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