Question

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, on-board Wi-Fi 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 servic 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 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 UCI) Where the infrastructure will be not totally · · Substitute all the old infrastructure (Use Case 2 = UC2) where the infrastructure and the equipment 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 »

Answer 1

1a) Equilibrium in the market can be found by equating the demand and supply equations:

UC1:

8300-0.5P=6000+4P

8300-6000=4P+0.5P

2300=4.5P

P=511.11, we can find Qd by substituting this in the demand equation,

Qd=8300-(0.5*511.11)

Qd=8044.5, we will approximate this to 8044, since a person cant buy half a ticket.

UC2:

8700-0.5P=6000+4P

8700-6000=4.5P

2700=4.5P

P=600, we can find Qd by substituting this in the demand equation,

Qd=8700-(0.5*600)

Qd=8400

1b) Annual total revenue for the municipality can be found by multiplying the price by quantity for both the use cases:

	Optimal Price	Optimal Quantity	Annual Total Revenue
UC1	511	8044	4,110,484
UC2	600	8400	5,040,000

2a.) NPV of UC1 turns out to be negative. UC2 can be accepted as it has a positive net present value.

Duration of project (years)	15
Rate (%)	4
	UC1	UC2
Initial outflow (z)	15000000	30000000
Calculation of cash flows
Revenue per year (a)	41,10,484	50,40,000
Annual Opex (b)	3000000	2000000
Annual Cash Flows (c = a-b)	11,10,484	30,40,000
Calculation of present value of inflows
PV of Annual inflows
Present value of Annuity factor (15 years, 4%) (d)	11.11838743	11.11838743
Present value of cash flows inflows (x=c*d)	12346791.35	33799897.79
PV of Residual value
Residual Value at the end (e)	500000	600000
Present value factor (15 years, 4%) (f)	0.555	0.555
Present value of Residual value(y=e*f)	277500	333000
Net Present value ((x+y)-z)	-2375708.651	4132897.794

2b.) At 7% interest rate UC2 also becomes unviable; NPV negative. reason for this change vis a vis scenario 1 is the increase in interest rate to 7%. As the rate rises, the present value of the inflows reduces-money becomes more valuable today, requiring a higher return to postpone consumption- as a result of which, both UC should be rejected.

Duration of project (years)	15
Rate (%)	7
	UC1	UC2
Initial outflow (z)	15000000	30000000
Calculation of cash flows
Revenue per year (a)	41,10,484	50,40,000
Annual Opex (b)	3000000	2000000
Annual Cash Flows (c = a-b)	11,10,484	30,40,000
Calculation of present value of inflows
PV of Annual inflows
Present value of Annuity factor (15 years, 7%) (d)	9.107914005	9.107914005
Present value of cash flows inflows (x=c*d)	10114192.78	27688058.58
PV of Residual value
Residual Value at the end (e)	500000	600000
Present value factor (15 years, 7%) (f)	0.362	0.362
Present value of Residual value(y=e*f)	181000	217200
Net Present value ((x+y)-z)	-4704807.224	-2094741.424

2c.)

Given that rate is 4% but demand of UC2; 8700-0.5P is equal to demand of UC1; 8300-0.5P, this means that in both UC1 and UC2, the optimal price and quantity given the supply equation will be P=600 and Qd=8400, taking the annual revenue to 5,040,000. In this scenario, the NPV of UC1 will also become positive. UC1 should be accepted from a financial standpoint as the NPV is higher.

Duration of project (years)	15
Rate (%)	4
	UC1	UC2
Initial outflow (z)	15000000	30000000
Calculation of cash flows
Revenue per year (a)	50,40,000	50,40,000
Annual Opex (b)	3000000	2000000
Annual Cash Flows (c = a-b)	20,40,000	30,40,000
Calculation of present value of inflows
PV of Annual inflows
Present value of Annuity factor (15 years, 4%) (d)	11.11838743	11.11838743
Present value of cash flows inflows (x=c*d)	22681510.36	33799897.79
PV of Residual value
Residual Value at the end (e)	500000	600000
Present value factor (15 years, 4%) (f)	0.555	0.555
Present value of Residual value(y=e*f)	277500	333000
Net Present value ((x+y)-z)	7959010.362	4132897.794

3. Scenario analysis gives an intuition about how the municipality can expect the viability of the use cases to change due to change in key variables such as interest rate and demand. If the interest rate is expected to increase, while everything else remains constant, the municipality should not undertake either of the use cases. Similarly, if the demand is expected to increase in future, UC1, appears to be delivering a higher value add, in terms of positive NPV.