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 the critical path(s) is (are) concluded after month 15. 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 15 000€ for each month of delay is applied in case the project is not concluded before month 14. 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 Pessimistic (months ) Std . deviation Duration Reduction (months ) Total Crashing Cost (€) A - 3 4 5 1 1 35 000€ B A 3 5 13 5 3 30 000 € C A 1 2 9 4 2 60 000 € D B 6 7 8 2 2 10 000 € E B 4 5 6 1 - - F C 5 9 19 7 5 9 000 € G C 5 5 5 0 3 21 000€ H D,E,F,G 2 3 4 1 - - Solution Activity Immediate Predecessor Time Optimistic (months ) Average Time (months ) Time Pessimistic (months ) Expected Duration Std . deviation Duration Reduction (months ) Total Crashing Cost (€) A - 3 4 5 4 1 1 35 000€ B A 3 5 13 6 5 3 39 000 € C A 1 2 9 3 4 2 60 000 € D B 6 7 8 7 2 2 10 000 € E B 4 5 6 5 1 - - F C 5 9 19 10 7 5 9 000 € G C 5 5 5 5 0 3 21 000€ H D,E,F,G 2 3 4 3 1 - - 4 7 3 C 4 7 0 4 10 6 B 4 10 0 10 17 7 D 10 17 0 10 15 5 E 12 17 2 7 17 10 F 7 17 0 The critical paths are A -B-D -H and A -C-F-H. The project duration is 20 months. Solution 0 4 4 A 0 4 0 7 12 5 G 12 17 5 17 20 3 H 17 20 0 Solution ➢ Path A -B-D -H: P(Duration > 15 ) = P(z > 15 −20 1+25 +4+1) = ������ ������ ≻ − 0.90 = 1 − ������ (������ > 0 .90 ) = 1 -(1 -P(z − 0.61 = ������ (������ < 0.61 ) = 72.91% Exercise 1 Activity Duration Reduction (months ) Total Crashing Cost (€) Unitary Crashing Cost (€) A 1 35 000€ 35 000€ B 3 39 000 € 13 000€ C 2 60 000 € 30 000 D 2 10 000 € 5 000€ E - - - F 5 9 000 € 1 800€ G 3 21 000€ 7 000€ H - - - Since in this case we have 2 critical paths (A-B-D-H and A -C-F-H) we need to crash either one activity in common to the two paths (A or H) or 2 activities at the same time (1 for each path). A is not convenient, since its unitary crashing cost is higher than the penalty and H cannot be crashed. Crashing B + C or F or C + B or D is not convenient since the total cost overcomes the benefit. The best solution is to crash D + F, see next slide. As we obtain a duration reduction of 2 months, the economic benefit is 3 0 0 00 – 10 000 – 9 000 = 11 000€ 4 7 3 C 4 7 0 4 10 6 B 4 10 0 10 15 5 D 10 15 0 10 15 5 E 10 15 0 7 12 5 F 12 15 3 The critical paths are A -B-D-H and A -B-E-H. The project duration is 18 months. Again, we can crash either one activity in common to the two paths (A, B or H) or 2 activities at the same time (1 for each path). As, D has already been crashed and A and H are not convenient the best solution is to crash B, see next slide. Solution 0 4 4 A 0 4 0 7 12 5 G 10 15 3 15 18 3 H 15 18 0 4 7 3 C 4 7 0 4 7 3 B 4 7 0 7 12 5 D 7 12 0 7 12 5 E 7 12 0 7 12 5 F 7 12 0 The critical paths are A -B-D-H and A -B-E-H, A -C-F-H, and A -C-G-H. The project duration is 15 months. Again, we can crash either one activity in common to the four paths or a combination of activities allowing to reduce the duration of all critical paths. As B and D have already been crashed and activities A and H are not economically convenient, we cannot further reduce the duration of the critical path A -B-D-H. Thus, we stop here. Solution 0 4 4 A 0 4 0 7 12 5 G 7 12 0 12 15 3 H 12 15 0 Exercise 1 Taking into account that Time Now = 10 month and the following budget information, compute the indicators: ACWP, BCWS, BCWP, BAC, CV, SV(€), SV(t). Consider that it was planned that at time 11 the BCWS had the same value that BCWP has at time now. Activity Expected Costs ( €) Real Costs ( €) BCWP criteria (milestones) POC A 25 000€ 30 000€ 0-50 -100 All Milestones completed B 40 000€ 45 000€ 0-50 -100 All Milestones completed C 32 000€ 15 000€ 20 -50 -100 Second Milestone completed D 28 000€ 10 000€ 20 -50 -100 First Milestone completed E 35 000€ 25 000€ 0-50 -100 Second Milestone completed F 60 000€ 40 000€ 20 -80 -100 Second Milestone completed G 30 000€ 5 000€ 0-50 -100 No Milestone Completed (0%) H 15 000€ - - - Exercise 1 ➢ BCWS = 25 000 + 40 000 + 32 000 + 3/10*60 000 +3/5*30 000 = 133 000 € ➢ BCWP = 25 000*1 + 40 000*1 + 32 000*0.5 + 28 000 * 0.2 + 35 000*0.5 + 60 000*0.8 + 30 000*0= 152 100€ ➢ ACWP = 30 000 + 45 000 + 15 000 + 10 000 + 25 000 + 40 000 + 5 000 = 170 000€ ➢ BAC = 25 000 + 40 000 + 32 000 + 28 000 + 35 000 + 60 000 + 30 000 + 15 000 = 265 000€ ➢ CV = BCWP – ACWP = 152 100 – 170 000 = -17 900€ (Cost Inefficient) ➢ SV(€) = BCWP – BCWS = 152 100 – 133 000 = 19 100 (Ahead Schedule) ➢ SV(t) = Earned Schedule – Time Now = 11 – 10 = 1 (one month in advance) Theoretical Questions ➢ What is the IRR? Write the formula and discuss its potential issues (6 Points). ➢ Define and comment different types of PPP contracts (6 Points). ➢ Given the following information for Company A and Company B compute for both companies the financial indicators “ROE” and “Cost of debt” and briefly comment the results (6 Points). Company A Company B Company A Company B EBIT 12 000 000€ 7 000 000€ ROE ?? ?? Net Income 3 000 000€ 5 000 000€ Cost of Debt ?? ?? Interest Expenses 5 000 000€ 950 000€ Non Financial Liabilities 8 000 000€ 5 000 000€ Financial Liabilities 20 000 000€ 10 000 000€ Equity 10 000 000€ 7 000 000€ Theoretical Questions ➢ What is the IRR? Write the formula and discuss its potential issues (6 Points) The internal rate of return (IRR) is the rate of return that makes the net present value of a stream of cash flows equal to zero. ෍ ������ ������������������ℎ ������������������������������ ������ (1 + ������������������ )������ = 0 Theoretical Questions ➢ Define and comment 4 different types of PPP contracts (e.g. BOT, DBO,…) (6 Points). Different types of PPP contracts that could be discussed: ▪ With a concession , the private counterpart receive a long term right to use all assets underlaying the agreement . The private is also charged with full or partial responsibility for the assets and it is usually required to investment in its concession .The ownership of assets is with the public counterpart .The private concessionaire receives its revenues from users and pay a concession fee to the granting authority . ▪ In a BOT framework, the concessionaire usually finances and builds the asset in compliance with the standards agreed with the public authority .It is then in charge of its operations and management for a given period of time after which it reverts the ownership to the public . The period conceded should give to the private the possibility to repay the investment with interests . ▪ A DBO is a framework where the private counterpart is in charge to design, build and operate for an agreed period a certain asset .If it is also in charge of finance it the model is the (DBFO) . Theoretical Questions ➢ Define and comment 4 different types of PPP contracts (e.g. BOT, DBO,…) (6 Points). Different types of PPP contracts that could be discussed: ▪ Lease/ Affermage :The private counterpart is in charge for operating and managing the infrastructure .Usually there is not the presence of great amounts of private investments with the exception of those cases where the lease is combined with other models of PPP (e .g.it build the infrastructure) .During the leasing period, the private operator collects revenues from users and pays its leasing fees to the public counterpart .In an affermage PPP all revenues are shared between the two parts .In a lease/ affermage framework the operator bears a greater amount of operating risks . ▪ Turn key contracts -DBF/BF ((design), build, finance) and BLT (build lease and transfer), also known as finance leases, in which the private sector partner bears construction risk but is remunerated by the public authority for the whole investment once it is completed - or through leasing installments over a 10 -20 year period . ▪ O&M contracts (Operation & Maintenance) of existing/brownfield infrastructure, in which the private sector partner is in charge of maintaining the infrastructure (i.e.energy efficiency improvement and energy management) . ▪ Availability based contracts , in which the private sector takes the responsibility to design, finance, build and maintain (DBFM) the infrastructure and delivers/operate non -core services (DBFMO) while the public authority retains the responsibility on the core service, generally funded through a mix of taxes and tariffs, and pays the private partner with availability based payments (for the remuneration of the investment and maintenance costs) and with no -core service charges . Theoretical Questions ➢ Given the following information for Company A and Company B compute for both companies the financial indicators “ROE” and “Cost of debt” and briefly comment the results (6 Points). Company A Company B Company A Company B EBIT 12,000,000 € 7,000,000 € ROE 0.300 0.714 Net Income 3,000,000 € 5,000,000 € Cost of Debt 0.250 0.095 Interest Expenses 5,000,000 € 950,000 € Non Financial Liabilities 8,000,000 € 5,000,000 € Financial Liabilities 20,000,000 € 10,000,000 € Equity 10,000,000 € 7,000,000 €