Mobility Engineering - Finance and Management of Infrastructure Investments

Full exam

Section I – Q1 4 7 3 C 8 11 4 0 2 2 B 2 4 2 4 11 7 D 4 11 0 2 3 1 E 9 10 7 2 8 6 F 4 10 2 The critical path is A -D -H -J. The project duration is 19 weeks. 0 4 4 A 0 4 0 2 4 2 G 8 10 6 8 12 4 I 10 14 2 11 14 3 H 11 14 0 Section I – Q1 (Solution) 14 19 5 J 14 19 0 ➢ Path A -D -H -J: P(Duration > 24 ) = P(z > 24 −19 4+1+4+4) = ������ � > 1 .39 = 1 − ������ (� < 1.39 ) = 1-0.9177 = 8.23 % ➢ Path B-F-I-J: P(Duration < 15 ) = P(z < 15 −17 1+9+4+4) = ������ � < − 0 .47 = 1 − ������ � < 0 .47 = 1 − 0.6808 = 31.92 % ➢ ACWP = 40 000 +15 000 +20 000 +70 000 +5 000 +48 000 +12 000 +2 000 = 212 000 € ➢ BCWS = 35 000 + 10 000 +24 000 + 63 000 *3/7 + 4 000 + 54 000 *5/6 + 10 000 = 155 000 € (Consider that at T= 7, activities D has been performed only for 3/7 and activity F for 5/6). ➢ BCWP = 35 000 + 10 000 +24 000 *0.2 + 63 000 + 4 000 + 54 000 *0.8 + 10 000 +25 000 *0 = 170 000 € Section I – Q1 (Solution) Section I – Q2 Section I – Q2 (Solution) ➢ EBITDA = Revenues – OPEX ➢ EBIT = EBITDA – Depreciations ➢ EBT = EBIT – Commission Fee – Senior Debt Interest ➢ Taxes = EBT * Tax Rate ➢ EAT = EBT – Taxes ➢ Distributions = min(EAT; Cash flows available to shareholders)Year 1 Year 2 Year 3 Revenues 10 000.00 € 15 000.00 € 20 000.00 € OPEX 2 000.00 € 2 000.00 € 2 000.00 € EBITDA 8 000.00 € 13 000.00 € 18 000.00 € Depreciations 300.00 € 300.00 € 300.00 € EBIT 7 700.00 € 12 700.00 € 17 700.00 € Commission Fee - € - € - € Senior Debt Interest 200.00 € 180.00 € 160.00 € EBT 7 500.00 € 12 520.00 € 17 540.00 € Taxes 3 750.00 € 6 260.00 € 8 770.00 € EAT 3 750.00 € 6 260.00 € 8 770.00 € Distributions 3 000.00 € 5 000.00 € 8 770.00 € Section I – Q 2 (Solution) ➢ ��� ℎ ���������� ��� �ℎ��� ℎ������ �������������� 0 = − 20 ,000 € ���� ������������� ��������������������� ➢ ��� ℎ ���������� ��� �ℎ��� ℎ������ �������������� 1 −�������������� 3 = ���������������������������� + ������������ ������������ ➢ 0 = ������������������ = σ �=1 ������ ������������ ������ (1+������������������ )������Year 0 Year 1 Year 2 Year 3 Cash Flows for Shareholders 20 000.00 €- 3 000.00 € 5 000.00 € 18 770.00 € IRR 12.05% Section II – Q3 Section II – Q3 (Solution) Section II – Q3 (Solution) ➢ ��� ℎ ���������� � = �������� � − ����� � ➢ ��������������� ��� ℎ ���������� � = ������������� ℎ �������������������� ������ (1+������������� ��������� )������ ➢ ������ ������������ = σ �=0 ������ ������������ ������ (1+�)������ ➢ Payback period = min � |������������������ ≥ 0 ➢ Payback period is year 3 since it is the first year in which the cumulated discounted cash flows are positive. ➢ It exists the IRR.Year 0 Year 1 Year 2 Year 3 Discount Rate Revenues - € 60 000.00 € 70 000.00 € 80 000.00 € 5% Costs 100 000.00 € 20 000.00 € 20 000.00 € 20 000.00 € CF 100 000.00 €- 40 000.00 € 50 000.00 € 60 000.00 € Discounted CF 100 000.00 €- 38 095.24 € 45 351.47 € 51 830.26 € Cumulated Discounted CF 100 000.00 €- 61 904.76 €- 16 553.29 €- 35 276.97 € NPV 35 276.97 € IRR (CF) 22% IRR ( Discounted CF) 16% Section II – Q4 Section II – Q4 (Solution) Consider a financial contract with an invested capital S=50, with N=10 and a compound interest rate law with i=2.5%. Select the correct value function W(t) in years t=2, t=3 and t=5. W(0) = 50 W(1) = 50 * (1+0.025)^1 = 51.25 W(2) = 50 * (1+0.025)^2 = 52.53125 W(3) = 50 * (1+0.025)^3 = 53.84453 W(4) = 50 * (1+0.025)^3 = 55.19064 W(5) = 50 * (1+0.025)^3 = 56.57041 Section II – Q5 Section II – Q 5 (Solution) Ex. Consider a financial contract that has the value of 98.5€ at time t0. After 84 days its value is equal to 101.2€. With respect to such interval [0; 84 days], select the correct answer. : • The interest I: 101.2 – 98.5 = 2.7€ • The interest rate i = 2.7/98.5 = 0.02741117 • The discount factor v = 98.5/101.2 = 0.9733202 • The accumulation factor m= 1/v = 1.027411 Section III – Q6 Please, see Slides 27 -39 of lecture “ cba_I ”. Section III – Q6 (Solution) The standard approach, consistent with international practice, is to convert and adjust financial cash -flows . Starting from the financial analysis, the following adjustments should be done to perform the economic analysis : ▪ fiscal corrections ; ▪ conversion from market to shadow prices ; ▪ evaluation of non -market impacts and correction for externalities . Section III – Q 6 (Solution) Fiscal Corrections Taxes and subsidies are transfer payments that do not represent real economic costs or benefits for society as they involve merely a transfer of control over certain resources from one group in society to another . To correct such distortions, the Economic Analysis requires that : prices for inputs and outputs must be considered net of VAT prices for inputs should be considered net of direct and indirect taxes Section III – Q6 (Solution) Conversion from market to shadow prices When market prices do not reflect the opportunity cost of inputs and outputs, the usual approach is to convert them into shadow prices to be applied to the items of the financial analysis . Transforming inputs market prices into shadow prices is completed through the application of Conversion Factors . In a nutshell, they represent the factor at which market prices have to be multiplied to obtain flows valued at shadow prices .Formally : ������� = �������∗ �������, where piis the market price for the good i,vi is shadow price for the same good and kiis the conversion factor . K> 1 -> the (social) opportunity cost is higher than that expressed by the market K< 1 -> e.g.due to market distortions or taxes adding to the marginal social value of the good Section III – Q6 (Solution) Externalities Impacts generated by the project, which are relevant for the society in general, but for which a proper market value is not available, should be included as project benefits or costs (namely, positive or negative externalities) in the economic analysis . Externalities : effects that do not occur in the transactions between the producer and the direct users of the project services but impact on uncompensated third parties .An externality is any cost or benefit that spills over from the project towards other parties without monetary compensation . Section III – Q7 Section III – Q7 (Solution) Please, see Slides 18 -23 of lecture “Public Private Partnership ”. The main policy measures that can be adopted in order to attract/increase financial resources for infrastructure projects are : 1. Grants 2. Availability Payment 3. Credit -Enhancement Tools 4. Direct Provision of Debt and Equity Capital 5. Other Measures Section III – Q 7 (Solution) Grants aim to reduce the capital requirements needed to implement the project or integrate project revenues during the operational phase . Grants are generally delivered by the contracting authority, even if some dedicated funds at national/regional level may exist . Grants can be of three main types : 1.1 Lump sum capital grant 1.2 Revenue grant 1.3 Grant on debt interests Availability payment means that the concessionaire receives a fixed amount of financial resources for ensuring a service with a certain availability target (set by Authority, or regulations) . Availability payment neutralizes the demand risk for the concessionaire : the payment is based on the availability of the service/facility, not on the effective exploitation of it by final users . However, the private concessionaire maintains its exposure to the performance risk and therefore needs to optimize the cost/income related to the project . Section III – Q7 (Solution) Credit enhancement tools : Realized directly by the government or by its own controlled agency( ies )or development bank(s) . Usually, they can assume three main types : 3.1 Minimum payment : paid by the contracting authority to reduce the demand risk for the private counterpart ; it is intended to guarantee a certain minimum level of revenues necessary to cover the debt service at some level of debt service cover ratio 3.2 Guarantee in case of default :it pays debt principal and interests in the case of concessionaire’s default 3.3 Guarantee in case of refinancing : it repays lenders if the concessionaire fails to refinance the loan or the used funding resources at maturity Section III – Q7 (Solution) Debt and Equity : 4.1 Subordinated (junior) debt aimed at enhancing the credit quality of the senior debt in order to attract investments from capital markets (losses are first covered by junior debt and then by debt tranches with higher seniority) 4.2 Debt : ➢ provided at market conditions to (promptly) respond to liquidity shortage, or ➢ at more favourable conditions to help the project to match the expectations of debt investors (e .g.in terms of yields or debt service cover ratio) ;such favourable terms may determine crowding out effects that should be monitored 4.3 Equity : public entities may enter as shareholders to fill the equity gap (at market or more favourable conditions), to reduce the financial gearing (mitigating credit risk) and to offer downside protection or upside leverage to the private shareholders Section III – Q7 (Solution) Other measures : 5.1 Officially mandated change to capital structure :specific regulations aimed to foster a change in the capital structure of the infrastructure project firm .In terms of capital structure, we refer to the percentage of debt and equity used to finance operations . As the project company matures, its financing needs evolve, calling for various adjustments of the capital structure that depend on the growth of the firm and the dynamics of the industry and market . 5.2 Favourable taxation schemes , e.g. for the Special Purpose Vehicle to sustain the general viability of the project (the effect is to increase free cash flow to operation) or for the equity investors on “certain qualified dividends" and long -term capital gains