Business and Law

Kilkennie plc., manufactures components for the automobile industry. The
company has recently been approached to supply components to eight
projects. The finance manager, Fredrick Wright, is concerned that the
existing funds available to the company are insufficient to execute all the
projects.
Based on Fredrick’s recommendation, management have decided to
allocate £660,000 to execute some of the projects. These projects are
labeled A-H. The projects are not mutually exclusive. The table below
provides you with the cost of each project, duration of each project and
expected cash inflows at the end of each year. All the cashflows are in
annuity. The estimated cost of capital is 10%.
Project Cost (in £) Project duration
(in years)
Annual cash
inflow (in £)
A 400,000 20 58,600
B 100,000 8 24,000
C 50,000 5 14,000
D 85,000 15 12,000
E 260,000 10 55,000
F 75,000 6 18,000
G 250,000 10 41,000
H 250,000 3 101,000
Kilkennie plc has sought your advice as to which of the above projects
should it select to invest the £660,000. The projects are divisible.
Required
1) Calculate the Net Present Value (NPV) for each project
a) State the NPV decision rule
b) Based on the NPV decision rule, select the projects that should be
financed with the £660,000 budget
c) Calculate the overall NPV for the selected projects in part b)
(Total: 25 marks)
2) Calculate the Profitability Index (PI) for each project
a) Use the calculation in part 2) to rank the projects from the most
preferred to the least preferred
b) Explain the PI decision rule
c) Based on the PI decision rule select which of the projects should be
financed with the £660,000 budget
d) Calculate the overall NPV for the selected projects in part c)
(Total: 25 marks)
3) Calculate the Internal rate of return of (i) Project A, which has an initial
cost of £400,000 and an annual cash inflow of £58,600 for 20 years; and
(ii) Project B, which has an initial cost of £100,000 and an annual cash
inflow of £24,000 for 8 years. All the cashflows are in annuity.
Given that Kilkennie plc. operates a 14% minimum required rate of return
policy, based on your IRR analysis, advice on which of the projects should
be accepted or rejected.
(Total: 25 marks)
4) Comment on the importance of investment appraisal and explain the
advantages and disadvantages for each of the following investment
appraisal techniques
I. Net Present Value
II. Internal rate of return
III. Profitability index
IV. Modified internal rate of return
(Total: 25 marks)
FORMULAE SHEET
FV = PV(1 + i)
n
𝑃𝑉𝐴𝐹 =
1
𝑖
(1 −
1
(1 + 𝑖)
𝑛
)
𝐹𝑉𝐴𝐹 =
1
𝑖
((1 + 𝑖)
𝑛 − 1)
𝐼𝑅𝑅 = 𝑎 + (𝑏 − 𝑎) (
𝑁𝑃𝑉𝑎
𝑁𝑃𝑉𝑎 − 𝑁𝑃𝑉𝑏
)
𝑀𝐼𝑅𝑅 = √
𝑇𝑉
𝑃𝑉
𝑛
− 1
𝐸𝐴𝐴 =
𝑁𝑃𝑉
𝑃𝑉𝐴𝐹
𝑃𝐼 =
𝐺𝑃𝑉
𝐶0
𝐸(𝑥) = ∑𝑥. 𝑝(𝑥)
𝜎𝑥
2 = ∑(𝑥 − 𝐸(𝑥))
2
. 𝑝(𝑥)
𝜎𝑥 = √𝜎𝑥
2
𝐶𝑜𝑉 =
𝜎𝑥
𝐸(𝑥)
𝑃0 =
𝑑
𝑘𝑒
𝑜𝑟
𝑑0(1 + 𝑔)
𝑘𝑒 − 𝑔
𝑔 = 𝑟𝑏 𝑜𝑟 √
𝑑0
𝑑−𝑛
𝑛
− 1
𝑘𝑒 = 𝑟𝑓 + 𝛽(𝑟𝑚 − 𝑟𝑓)
𝑊𝐴𝐶𝐶 = 𝑘𝑒 (
𝑉𝑒
𝑉𝑒 + 𝑉𝑑
) + 𝑘𝑑𝑎𝑡 (
𝑉𝑑
𝑉𝑒 + 𝑉𝑑
)
Present value of £1 at i% for n periods, PVIF(i,n).
Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
1 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
4 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
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
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
11 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350
12 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319
13 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290
14 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263
15 0.861 0.743 0.642 0.555 0.481 0.417 0.362 0.315 0.275 0.239
16 0.853 0.728 0.623 0.534 0.458 0.394 0.339 0.292 0.252 0.218
17 0.844 0.714 0.605 0.513 0.436 0.371 0.317 0.270 0.231 0.198
18 0.836 0.700 0.587 0.494 0.416 0.350 0.296 0.250 0.212 0.180
19 0.828 0.686 0.570 0.475 0.396 0.331 0.277 0.232 0.194 0.164
20 0.820 0.673 0.554 0.456 0.377 0.312 0.258 0.215 0.178 0.149
Period 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
2 0.812 0.797 0.783 0.769 0.756 0.743 0.731 0.718 0.706 0.694
3 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
5 0.593 0.567 0.543 0.519 0.497 0.476 0.456 0.437 0.419 0.402
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
10 0.352 0.322 0.295 0.270 0.247 0.227 0.208 0.191 0.176 0.162
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
16 0.188 0.163 0.141 0.123 0.107 0.093 0.081 0.071 0.062 0.054
17 0.170 0.146 0.125 0.108 0.093 0.080 0.069 0.060 0.052 0.045
18 0.153 0.130 0.111 0.095 0.081 0.069 0.059 0.051 0.044 0.038
19 0.138 0.116 0.098 0.083 0.070 0.060 0.051 0.043 0.037 0.031
20 0.124 0.104 0.087 0.073 0.061 0.051 0.043 0.037 0.031 0.026
Future value of £1 at i% for n periods, FVIF(i,n).
Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
1 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100
2 1.020 1.040 1.061 1.082 1.103 1.124 1.145 1.166 1.188 1.210
3 1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1.331
4 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464
5 1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539 1.611
6 1.062 1.126 1.194 1.265 1.340 1.419 1.501 1.587 1.677 1.772
7 1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828 1.949
8 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.851 1.993 2.144
9 1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172 2.358
10 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367 2.594
11 1.116 1.243 1.384 1.539 1.710 1.898 2.105 2.332 2.580 2.853
12 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138
13 1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066 3.452
14 1.149 1.319 1.513 1.732 1.980 2.261 2.579 2.937 3.342 3.797
15 1.161 1.346 1.558 1.801 2.079 2.397 2.759 3.172 3.642 4.177
16 1.173 1.373 1.605 1.873 2.183 2.540 2.952 3.426 3.970 4.595
17 1.184 1.400 1.653 1.948 2.292 2.693 3.159 3.700 4.328 5.054
18 1.196 1.428 1.702 2.026 2.407 2.854 3.380 3.996 4.717 5.560
19 1.208 1.457 1.754 2.107 2.527 3.026 3.617 4.316 5.142 6.116
20 1.220 1.486 1.806 2.191 2.653 3.207 3.870 4.661 5.604 6.727
Period 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%
1 1.110 1.120 1.130 1.140 1.150 1.160 1.170 1.180 1.190 1.200
2 1.232 1.254 1.277 1.300 1.323 1.346 1.369 1.392 1.416 1.440
3 1.368 1.405 1.443 1.482 1.521 1.561 1.602 1.643 1.685 1.728
4 1.518 1.574 1.630 1.689 1.749 1.811 1.874 1.939 2.005 2.074
5 1.685 1.762 1.842 1.925 2.011 2.100 2.192 2.288 2.386 2.488
6 1.870 1.974 2.082 2.195 2.313 2.436 2.565 2.700 2.840 2.986
7 2.076 2.211 2.353 2.502 2.660 2.826 3.001 3.185 3.379 3.583
8 2.305 2.476 2.658 2.853 3.059 3.278 3.511 3.759 4.021 4.300
9 2.558 2.773 3.004 3.252 3.518 3.803 4.108 4.435 4.785 5.160
10 2.839 3.106 3.395 3.707 4.046 4.411 4.807 5.234 5.695 6.192
11 3.152 3.479 3.836 4.226 4.652 5.117 5.624 6.176 6.777 7.430
12 3.498 3.896 4.335 4.818 5.350 5.936 6.580 7.288 8.064 8.916
13 3.883 4.363 4.898 5.492 6.153 6.886 7.699 8.599 9.596 10.699
14 4.310 4.887 5.535 6.261 7.076 7.988 9.007 10.147 11.420 12.839
15 4.785 5.474 6.254 7.138 8.137 9.266 10.539 11.974 13.590 15.407
16 5.311 6.130 7.067 8.137 9.358 10.748 12.330 14.129 16.172 18.488
17 5.895 6.866 7.986 9.276 10.761 12.468 14.426 16.672 19.244 22.186
18 6.544 7.690 9.024 10.575 12.375 14.463 16.879 19.673 22.901 26.623
19 7.263 8.613 10.197 12.056 14.232 16.777 19.748 23.214 27.252 31.948
20 8.062 9.646 11.523 13.743 16.367 19.461 23.106 27.393 32.429 38.338
Present value of an ordinary annuity of £1 at i% for n periods, PVAIF(i,n).
Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909
2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736
3 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487
4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170
5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791
6 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
8 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335
9 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
11 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495
12 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814
13 12.134 11.348 10.635 9.986 9.394 8.853 8.358 7.904 7.487 7.103
14 13.004 12.106 11.296 10.563 9.899 9.295 8.745 8.244 7.786 7.367
15 13.865 12.849 11.938 11.118 10.380 9.712 9.108 8.559 8.061 7.606
16 14.718 13.578 12.561 11.652 10.838 10.106 9.447 8.851 8.313 7.824
17 15.562 14.292 13.166 12.166 11.274 10.477 9.763 9.122 8.544 8.022
18 16.398 14.992 13.754 12.659 11.690 10.828 10.059 9.372 8.756 8.201
19 17.226 15.678 14.324 13.134 12.085 11.158 10.336 9.604 8.950 8.365
20 18.046 16.351 14.877 13.590 12.462 11.470 10.594 9.818 9.129 8.514
Period 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
2 1.713 1.690 1.668 1.647 1.626 1.605 1.585 1.566 1.547 1.528
3 2.444 2.402 2.361 2.322 2.283 2.246 2.210 2.174 2.140 2.106
4 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
6 4.231 4.111 3.998 3.889 3.784 3.685 3.589 3.498 3.410 3.326
7 4.712 4.564 4.423 4.288 4.160 4.039 3.922 3.812 3.706 3.605
8 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
10 5.889 5.650 5.426 5.216 5.019 4.833 4.659 4.494 4.339 4.192
11 6.207 5.938 5.687 5.453 5.234 5.029 4.836 4.656 4.486 4.327
12 6.492 6.194 5.918 5.660 5.421 5.197 4.988 4.793 4.611 4.439
13 6.750 6.424 6.122 5.842 5.583 5.342 5.118 4.910 4.715 4.533
14 6.982 6.628 6.302 6.002 5.724 5.468 5.229 5.008 4.802 4.611
15 7.191 6.811 6.462 6.142 5.847 5.575 5.324 5.092 4.876 4.675
16 7.379 6.974 6.604 6.265 5.954 5.668 5.405 5.162 4.938 4.730
17 7.549 7.120 6.729 6.373 6.047 5.749 5.475 5.222 4.990 4.775
18 7.702 7.250 6.840 6.467 6.128 5.818 5.534 5.273 5.033 4.812
19 7.839 7.366 6.938 6.550 6.198 5.877 5.584 5.316 5.070 4.843
20 7.963 7.469 7.025 6.623 6.259 5.929 5.628 5.353 5.101 4.870
Future value of an ordinary annuity of £1 at i% for n periods, FVAIF(i,n).
Period 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2 2.010 2.020 2.030 2.040 2.050 2.060 2.070 2.080 2.090 2.100
3 3.030 3.060 3.091 3.122 3.153 3.184 3.215 3.246 3.278 3.310
4 4.060 4.122 4.184 4.246 4.310 4.375 4.440 4.506 4.573 4.641
5 5.101 5.204 5.309 5.416 5.526 5.637 5.751 5.867 5.985 6.105
6 6.152 6.308 6.468 6.633 6.802 6.975 7.153 7.336 7.523 7.716
7 7.214 7.434 7.662 7.898 8.142 8.394 8.654 8.923 9.200 9.487
8 8.286 8.583 8.892 9.214 9.549 9.897 10.260 10.637 11.028 11.436
9 9.369 9.755 10.159 10.583 11.027 11.491 11.978 12.488 13.021 13.579
10 10.462 10.950 11.464 12.006 12.578 13.181 13.816 14.487 15.193 15.937
11 11.567 12.169 12.808 13.486 14.207 14.972 15.784 16.645 17.560 18.531
12 12.683 13.412 14.192 15.026 15.917 16.870 17.888 18.977 20.141 21.384
13 13.809 14.680 15.618 16.627 17.713 18.882 20.141 21.495 22.953 24.523
14 14.947 15.974 17.086 18.292 19.599 21.015 22.550 24.215 26.019 27.975
15 16.097 17.293 18.599 20.024 21.579 23.276 25.129 27.152 29.361 31.772
16 17.258 18.639 20.157 21.825 23.657 25.673 27.888 30.324 33.003 35.950
17 18.430 20.012 21.762 23.698 25.840 28.213 30.840 33.750 36.974 40.545
18 19.615 21.412 23.414 25.645 28.132 30.906 33.999 37.450 41.301 45.599
19 20.811 22.841 25.117 27.671 30.539 33.760 37.379 41.446 46.018 51.159
20 22.019 24.297 26.870 29.778 33.066 36.786 40.995 45.762 51.160 57.275
Period 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%
1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
2 2.110 2.120 2.130 2.140 2.150 2.160 2.170 2.180 2.190 2.200
3 3.342 3.374 3.407 3.440 3.473 3.506 3.539 3.572 3.606 3.640
4 4.710 4.779 4.850 4.921 4.993 5.066 5.141 5.215 5.291 5.368
5 6.228 6.353 6.480 6.610 6.742 6.877 7.014 7.154 7.297 7.442
6 7.913 8.115 8.323 8.536 8.754 8.977 9.207 9.442 9.683 9.930
7 9.783 10.089 10.405 10.730 11.067 11.414 11.772 12.142 12.523 12.916
8 11.859 12.300 12.757 13.233 13.727 14.240 14.773 15.327 15.902 16.499
9 14.164 14.776 15.416 16.085 16.786 17.519 18.285 19.086 19.923 20.799
10 16.722 17.549 18.420 19.337 20.304 21.321 22.393 23.521 24.709 25.959
11 19.561 20.655 21.814 23.045 24.349 25.733 27.200 28.755 30.404 32.150
12 22.713 24.133 25.650 27.271 29.002 30.850 32.824 34.931 37.180 39.581
13 26.212 28.029 29.985 32.089 34.352 36.786 39.404 42.219 45.244 48.497
14 30.095 32.393 34.883 37.581 40.505 43.672 47.103 50.818 54.841 59.196
15 34.405 37.280 40.417 43.842 47.580 51.660 56.110 60.965 66.261 72.035
16 39.190 42.753 46.672 50.980 55.717 60.925 66.649 72.939 79.850 87.442
17 44.501 48.884 53.739 59.118 65.075 71.673 78.979 87.068 96.022 105.931
18 50.396 55.750 61.725 68.394 75.836 84.141 93.406 103.740 115.266 128.117
19 56.939 63.440 70.749 78.969 88.212 98.603 110.285 123.414 138.166 154.740
20 64.203 72.052 80.947 91.025 102.444 115.380 130.033 146.628 165.418 186.688