compute the NPV for both the investment solutions (UC1 and UC2), if you consider an average interest rate (i) of 4% per year (please, consider the compounded interest rate regime) and explain which investment is more profitable from a financial point
You are the financial analyst of the Management and Budgeting Office (MBO) for the Procurement Agency of your Municipality.
The Transport system of your city needs to have an extension/renovation of the existing equipment (e.g., vehicles, onboard WiFi network, etc.) and infrastructure (e.g. binary for bus, etc.). The transport system is totally owned by the municipality, hence it is in charge of investment decision and business activity for this service.
Today, the goals for your municipality are several, as to increase the number of passengers for public transport in your city, to decrease the number of people using cars by providing a better transport services, to decrease the environmental pollution, to build a more efficient transport system in terms of saving of costs.
On the other side, your municipality has a budget constraint due to the lack of financial resources.
For this reason, the municipality has to decide among different kind of investments, and it has to consider some uncertain future variables (e.g., as the expected demand of passengers, expected prices, costs of infrastructures, interest rate, expected revenues from passengers’ services, etc.).
Your MBO office analysed two possible ways for investing in a new transport system:
 Renovate the old infrastructure (Use Case 1 = UC1) where the infrastructure will be not totally substituted but only renewed with some new equipment in order to become more efficient, since the current equipment is becoming obsolete and needs to be changed;
 Substitute all the old infrastructure (Use Case 2 = UC2) where the infrastructure and the equipment will be totally substituted with new one. The new infrastructure will be more environmental friendly and more efficient, and it will include new services for passengers related to wireless connection and smart mobility, hence, more attractive for people.
Since you are the consultant for the municipality, for each of the two solutions you have considered several variables to be analysed in order to provide to the municipality your financial evaluation:
 Initial costs of the investment (CapEx) that represents the initial outflow for the investment coming from the purchasing of material, equipment, work force and building or renovating the infrastructure
 Operating cost of maintenance of infrastructure and equipment (OpEx) that represents the yearly cost for maintaining the infrastructure
 Interest rate, that will be chosen with an average value of the expected future interest rates
 Residual value (salvage value) at the end of life of your infrastructure
 The ‘expected’ demand of passengers in the next 15 years (the demand of passengers is expected to increase in the future if the infrastructure will be improved). The increasing of demand will be different according to the difference of use cases (UC1 or UC2)
 Prices for passengers: this value is chosen by considering the demand and supply market clearing.
The figures of the variables are shown in the following table (for each use case):
Variables

UC1

UC2

Initial cost of investment (CapEx in Euro)

 € 15,000,000

 € 30,000,000

Cost of maintenance of equipment and infrastructure (OpEx in Euro)

 € 3,000,000

 € 2,000,000

Residual value (at the end of the project) in Euro

€ 500,000

€ 600,000

Duration of the project investment (years)

15

15

Interest rate

4%

4%

Let suppose that the expected (estimated) annual demand of passengers (from year 1 to 15) in the current market is represented by the following equations (hence, you expected the demand is constant for all the years, from year 1 to year 15):
UC1 è Qd = a + bP è 8,300 – 0.5P
UC2 è Qd = a + bP è 8,700 – 0.5P
Where Q is the demanded quantity of passengers (tickets) and P is the price for the ticket of transport for each passenger.
Let suppose, also, your expected (estimated) annual supply function for offering transport services to passengers (from year 1 to 15) will be represented by the following equation:
UC1 = UC2 è Qs = c + dP è Qs = 6,000 + 4P
 1. Please, compute:
 The equilibrium in the market (i.e., optimal price and optimal quantity) by considering the demand and supply equation;
 The annual total revenue for the municipality by considering optimal quantity and price computed before.
N.B. Remember that Total Revenue = P*Q
 2. Please, consider the following ‘Scenario Analysis’ (or sensitivity analysis) you should make in order to provide a better final evaluation of the two use cases (UC1 and UC2):
 SCENARIO 1: compute the NPV for both the investment solutions (UC1 and UC2), if you consider an average interest rate (i) of 4% per year (please, consider the compounded interest rate regime) and explain which investment is more profitable from a financial point of view (UC1 or UC2)?
HINT: in the computation of the net cash flows you have to consider also the total revenue per year that you have computed in the question 1b, hence, the value computed in question 1b will be constant for every year.
N.B. According to Article 19 (Discounting of cash flows) of Commission Delegated Regulation (EU) No 480/2014, for the programming period 20142020, the European Commission recommends that a 4% discount rate in real terms is considered as the reference parameter for the real opportunity cost of capital in the long term. Values differing from the 4% benchmark may, however, be justified on the grounds of international macroeconomic trends and conjunctures, the Member State’s specific macroeconomic conditions and the nature of the investor and/or the sector concerned. To ensure consistency amongst the discount rates used for similar projects in the same country, the Commission encourages the Member States to provide their own benchmark for the financial discount rate in their guidance documents and then to apply it consistently in project appraisal at national level.
 SCENARIO 2: compute the NPV for both the investment solutions (UC1 and UC2) if you consider an average interest rate (i) of 7% per year (please, consider the compounded interest rate regime): which investment is more profitable from a financial point of view (UC1 or UC2)? Explain if the solution is different with respect to Scenario 1 and explain how a change in the interest rate can affect your final decision.
 SCENARIO 3: compute the NPV for both the investment solutions (UC1 and UC2) if you consider an average interest rate (i) of 4% per year (please, consider the compounded interest rate regime) and if the Demand of UC2 is equal to the Demand of UC1: which investment is more profitable from a financial point of view (UC1 or UC2)? Explain if there are some difference respect to Scenario 0.
HINT: in this case, consider the same demand and supply functions for UC1 and UC2.
 3. Provide your intuition about how the scenario analysis can help you to understand which investment can be more profitable/viable and describe which suggestion you can give to the municipality in order to help it to make the optimal choice.
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