Mobility Engineering - Finance and Management of Infrastructure Investments

Full exam

Exercise 1 The manager of a company is responsible for the following project. 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 program. A penalty of 30 000€ for each month of delay is applied in case the project is not concluded before month 9. At the end of each step of the crashing algorithm write which is the margin gained and the critical path/s (only Crashing ON/OFF can be applied) . Activity Immediate Predecessor Duration (months ) Duration Reduction (Crashing) Total Crashing Cost (€) A - 2 1 28000€ B - 5 3 10000€ C A 6 2 45000€ D A 5 4 150000€ E B 3 1 5000€ F C 4 1 20000€ G D 2 1 10000€ H D 4 2 6000€ I E,F,G,H 1 - - 2 7 5 D 3 8 1 0 5 5 B 4 9 4 5 8 3 E 9 12 4 2 8 6 C 2 8 0 8 12 4 F 8 12 0 The critical path is A -C-F-I. The project duration is 13 months. Solution 0 2 2 A 0 2 0 7 9 2 G 10 12 3 7 11 4 H 8 12 1 12 13 1 I 12 13 0 Solution For crashing, we focus only on activities belonging to the critical path. The activity providing the highest real benefit is activity F. Indeed, Crashing C would lead to a reduction of only 1 month of total duration reduction, due to the fact that a new critical path (A -D - H -I) would emerge. Moreover, crashing C + H would allow to achieve a duration reduction of 2 months, but the overall benefit is lower than crashing only F. Therefore, we start crashing F, see next slide. Activity Immediate Predecessor Duration (months ) Duration Reduction (Crashing) Total Crashing Cost (€) Unitary Crashing Cost €) Real benefit A - 2 1 28000€ 28000€ 2000€ B - 5 3 10000€ 3333.33€ C A 6 2 45000€ 22500€ -15000€ D A 5 4 150000€ 37500€ E B 3 1 5000€ 5000€ F C 4 1 20000€ 20000€ 10000€ G D 2 1 10000€ 10000€ H D 4 2 6000€ 3000€ I E,F,G,H 1 - - - 2 7 5 D 2 7 0 0 5 5 B 3 8 3 5 8 3 E 8 11 3 2 8 6 C 2 8 0 8 11 3 F 8 11 0 The critical paths are A -C-F-I and A -D-H-I. The project duration is 12 months. Having two critical paths we need to crash 1 activity in common to the two paths (A), or two activities of the two paths (C+H, as F has already been crashed, D is not convenient since its unitary crashing cost is higher than the penalty and I cannot be crashed). Crashing C+H is more convenient, as it allows to achieve 2 months of duration reduction with a economic benefit of 9000€ (60000 – 45000 – 6000). Crashing A activity allows to achieve a benefit of 2000€ (30000 -28000) and only 1 month of duration reduction. Thus we crash C+H, see next slide. Solution 0 2 2 A 0 2 0 7 9 2 G 8 11 2 7 11 4 H 7 11 0 11 12 1 I 11 12 0 2 7 5 D 2 7 0 0 5 5 B 1 6 1 5 8 3 E 6 9 1 2 6 4 C 2 6 0 6 9 3 F 6 9 0 The critical paths are A -C-F-I, A -D-H-I and A - D-G -I. The project duration is 10 months. Having three critical paths we need to crash 1 activity in common to the three paths (A), or a combination of activities of the three paths (no alternatives). Crashing A is economically convenient (benefit equal to 2000€ (30000 -28000). Thus we crash A, see next slide. Solution 0 2 2 A 0 2 0 7 9 2 G 7 9 0 7 9 2 H 7 9 0 9 10 1 I 9 10 0 1 6 5 D 1 6 0 0 5 5 B 0 5 0 5 8 3 E 5 8 0 1 5 4 C 1 5 0 5 8 3 F 5 8 0 The critical paths are A -C-F-I, A -D-H-I, A -D-G - I and B -E-I. The project duration is 9 months. Since there is no more penalty for a project with a duration of 9 months, there is no more economic incentive to further reduce the project duration. Thus, we stop here the crashing algorithm. Solution 0 1 1 A 0 2 0 6 8 2 G 6 8 0 6 8 2 H 6 8 0 8 9 1 I 8 9 0 Solution Activity Expected Costs ( €) Real Costs ( €) BCWP criteria (milestones) POC A 30000€ 32000€ 0-50 -100 All Milestones completed B 25000€ 30000€ 20 -80 -100 All Milestones completed C 40000€ 38000€ 20 -80 -100 Second Milestone Completed D 35000€ 40000€ 20 -80 -100 All Milestones completed E 20000€ 20000€ 0-50 -100 All Milestones completed F 50000€ 15000€ 20 -50 -100 First Milestone Completed G 32000€ 20000€ 20 -50 -100 First Milestone Completed H 28000€ - I 12000€ - 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 = 8 (month) and that it was planned that at month 7.5 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 ➢ ACWP = 32 000 + 30 000 + 38 000 + 40 000 + 20 000 + 15 000 + 20 000 = 195 000€ ➢ BCWS = 30 000 + 25 000 + 40 000 + 35 000 + 20 000 + 32 000*1/2 + 28 000*1/4 = 173 000€ ➢ BCWP = 30 000 + 25 000 + 40 000*0.8 + 35 000 + 20 000 + 50 000*0.2 + 32 000*0.2 = 158 400€ ➢ CV = BCWP – ACWP = 158 400 – 195 000 = -36 600€ (cost inefficiency) ➢ SV(€) = BCWP – BCWS = 158 400 – 173 000 = -14 600€ (behind schedule) ➢ SV(t) = Earned Schedule – Time Now = 7.5 – 8 = -0.5 (behind schedule) ➢ CPI = BCWP/ACWP = 158 400/195 000 = 0.812 ➢ SPI = BCWP/BCWS = 158 400/173 000 = 0.915 Contingent Error ➢ EAC(t) = Project Duration – SV t= 13 – (-0.5) = 13.5 ➢ EAC(€) = BAC – CV = 272 000 – (-36 600) = 308 600€ ➢ BAC = 30 000 + 25 000 + 40 000 + 35 000 + 20 000 + 50 000 + 32 000 + 28000 + 12000 = 272 000€ Structural Error ➢ EAC(t) =Time Now + ART = 8 + 6.01 = 14.01 ➢ ART = BRT/SPI = 5.5/0.915 = 6.01 ➢ BRT = Project Duration – Earned Schedule = 13 – 7.5 = 5.5 ➢ EAC(€) = ACWP + ACWR = 195 000 + 139901.4 = 334 901.4€ ➢ ACWR = BCWR/CPI = 113 600/0.812 = 139 901.4€ ➢ BCWR = BAC – BCWP = 272 000 – 158 400 = 113 600€ Theoretical Questions ➢ (6 Points) Which are the main actors that might be involved in a PPP? List them and provide a brief description of their role . ➢ (6 Points) Discuss how it is possible to compute the Weighted Average Cost of Capital (WACC), providing a definition of its main components. ➢ (6 Points) Which are the main adjustments that should be considered in case financial cash flows should be converted into economic cash -flows? Discuss them theoretically and then compute financial cash -flows and economic cash -flows in 2021 with respect to the project summarized in the following table. Moreover it is known that: ▪ The manpower cost (corresponding to 30% of the overall Operating Cost item) does not reflect a competitive cost for manpower. Its conversion factor is 1.25. ▪ The project generated 1 000 tons of CO 2 with a cost of 0.1€/kg of C0 2. ▪ Corporate Taxes represent a distribution of financial resources across different groups of society. Item 2021 Operating Costs 1 500 000 Revenues 2 000 000 Corporate Taxes 250 000 Solutions ➢ Which are the main actors that might be involved in a PPP? List them and provide a brief description of their role (6 Points). Solution ➢ Discuss how it is possible to compute the Weighted Average Cost of Capital (WACC), providing a definition of its main components (6 Points). Solution ➢ Which are the main adjustments that should be considered in case financial cash flows should be converted into economic cash -flows? Discuss them theoretically and then compute financial cash -flows and economic cash -flows in 2021 with respect to the project summarized in the following table . Moreover it is known that : ▪ The manpower cost (corresponding to 30% of the overall Operating Cost item) does not reflect a competitive cost for manpower. Its conversion factor is 1.25. ▪ The project generated 1 000 tons of CO 2 with a cost of 0.1€/kg (6 Points). ▪ Corporate Taxes represent a distribution of financial resources across different groups of society. Item 2021 Operating Costs 1 500 000 Revenues 2 000 000 Corporate Taxes 250 000Item 2021 Item 2021 Operating Costs 1,500,000.00 € Operating Costs 1,612,500.00 € Revenues 2,000,000.00 € Revenues 2,000,000.00 € Corporate Taxes 250,000.00 € Corporate Taxes 250,000.00 € Environmental Externalities 100,000.00 € FCF 250,000.00 € ECF 287,500.00 € Financial Analysis Economic Analysis Solution FCF = Revenues – Operating Costs – Corporate Taxes ECF = Revenues – Operating Costs – Environmental Externalities Operating Costs (in the economic analysis ) = Operating Costs (in the Financial Analysis)*0.7 + Operating Costs (in the Financial Analysis)*0.3*1.25 Environmental Externalities = 0.1*1000*1000Item 2021 Item 2021 Operating Costs 1,500,000.00 € Operating Costs 1,612,500.00 € Revenues 2,000,000.00 € Revenues 2,000,000.00 € Corporate Taxes 250,000.00 € Corporate Taxes 250,000.00 € Environmental Externalities 100,000.00 € FCF 250,000.00 € ECF 287,500.00 € Financial Analysis Economic Analysis