Present value of an annuity of 1 i.e. 1-(1+r)^ Where r = discount rate n = number of periods Annuity Table Discount rate (r) Periods (n) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12345 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 12345 5 68029 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.355 7 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759 10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145 68029 10 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 11.35 10.63 9.986 9.394 8.853 8.358 7.904 7.487 7.103 14 13.00 12.11 11.30 10.56 9.899 9.295 8.745 8.244 7.786 7.367 15 13.87 12.85 11.94 11.12 10.38 9.712 9.108 8.559 8.061 7.606 12345 11 (n) 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 12345 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 1.713 1.690 1.668 1.647 1.626 1.605 1.585 1.566 1.547 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 2.855 2.798 2.743 2.690 2.639 2.589 5 3.696 3.605 3.517 3.433 3.352 3.274 3.199 3.127 3.058 2.991 12345 1 678 4.231 4.111 3.998 3.889 3.784 3.685 3.589 3.498 3.410 3.326 6 4.712 4.564 4.423 4.288 4.160 4.039 3.922 3.812 3.706 3.605 7 5.146 4.968 4.799 4.639 4.487 4.344 4.207 4.078 3.954 3.837 9 5.537 5.328 5.132 4.946 4.772 4.607 4.451 4.303 4.163 4.031 6812 9 10 5.889 5.650 5.426 5.216 5.019 4.833 4.659 4.494 4.339 4.192 10 11 13 14 15 12345 6.207 5.938 5.687 5.453 5.234 5.029 4.836 4.656 4.486 4.327 11 12 6.492 6.194 5.918 5.660 5.421 5.197 4.988 4.793 4.611 4.439 6.750 6.424 6.122 5.842 5.583 5.342 5.118 4.910 4.715 4.533 6.982 6.628 6.302 6.002 5.724 5.468 5.229 5.008 4.802 4.611 7.191 6.811 6.462 6.142 5.847 5.575 5.324 5.092 4.876 4.675 12345 Present Value Table Present value of 1 i.e. (1+r)-n Where r = discount rate n = number of periods until payment Discount rate (r) Periods (n) 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12345 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 3 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683 5 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 12345 5 6 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 7 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 7 8 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467 9 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 10 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386 68119 10 11 12345 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.861 0.743 0.642 0.555 0.481 0.417 0.362 0.315 0.275 0.239 (n) 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 1 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 2345 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579 4 0.659 0.636 0.613 0.592 0.572 0.552 0.534 0.516 0.499 0.482 0.593 0.567 0.543 0.519 0.497 0.476 0.456 0.437 0.419 0.402 12345 12345 11 6 0.535 0.507 0.480 0.456 0.432 0.410 0.390 0.370 0.352 0.335 7 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279 8 0.434 0.404 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233 9 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225 0.209 0.194 6881 7 9 10 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162 10 11 0.317 0.287 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135 12 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0.137 0.124 0.112 13 0.258 0.229 0.204 0.182 0.163 0.145 0.130 0.116 0.104 0.093 14 0.232 0.205 0.181 0.160 0.141 0.125 0.111 0.099 0.088 0.078 15 0.209 0.183 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065 12375 11 14 QUESTION 2 Amber Plc has the opportunity to invest in a new project 'Gem' which is estimated to have a 3-year market life. Amber plc has already incurred 50,000 expenses on a market survey to estimate future demand levels for 'Gem', which are as follows: Demand for Gem Year 1 10,000 units Year 2 7,000 units Year 3 5,000 units Production of Gem would commence immediately, with all sales and variable costs arising at the end of each year. The following unit costs and revenues are expected for the Gem, all at current prices: Selling price per unit Costs per unit: 40 Variable materials 9 Variable labour 12 Note (2) Other overheads 10 Depreciation 8 Interest 3 Loss per unit (42) (2) Additional information: (1) (2) (3) (4) Amber Plc will purchase a new machine to fufil production of Gem. The machine cost will be payable immediately at a current price of 180,000. It is estimated the machine will be sold for 30,000 at the end of the project. Other overheads of 10 per unit (at current prices) comprise of variable overheads of 6 per unit and apportioned general fixed overheads of 4 per unit. The general inflation rate is expected to be 5% per annum for the next three years. The selling price and any cash flows not specified below are also expected to increase at the same general rate. Variable costs are expected to increase with inflation at the following rates: Variable materials Variable labour Variable overheads Increase % 6 10 3 Amber Plc pays corporation tax on taxable profits at a rate of 20% p.a. and tax is paid one year in arrears. Capital allowances are available on the machine at 25% p.a. on a reducing balance basis. (5) Amber Plc has a real after-tax cost of capital of 5.7% per annum. QUESTION 2 (continued) Required: a) Calculate the Net Present Value of the project, taking into account the effects of inflation and taxation. Please show all workings and round all figures to the nearest thousand pounds (000). (16 marks) b) Advise Amber Plc whether they should undertake the project, explaining which cash flows have not been considered during your investment appraisal. (5 marks) c) Critically evaluate the difference between real rates of return and nominal rates of return, indicating which approach you have applied in part a). (4 marks) Total: 25 marks