Smith Inc. operates a chain of doughnut shops. The company is considering two possible expansion plans. Plan A would open eight smaller shops at a cost of $8,840,000. Expected annual net cash inflows are $1,450,000 with zero residual value at the end of ten years. Under Plan B, Smith would open three larger shops at a cost of $8,540,000. This plan is expected to generate net cash inflows of $1,100,000 per year for ten years, the estimated life of the properties. Estimated residual value is $900,000. Smith uses straight-line depreciation and requires an annual return of 10%.

1.	Compute the payback period, the ARR, and the NPV of these two plans. What are the strengths and weaknesses of these capital budgeting models?
2.	Which expansion plan should Smith choose? Why?
3.	Estimate Plan A's IRR. How does the IRR compare with the company's required rate of return?

18% 1.000 3.572 5.215 7.154 9.442 12.142 15.327 19.086 23.521 20% 1.000 2.200 3.640 5.368 7.442 9.930 12.916 16.499 20.799 25.959 Future Value of Annuity of $1 Periods 1% 2% 3% 4% 5% 6% 8% 10% 12% 14% 16% Period 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 Period 2 2.010 2020 2030 2040 2050 2.060 2.080 2.120 2.140 2.160 Period 3 3.030 3.060 3.091 3.122 3.153 3.184 3.246 3.310 3.374 3.440 3.506 Period 4 4.060 | 4.122 4.184 4.246 4.310 4.375 4.506 4.641 4.779 4.921 5.066 Period 5 5.101 5.204 5.309 5.416 5.526 5.637 5.867 6.105 6.353 6.610 6.877 Period 66.152 6.308 6.468 6.633 6.802 6.975 7.336 7.716 8.115 8.536 8.977 Period 77.214 7.434 7.662 7.898 8.142 8.394 8.923 9.487 10.089 10.730 11.414 Period 8 8.286 8.583 8.892 9.214 9.549 9.897 10.637 11.436 12.300 13.233 14.240 Period 9 9.369 9.755 10.159 10.583 11.027 11.491 12.488 13.579 14.776 16.085 17.519 Period 10.462 10.950 11.464 12.006 12.578 13.181 14.48715.937 17.549 19.337 21.321 10 Period 11.567 12.169 12.80813.486 14.207 14.972 16.645 18.531 20.655 23.045 25.733 11 Period 12.68313.412 14.192 15.026 15.917 16.870 18.977 21.384 24.133 27.271 30.850 12 Period 13.809 14.680 15.618 16.627 17.713 18.882 21.495 24.523 28.029 32.089 36.786 13 Period 14.947 15.974 17.086 18.292 19.599 21.015 24.215 27.975 32.393 37.581 43.672 14 Period 16.097 17.29318.599 20.024 21.579 23.276 27.152 31.772 37.280 43.842 51.660 15 Period 22.019 24.297 26.870 29.778 33.066 36.786 45.762 57.275 72.052 91.025 115.380 20 Period 28.243 32.03036.459 41.646 47.727 54.865 73.106 98.347 133.334 181.871 249.214 28.755 32.150 34.931 39.581 42.219 48.497 50.818 59.196 60.965 72.035 146.628 186.688 342.603 471.981 Period 34.785 40.568 47.575 56.085 66.439 79.058 113.283 164.494 241.333 356.787 530.312 790.948 1,181.882 30 Period 48.88660.402 75.401 95.026120.800 154.762 259.057 442.593767.091 1,342.0252,360.757 4,163.2137.343.858 40 Periods Period 1 Period 2 Period 3 Period 4 Period 5 Period 6 Period 7 Period 8 Period 9 Period 10 Period 11 Period 12 Period 13 Period 14 Period 15 Period 20 Period 25 Period 30 Period 40 Present Value of $1 1% 2% 3% 4% 5% 6% 8% 0.990 0.980 0.971 0.962 0.952 0.943 0.926 0.980 0.961 0.943 0.925 0.907 0.890 0.857 0.971 0.942 0.915 0.889 0.864 0.840 0.794 0.961 0.924 0.888 0.855 0.823 0.792 0.735 0.951 0.906 0.863 0.822 0.784 0.747 0.681 0.942 0.888 0.837 0.790 0.746 0.705 0.630 0.933 0.871 0.813 0.760 0.711 0.665 0.583 0.923 0.853 0.789 0.731 0.677 0.627 0.540 0.914 0.837 0.766 0.703 0.6450.5920.500 0.905 0.820 0.744 0.676 0.614 0.558 0.463 0.896 0.804 0.722 0.650 0.585 0.527 0.429 0.887 0.788 0.701 0.625 0.557 0.497 0.397 0.879 0.773 0.681 0.601 0.530 0.469 0.368 0.870 0.758 0.661 0.577 0.505 0.442 0.340 0.861 0.743 0.642 0.555 0.481 0.417 0.315 0.820 0.673 0.554 0.456 0.377 0.312 0.215 0.780 0.610 0.478 0.375 0.295 0.233 0.146 0.742 0.552 0.412 0.308 0.231 0.174 0.099 0.672 0.453 0.307 0.208 0.142 0.097 0.046 10% 12% 14% 16% 18% 20% 0.909 0.893 0.877 0.862 0.847 0.833 0.826 0.797 0.769 0.743 0.718 0.694 0.751 0.712 0.675 0.641 0.609 0.579 0.683 0.636 0.592 0.552 0.516 0.482 0.621 0.567 0.519 0.476 0.437 0.402 0.564 0.507 0.456 0.410 0.370 0.335 0.513 0.452 0.400 0.354 0.314 0.279 0.467 0.404 0.351 0.305 0.266 0.233 0.424 0.361 0.308 0.263 0.225 0.194 0.386 0.322 0.270 0.227 0.191 0.162 0.350 0.287 0.237 0.1950.162 0.135 0.319 0.257 0.208 0.168 0.1370.112 0.290 0.229 0.1820.145 0.116 0.093 0.263 0.2050.160 0.125 0.099 0.078 0.239 0.183 0.140 0.108 0.084 0.065 0.149 0.104 0.073 0.051 0.037 0.026 0.092 0.059 0.038 0.024 0.0160.010 0.057 0.033 0.020 0.012 0.007 0.004 0.022 0.0110.005 0.003 0.001 0.001 Periods Period 1 Period 2 Period 3 Period 4 Period 5 Period 6 Period 7 Period 8 Period 9 Period 10 Period 11 Period 12 Period 13 Period 14 Period 15 Period 20 Period 25 Period 30 Period 40 Future Value of $1 1% 2% 3% 4% 5% 6% 8% 10% 12% 14% 16% 18% 20% 1.010 1.020 1.030 1.040 1.050 1.060 1.080 1.100 1.120 1.140 1.160 1.180 1.200 1.020 1.040 1.061 1.0821.103 1.124 1.166 1.210 1.254 1.300 1.346 1.392 1.440 1.030 1.061 1.093 1.125 1.158 1.191 1.260 1.331 1.405 1.482 1.561 1.643 1.728 1.041 1.082 1.126 1.170 1.216 1.262 1.360 1.464 1.574 1.689 1.811 1.939 2.074 1.0511.104 1.159 1.217 1.276 1.338 1.469 1.611 1.762 1.925 2.100 2.288 2.488 1.062 1.126 1.194 1.265 1.340 1.419 1.587 1.772 1.974 2.196 2.436 2.700 2.986 1.072 1.149 1.230 1.316 1.407 1.504 1.714 1.949 2.211 2.502 2.826 3.185 3.583 1.083|1.1721.267 1.369 1.477 1.594 1.851 2.144 2.476 2.853 3.278 3.759 4.300 1.094 1.195 1.305 1.423 1.551 1.689 1.999 2.358 2.773 3.252 3.803 4.435 5.160 1.105 | 1.219 1.344 1.480 1.629 1.791 2.159 2.594 3.106 3.707 4.411 5.234 6.192 1.116 1.243 1.384 1.539 1.710 1.898 2.332 2.853 3.479 4.226 5.117 6.176 7.430 1.127 | 1.268 1.426 | 1.601 | 1.796 2.012 2.518 3.138 3.896 4.818 5.936 7.288 8.916 1.138 1.294 1.469 1.665 1.886 2.133 2.720 3.452 4.363 5.492 6.886 8.599 10.699 1.1491.319 1.513 1.732 1.980 2.261 2.937 3.797 4.887 6.261 7.988 10.147 12.839 1.1611.346 1.558 1.801 2.079 2.397 3.172 4.177 5.474 7.138 9.266 11.974 15.407 1.220 1.486 1.806 2.1912.653 3.207 4.661 6.727 9.646 13.743 19.461 27.393 38.338 1.282 1.641 2.094 2.666 3.386 4.292 6.848 10.835| 17.000 26.462 40.874 62.669 95.396 1.348 1.811 2.427 3.243 4.322 5.743 10.063 | 17.449 29.960 50.950 85.850 143.371 237.376 1.489 2.208 3.262 4.801 7.040 10.286 21.725 45.25993.051 188.884 378.721 | 750.3781,469.772 Periods Period 1 Period 2 Period 3 Period 4 Period 5 Period 6 Period 7 Period 8 Period 9 Period 10 Period 11 Period 12 Period 13 Period 14 Period 15 Period 20 Period 25 Period 30 Period 40 Present Value of Annuity of $1 1% 2% 3% 4% 5% 6% 8% 10% 12% 14% 16% 18% 20% 0.990 0.980 0.971 0.962 0.952 0.943 0.926 0.909 0.893 0.877 0.862 0.847 0.833 1.970 1.942 1.913 1.886 1.859 1.833 1.783 1.736 1.6901.647 1.605 1.566 1.528 2.941 2.884 2.829 2.775 2.723 2.673 2.577 2.487 2.402 2.322 2.246 2.174 2.106 3.902 3.808 3.717 3.630 3.546 3.465 3.312 3.1703.037 2.914 2.798 2.690 2.589 4.853 4.713 4.580 4.452 4.329 4.212 3.993 3.791 3.605 3.433 3.274 3.127 2.991 5.795 5.601 5.417 5.242 5.076 4.917 4.623 4.355 4.111 3.8893.685 3.498 3.326 6.728 6.472 6.230 6.002 5.786 5.582 5.206 4.868 4.564 4.288 4.0393.812 3.605 7.652 7.325 7.020 6.733 6.463 6.210 5.747 5.335 4.968 |4.639 | 4.344 4.078 3.837 8.566 8.162 7.786 7.435 7.108 6.802 6.247 5.759 5.328 | 4.946 | 4.607 4.303 4.031 9.471 8.983 8.530 8.111 7.722 7.360 6.710 6.145 5.6505.216 4.833 4.494 4.192 10.368 9.787 9.253 8.760 8.306 7.887 7.139 6.495 5.938 5.453 5.0294.656 4.327 11.255 10.575 9.954 9.385 8.863 8.384 7.536 6.814 6.194 5.6605.1974.793 4.439 12.134 11.348 10.635 9.986 9.394 8.853 7.904 7.103 6.424 5.842 5.342 4.910 4.533 13.004 12.106 | 11.296 10.563 9.899 9.295 8.244 7.3676.628 6.0025.468 5.008 4.611 13.865 12.849 11.938 11.118 10.380 9.712 8.559 7.606 6.811 6.142 5.575 5.0924.675 18.046 16.351 14.877 13.590 12.462 11.470 9.818 8.5147.469 6.623 5.929 5.353 4.870 22.023 19.523 17.413 15.622 14.094 12.783 10.675 9.077 7.843 6.873 6.097 5.4674.948 25.808 22.396 | 19.600 17.292 15.372 13.765 11.258 9.427 8.055 7.003 6.1775.517 4.979 32.835 27.355 23.115 19.793 17.159 15.046 | 11.925 9.7798.244 7.105 | 6.233 5.548 | 4.997