Mobility Engineering - Finance and Management of Infrastructure Investments

Full exam

Exercise 1 The following project is assigned. Identify the critical path. Consider the possibility to crash the activities as shown in the following table. Identify the optimal solution according to a crashing programme . A penalty of 20 000€ for each week of delay is applied in case the project is not concluded before week 11. At the end of each step of the crashing algorithm write which is the margin gained and the critical path/s. Activity Immediate Predecessor Duration (Weeks) Duration Reduction (Crashing) Total Crashing Cost (€) A - 2 1 5 000€ B - 4 - - C A 5 1 3 000 € D A 3 2 22 000€ E B 5 3 54 000€ F C,D,E 4 1 31 000 € G F 3 2 36 000 € 2 7 5 C 4 9 2 0 4 4 B 0 4 0 2 5 3 D 6 9 4 9 13 4 F 9 13 0 4 9 5 E 4 9 0 The critical path is B -E-F-G. The project duration is 16 weeks. Solution 0 2 2 A 2 4 2 13 16 3 G 13 16 0 Exercise 1 Activity Immediate Predecessor Duration (Weeks) Duration Reduction (Crashing) Total Crashing Cost (€) Unitary crashing cost (€) A - 2 1 5 000€ 5 000€ B - 4 - - - C A 5 1 3 000 € 3 000€ D A 3 2 22 000€ 11 000€ E B 5 3 54 000€ 18 000€ F C,D,E 4 1 31 000 € 31 000€ G F 3 2 36 000 € 18 000€ The following project is assigned. Identify the critical path. Consider the possibility to crash the activities as shown in the following table. Identify the optimal solution according to a crashing programme . A penalty of 20 000€ for each week of delay is applied in case the project is not concluded before week 11. At the end of each step of the crashing algorithm write which is the margin gained and the critical path/s. Crash G, as it is the most convenient activity. Solution The critical path is B -E-F-G. The project duration is 14 weeks. Benefit = 40 000 – 36 000 = 4 000€ 2 7 5 C 4 9 2 0 4 4 B 0 4 0 2 5 3 D 6 9 4 9 13 4 F 9 13 0 4 9 5 E 4 9 0 0 2 2 A 2 4 2 13 14 1 G 13 14 0 Crash C+E. Indeed, crashing only E is not convenient. As we have reached the target duration of 11 weeks and there is no more penalty, we stop crashing. Solution The critical paths are: A -C-F-G and B -E-F-G. The project duration is 11 weeks. Benefit = 60 000 – (54 000 + 3000)= 3 000€ 2 6 4 C 2 6 0 0 4 4 B 0 4 0 2 5 3 D 3 6 1 6 10 4 F 6 10 0 4 6 2 E 4 6 0 0 2 2 A 0 2 0 10 11 1 G 10 11 0 Solution Activity Expected Costs ( €) Real Costs ( €) BCWP criteria (milestones) POC A 42 000 € 30 000 € 20 -80 -100 All Milestones completed B 40 000 € 30 000 € 0-100 All Milestones completed C 20 000 € 18 000 € 0-50 -100 Second Milestone Completed (50%) D 35 000 € 15 000 € 20 -80 -100 First Milestone completed E 30 000 € 5 000 € 20 -80 -100 First Milestone completed F 30 000 € 25 000€ 0-100 All Milestones completed G 20 000 € - 20 -80 -100 The following additional information is provided: • Considering the budget information contained in the following table compute the project performances (no crashing is considered). Consider that Time Now = 6 (week) and that it was planned that at time (week) 5 the BCWS had the same value that BCWP has at time now. • Compute the estimate at completion in case of Structural Error and Contingent Error. NO Crashing is Considered Solution ➢ BCWS = 42 000 + 40 000 + 20 000*4/5 + 35 000 + 30 000*2/5 = 145 000€ ➢ ACWP = 30 000 + 30 000 + 18 000 + 15 000 + 5 000 + 25 000 = 123 000€ ➢ BCWP = 42 000 + 40 000 + 20 000*0.5 + 0.2*35 000 + 0.2*30 000 + 30 000 = 135 000€ ➢ CV = BCWP – ACWP = 135 000 – 123 000 = 12 000€ (cost efficiency) ➢ SV(€) = BCWP – BCWS = 135 000 – 145 000 = -10 000€ (behind schedule) ➢ SV(t) = Earned Schedule – Time Now = 5 – 6 = -1 (behind schedule) ➢ CPI = BCWP/ACWP = 135 000/123 000 = 1.097 ➢ SPI = BCWP/BCWS = 135 000/145 000 = 0.931 Contingent Error ➢ EAC(t) = Project Duration – SV t= 16 – (-1) = 17 ➢ EAC(€) = BAC – CV = 217 000 – (12 000) = 205 000€ ➢ BAC = 42 000 + 40 000 + 20 000 + 35 000 + 30 000 + 30 000 + 20 000 = 217 000€ Structural Error ➢ EAC(t) = Time Now + ART = 6 + 11.82 = 17.82 ➢ ART = BRT/SPI = 11/0.931 = 11.82 ➢ BRT = Project Duration – Earned Schedule = 16 – 5 = 11 ➢ EAC(€) = ACWP + ACWR = 123 000 + 74 749 = 197 749€ ➢ ACWR = BCWR/CPI = 82 000/1.097 = 74 749€ ➢ BCWR = BAC – BCWP = 217 000 – 135 000 = 82 000€ Theoretical Questions 1 ➢ Based on the information in the following table, compute the Return on Investment (ROI) and the quick ratio (known also as acid test ratio) for Company A and Company B (6 Points). Company A Company B Net Profit 18,000,000 € 7,000,000 € Operating Profit 50,000,000 € 20,000,000 € Total Assets 120,000,000 € 90,000,000 € Non Financial Liabilities 28,000,000 € 15,000,000 € Cash 7,000,000 € 2,000,000 € Short Term Investments 3,000,000 € 1,000,000 € Financial Liabilities 60,000,000 € 40,000,000 € Receivables 15,000,000 € 500,000 € Current Liabilities 32,000,000 € 3,000,000 € Theoretical Questions 2 ➢ Define the different categories of financial instruments that can be used to finance an infrastructure project and provide 1 example of financial instrument belonging to each category (6 Points). Theoretical Questions 3 ➢ Based on the Cash Flows (CF) in the following table, compute the Net Present Value (NPV) and the Payback Time (PBT) for Project A and B, respectively. Furthermore, comment which investment is preferable according to the different indicators, explaining and discussing potential different indications provided by these indicators. Include in the discussion also the IR R (the value is already computed both for project A and project B) ( 6 Points).Year 0 Year 1 Year 2 Year 3 IRR Discount Rate CF Scenario A -1,000,000.00 € 500,000.00 € 300,000.00 € 900,000.00 € 28% 3% CF Scenario B -100,000.00 € 80,000.00 € 25,000.00 € 5,000.00 € 8% 3% NPV A??? NPV B??? PBT A??? PBT B??? Theoretical Questions 1: Solution ➢ Based on the information in the following table, compute the Return on Investment (ROI) and the quick ratio (known also as acid test ratio) for Company A and Company B (6 Points). �������� = �������������� ����������� (��������� ) ����� ������ − ��� ������������������� ������������������������������������ ���������� ���������� = ���ℎ + �ℎ��� ���� ���������������� + ���������������� ������� ������������������������������������Company A Company B Net Profit 18,000,000 € 7,000,000 € Operating Profit 50,000,000 € 20,000,000 € Total Assets 120,000,000 € 90,000,000 € Non Financial Liabilities 28,000,000 € 15,000,000 € Cash 7,000,000 € 2,000,000 € Short Term Investments 3,000,000 € 1,000,000 € Financial Liabilities 60,000,000 € 40,000,000 € Receivables 15,000,000 € 500,000 € Current Liabilities 32,000,000 € 3,000,000 € Solution Company A Company B ROI 0.543 0.267 Quick Ratio 0.781 1.167 Theoretical Questions 2: Solution ➢ Define the different categories of financial instruments that can be used to finance an infrastructure project and provide 1 example of financial instrument belonging to each category (6 Points). Theoretical Questions 3: Solution ��������������� �� ������ = �� ������ (1 + ������������� ���� )������ � ������� = ෍ ������=1 ������ �� ������ (1 + �)������ = ෍ ������=1 ������ ��������������� �� ������ ��������������� ��������������� �� ������ = ��������������� ��������������� �� ������−1 + ��������������� �� ������ The Payback Time is the minimum number of years after which the Cumulative Discounted CF are positive. It is Year 3 for project A and Year 2 for project B.Year 0 Year 1 Year 2 Year 3 Discounted CF Scenario A -1,000,000.00 € 485,436.89 € 282,778.77 € 823,627.49 € Discounted CF Scenario B -100,000.00 € 77,669.90 € 23,564.90 € 4,575.71 € NPV A 591,843.1594 € NPV B 5,810.5089 € Year 0 Year 1 Year 2 Year 3 Cumulative DCF Scenario A -1,000,000.00 € -514,563.11 € -231,784.33 € 591,843.16 € Cumulative DCF Scenario B -100,000.00 € -22,330.10 € 1,234.80 € 5,810.51 € PBT A 3 Years PBT B 2 Years