10.2857 21.7245 40 1.4889 2.2080 3.2620 4.8010 7.0400 14.9745 31.4094 45.2593 93.0510 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) O stLO N 00