Mobility Engineering - Finance and Management of Infrastructure Investments

Full exam

Exercise 1 The manager of a company is responsible for the following project. Using the PERT algorithm identify the critical path. Compute the probability that paths A -C-H and A -E-H are concluded after month 30. 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 30 000€ for each month of delay is applied in case the project is concluded after month 20 (>20 month) . In addition, a market opportunity equal to 45 000€/month is achieved in case the project is reduced by month 20 to month 18. At the end of each step of the crashing algorithm write which is the margin gained and the critical path/s. Activity Immediate Predecessor Time Optimistic (months ) Average Time (months ) Time Pessimisti c(months ) Std . deviation Duration Reduction (months ) Total Crashing Cost (€) A - 6 7 14 4 2 74 000€ B - 2 4 12 3 3 45 000 € C A 5 7 15 7 3 45 000 € D A 3 4 5 1 2 1 000 € E A 9 10 11 1 5 80 000€ F B 5 6 7 1 5 10 000 € G B 5 6 19 6 3 9 000€ H C,D,E,F,G 3 5 19 4 - - Solution Activity Immediate Predecessor Time Optimistic (months ) Average Time (months ) Time Pessimistic (months ) Expected duration (months ) Std . deviation Duration Reduction (months ) Total Crashing Cost (€) A - 6 7 14 8 4 2 74 000€ B - 2 4 12 5 3 3 45 000 € C A 5 7 15 8 7 3 45 000 € D A 3 4 5 4 1 2 1 000 € E A 9 10 11 10 1 5 80 000€ F B 5 6 7 6 1 5 10 000 € G B 5 6 19 8 6 3 9 000€ H C,D,E,F,G 3 5 19 7 4 - - 8 16 8 C 10 18 2 0 5 5 B 5 10 5 8 12 4 D 14 18 6 8 18 10 E 8 18 0 5 11 6 F 12 18 7 The critical path is A -E-H. The project duration is 25 months. Solution 0 8 8 A 0 8 0 5 13 8 G 10 18 5 18 25 7 H 18 25 0 Solution ➢ Path A -C-H: P(Duration > 30 ) = P(z > 30 −23 16 +49 +16 ) = ������ � ≻ 0 .78 = 1 − ������ (� < 0.78 ) = 1 -0.7823 = 21.77% ➢ Path A -E-H: P(Duration > 30 ) = P(z > 30 −25 16 +1+16 ) ������ � > 0.87 = 1 − ������ (� < 0.87 ) = 1 -0.8078 = 19.22% Exercise 1 Activity Duration Reduction (months ) Total Crashing Cost (€) Unitary Crashing Cost (€) A 2 74 000€ 37 000€ B 3 45 000 € 15 000€ C 3 45 000 € 15 000€ D 2 1 000 € 500€ E 5 80 000€ 16 000€ F 5 10 000 € 2 000€ G 3 9 000€ 3 000€ H - - - In this case we have 1 critical path A -E-H. Only activity E has a unitary crashing cost below the penalty (30 000€). Therefore, we should start crashing activity E. However, crashing only activity E would lead to the emergence of another critical path (A -C-H) with a real duration reduction equal to 2 months. This scenario would not be economically convenient, since we would spend 80 000€ with a saving of 60 000€. Consequently, E should be crashed in parallel with another activity of the path A -C-H. The best solution is t o crash E and C in parallel. In this way, we achieve a real project duration reduction equal to 5 months. Benefit = 30 000 * 5 – 80 000 – 45 000 = 25 000€ 8 13 5 C 8 13 0 0 5 5 B 0 5 0 8 12 4 D 9 13 1 8 13 5 E 8 13 0 5 11 6 F 7 13 2 The critical paths are A -C-H, A -E-H and B -G -H. The project duration is 20 months. As we have three critical paths we need to crash a combination of activities allowing to reduce the duration of all the 3 critical paths. The best solution is to crash activity A and activity G. The project duration is reduced by 2 months. The benefit is equal to: 45 000*2 – 74 000 – 9000 = 7 000€ Solution 0 8 8 A 0 8 0 5 13 8 G 5 13 0 13 20 7 H 13 20 0 6 11 5 C 6 11 0 0 5 5 B 0 5 0 6 10 4 D 7 11 1 6 11 5 E 6 11 0 5 11 6 F 5 11 0 The critical paths are A -C-H, A -E-H and B -F-H. The project duration is 18 months. Since there is not anymore penalty or market opportunity there is no more incentive to further reduce the project duration. Solution 0 6 6 A 0 6 0 5 10 5 G 6 11 1 11 18 7 H 11 18 0 Exercise 1 Taking into account that Time Now = month 13 and given the following budget information compute the indicators: ACWP, BCWS, BCWP, BAC, CV, SV(€), SV(t). Consider that it was planned that at time 12 the BCWS had the same value that BCWP has at time now. Activity Expected Costs ( €) Real Costs ( €) BCWP criteria (milestones) POC A 40 000€ 50 000€ 20 -80 -100 All Milestones completed B 35 000€ 40 000€ 0-50 -100 All Milestones completed C 40 000€ 45 000€ 20 -50 -100 All Milestone completed D 32 000€ 30 000€ 20 -80 -100 Second Milestone completed E 40 000€ 55 000€ 0-50 -100 All Milestones completed F 50 000€ 40 000€ 20 -80 -100 Second Milestone completed G 25 000€ 20 000€ 20 -50 -100 First Milestone Completed H 10 000€ - - No Milestone Completed Exercise 1 ➢ BCWS = 40 000 + 35 000 + 40 000 * 5/8 + 32 000 + 40 000*5/10 + 50 000 + 25 000 = 227 000 € ➢ BCWP = 40 000*1 + 35 000*1 + 40 000*1 + 32 000 * 0.8 + 40 000*1 + 50 000*0.8 + 25 000*0.2= 225 600€ ➢ ACWP = 50 000 + 40 000 + 45 000 + 30 000 + 55 000 + 40 000 + 20 000 = 280 000€ ➢ BAC = 40 000 + 35 000 + 40 000 + 32 000 + 40 000 + 50 000 + 25 000 + 10 000 = 272 000€ ➢ CV = BCWP – ACWP = 225 600 – 280 000 = -54 400€ (Cost Inefficient) ➢ SV(€) = BCWP – BCWS = 225 600 – 227 000 = -1 400 (Behind Schedule) ➢ SV(t) = Earned Schedule – Time Now = 12 – 13 = -1 (one month in delay) Theoretical Question 1 ➢ G iven the information in the following table, compute the Debt Service Cover Ratio (DSCR) for Year 0, Year 1, Year 2, Year 3 and the Loan Life Cover Ratio (LLCR) for the whole project (6 Points).Year 0 Year 1 Year 2 Year 3 Discount Rate CF 200,000.00 € 300,000.00 € 350,000.00 € 400,000.00 € 5% Debt Repayment 150,000.00 € 165,000.00 € 178,000.00 € 188,000.00 € Financial Interests 7,500.00 € 8,250.00 € 8,900.00 € 9,400.00 € DSCR ??? ??? ??? ??? LLCR ??? Theoretical Question 2 ➢ Define what a PPP is and explain how the main risks can be allocated to the different actors involved in the PPP (6 Points). Theoretical Question 3 ➢ Explain the difference between the Internal return rate (IRR) and the modified internal return rate (MIRR). Moreover, based on the information available in the following table (the MIRR is computed assuming that cash generated can be re - invested at a discount rate equal to 4%), demonstrate that the IRR and the MIRR are equal to the compound annual growth rate in case in case we assume to have the possibility to invest in each year the available cash flows (CF) at the respective interest rate. (6 Points).Year 0 Year 1 Year 2 Year 3 IRR MIRR Discount Rate CF -50,000.00 € 25,000.00 € 25,000.00 € 30,000.00 € 26.774% 18.424% 4.00% Theoretical Question 1: Solution ➢ G iven the information in the following table, compute the Debt Service Cover Ratio (DSCR) for Year 0, Year 1, Year 2, Year 3 and the Loan Life Cover Ratio (LLCR) for the whole project. ��� � ������ = �� ������ ���� ��������� ������ + ��������� ������������� ������ ���������� �� ������ = �� ������ (1 + �������� ���� ������)������ ���������� ���� ��������� ������ = ���� ��������� ������ (1 + �������� ���� ������)������ ���� = σ ���������������� �� ������ σ ���������������� ���� ��������� ������Year 0 Year 1 Year 2 Year 3 CF 200,000.00 € 300,000.00 € 350,000.00 € 400,000.00 € Debt Repayment 150,000.00 € 165,000.00 € 178,000.00 € 188,000.00 € Financial Interests 7,500.00 € 8,250.00 € 8,900.00 € 9,400.00 € DSCR 1.270 1.732 1.873 2.026 Discounted CF 200,000.00 € 285,714.29 € 317,460.32 € 345,535.04 € Discounted Debt Repayment 150,000.00 € 157,142.86 € 161,451.25 € 162,401.47 € LLCR 1.820 Theoretical Question 2: Solution ➢ Define what a PPP is and explain how the main risks can be allocated to the different actors involved in the PPP (6 Points). PPP: a long -term contract between a private party and a government entity, for providing a public asset or service, in which the private party bears significant risk and management responsibility, and remuneration is linked to performance Theoretical Question 2: Solution PPP is an effective instrument for combining the pros of a competitive tender and shifting risks and costs from public balances .Nevertheless, it is important to understand that in PPP there are potential source of risks as well : ➢ Construction and Completion risks : • Cost of Construction : During the completion of the project costs increase diverging from the budget (EPC Contractor can bear the construction risk) . • Delay :The project is not able to keep -up with the expected time schedule . • Performance :The infrastructure delivered might not be able to pass the set of agreed tests . ➢ Operating risks : The financial model and the assumption made about the sustainability of the project (e .g. operating costs or demand) diverge from the consumptive (The O&M Contractor can bear the operation risk) . Theoretical Question 2: Solution ➢ Political and Regulatory Risk : A government may decide to end a project or to unilaterally modify the terms of it or not honour them . A government may also decide to nationalize and thus expropriate the assets from the private counterpart before the end of the agreed period . ➢ Environmental Risk :compliance environmental requirements may increase substantially costs in order to meet them . Also, some lenders may be tempted to avoid project that not meet with their environmental standards (e .g.Equator Principles) . Theoretical Question 3: Solution �� ������������ � �������� ������ = �� ������ ∗ (1 + �������� )3−������ ��������� �������� = ( σ �������� ������������ � �������� ������ − �� ������������������������ 0 ) 1 3− 1 �� ������������ � ��������� ������ = �� ������ ∗ (1 + �������� ���� )3−������ ��������� ��������� = ( σ �������� ������������ � � �������� ������ − �� ������������������������ 0 ) 1 3− 1Year 0 Year 1 Year 2 Year 3 IRR MIRR Discount Rate CF -50,000.00 € 25,000.00 € 25,000.00 € 30,000.00 € 26.774% 18.424% 4.00% Solution Year 1 Year 2 Year 3 Total CF (Year 1-3) CF 25,000.00 € 25,000.00 € 30,000.00 € 80,000.000 € CF Adjusted IRR 40,178.814 € 31,693.380 € 30,000.000 € 101,872.194 € CAGR (IRR) 26.774% Year 1 Year 2 Year 3 Total CF (Year 1-3) CF 25,000.00 € 25,000.00 € 30,000.00 € 80,000.000 € CF Adjusted MIRR 27,040.000 € 26,000.000 € 30,000.000 € 83,040.000 € CAGR (MIRR) 18.424%