Present value tables Present value of 1 in n years at discount rate r. Discount rate (r) Periods (n) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 123456789 0.990 0.980 0.971 0.980 0.961 0.943 0.962 0.925 0.971 0.942 0.915 0.889 0.961 0.924 0.888 0.855 0.823 0.952 0.943 0.935 0.926 0.917 0.909 0.907 0.890 0.873 0.857 0.842 0.826 0.864 0.840 0.816 0.794 0.772 0.751 0.792 0.763 0.735 0.708 0.683 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 123456789 10 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386 10 11 12345 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 11 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 12 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 13 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.861 0.743 0.642 0.555 0.481 0.417 0.362 0.340 0.315 0.299 0.263 0.275 0.239 14 15 2345 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 1 -234567842-2374 0.901 0.893 0.885 0.877 0.870 0.812 0.797 0.783 0.769 0.756 0.862 0.743 0.731 0.712 0.693 0.675 0.658 0.659 0.636 0.613 0.592 0.572 0.593 0.567 0.543 0.519 0.497 0.535 0.507 0.480 0.456 0.432 0.482 0.452 0.425 0.400 0.376 0.434 0.404 0.376 0.351 0.327 9 0.391 0.361 0.333 0.308 0.284 10 0.352 0.322 0.295 0.270 11 0.317 0.287 0.261 0.237 12 0.286 0.257 0.231 0.208 0.187 13 0.258 0.229 0.204 0.182 0.163 14 0.232 0.205 0.181 0.160 0.141 15 0.209 0.183 0.160 0.140 0.123 0.855 0.847 0.840 0.833 0.731 0.718 0.706 0.694 0.641 0.624 0.609 0.593 0.579 0.552 0.534 0.516 0.499 0.482 0.476 0.456 0.437 0.419 0.402 0.410 0.390 0.370 0.352 0.335 0.354 0.333 0.314 0.296 0.279 0.305 0.285 0.266 0.249 0.233 0.263 0.243 0.225 0.209 0.194 0.247 0.227 0.208 0.191 0.176 0.162 0.215 0.195 0.178 0.162 0.148 0.135 0.168 0.152 0.137 0.124 0.112 0.145 0.130 0.116 0.104 0.093 0.125 0.111 0.108 0.095 -234567890; 1 10 11 12 13 0.099 0.088 0.078 0.084 14 0.074 0.065 15 Annuity table Present value of 1 receivable at the end of each year for n years at discount rate r. Discount rate (r) Years (u) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 1 9 -234567842-2345 0.990 0.980 0.971 1.970 1.942 1.913 2.941 2.884 2.829 0.962 1.886 2.775 2.723 10 3.902 3.808 3.717 3.630 3.546 4.853 4.713 4.580 4.452 4.329 5.795 5.601 5.417 5.242 5.076 6.728 6.472 6.230 6.002 5.786 7.652 7.325 7.020 6.733 6.463 8.566 8.162 7.786 7.435 7.108 9.471 8.983 8.530 8.111 7.722 7.360 7.024 0.952 0.943 0.935 0.926 0.917 0.909 1.859 1.833 1.808 1.783 1.759 1.736 2.673 2.624 2.577 3.465 3.387 3.312 3.240 3.170 4.212 4.100 3.993 3.890 3.791 4.917 4.767 4.623 4.486 4.355 5.582 5.389 5.206 5.033 4.868 6.210 5.971 5.747 5.535 5.335 6.802 6.515 6.247 5.759 6.145 2.531 2.487 1234567 8 5.995 9 6.710 6.418 11 10.37 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495 12 11.26 10.58 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814 13 12.13 14 13.00 15 13.87 11.35 12.11 11.30 12.85 11.94 10.63 9.986 9.394 8.853 8.358 7.904 7.487 7.103 10.56 9.899 9.295 11.12 10.38 9.712 8.745 9.108 8.559 8.244 7.786 7.367 8.061 7.606 012345 11 12 13 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 1 8 9 -23456700FF2375 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 1.713 1.690 1.668 1.647 1.626 1.605 1.585 0.840 1.566 1.547 0.833 1.528 2.444 2.402 2.361 2.322 2.283 2.246 2.210 2.174 2.140 2.106 3.102 3.037 2.974 2.914 3.696 3.605 3.517 3.433 4.231 4.111 3.998 3.889 4.712 4.564 4.423 4.288 5.146 4.968 4.799 4.639 5.537 2.855 2.798 2.743 2.690 2.639 2.589 3.352 3.274 3.199 3.127 3.058 2.991 10 5.889 11 6.207 12 6.492 6.194 13 14 15 3.784 3.685 3.589 3.498 3.410 3.326 4.160 4.039 4.487 4.344 5.328 5.132 4.946 4.772 5.650 5.426 5.216 5.019 5.938 5.687 5.453 5.234 5.918 5.660 5.421 6.750 6.424 6.122 5.842 5.583 6.982 6.628 6.302 6.002 5.724 7.191 6.811 6.462 6.142 5.847 3.922 4.207 4.607 4.451 4.833 4.659 4.494 5.029 4.836 4.656 5.197 4.988 4.793 5.342 5.118 4.910 5.468 5.229 5.008 5.575 5.324 5.092 3.812 3.706 4.078 3.605 3.954 3.837 4.303 4.163 4.031 4.339 4.192 4.486 4.327 4.611 4.439 10 -234567890 11 12 4.715 4.533 13 4.802 4.876 4.611 14 4.675 15 BJ Joinery is a medium sized family-owned business that makes bespoke furniture in the UK. The family rely on the business for an income and have expressed a desire to reduce the company's environmental footprint. It has one combined factory and office site which uses large amounts of energy for power, heat, and light. BJ is concerned about the rising cost of energy as well as wanting to reduce its environmental impact. BJ has implemented several initiatives which have improved the sustainability of raw material supply and the repair and recycling of old furniture. The company is now looking to invest in on-site energy production and has three possible investments, however, owing to the shortage of funds the company can only undertake one of these investments this year. Details of the three investments are: 1) Solar power electricity generation, installed on the factory roof. Initial Investment 2m with a life of 15 years. Owing to the variability of sunny days in the UK there are three estimates of energy savings per year: Worst case Best case (20% probability) 0.2m per year (30% probability) 1.0m per year Average case (50% probability) 0.6m per year The Solar installation will have a value of 0.5m at the end of 15 years. The solar power installation will reduce carbon emissions by 30%. 2) Ground heat pump, installed under the existing lorry delivery area. Initial investment 2.2m with a life of 15 years and estimate average energy savings of 0.3m per year for 15 years with no residual value. The ground heat pump is estimated to cut carbon emissions by 50%. 3) Bio-mass boiler installation, using sustainable wood pellets. Initial investment 1.5m with a life of 12 years and estimate energy saving of 1.2m per year for 12 years, however the boiler will need to burn wood pellets at a cost of 0.9m per year for the first 5 years increasing to 1.1m per year for year 6 to year 12. The bio-mass boiler will have no residual value and reduce net carbon emissions by 70%. Note: The costs and savings for options 1, 2 & 3 are guaranteed by the UK government and so are NOT subject to any inflation or uncertainty. Required: (a) If the required cost of capital is 10%, calculate the expected net present value for each of the three projects. (50 marks) (b) Calculate the payback period for each of the 3 projects. (20 marks) (c) Advise the family on which project BJ Joinery should undertake, include a discussion of the non-financial environmental benefits of each project. Limit of 300 words (30 marks) [Total 100 marks]