Two options (shown in Table Q3a) are being considered to supply water to yard taps in a section of the township (very low-income population) whose 2030 population was forecasted in Question 2. As Municipal Manager, you have setup a project task team (comprising the councillor, youth leaders, political party representatives, interested stakeholders and the Johannesburg Water representatives). The task team has agreed on one project objective i.e.: to provide each household with at least 200 litres per day The preferred option will cater for 300 households. Assume that each household will contribute a total of R240 during the first year and this annual contribution will increase by the prevailing interest rate until the end of the 10-year period. Both options have a life span of 10 years and the prevailing annual interest rate is 5%. The council will pay for 90% of the capital cost of the preferred option while households will pay 10% of the capital cost PLUS 100% of the Operation, Maintenance and Replacement (OMR) costs. The OMR cost will increase by a fixed amount annually from the end of the 2nd year. Develop a matrix to screen the two options below. After developing the matrix, screen the 2 options and recommend the preferred option to the Mayor. Table Q3b lists the typical steps involved in developing a screening matrix and the mark allocation. Table Q3a Option 1 -Yard taps receive water from a bulk municipal water supply connection Option 2 - Taps receive water from a system of boreholes, pumps and tanks R1 200 000 R1 000 000 Capital cost OMR cost: i. At the end of the 1st year R8 000 R12 000 ii. R2 000 R4 000 Annual increase from the end of the 2nd year until the end of the 10th year Table Q3b Steps Steps Mark allocation Mark allocation 4.0 Step 1: State the objective 2.0 Step 2: Agree on the criteria that support the objective Step 3: Gather information 0.5 Step 6: Develop Criteria and four (4) Measures of Effectiveness (MOE) Step 7: Decide on the scale for scoring and description of scale for each MOE Step 8: Decide on the weights for each criteria Step 9: Develop the Evaluation Outcome Step 10: Screen the options and recommend the preferred option(s) Step 4: Identify the options 1.0 7.5 2.0 Step 5: Preliminary designs including lifecycle costs 5% 5% n n 1 2 3 3 4 4 5 5 6 7 7 8 9 10 11 1 2 3 4 5 6 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 12 13 14 15 16 17 18 Single Payment Compound Present Amount Worth Factor Factor Find F Find P Given P Given F F/P P/F 1.050 .9524 1.102 9070 1.158 .8638 1.216 .8227 1.276 .7835 1.340 .7462 1.407 .7107 1.477 .6768 1.551 .6446 1.629 .6139 1.710 .5847 1.796 ,5568 1.886 .5303 1.980 ,5051 2.079 .4810 2.183 .4581 2.292 .4363 2.407 .4155 2.527 .3957 2.653 .3769 2.786 .3589 2.925 .3419 3.072 .3256 3.225 .3101 3.386 .2953 3.556 .2812 3.733 .2678 3.920 .2551 4.116 .2429 4.322 .2314 4.538 .2204 4.765 .2099 5.003 .1999 5.253 .1904 5.516 .1813 7.040 .1420 8.985 .1113 11.467 .0872 14.636 .0683 18.679 .0535 23.840 .0419 30.426 .0329 38,832 .0258 49.561 .0202 63.254 .0158 80.730 .0124 103.034 .00971 131.500 .00760 Sinking Fund Factor Find A Given F A/F 10000 .4878 .3172 .2320 .1810 .1470 .1228 .1047 .0907 .0795 .0704 .0628 .0565 .0510 0463 .0423 ,0387 0355 0327 .0302 .0280 .0260 .0241 .0225 0210 .0196 .0183 .0171 .0160 .0151 .0141 .0133 .0125 .0118 .0111 .00828 .00626 .00478 .00367 .00283 .00219 .00170 .00132 .00103 .00080 .00063 .00049 .00038 Compound Interest Factors Uniform Payment Series Capital Compound Recovery Amount Factor Factor Find A Find F Given P Given A A/P F/A 1.0500 1.000 .5378 2.050 .3672 3.152 .2820 4.310 2310 5.526 .1970 6.802 .1728 8.142 1547 9.549 1407 11.027 .1295 12.578 1204 14.207 1128 15.917 . 1065 17.713 .1010 19.599 0963 21.579 .0923 23.657 .0887 25.840 0855 28.132 .0827 30.539 .0802 33,066 .0780 35.719 .0760 38.505 .0741 41.430 .0725 44.502 .0710 47.727 .0696 51.113 .0683 54,669 .0671 58.402 .0660 62.323 .0651 66.439 0641 70.761 .0633 75.299 .0625 80.063 .0618 85.067 .0611 90.320 .0583 120.799 0563 159.699 .0548 209.347 .0537 272.711 0528 353.582 0522 456.795 .0517 588,525 .0513 756.649 .0510 971.222 0508 1 245.1 .0506 1 594.6 0505 2040.7 0504 2610.0 Present Worth Factor Find P Given A P/A 0.952 1.859 2.723 3.546 4.329 5.076 5.786 6.463 7.108 7.722 8.306 8.863 9.394 9.899 10.380 10.838 11.274 11.690 12.085 12.462 12.821 13.163 13.489 13.799 14.094 14.375 14.643 14.898 15.141 15.372 15.593 15.803 16.003 16.193 16.374 17.159 17.774 18.256 18.633 18.929 19.161 19.343 19.485 19.596 19.684 19.752 19.806 19.848 Arithmetic Gradient Gradient Gradient Uniform Present Series Worth Find A Find P Given G Given G A/G P/G 0 0 0.488 0.907 0.967 2.635 1.439 5.103 1.902 8.237 2.358 11.968 2.805 16.232 3.244 20.970 3.676 26.127 4.099 31.652 4.514 37.499 4.922 43.624 5.321 49.988 5.713 56,553 6.097 63.288 6,474 70.159 6.842 77.140 7.203 84.204 7.557 91.327 7.903 98.488 8.242 105.667 8.573 112.846 8.897 120.008 9.214 127.140 9.524 134.227 9.827 141.258 10.122 148.222 10.411 155.110 10.694 161.912 10.969 168,622 11.238 175.233 11.501 181.739 11.757 188.135 12.006 194.416 12.250 200.580 13.377 229.545 14.364 255.314 15.223 277.914 15.966 297.510 16.606 314.343 17.154 328.691 17.621 340.841 18.018 351.072 18.353 359.646 18,635 366.800 18,871 372.749 19,069 377.677 19.234 381.749 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Two options (shown in Table Q3a) are being considered to supply water to yard taps in a section of the township (very low-income population) whose 2030 population was forecasted in Question 2. As Municipal Manager, you have setup a project task team (comprising the councillor, youth leaders, political party representatives, interested stakeholders and the Johannesburg Water representatives). The task team has agreed on one project objective i.e.: to provide each household with at least 200 litres per day The preferred option will cater for 300 households. Assume that each household will contribute a total of R240 during the first year and this annual contribution will increase by the prevailing interest rate until the end of the 10-year period. Both options have a life span of 10 years and the prevailing annual interest rate is 5%. The council will pay for 90% of the capital cost of the preferred option while households will pay 10% of the capital cost PLUS 100% of the Operation, Maintenance and Replacement (OMR) costs. The OMR cost will increase by a fixed amount annually from the end of the 2nd year. Develop a matrix to screen the two options below. After developing the matrix, screen the 2 options and recommend the preferred option to the Mayor. Table Q3b lists the typical steps involved in developing a screening matrix and the mark allocation. Table Q3a Option 1 -Yard taps receive water from a bulk municipal water supply connection Option 2 - Taps receive water from a system of boreholes, pumps and tanks R1 200 000 R1 000 000 Capital cost OMR cost: i. At the end of the 1st year R8 000 R12 000 ii. R2 000 R4 000 Annual increase from the end of the 2nd year until the end of the 10th year Table Q3b Steps Steps Mark allocation Mark allocation 4.0 Step 1: State the objective 2.0 Step 2: Agree on the criteria that support the objective Step 3: Gather information 0.5 Step 6: Develop Criteria and four (4) Measures of Effectiveness (MOE) Step 7: Decide on the scale for scoring and description of scale for each MOE Step 8: Decide on the weights for each criteria Step 9: Develop the Evaluation Outcome Step 10: Screen the options and recommend the preferred option(s) Step 4: Identify the options 1.0 7.5 2.0 Step 5: Preliminary designs including lifecycle costs 5% 5% n n 1 2 3 3 4 4 5 5 6 7 7 8 9 10 11 1 2 3 4 5 6 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 12 13 14 15 16 17 18 Single Payment Compound Present Amount Worth Factor Factor Find F Find P Given P Given F F/P P/F 1.050 .9524 1.102 9070 1.158 .8638 1.216 .8227 1.276 .7835 1.340 .7462 1.407 .7107 1.477 .6768 1.551 .6446 1.629 .6139 1.710 .5847 1.796 ,5568 1.886 .5303 1.980 ,5051 2.079 .4810 2.183 .4581 2.292 .4363 2.407 .4155 2.527 .3957 2.653 .3769 2.786 .3589 2.925 .3419 3.072 .3256 3.225 .3101 3.386 .2953 3.556 .2812 3.733 .2678 3.920 .2551 4.116 .2429 4.322 .2314 4.538 .2204 4.765 .2099 5.003 .1999 5.253 .1904 5.516 .1813 7.040 .1420 8.985 .1113 11.467 .0872 14.636 .0683 18.679 .0535 23.840 .0419 30.426 .0329 38,832 .0258 49.561 .0202 63.254 .0158 80.730 .0124 103.034 .00971 131.500 .00760 Sinking Fund Factor Find A Given F A/F 10000 .4878 .3172 .2320 .1810 .1470 .1228 .1047 .0907 .0795 .0704 .0628 .0565 .0510 0463 .0423 ,0387 0355 0327 .0302 .0280 .0260 .0241 .0225 0210 .0196 .0183 .0171 .0160 .0151 .0141 .0133 .0125 .0118 .0111 .00828 .00626 .00478 .00367 .00283 .00219 .00170 .00132 .00103 .00080 .00063 .00049 .00038 Compound Interest Factors Uniform Payment Series Capital Compound Recovery Amount Factor Factor Find A Find F Given P Given A A/P F/A 1.0500 1.000 .5378 2.050 .3672 3.152 .2820 4.310 2310 5.526 .1970 6.802 .1728 8.142 1547 9.549 1407 11.027 .1295 12.578 1204 14.207 1128 15.917 . 1065 17.713 .1010 19.599 0963 21.579 .0923 23.657 .0887 25.840 0855 28.132 .0827 30.539 .0802 33,066 .0780 35.719 .0760 38.505 .0741 41.430 .0725 44.502 .0710 47.727 .0696 51.113 .0683 54,669 .0671 58.402 .0660 62.323 .0651 66.439 0641 70.761 .0633 75.299 .0625 80.063 .0618 85.067 .0611 90.320 .0583 120.799 0563 159.699 .0548 209.347 .0537 272.711 0528 353.582 0522 456.795 .0517 588,525 .0513 756.649 .0510 971.222 0508 1 245.1 .0506 1 594.6 0505 2040.7 0504 2610.0 Present Worth Factor Find P Given A P/A 0.952 1.859 2.723 3.546 4.329 5.076 5.786 6.463 7.108 7.722 8.306 8.863 9.394 9.899 10.380 10.838 11.274 11.690 12.085 12.462 12.821 13.163 13.489 13.799 14.094 14.375 14.643 14.898 15.141 15.372 15.593 15.803 16.003 16.193 16.374 17.159 17.774 18.256 18.633 18.929 19.161 19.343 19.485 19.596 19.684 19.752 19.806 19.848 Arithmetic Gradient Gradient Gradient Uniform Present Series Worth Find A Find P Given G Given G A/G P/G 0 0 0.488 0.907 0.967 2.635 1.439 5.103 1.902 8.237 2.358 11.968 2.805 16.232 3.244 20.970 3.676 26.127 4.099 31.652 4.514 37.499 4.922 43.624 5.321 49.988 5.713 56,553 6.097 63.288 6,474 70.159 6.842 77.140 7.203 84.204 7.557 91.327 7.903 98.488 8.242 105.667 8.573 112.846 8.897 120.008 9.214 127.140 9.524 134.227 9.827 141.258 10.122 148.222 10.411 155.110 10.694 161.912 10.969 168,622 11.238 175.233 11.501 181.739 11.757 188.135 12.006 194.416 12.250 200.580 13.377 229.545 14.364 255.314 15.223 277.914 15.966 297.510 16.606 314.343 17.154 328.691 17.621 340.841 18.018 351.072 18.353 359.646 18,635 366.800 18,871 372.749 19,069 377.677 19.234 381.749 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 26 27 28 29 30 31 32 33 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100 34 35 40 45 50 55 60 65 70 75 80 85 90 95 100