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Exercise 13-3 Internal Rate of Return [LO13-3) Wendell's Donut Shoppe is investigating the purchase of a new $52,100 donut making machine. The new machine would permit the company to reduce the amount of part-time help needed, at a cost savings of $6,100 per year. In addition, the new machine would allow the company to produce one new style of donut, resulting in the sale of 2,800 dozen more donuts each year. The company realizes a contribution margin of $170 per dozen donuts sold. The new machine would have a six-year useful life. Click here to view Exhibit 13B-1 and Exhibit 13B 2 to determine the appropriate discount factor(s) using tables. Required: 1. What would be the total annual cash inflows associated with the new machine for capital budgeting purposes? 2. What discount factor should be used to compute the new machine's Internal rate of return? (Round your answers to 3 decimal places.) 3. What is the new machine's internal rate of return? (Round your final answer to nearest whole percentage.) 4. In addition to the data given previously, assume that the machine will have a $11,500 salvage value at the end of six years. Under these conditions, what is the internal rate of return? (Hint You may find it helpful to use the net present value approach, find the discount rate that will cause the net present value to be closest to zero.) (Round your final answer to nearest whole percentage.) Required: 1. What would be the total annual cash inflows associated with the new machine for capital budgeting purposes? 2. What discount factor should be used to compute the new machine's internal rate of return? (Round your answers to 3 decimal places.) 3. What is the new machine's internal rate of return? (Round your final answer to nearest whole percentage.) 4. In addition to the data given previously, assume that the machine will have a $11,500 salvage value at the end of six years. Under these conditions, what is the internal rate of return? (Hint: You may find it helpful to use the net present value approach: find the discount rate that will cause the net present value to be closest to zero) (Round your final answer to nearest whole percentage.) 1 2 3 4 Annual cash inflows Discount factor Internal rate of return Internal rate of retum EXHIBIT 130-1 Present of the Periods 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 245 255 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 0.826 0.820 0813 0.806 0.800 2 0.925 0.907 0.890 0.873 0.857 0.842 0.826 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694 0.683 0.672 0.661 0.650 0.540 3 0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579 0.564 0.551 0.537 0.524 0.512 4 0.855 0.823 0.792 0.763 0.735 0.708 0.683 0659 0.636 0.613 0.592 0.572 0.552 0.534 0.516 0.499 0482 0.467 0.451 0.437 0.423 0410 5 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.593 0.567 0.543 0.519 0.497 0.476 0.456 0.437 0.419 0402 0.386 0.370 0.355 0.341 0.328 5 7 0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.535 0.507 0.480 0.456 0.432 0.410 0.390 0.370 0.352 0.335 0.319 0.303 0.289 0.275 0.262 0.750 0.711 0.665 0.623 0.583 0.547 0.513 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279 0.263 0249 0215 0222 0210 0.71 0.677 0.627 052 0 540 0 502 0.467 0.434 0.404 0.376 0.351 0.327 0.305 0.295 0.266 0249 0233 0.218 0204 0 191 179 0168 0.703 0.545 0.592 0.544 0.500 0.460 0.424 0.391 0.361 0.333 0.300 0.204 0.263 0.243 0225 0.209 0.194 0.180 0.167 0.155 0 144 0.134 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0191 0.176 0162 0.149 0137 0.125 0.116 0.107 10 11 050 055 0527 0.475 0429 0.18 0150 0317 0207 0.251 0237 0215 0 195 0.178 0162 0148 0.135 01230112 0 103 0094 0.086 0625 0.557 0.497 0.444 0.397 0.356 0.319 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0 137 0.124 0 112 0.102 0092 0.083 0076 0.069 13 0 601 0500469 0415 0368 0.326 0.290 0.250 0.229 0.204 0.182 0.163 0145 0.130 0 116 0104 0093 0.084 0.075 0068 0.0510055 14 0577 0.505 0442 0.38 0 140 0.299 0.263 0.232 0.205 0.181 0 160 0141 0.125 0.111 0009 008 0078 0.069 0062 0055 004 0044 15 0.555 0.481 0.417 0.362 0315 0.275 0239 0.200 0.13 0.160 0.40 0.123 0.00 0.095 084 0.074 0.065 0.057 0.051 0.045 0010 0035 16 0514049201040310 0202 0252 020 0.163 01410120107 000 001 0071 0062 0054 0047 0042 0036 002 00 17 0513 0.435 0.371 03170270 0231 0.19 0.10 0.146 0125 000 000 000 000 0060 0052 0.045 0.00 0.034 000 002 0023 13 04040416 030 0.205 0.250 0212 OTRO 0.1510110 0111 0005 DORT 000 0050 051 0044 0018 0012 0028 0024 002 001 10 0.375 0.06 0331 0.277 0232 01040154 01 0.116 0.0000 007000600051 0.043 001 0.031 0.027 002002000170014 20 0.456 0377 0.312 0258 0215 0.17 0.140 0.124 0104 0.007 007 006 005 004 003 0031 0.026 0022 0010 0016 0.014 0012 21 0430 0.359 0.294 0242 0.19 0.164 0.135 0.112 0.003 0.027 0064 005 0044 0.037 0.031 0.025 0.022 018 0015 0.013 001T 0.009 22 0.422 0.342 0.278 0.226 0.184 0150 0.123 0.101 0.00 0.068 0056 0046 0038 0032 0.026 0.022 018 015 2013 0.01 0.000 0.007 23 0060326 0.262 0.211 0.170 0138 0.12 0.091 0.074 060 0.049 0040 0033 0027 0022 0.018 00 15 0012 0.010 0.000 0.007 0.006 24 0 190 0.310 0247 0.17 0.15 0.126 0102 0.002 0.06 005 004 003 002 003 0019 2015 2013 0010 0.00 0.00 0.00 0.005 25 0.375 0.295 0.23 0.14 0.146 0110 0002 0.074 0.059 0047 003 00:30 0024 0.020 0,016 0013 0010 0000 0.007 0.005 0.005 0.004 26 0.301 0281 0.220 0.172 0.135 0.106 oon o006 ooss 0012 onas 0026 0.021 0.017 0.014 0.011 0000 0.007 0.006 ooos aoot 0003 27 0 147 0268 0.207 0.151 0.125 0.098 007 0060 004 003 0029 0023 0.018 0014 0011 0.009 0007 0006 0.005 0.004 000 0002 28 0332 0265 0 195 0.150 a116 0090 0.000 0.00 0.002 0.025 0.025 0.0200.0160.012 0010 0.008 0.000 0.00 0.004 0.003 0.002 0.002 0321 0243 0.185 0.141 0.107 0.02 0063 004 0037 0.029 002 0017 001 0011 000 000 000 0004 0.003 0.002 0002 0.002 30 0 231 0.17 0.1310099 0050057 0044 033 0.026 00200015 0.012 0.000 0.00 0.00 0.004 00030003 0.0020002 0001 40 2 08 0.142 0097 0.067 0.046 0032 0.022 0015 01 000 000 0004 003 0.002 0001 0001 0.001 0000 0000 0000 0.000 0.000 EXHIBIT 133-2 Present Value of an Annuity of $1 in Arrears 1- " Periods 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 1 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 0.826 0.820 0.813 0.806 0.800 2 1.886 1.859 1.833 1.808 1.783 1759 1.736 1.713 1.690 1.668 1.647 1.626 1605 1.585 1.566 1.547 1.528 1.509 1.492 1.474 1.457 1.440 3 2.775 2.723 2.673 2624 2.577 2.531 2.487 2444 2.402 2.361 2322 2.283 2.246 2.210 2.174 2.140 2.106 2074 2.042 2011 1.981 1952 4 3.630 3.546 3.465 3.387 3.312 3.240 3.170 3.102 3.037 2.974 2.914 2.855 2.798 2743 2.690 2.639 2.589 2540 2.494 2.448 2.404 2.362 5 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.696 3.605 3.517 3.433 3.352 3.274 3.199 3.127 3.058 2.991 2.926 2.864 2.803 2.745 2.689 6 5.242 5.076 4.917 4.767 4623 4.486 4.355 4 231 4.111 3.998 3.889 3.784 3.685 3.589 3.498 3.410 3326 3.245 3.167 3.092 3.020 2.951 6.002 5.786 5.582 5.389 5.206 5.033 4.868 4.712 4.564 4.423 4.288 4.160 4,039 3.922 3.812 3.706 3 605 3.508 3.416 3.327 3.242 3.161 8 6.733 6.463 6.210 5.971 57475.535 5.335 5.146 4.968 4.799 4.639 4.487 4 344 4.207 4.078 3.954 3.837 3.726 3.619 3.518 3.421 3.329 9 7.435 7.108 6.802 6.515 6.247 5.995 5.759 5.537 5.328 5.132 4.946 4.772 4.607 4.451 4.303 4.163 4.031 3.905 3.786 3.673 3.566 3.463 10 8.111 7.722 7360 7.024 6.710 6.418 6.145 5.889 5.650 5.426 5.216 5,019 4.833 4.659 4.494 4.339 4.192 4.054 3.923 3.799 3.682 3.571 11 8.760 8.306 7.887 7.499 7.139 6.805 6.495 6.207 5.938 5.687 5.453 5.234 5.029 4.836 4.656 4.486 4.327 4.177 4,035 3.902 3.776 3.656 12 93858.863 8 384 7943 7536 7161 6.814 6.492 6.194 5.918 5.660 5.421 5.197 4988 4.793 4.611 4.439 4278 4.127 3985 3.851 3.725 13 9.986 9.394 8.853 8 358 7904 7487 7.103 6.750 5.424 6.122 5,842 5.583 5 342 5.118 4.910 4715 4533 4 362 4203 4053 3.912 3.780 14 10.563 9.899 9.295 8.745 8.244 7.786 7.367 6.982 5.628 6.302 6.002 5.724 5.468 5.229 5.008 4 802 4,611 4.432 4.265 4.108 3.962 3.824 15 11.118 10 380 9.712 9.10B 8.559 8061 7.606 7191 5.811 6.462 6.142 5.847 5.575 5 324 5.092 4.876 4.675 4.489 4.315 4.153 4001 3.859 16 17 18 19 20 11.652 10.838 10.106 9.447 8.851 8.313 7.824 7 379 6974 6,604 6.265 5.954 5668 5.405 5.162 4.938 4.730 4.536 4.357 4.189 4.033 3 897 12.166 11 274 10.477 9.763 9.122 8544 8022 7549 7.120 6.229 6.373 6.047 5749 5.475 5.222 4.990 4.775 4.576 4.391 4.219 4.059 3910 12.559 11.690 10 828 10.0599372 8.756 3.201 7.702 7.250 6.40 6.467 6.128 5.818 5534 5 273 5033 48124.608 4.419 4243 4080 3928 13.134 12.085 11.158 10.336 9.604 8.950 8.365 7.839 7 366 6.938 6.5506.198 5.877 5584 5316 5070 4.843 4.635 4.442 4.263 4 097 3.942 13.590 12.462 11.470 10.5949818 9.129 3514 7963 7.469 2025 6623 6.259 5929 5.628 5353 51014870 4657 4.460 4279 4 110 3954 21 22 24 14.029 12.821 11.764 10.836 10 017 9.292 3.649 8,075 7562 7.102 6.687 6.312 5.923 5.665 5384 5 127 4 891 4675 4.476 4.292 4.121 3.963 14.451 13.163 12.042 11.061 10.2019.442 87728.176 2645 7 120 6.743 6.259 6011 5.506 5410 5.149 4909 4.690 4.488 4.302 4.130 3.970 14.857 13.489 12 303 11.272 10 371 9.580 8 883 3.266 7718 7230 6.792 6.399 6044 5723 5.432 5 167 4925 4.703 4.499 4.311 4.137 3.976 15.247 13 799 12 550 11.469 10529 9707 BB5 7784720163564246 073 5746 5.451 5.182 4937 4.713 4.507 4 318 4.143 3.981 15.622 14.094 12.783 11.654 10.675 9.823 9077 8.422 743 7330 6.873 6.464 6.097 5.766 5.467 5.1954.948 4721 4514 4 323 4.147 3.985 15.983 14 375 13003 11826 10 810 0.0299 161 707779 006 6401 611 573 5 05 206 4056 4728 4520 4328 4 151 3988 15 330 14 543 13 211 11987 10 935 10.027 9237 548 7043 7.000 6.935 6514 6136 5.798 5.492 5215 4.964 4.734 4524 4332 4. 154 3.990 16.663 14.898 13.406 12.137 11.051 10.116 9.307 1.602 79847641 6.961 6.514 6.152 5810 5.502 5.223 4.970 4.739 4.528 4 335 4.157 3.992 16,984 15.141 13.591 12278 11 158 10.1989 370 8650 80227.470 6.983 6.551 6.166 5320 5510 529 4.975 4.743 4531 4337 4.159 3994 17.292 15.372 13.765 12 400 11.258 10.274 427 3 604 2055 2006 200560615 05517 5225 4070 4.7464.534 4.329 4.160 2995 19.793 17.159 15.046 13.332 11.925 10.757 9.779 8.951 8.244 7634 7.105 6.642 6 233 5.871 5548 5.258 4.997 4.760 4.544 4.347 4.166 3.999 27 28 29 30 40

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