Interstate Manufacturing is considering either replacing one of its old machines with a new machine or having the old machine overhauled. Information about the two alternatives follows. Management requires a 8% rate of return on its investments. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)
Factor tables:
PV of $1
FV of $1
PVA of $1
FVA of $1
Alternative 1: Keep the old machine and have it overhauled. If the old machine is overhauled, it will be kept for another five years and then sold for its salvage value. Cost of old machine Cost of overhaul Annual expected revenues generated Annual cash operating costs after overhaul Salvage value of old machine in 5 years $105,000 143,000 87,000 52.000 19.000 Alternative 2: Sell the old machine and buy a new one. The new machine is more efficient and will yield substantial operating cost savings with more product being produced and sold. Cost of new machine Salvage value of old machine now Annual expected revenues generated Annual cash operating costs Salvage value of new machine in 5 years $ 294,000 29,000 118.000 25,000 11,000 Required: 1. Determine the net present value of alternative 1. Initial cash investment (net) Chart values are based on: Year Subsequent Cash inflow (outflow) x Table factor = Present Value = 2 3 2. Determine the net present value of alternative 2. Initial cash investment (net) Year Subsequent Cash Inflow (outflow) x Table factor Present Value 2 3. Which alternative should management select? 1. Determine the net present value of alternative 1. Initial cash investment (net) Chart values are based on: Year Subsequent Cash inflow (outflow) x Table factor = Present Value Present value of cash inflows Present value of cash outflows Net present value Taure T UT Present Value inflow (outflow) * 2 3 Now $ 0 3. Which alternative should management select? 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% OOoo OWN 0.9901 0.9803 0.9706 0.9610 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 0.9615 0.9426 0.9246 0.9151 0.8890 0.8885 0.8548 0.8626 0.8219 0.8375 0.7903 0.8131 0.7599 0.7894 0.7307 0.7664 0.7026 0.7441 0.6756 0.7224 0.6496 0.7014 0.6246 0.6810 0.6006 0.6611 0.5775 0.64190.5553 0.6232 0.5339 0.6050 0.5134 0.5874 0.4936 0.5703 0.4746 0.5537 0.4564 0.4776 0.3751 0.4120 0.3083 0.3554 0.2534 0.3066 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 0.9091 0.8417 0.8264 0.7722 0.7513 0.7084 0.6830 0.6499 0.6209 0.5963 0.5645 0.5470 0.5132 0.50190.4665 0.4604 0.4241 0.4224 0.3855 0.3875 0.3505 0.3555 0.3186 0.3262 0.2897 0.2992 0.2633 0.27450.2394 0.2519 0.2176 0.2311 0.1978 0.2120 0.1799 0.1945 0.1635 0.1784 0.1486 0.1160 0.0923 0.0754 0.0573 0.0490 0.0356 0.0318 0.0221 0.8929 0.8696 0.7972 0.7118 0.6355 0.5718 0.5674 0.4972 0.5066 0.4323 0.4523 0.3759 0.40390.3269 0.3606 0.2843 0.3220 0.2472 0.2875 0.2149 0.2567 0.1869 0.2292 0.1625 0.2046 0.1413 0.1827 0.1229 0.1631 0.1069 0.1456 0.0929 0.1300 0.0808 0.1161 0.0703 0.1037 0.0611 0.0588 0.0304 0.0334 0.0151 0.0189 0.0075 0.0107 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 Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 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 1.00001.0000 1.0000 1.0000 1.0000 1.0000 1.0200 1.0300 1.0400 1.0500 1.0600 1.0700 1.0404 1.0609 1.0816 1.1025 1.1236 1.1449 1.0612 1.0927 1.1249 1.1576 1.1910 1.2250 1.0824 1.1255 1.1699 1.2155 1.2625 1.3108 1.10411.15931.2167 1.2763 1.3382 1.4026 1.1262 1.1941 1.2653 1.3401 1.4185 1.5007 1.1487 1.2299 1.3159 1.4071 1.5036 1.6058 1.1717 1.2668 1.3686 1.4775 1.5938 1.7182 1.1951 1.3048 1.4233 1.5513 1.6895 1.8385 1.21901.3439 1.4802 1.6289 1.7908 1.9672 1.2434 1.3842 1.5395 1.7103 1.8983 2.1049 1.2682 1.4258 1.6010 1.7959 2 .0122 2.2522 1.2936 1.4685 1.6651 1.8856 2.1329 2.4098 1.31951.5126 1.73171.9799 2.26092.5785 1.34591.5580 1.8009 2.0789 2.3966 2.7590 1.3728 1.60471.8730 2.1829 2.5404 2.9522 1.4002 1.6528 1.9479 2.2920 2.6928 3.1588 1.4282 1.7024 2.0258 2.4066 2.8543 3.3799 1.4568 1.75352.1068 2.5270 3.0256 3.6165 1.4859 1.8061 2.1911 2.6533 3.2071 3.8697 1.6406 2.0938 2.6658 3.3864 4.2919 5.4274 1.8114 2.4273 3.2434 4.32195 .7435 7 .6123 1.99992.8139 3.9461 5.5160 7.6861 10.6766 2.2080 3.2620 4.8010 7.0400 10.2857 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 1.0000 1.1000 1.1200 1.2100 1.2544 1.3310 1.4049 1.4641 1.5735 1.6105 1.7623 1.7716 1.9738 1.9487 2.2107 2.1436 2.4760 2.3579 2.7731 2.5937 3.1058 2.8531 3.4785 3.1384 3.8960 3.4523 4.3635 3.7975 4.8871 4.1772 5.4736 4.5950 6.1304 5.0545 6.8660 5.5599 7.6900 6.1159 8.6128 6.7275 9.6463 10.8347 17.0001 17.4494 29.9599 28.1024 52.7996 45.2593 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 30 35 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). -=[v-ation] TABLE B.3 Present Value of an Annuity of 1 Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% 0 WN o co 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 0.9709 1.9416 1.9135 2.8839 2.8286 3.8077 3.7171 4.71354.5797 5.60145.4172 6.4720 6.2303 7.3255 7.0197 8.1622 7.7861 8.9826 8.5302 9.7868 9.2526 10.5753 9.9540 11.3484 10.6350 12.1062 11.2961 12.8493 11.9379 13.5777 12.5611 14.29191 3.1661 14.9920 13.7535 15.6785 14.3238 16.3514 14.8775 19.5235 17.4131 22.3965 19.6004 24.9986 21.4872 27.3555 23.1148 .9615 0.9524 0.9434 0.9346 1.8861 1.8594 1.8334 1.8080 2.7751 2.7232 2.6730 2.6243 3.6299 3.5460 3.4651 3.3872 4.4518 4.3295 4.2124 4.1002 5.24215.0757 4.9173 4.7665 6.0021 5.7864 5.5824 5.3893 6.7327 6.4632 6.2098 5.9713 7.4353 7.1078 6.8017 6.5152 8.11097.7217 7.3601 7.0236 8.7605 8.3064 7.8869 7.4987 9.3851 8.8633 8.3838 7.9427 9.9856 9.3936 8.8527 8.3577 10.5631 9.8986 9.2950 8.7455 11.1184 10.37979.71229.1079 11.6523 10.8378 10.1059 9.4466 12.1657 11.2741 10.4773 9.7632 12.6593 11.6896 10.8276 10.0591 13.1339 12.0853 11.158110.3356 13.5903 12.4622 11.469910.5940 15.6221 14.093912.7834 11.6536 17.2920 15.3725 13.7648 12.4090 18.6646 16.3742 14.4982 12.9477 19.7928 17.1591 15.0463 13.3317 0.9259 0.9174 0.9091 0.8929 0.8696 1.7833 1.7591 1.7355 1.6901 1.6257 2.5771 2.5313 2.4869 2.4018 2.2832 3.3121 3.2397 3.1699 3.0373 2.8550 3.9927 3.8897 3.7908 3.6048 3.3522 4.62294.48594.3553 4.1114 3.7845 5.2064 5.0330 4.8684 4.5638 4.1604 5.7466 5.5348 5.33494.9676 4.4873 6.2469 5.9952 5.7590 5.3282 4.7716 6.71016.4177 6.1446 5.6502 5.0188 7.1390 6.8052 6.4951 5.9377 5.2337 7.5361 7.1607 6.8137 6.1944 5.4206 7.9038 7.48697.1034 6.4235 5.5831 8.2442 7.78627.3667 6.6282 5.7245 8.5595 8.0607 7.6061 6.81095.8474 8.8514 8.3126 7.8237 6.9740 5.9542 9.1216 8.5436 8.0216 7.1196 6.0472 9.3719 8.7556 8.2014 7.2497 6.1280 9.6036 8.9501 8.36497.3658 6.1982 9.8181 9.1285 8.5136 7.4694 6.2593 10.6748 9.8226 9.0770 7.8431 6.4641 11.2578 10.27379.42698.0552 6.5660 11.6546 10.56689.6442 8.1755 6.6166 11.9246 10.7574 9.77918.2438 6.6418 40 *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]/i TABLE B.4 Future Value of an Annuity of 1 Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% LO 1.0000 10000 10000 10000 10000 10000 2.0100 2.0200 2.0300 2.0400 2.0500 2.0600 3.0301 3.0604 3.0909 3.1216 3.1525 3.1836 4.0604 4.1216 4.1836 4.2465 4.3101 4.3746 5.1010 5.2040 5.30915.4163 5.5256 5.6371 6.1520 6.3081 6.4684 6.6330 6.80196.9753 7.2135 7.4343 7.66257.89838.1420 8.3938 8.2857 8.5830 8.89239.2142 9.54919.8975 9.3685 9.7546 10.1591 10.5828 11.0266 11.4913 10.4622 10.9497 11.4639 12.0061 12.5779 13.1808 11.5668 12.1687 12.8078 13.4864 14.2068 14.9716 12.6825 13.4121 14.1920 15.0258 15.9171 16.8699 13.8093 14.6803 15.6178 16.6268 17.7130 18.8821 14.9474 15.9739 17.0863 18.2919 19.5986 21.0151 16.0969 17.2934 18.5989 20.0236 21.5786 23.2760 17.2579 18.6393 20.1569 21.8245 23.6575 25.6725 18.4304 20.0121 21.7616 23.6975 25.8404 28.2129 19.6147 21.4123 23.4144 25.6454 28.1324 30.9057 20.8109 22.8406 25.1169 27.6712 30.5390 33.7600 22.0190 24.2974 26.8704 29.7781 33.0660 36.7856 28.2432 32.0303 36.4593 41.6459 47.7271 54.8645 34.7849 40.5681 47.5754 56.084966.4388 79.0582 41.6603 49.994560.4621 73.6522 90.3203 111.4348 48.8864 60.4020 75.4013 95.0255 120.7998 154.7620 10000 1.0000 1.0000 1.0000 1.0000 1.0000 2.0700 2.0800 2.0900 2.1000 2.1200 2.1500 3.2149 3.2464 3.2781 3.3100 3.3744 3.4725 4.4399 4.5061 4.5731 4.6410 4.7793 4.9934 5.75075 .8666 5.9847 6.1051 6.3528 6.7424 7.15337.33597.52337.7156 8.1152 8.7537 8.65408 .9228 9.2004 9.4872 10.0890 11.0668 10.2598 10.6366 11.028511.4359 12.2997 13.7268 11.9780 12.4876 13.0210 13.5795 14.7757 16.7858 13.8164 14.4866 15.1929 15.9374 17.5487 20.3037 15.7836 16.6455 17.5603 18.5312 20.6546 24.3493 17.8885 18.9771 20.1407 21.3843 24.1331 29.0017 20.1406 21.4953 22.9534 24.5227 28.0291 34.3519 22.5505 24.2149 26.0192 27.9750 32.3926 40.5047 25.1290 27.1521 29.360931.7725 37.2797 47.5804 27.8881 30.3243 33.0034 35.9497 42.7533 55.7175 30.8402 33.7502 36.9737 40.5447 48.8837 65.0751 33.9990 37.4502 41.3013 45.5992 55.7497 75.8364 37.3790 41.4463 46.0185 51.1591 63.4397 88.2118 40.9955 45.7620 51.1601 57.2750 72.0524 102.4436 63.2490 73.1059 84.700998.3471 133.3339 212.7930 94.4608 113.2832 136.3075 164.4940 241.3327 434.7451 138.2369 172.3168 215.7108 271.0244 431.6635 881.1702 199.6351 259.0565 337.8824 442.5926 767.0914 1,779.0903 20 30 40 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)
