Question 2 Slugsey plc makes slug traps for commercial food growers. A new slug trap, the Slugmatic, has been developed which requires a machine to be bought costing 1,400,000 A net present value appraisal has been carried out that indicates a positive net present value (NPV) of 19,500. This appraisal was followed up with an assessment of the riskiness of the project. This was achieved by taking each of the input factors in turn and estimating the value for it at which the project would have a zero NPV. Data on the original estimates are as follows. Cost of machine Selling price (per trap) Material cost (per trap) Labour cost (per trap) Variable overheads (per trap) Sales life Original estimate 1,400,000 250 40 90 15 10 years The above assessment is based on the assumptions of a discount rate of 10% and of constant sales of 2,200 traps per annum. At a recent board meeting held to discuss whether the new slug trap project should go ahead the following comments were made: Robert Hillier Managing Director): '1 favour the sensitivity analysis we have performed as it lets us see the effect of all the investment appraisal variables changing at the same time. Malcolm Hillier (Production Director): 'We haven't considered whether the project reduces the company's and the directors' risk. We should use a portfolio theory approach to identify the systematic risk diversified away by the project.' Steve Jay (Marketing Director): 'What about our shareholders' risk? They are interested in unsystematic risk so we should use CAPM to make the decision.' Question 2 continued Requirements (a) To generate a zero NPV, estimate the values for (0) the discount rate, (ii) the annual sales volume, (ii) the cost of the machine and discuss how sensitive the project is to each of these input factors. Ignore taxation and inflation. (12 marks) (b) Compare and contrast sensitivity analysis, portfolio theory and the capital asset pricing model as techniques for dealing with risk in project appraisal, identifying any errors made by the directors in their comments. (13 marks) (Total 25 marks) APPENDIX Present value tables Present value of 1 in n years at discount rater Periods Discount rate (r) (n) 1% 2% % 7% 8% 9 10% 1 2 3 1 2 3 4 5 6 7 8 9 10 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 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 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 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386 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 0319 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 5 6 7 8 9 10 12 13 14 15 12 13 14 15 11% 12% 13% 15% 16% 17% 18% 19% 20% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.901 0.893 0.885 0.877 0.870 0.862 0.855 0.847 0.840 0.833 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.7180.706 0.694 0.731 0.712 0.693 0.675 0.658 0.641 0.624 0.609 0.593 0.579 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 0.535 0.507 0.480 0.456 0.432 0.410 0.390 0.370 0352 0.335 0.482 0.452 0.425 0.400 0.376 0.354 0.333 0.314 0.296 0.279 0.434 0.404 0.376 0.351 0.327 0.305 0.285 0.266 0.249 0.233 0.391 0.361 0.333 0.308 0.284 0.263 0.243 0.225 0.209 0.194 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162 0.317 0.287 0.261 0.237 0.215 0.195 0.178 0.162 0.148 0.135 0.286 0.257 0.231 0.208 0.187 0.168 0.152 0.137 0.124 0.112 0.258 0.229 0.204 0.182 0.163 0.145 0.130 0.116 0.104 0.093 0.232 0.205 0.181 0.160 0.141 0.125 0.111 0.099 0.088 0.078 0.209 0.183 0.160 0.140 0.123 0.108 0.095 0.084 0.074 0.065 4 5 6 7 8 9 10 11 12 13 14 15 Annuity tables Present value of l receivable at the end of each year for n years at discount rater Periods Discount rate (1) 1% 2% 3% 4% 5% 7% 8% 9% 10% 1 2 3 4 5 6 7 8 9 10 11 12 13 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536 7.161 12.134 11.348 10.635 9.986 9.394 8.853 8.358 7.904 7.487 13.004 12.106 11.296 10.563 9.899 9.295 8.745 8.244 7.786 13.865 12.849 11.938 11.118 10.380 9.712 9.108 8.559 8.061 0.909 1.736 2.487 3.170 3.791 4.355 4.868 5.335 5.759 6.145 6.495 6,814 7.103 7.367 7.606 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 15 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 1 2 3 4 6 7 8 9 10 11 12 13 14 0.901 0.893 1.713 1.690 2.444 2.402 3.102 3.037 3.696 3.605 4.231 4.111 4.712 4.564 5.146 4.968 5.537 5.328 5.889 5.650 6.207 5.938 6.492 6.194 6.750 6.424 6.982 6.618 7.191 6.811 0.885 0.877 1.668 1.647 2.361 2.322 2.974 2.914 3.517 3.433 3.998 3.889 4.423 4.288 4.799 4.639 5.132 4.946 5.426 5.216 5.687 5.453 5.918 5.660 6.122 5.842 6.302 6.002 6.462 6.142 0.870 1.626 2.283 2.855 3.352 3.784 4.160 4.487 4.772 5.019 5.234 5.421 5.583 5.724 5.847 0.862 0.855 0.847 0.840 1.605 1.585 1.566 1.547 2.246 2.210 2.174 2.140 2.798 2.743 2.690 2.639 3.274 3.199 3.127 3.058 3.685 3.589 3.498 3.410 4.039 3.922 3.812 3.706 4.344 4.207 4.078 3.954 4.607 4.451 4.303 4.163 4.833 4.659 4.494 4.339 5.029 4.836 4.656 4.486 5.197 4.988 4.793 4.611 5.342 5.118 4.910 4.715 5.468 5.229 5.008 4.802 5.575 5.324 5.092 4.876 0.833 1.528 2.106 2.589 2.991 3.326 3.605 3.837 4.031 4.192 4.327 4.439 4.533 4.611 4.675 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Formulae sheet 1. Expected retum xp Ix outcome, p = probability of outcome) 1 2. Variance of 3. Standard deviation of 4. Expected retur on a 2 asset portfolio i, ai, ai, [a= proportion of funds invested in A whose mean retumis ij 5. Risk (standard deviation) of a 2 asset portfolio , vao (1-a) o 23(1-2)covit..ta) 6. Covariance coven) (MP [ta= outcomes for Aj CO2 7. Correlation con 8. CAPM required rate of return = r, B,(r. 1) In = risk free rate, tm = retum an market portfolio. B = beta of investment cov,) com 10 = standard deviation of j's retums 10. Beta of a firm with various activities B x, where x is the weighting for each activity D 11. Dividend valuation model generally P, IP = share price at time of D 12. DVM with constant growth P. D.01 ) D.(1 ) P & D P D. = current dividend D. = dividend in ne year 9- growth in dividends k = cost of equity] = interest on face value. T=tax] 13. After tax cost of irredeemable debtk (1 T) P 14. After tax cost of redeemable debt solve 0 (P) (I-TXAF. RV (I k.) where AF is an annuity factor and RV is the redemption value NPV NPV, NPV) Irdiscount rate giving NPV) UMADFR-15-3 Page 11 of 13 15. IRR