Information on assumed capital investments in the current year for Google and Apple follow. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.) $ millions Initial investment Annual net cash flows, years 1-10 Required rate of return on investment Google $ (23,548) $ 4,000 6% Apple $ (10,495) $ 3,000 7% Required: 1. Compute break-even time for both companies. 2. Based on break-even time, which company can expect its investment to more quickly yield positive net cash flows? Complete this question by entering your answers in the tabs below. Required 1 Required 2 Compute break-even time for both companies. (Round "Break even time" answers to 1 decimal place.) Google Apple 4.2 years Break-even time years Required 1 Required 2 Based on break-even time, which company can expect its investment to more quickly yield positive net cash flows? Which company can expect its investment to more quickly yield positive net cash flows? Apple Table B.1* Present Value of 1 p=1/(1+i)" Rate Periods 1% 2% 3% 4% 6% 7% 8% 9% 10% 12% 15% Periods 5% 0.9524 1 0.9901 0.9804 0.9709 0.9615 0.9434 0.9346 0.9259 0.9174 0.9091 0.8929 0.8696 1 2 0.9803 0.9612 0.9426 0.9246 0.9070 0.8734 0.8573 0.8417 0.8264 0.7972 0.7561 2 0.8900 0.8396 3 0.9706 0.9423 0.9151 0.8890 0.8638 0.8163 0.7938 0.7722 0.7513 0.7118 0.6575 3 4 0.9610 0.9238 0.7350 J. 0.7084 0.6830 0.5718 0.8885 0.8626 4 0.8548 0.8219 0.8227 0.7835 0.7921 0.7473 0.7629 0.7130 0.6355 0.5674 5 0.9515 0.9057 0.6806 0.6499 0.6209 0.4972 5 6 0.9420 0.8880 0.8375 0.7903 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645 0.5066 0.4323 6 7 0.8706 0.8131 0.7599 0.7107 0.6651 0.6227 0.5835 0.5470 7 0.9327 0.9235 0.5132 0.4665 0.4523 0.4039 0.3759 0.3269 8 0.8535 0.7894 0.6768 0.6274 0.5820 0.5403 0.5019 8 0.7307 0.7026 9 0.9143 0.8368 0.7664 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3606 0.2843 9 10 0.9053 0.8203 0.7441 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 0.3220 0.2472 10 11 0.8963 0.8043 0.7224 0.6496 0.5847 0.5268 0.4751 0.4289 0.3875 0.3505 0.2875 0.2149 11 12 0.8874 0.7014 0.6246 0.5568 0.4970 0.3971 0.2567 0.1869 12 0.7885 0.7730 0.4440 0.4150 0.3555 0.3262 0.3186 0.2897 13 0.6810 0.6006 0.5303 0.4688 0.3677 0.2292 0.1625 13 0.8787 0.8700 14 0.7579 0.6611 0.5775 0.5051 0.4423 0.3878 0.3405 0.2992 0.2633 0.2046 0.1413 14 15 0.8613 0.7430 0.6419 0.5553 0.4810 0.4173 0.3624 0.2745 0.2394 0.1827 0.1229 15 16 0.7284 0.6232 0.5339 0.4581 0.3936 0.3387 0.3152 0.2919 0.2703 0.2519 0.2176 0.1631 0.1069 16 0.8528 0.8444 0.8360 17 0.7142 0.6050 0.5134 0.4363 0.1978 0.1456 0.0929 17 18 0.7002 0.5874 0.4936 0.3714 0.3503 0.3305 0.3166 0.2959 0.2765 0.4155 0.3957 0.1300 0.2311 0.2120 0.1945 0.0808 18 19 0.1799 0.1635 0.6864 0.5703 0.2502 0.2317 0.2145 0.4746 elele 0.1161 0.8277 0.8195 0.0703 19 20 0.6730 0.5537 0.4564 0.3118 0.2584 0.1784 0.1486 0.1037 0.0611 20 0.3769 0.2953 25 0.7798 0.6095 0.4776 0.3751 0.1160 0.0923 0.0588 0.0304 25 0.2330 0.1741 30 0.5521 0.0334 0.0151 0.7419 0.7059 30 0.4120 0.3554 0.1460 0.0994 0.0676 0.3083 0.2534 0.2314 0.1813 0.1842 0.1314 0.0937 0.0668 0.0754 0.0490 0.0573 0.0356 35 0.5000 0.1301 0.0189 0.0075 35 40 0.6717 0.4529 0.3066 0.2083 0.1420 0.0972 0.0460 0.0318 0.0221 0.0107 0.0037 40 *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). f = (1 + i)" Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% Periods 0 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0 1 1.0100 1.0200 1.0300 1.0500 1.0600 1.0800 1.0900 1.1200 1.1500 1 1.0400 1.0816 1.0700 1.1449 2 1.0201 1.0404 1.0609 1.1025 1.1664 1.1881 1.1000 1.2100 1.3310 1.1236 1.1910 2 1.2544 1.4049 1.3225 1.5209 3 1.0303 1.0612 1.0927 1.1249 1.1576 1.2250 1.2597 1.2950 3 4 1.0406 1.0824 1.1255 1.1699 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641 1.5735 1.7490 4 5 1.0510 1.1041 1.1593 1.2167 1.2763 1.3382 1.4026 1.4693 1.7623 2.0114 5 1.5386 1.6771 1.6105 1.7716 6 1.0615 1.1262 1.2653 1.5007 1.9738 2.3131 6 1.1941 1.2299 1.3401 1.4071 1.4185 1.5036 1.5869 1.7138 7 1.0721 1.1487 1.3159 1.6058 1.8280 1.9487 2.2107 2.6600 7 8 1.0829 1.1717 1.3686 1.4775 1.5938 1.7182 1.8509 1.9926 2.4760 3.0590 8 1.2668 1.3048 9 1.0937 1.1951 1.4233 1.5513 1.9990 2.1719 2.7731 3.5179 9 1.8385 1.9672 10 1.1046 1.4802 2.3674 1.6895 1.7908 1.8983 4.0456 1.2190 1.2434 10 1.3439 1.3842 1.6289 1.7103 2.1589 2.3316 2.1436 2.3579 2.5937 2.8531 3.1384 3.4523 3.1058 3.4785 11 1.1157 1.5395 2.1049 2.5804 4.6524 11 12 1.1268 1.2682 1.4258 1.6010 1.7959 2.0122 2.2522 2.5182 2.8127 3.8960 5.3503 12 13 1.4685 1.6651 1.8856 2.1329 2.4098 3.0658 4.3635 6.1528 13 1.1381 1.1495 1.2936 1.3195 2.7196 2.9372 14 1.5126 1.9799 2.2609 3.3417 3.7975 4.8871 14 1.7317 1.8009 7.0757 8.1371 15 1.1610 2.0789 2.3966 2.5785 2.7590 2.9522 3.1722 3.6425 4.1772 5.4736 1.3459 1.3728 15 16 1.5580 1.6047 1.6528 1.8730 2.5404 3.4259 3.9703 9.3576 1.1726 1.1843 16 2.1829 2.2920 4.5950 5.0545 6.1304 6.8660 17 1.9479 3.1588 3.7000 4.3276 10.7613 17 1.4002 1.4282 2.6928 2.8543 18 1.1961 1.7024 2.0258 2.4066 3.3799 3.9960 4.7171 5.5599 7.6900 12.3755 18 19 1.7535 3.0256 3.6165 6.1159 8.6128 14.2318 19 1.2081 1.2202 1.4568 1.4859 2.1068 2.1911 2.5270 2.6533 5.1417 5.6044 20 1.8061 3.8697 4.3157 4.6610 6.8485 9.6463 20 6.7275 10.8347 16.3665 32.9190 25 1.2824 TTTT 1.6406 2.0938 2.6658 3.3864 5.4274 17.0001 25 3.2071 4.2919 5.7435 7.6861 8.6231 13.2677 30 1.3478 1.8114 2.4273 3.2434 4.3219 7.6123 10.0627 29.9599 66.2118 30 T 17.4494 28.1024 35 1.4166 1.9999 2.8139 3.9461 5.5160 10.6766 14.7853 52.7996 133.1755 35 20.4140 31.4094 40 1.4889 2.2080 3.2620 4.8010 7.0400 10.2857 14.9745 21.7245 45.2593 93.0510 267.8635 40 * 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). Table B.3 Present Value of an Annuity of 1 p= [1 - 1/(1 + i)"]/i Rate Periods 1% 2% 3% 4% 6% 7% 8% 9% 10% 12% 15% Periods 1 0.9901 0.9804 0.9709 0.9615 0.9346 el 0.9259 0.9091 0.8929 0.8696 1 5% 0.9524 1.8594 2.7232 0.9174 1.7591 2 1.9704 1.9416 1.9135 0.9434 1.8334 2.6730 1.8861 1.8080 1.7833 1.7355 1.6901 1.6257 2 3 2.8839 2.7751 2.6243 2.5771 2.5313 2.4869 "T 2.4018 2.2832 3 T T 4 2.9410 3.9020 4.8534 2.8286 3.7171 4.5797 3.6299 3.3121 3.1699 3.0373 4 3.8077 4.7135 5.6014 3.5460 4.3295 3.4651 4.2124 3.3872 4.1002 3.2397 3.8897 5 2.8550 3.3522 4.4518 "T 3.9927 3.7908 3.6048 5 alulel 5.7955 6 5.4172 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.1114 3.7845 6 5.2421 6.0021 7 6.4720 6.2303 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.5638 7 8 6.7282 7.6517 8.5660 7.3255 lalala 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 4.9676 7.0197 7.7861 8 4.1604 4.4873 4.7716 5.3349 5.7590 9 8.1622 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.3282 9 10 9.4713 8.9826 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.0188 10 11 10.3676 9.7868 9.2526 8.3064 7.8869 7.4987 7.1390 6.8052 6.4951 5.6502 5.9377 6.1944 5.2337 11 12 10.5753 9.9540 8.7605 9.3851 9.9856 8.8633 7.9427 7.1607 6.8137 5.4206 11.2551 12.1337 12 8.3838 8.8527 7.5361 7.9038 13 11.3484 9.3936 8.3577 7.4869 7.1034 6.4235 5.5831 13 10.6350 11.2961 14 12.1062 9.8986 9.2950 8.7455 8.2442 7.7862 7.3667 6.6282 5.7245 14 13.0037 13.8651 10.5631 11.1184 15 12.8493 10.3797 9.7122 9.1079 8.5595 8.0607 7.6061 6.8109 5.8474 15 11.9379 12.5611 16 14.7179 13.5777 11.6523 10.8378 10.1059 9.4466 8.8514 8.3126 7.8237 6.9740 5.9542 16 17 15.5623 14.2919 13.1661 12.1657 10.4773 9.7632 9.1216 8.5436 8.0216 6.0472 17 7.1196 7.2497 18 16.3983 14.9920 12.6593 11.2741 11.6896 12.0853 10.8276 10.0591 9.3719 8.2014 13.7535 14.3238 18 8.7556 8.9501 6.1280 6.1982 19 17.2260 15.6785 10.3356 9.6036 8.3649 7.3658 19 13.1339 13.5903 11.1581 11.4699 20 18.0456 16.3514 14.8775 10.5940 9.8181 9.1285 8.5136 7.4694 6.2593 20 12.4622 14.0939 25 22.0232 17.4131 15.6221 12.7834 11.6536 10.6748 9.8226 9.0770 7.8431 6.4641 25 30 19.6004 17.2920 13.7648 12.4090 9.4269 8.0552 6.5660 30 25.8077 29.4086 19.5235 22.3965 24.9986 27.3555 15.3725 16.3742 11.2578 11.6546 35 21.4872 18.6646 12.9477 10.2737 10.5668 10.7574 8.1755 6.6166 14.4982 15.0463 35 9.6442 9.7791 40 32.8347 23.1148 19.7928 17.1591 13.3317 11.9246 8.2438 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). Table B.4%Future Value of an Annuity of 1 f = [(1 + i)" - 13/1 Rate Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 15% Periods 1 1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1 2 2.0100 2.0200 2.0300 IT 2.0400 2.0500 2.0800 2.0900 2.1200 2.1500 2 2.0600 3.1836 2.0700 3.2149 I 2.1000 3.3100 3 3.0301 3.0604 3.0909 3.1216 3.1525 3.2464 3.2781 3.3744 3.4725 3 4 4.0604 4.1216 4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 4.7793 4.9934 4 5 5.1010 4.1836 5.3091 6.4684 5.4163 5.5256 5.8666 6.1051 6.3528 6.7424 5 5.2040 6.3081 T 5.6371 6.9753 5.7507 7.1533 5.9847 7.5233 6 6.1520 6.6330 6.8019 7.3359 7.7156 8.1152 8.7537 6 7 7.2135 7.4343 7.6625 7.8983 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872 10.0890 11.0668 7 8 8.2857 8.5830 8.8923 9.2142 9.5491 9.8975 10.2598 10.6366 11.0285 12.2997 13.7268 8 9 9.3685 9.7546 10.5828 11.0266 11.9780 13.0210 10.1591 11.4639 9 11.4359 13.5795 15.9374 12.4876 14.4866 14.7757 17.5487 11.4913 13.1808 14.9716 16.7858 20.3037 10 10.4622 10.9497 12.0061 12.5779 13.8164 15.1929 10 11 12.1687 12.8078 13.4864 14.2068 15.7836 16.6455 17.5603 18.5312 20.6546 24.3493 11 11.5668 12.6825 12 13.4121 15.0258 15.9171 16.8699 17.8885 18.9771 20.1407 12 13 14.6803 16.6268 18.8821 20.1406 22.9534 13 13.8093 14.9474 14.1920 15.6178 17.0863 18.5989 21.4953 24.2149 14 15.9739 18.2919 26.0192 17.7130 19.5986 21.5786 23.6575 14 15 16.0969 17.2934 20.0236 21.0151 23.2760 25.6725 22.5505 25.1290 27.8881 15 29.3609 33.0034 16 17.2579 18.6393 20.1569 21.8245 16 27.1521 30.3243 33.7502 37.4502 17 18.4304 20.0121 21.7616 23.6975 25.8404 28.2129 30.8402 36.9737 17 18 19.6147 21.4123 23.4144 25.6454 28.1324 33.9990 41.3013 21.3843 24.1331 29.0017 24.5227 28.0291 34.3519 27.9750 32.3926 40.5047 31.7725 37.2797 47.5804 35.9497 42.7533 55.7175 40.5447 48.8837 65.0751 45.5992 55.7497 75.8364 51.1591 63.4397 88.2118 57.2750 72.0524 102.4436 98.3471 133.3339 212.7930 164.4940 241.3327 434.7451 271.0244 431.6635 881.1702 442.5926 767.0914 1,779.0903 18 19 25.1169 30.5390 41.4463 19 20.8109 22.0190 28.2432 30.9057 33.7600 36.7856 54.8645 22.8406 24.2974 32.0303 27.6712 29.7781 37.3790 40.9955 46.0185 51.1601 20 20 26.8704 36.4593 45.7620 73.1059 25 33.0660 47.7271 66.4388 41.6459 63.2490 84.7009 25 30 34.7849 40.5681 47.5754 56.0849 79.0582 94.4608 113.2832 136.3075 30 35 60.4621 73.6522 90.3203 111.4348 138.2369 35 41.6603 48.8864 49.9945 60.4020 172.3168 259.0565 215.7108 337.8824 40 75.4013 95.0255 120.7998 154.7620 199.6351 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)