TopCap Co. is evaluating the purchase of another sewing machine that will be used to manufacture sport caps. The invoice price of the machine is $124,500. In addition, delivery and installation costs will total $4,000. The machine has the capacity to produce 12,000 dozen caps per year. Sales are forecast to increase gradually, and production volumes for each of the five years of the machine's life are expected to be as follows: Use Table 6-4. (Use appropriate factor(s) from the tables provided. Round the PV factors to 4 decimals.)
| | | |
| 2019 | 3,600 | dozen |
| 2020 | 5,600 | dozen |
| 2021 | 8,500 | dozen |
| 2022 | 11,300 | dozen |
| 2023 | 12,000 | dozen |
| |
The caps have a contribution margin of $8.00 per dozen. Fixed costs associated with the additional production (other than depreciation expense) will be negligible. Salvage value and the investment in working capital should be ignored. TopCap Co.'s cost of capital for this capacity expansion has been set at 8%. Required:
- Calculate the net present value of the proposed investment in the new sewing machine.
- Calculate the present value ratio of the investment.
- What is the internal rate of return of this investment relative to the cost of capital?
- Calculate the payback period of the investment.
A. Calculate the net present value of the proposed investment. (Round your intermediate calculations to 2 decimals.) (Negative amount should be indicated by a minus sign.)
B. Calculate the present value ratio of the investment. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
C. What is the internal rate of return of this investment, relative to the cost of capital?
Internal rate of return of this investment: _____the cost of capital of 8%
D. Calculate the payback period of the investment. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Payback period: years
TABLE 6.4 FACTORS FOR CALCULATING THE PRESENT VALUE OF $1 Discount Rate No. of Periods 14% 16% 18% 2% 4% 6% 8% 10% 12% 20% 0.8333 0.980 0.9615 0.9434 0.9259 0.9091 0.8929 0.8772 0.8621 0.8475 1 0.7695 0.7182 2 0.961 0.9246 0.8900 0.8573 0.8264 0.7972 0.7432 0.6944 0.5787 3 0.942 0.8890 0.8396 0.7938 0.7513 0.6750 0.6407 0.6086 0.7118 0.7921 0.7350 0.6830 4 0.924 0.8548 0.6355 0.5921 0.5523 0.5158 0.4823 0.906 0.7473 0.6209 0.5674 0.8219 0.6806 0.5194 0.4761 0.4371 0.4019 0.6302 0.7050 0.3704 6 0.888 0.7903 0.5645 0.5066 0.4556 0.4104 0.3349 0.5835 7 0.871 0.7599 0.6651 0.5132 0.4523 0.3538 0.3139 0.2791 0.3996 0.4039 0.2326 0.853 0.7307 0.6274 0.5403 0.4665 0.3506 0.3050 0.2660 O.1938 0.837 0.7026 0.5919 0.5002 0.4241 0.3606 0.3075 0.2630 0.2255 0.2267 0.3855 0.1911 10 0.820 0.6756 0.5584 0.4632 0.3220 0.2697 0.1615 0.6496 0.3505 0.1954 11 0.804 0.5268 0.4289 0.2875 0.2366 0.1619 0.1346 0.3186 0.788 0.6246 0.4970 0.3971 0.2567 0.2076 0.1685 0.1372 0.1122 12 0.773 0.2897 13 0.6006 0.4688 0.3677 0.2292 0.1821 0.1452 0.1163 0.0935 0.4423 0.1252 14 0.758 0.5775 0.3405 0.2633 0.2046 0.1597 0.0985 0.0779 0.5553 0.1079 0.0835 15 0.743 0.4173 0.3152 0.2394 0.1827 0.1401 0.0649 0.3936 16 0.728 0.5339 0.2919 0.2176 0.1631 0.1229 0.0930 0.0708 O.0541 17 0.3714 0.2703 0.1978 0.0802 0.0451 0.714 0.5134 0.1456 0.1078 0.0600 0.0691 0.3503 0.1799 0.0376 18 0.700 0.4936 0.2502 0.1300 0.0946 0.0508 0.1635 0.686 0.1161 0.0829 19 0.4746 0.3305 0.2317 0.0596 0.0431 0.0313 0.3118 0.0514 0.0365 0.0261 20 0.673 0.4564 0.2145 0.1486 0.1037 0.0728 0.1987 O.0926 0.0217 21 0.660 0.4388 0.2942 0.1351 0.0638 0.0443 0.0309 0.647 0.4220 0.2775 0.1228 0.0560 0.0382 0.0262 O.0181 22 0.1839 0.0826 0.2618 0.1703 0.1117 0.0491 0.0222 0.0151 23 0.634 0.4057 0.0738 0.0329 0.1015 0.0188 0.3901 0.0284 24 0.622 0.2470 0.1577 0.0659 0.0431 0.0126 25 0.610 0.2330 0.1460 0.0588 0.0378 0.0245 0.0160 0.0105 0.3751 0.0923 0.0334 0.0070 30 0.552 0.3083 0.1741 0.0994 0.0573 0.0196 0.01 16 0.0042 0.0356 0.0055 O.0017 35 0.500 0.2534 0.1301 0.0676 0.0189 0.0102 0.0030 0.0013 0.2083 0.0972 0.0460 0.0221 0.0107 0.0007 40 0.453 0.0053 0.0026 0.1712 0.0313 0.0006 45 0.410 0.0727 0.0137 0.0061 0.0027 0.0013 0.0003 0.1407 0.0035 0.0006 0.0001 50 0.372 0.0543 0.0213 0.0085 0.0014 0.0003 FACTORS FOR CALCULATING THE PRESENT VALUE OF AN ANNUITY OF $1 TABLE 6.5 Discount Rate No. of 14% Periods 2% 4% 6% 16% 20% 8% 10% 12% 18% 0.980 0.9259 0.8333 1 0.9615 0.9434 0.9091 0.8929 0.8772 0.8621 0.8475 1.942 1.7833 1.5278 2 1.8861 1.8334 1.7355 1.6901 1.6467 1.6052 1.5656 2.4869 2.1065 3 2.884 2.7751 2.6730 2.5771 2.4018 2.3216 2.2459 2.1743 3.1699 3.808 3.6299 3.4651 3.3121 3.0373 2.9137 2.7982 2.6901 2.5887 4.713 4.4518 4.2124 3.9927 3.7908 3.6048 3.4331 3.2743 3.1272 2.9906 4.3553 6 5.601 5.2421 4.9173 4.6229 4.1114 3.8887 3.6847 3.4976 3.3255 5.5824 4.8684 4.5638 4.0386 7 6.472 6.0021 5.2064 4.2883 3.8115 3.6046 4.3436 7.325 6.7327 5.7466 4.9676 4.6389 4.0776 3.8372 6.2098 5.3349 6.8017 4.6065 6.2469 8.162 7.4353 5.7590 5.3282 4.9464 4.3030 4.0310 8.983 8.1109 6.1446 5.6502 4.4941 10 7.3601 6.7101 5.2161 4.8332 4.1925 7.8869 9.787 8.7605 7.1390 6.4951 5.9377 5.4527 5.0286 11 4.6560 4.3271 10.575 4.4392 12 9.3851 8.3838 7.5361 6.8137 6.1944 5.6603 5.1971 4.7932 7.1034 13 11.348 9.9856 8.8527 7.9038 6.4235 5.8424 5.3423 4.9095 4.5327 5.4675 12.106 10.5631 9.2950 7.3667 6.6282 6.0021 5.0081 14 8.2442 4.6106 6.8109 12.849 11.1184 9.7122 8.5595 7.6061 5.5755 4.6755 15 6.1422 5.0916 4.7296 16 13.578 11.6523 10.1059 8.8514 7.8237 6.9740 6.2651 5.6685 5.1624 9.1216 5.2223 17 14.292 12.1657 10.4773 8.0216 7.1196 6.3729 5.7487 4.7746 14.992 12.6593 10.8276 9.3719 8.2014 7.2497 6.4674 5.8178 5.2732 4.8122 18 19 15.678 13.1339 11.1581 9.6036 8.3649 7.3658 6.5504 5.8775 5.3162 4.8435 4.8696 20 16.351 13.5903 11.4699 9.8181 8.5136 7.4694 6.6231 5.9288 5.3527 8.6487 6.6870 21 17.011 14.0292 11.7641 10.0168 7.5620 5.9731 5.3837 4.8913 17.658 14.4511 8.7715 7.6446 4.9094 22 12.0416 10.2007 6.7429 6.0113 5.4099 8.8832 14.8568 12.3034 6.7921 4.9245 23 18.292 10.3711 7.7184 6.0442 5.4321 24 18.914 15.2470 12.5504 10.5288 8.9847 7.7843 6.8351 6.0726 5.4509 4.9371 19.523 4.9476 25 15.6221 12.7834 10.6748 9.0770 7.8431 6.8729 6.0971 5.4669 17.2920 13.7648 11.2578 8.0552 7.0027 6.1772 5.5168 4.9789 30 22.396 9.4269 9.6442 35 24.999 18.6646 14.4982 11.6546 8.1755 7.0700 6.2153 5.5386 4.9915 4.9966 40 27.355 19.7928 15.0463 11.9246 9.7791 8.2438 7.1050 6.2335 5.5482 45 20.7200 15.4558 9.8628 8.2825 7.1232 5.5523 4.9986 29.490 12.1084 6.2421 12.2335 50 31.424 21.4822 15.7619 9.9148 8.3045 7.1327 6.2463 5.5541 4.9995 TABLE 6.4 FACTORS FOR CALCULATING THE PRESENT VALUE OF $1 Discount Rate No. of Periods 14% 16% 18% 2% 4% 6% 8% 10% 12% 20% 0.8333 0.980 0.9615 0.9434 0.9259 0.9091 0.8929 0.8772 0.8621 0.8475 1 0.7695 0.7182 2 0.961 0.9246 0.8900 0.8573 0.8264 0.7972 0.7432 0.6944 0.5787 3 0.942 0.8890 0.8396 0.7938 0.7513 0.6750 0.6407 0.6086 0.7118 0.7921 0.7350 0.6830 4 0.924 0.8548 0.6355 0.5921 0.5523 0.5158 0.4823 0.906 0.7473 0.6209 0.5674 0.8219 0.6806 0.5194 0.4761 0.4371 0.4019 0.6302 0.7050 0.3704 6 0.888 0.7903 0.5645 0.5066 0.4556 0.4104 0.3349 0.5835 7 0.871 0.7599 0.6651 0.5132 0.4523 0.3538 0.3139 0.2791 0.3996 0.4039 0.2326 0.853 0.7307 0.6274 0.5403 0.4665 0.3506 0.3050 0.2660 O.1938 0.837 0.7026 0.5919 0.5002 0.4241 0.3606 0.3075 0.2630 0.2255 0.2267 0.3855 0.1911 10 0.820 0.6756 0.5584 0.4632 0.3220 0.2697 0.1615 0.6496 0.3505 0.1954 11 0.804 0.5268 0.4289 0.2875 0.2366 0.1619 0.1346 0.3186 0.788 0.6246 0.4970 0.3971 0.2567 0.2076 0.1685 0.1372 0.1122 12 0.773 0.2897 13 0.6006 0.4688 0.3677 0.2292 0.1821 0.1452 0.1163 0.0935 0.4423 0.1252 14 0.758 0.5775 0.3405 0.2633 0.2046 0.1597 0.0985 0.0779 0.5553 0.1079 0.0835 15 0.743 0.4173 0.3152 0.2394 0.1827 0.1401 0.0649 0.3936 16 0.728 0.5339 0.2919 0.2176 0.1631 0.1229 0.0930 0.0708 O.0541 17 0.3714 0.2703 0.1978 0.0802 0.0451 0.714 0.5134 0.1456 0.1078 0.0600 0.0691 0.3503 0.1799 0.0376 18 0.700 0.4936 0.2502 0.1300 0.0946 0.0508 0.1635 0.686 0.1161 0.0829 19 0.4746 0.3305 0.2317 0.0596 0.0431 0.0313 0.3118 0.0514 0.0365 0.0261 20 0.673 0.4564 0.2145 0.1486 0.1037 0.0728 0.1987 O.0926 0.0217 21 0.660 0.4388 0.2942 0.1351 0.0638 0.0443 0.0309 0.647 0.4220 0.2775 0.1228 0.0560 0.0382 0.0262 O.0181 22 0.1839 0.0826 0.2618 0.1703 0.1117 0.0491 0.0222 0.0151 23 0.634 0.4057 0.0738 0.0329 0.1015 0.0188 0.3901 0.0284 24 0.622 0.2470 0.1577 0.0659 0.0431 0.0126 25 0.610 0.2330 0.1460 0.0588 0.0378 0.0245 0.0160 0.0105 0.3751 0.0923 0.0334 0.0070 30 0.552 0.3083 0.1741 0.0994 0.0573 0.0196 0.01 16 0.0042 0.0356 0.0055 O.0017 35 0.500 0.2534 0.1301 0.0676 0.0189 0.0102 0.0030 0.0013 0.2083 0.0972 0.0460 0.0221 0.0107 0.0007 40 0.453 0.0053 0.0026 0.1712 0.0313 0.0006 45 0.410 0.0727 0.0137 0.0061 0.0027 0.0013 0.0003 0.1407 0.0035 0.0006 0.0001 50 0.372 0.0543 0.0213 0.0085 0.0014 0.0003 FACTORS FOR CALCULATING THE PRESENT VALUE OF AN ANNUITY OF $1 TABLE 6.5 Discount Rate No. of 14% Periods 2% 4% 6% 16% 20% 8% 10% 12% 18% 0.980 0.9259 0.8333 1 0.9615 0.9434 0.9091 0.8929 0.8772 0.8621 0.8475 1.942 1.7833 1.5278 2 1.8861 1.8334 1.7355 1.6901 1.6467 1.6052 1.5656 2.4869 2.1065 3 2.884 2.7751 2.6730 2.5771 2.4018 2.3216 2.2459 2.1743 3.1699 3.808 3.6299 3.4651 3.3121 3.0373 2.9137 2.7982 2.6901 2.5887 4.713 4.4518 4.2124 3.9927 3.7908 3.6048 3.4331 3.2743 3.1272 2.9906 4.3553 6 5.601 5.2421 4.9173 4.6229 4.1114 3.8887 3.6847 3.4976 3.3255 5.5824 4.8684 4.5638 4.0386 7 6.472 6.0021 5.2064 4.2883 3.8115 3.6046 4.3436 7.325 6.7327 5.7466 4.9676 4.6389 4.0776 3.8372 6.2098 5.3349 6.8017 4.6065 6.2469 8.162 7.4353 5.7590 5.3282 4.9464 4.3030 4.0310 8.983 8.1109 6.1446 5.6502 4.4941 10 7.3601 6.7101 5.2161 4.8332 4.1925 7.8869 9.787 8.7605 7.1390 6.4951 5.9377 5.4527 5.0286 11 4.6560 4.3271 10.575 4.4392 12 9.3851 8.3838 7.5361 6.8137 6.1944 5.6603 5.1971 4.7932 7.1034 13 11.348 9.9856 8.8527 7.9038 6.4235 5.8424 5.3423 4.9095 4.5327 5.4675 12.106 10.5631 9.2950 7.3667 6.6282 6.0021 5.0081 14 8.2442 4.6106 6.8109 12.849 11.1184 9.7122 8.5595 7.6061 5.5755 4.6755 15 6.1422 5.0916 4.7296 16 13.578 11.6523 10.1059 8.8514 7.8237 6.9740 6.2651 5.6685 5.1624 9.1216 5.2223 17 14.292 12.1657 10.4773 8.0216 7.1196 6.3729 5.7487 4.7746 14.992 12.6593 10.8276 9.3719 8.2014 7.2497 6.4674 5.8178 5.2732 4.8122 18 19 15.678 13.1339 11.1581 9.6036 8.3649 7.3658 6.5504 5.8775 5.3162 4.8435 4.8696 20 16.351 13.5903 11.4699 9.8181 8.5136 7.4694 6.6231 5.9288 5.3527 8.6487 6.6870 21 17.011 14.0292 11.7641 10.0168 7.5620 5.9731 5.3837 4.8913 17.658 14.4511 8.7715 7.6446 4.9094 22 12.0416 10.2007 6.7429 6.0113 5.4099 8.8832 14.8568 12.3034 6.7921 4.9245 23 18.292 10.3711 7.7184 6.0442 5.4321 24 18.914 15.2470 12.5504 10.5288 8.9847 7.7843 6.8351 6.0726 5.4509 4.9371 19.523 4.9476 25 15.6221 12.7834 10.6748 9.0770 7.8431 6.8729 6.0971 5.4669 17.2920 13.7648 11.2578 8.0552 7.0027 6.1772 5.5168 4.9789 30 22.396 9.4269 9.6442 35 24.999 18.6646 14.4982 11.6546 8.1755 7.0700 6.2153 5.5386 4.9915 4.9966 40 27.355 19.7928 15.0463 11.9246 9.7791 8.2438 7.1050 6.2335 5.5482 45 20.7200 15.4558 9.8628 8.2825 7.1232 5.5523 4.9986 29.490 12.1084 6.2421 12.2335 50 31.424 21.4822 15.7619 9.9148 8.3045 7.1327 6.2463 5.5541 4.9995
