Question

The city of Ottawa is planning a new expansion for its bike routes, the project cost is estimated to be $27,000,000 and is to be paid in 6 equal payments of $4,500,000 each (Payment 1 is due before commencement (now), Payments 2-6 at the end of years 1, 2, 3, 4, and when the construction is done by the end of year 5). The feasibility assessment period of this project is 20 years after construction. This proposal benefits the city a total of $2,600,000 by reducing congestion and air pollution. The O & M costs for the proposed routes is expected to be $500,000 per year. If the social discount rate for this project is chosen to be 5%. A] Draw a cash flow diagram. B] Calculate the benefit/cost ratio of this project and comment on its feasibility. C] if the feasibility assessment period is changed to 50 years after construction, how would that impact the project’s feasibility.

Answer 1

Answer: A) Cash flow diagram:
```
Year 0: - $4,500,000 (Payment 1)
Year 1: $2,600,000 - $500,000 = $2,100,000
Year 2: -$4,500,000 - $500,000 = -$5,000,000
Year 3: $2,100,000 - $500,000 = $1,600,000
Year 4: -$4,500,000 - $500,000 = -$5,000,000
Year 5: $2,100,000 - $500,000 + $4,500,000 = $6,100,000
```

B) Benefit/cost ratio:
```
Benefit = $2,600,000
Cost = $27,000,000 + 5*$500,000 = $29,500,000
PV of benefits = $2,600,000/(1+0.05)^1 + $2,100,000/(1+0.05)^3 + $1,600,000/(1+0.05)^5 + $6,100,000/(1+0.05)^5
= $2,314,553.54
PV of costs = $4,500,000 + $4,500,000/(1+0.05)^2 + $4,500,000/(1+0.05)^3 + $4,500,000/(1+0.05)^4 + $4,500,000/(1+0.05)^5 + $500,000*(1-(1/((1+0.05)^5/0.05)))
= $24,645,699.67
Benefit/cost ratio = PV of benefits / PV of costs = $2,314,553.54 / $24,645,699.67 = 0.094
```

The benefit/cost ratio of this project is less than one, which indicates that the project is not economically feasible. The cost of the project exceeds the present value of its benefits.

C) If the feasibility assessment period is changed to 50 years after construction, the present value of benefits will increase and the project may become more feasible. However, the cost of the project will remain the same. A new analysis would need to be done to determine the new benefit/cost ratio.

Answer 2

The project's feasibility is analyzed by evaluating a cash flow diagram, calculating the benefit/cost ratio, and considering the impact of extending the assessment period to 50 years.

Step-by-step explanation:

The question asks to evaluate the feasibility of a new bike route expansion in Ottawa with specified financials using a cash flow diagram and calculating the benefit/cost ratio. A cash flow diagram can be drawn with an initial payment of $4,500,000, followed by five annual payments of the same amount, yearly O & M costs of $500,000, and benefits of $2,600,000 reducing congestion and pollution. The project's feasibility over 20 years is assessed using a 5% social discount rate.

The benefit/cost ratio is calculated by comparing the present value of benefits over the cost across the projected lifespan of the project. If the project’s benefits surpass the costs, it is considered feasible. The extension of the feasibility assessment period to 50 years would typically increase the accrued benefits and could improve the project's feasibility depending on the discount rate applied over the extended period.