Question

A toll bridge across Mississippi River is being considered as a replacement for the current I-40 bridge linking Tennessee to Arkansas. Because this bridge, if approved, will become a part of the U.S. Interstate Highway system, the B-C ratio method must be applied in the evaluation. Investment cost of the structure are estimated to be $17,000,000 and $325,000 per year in operating and maintenance costs are anticipated. In addition, the bridge must be resurfaced every fifth year of its 30-year projected lie at a cost of $1,250,00per occurrence (no resurfacing cost in year 30). Revenues generated from the roll are anticipated to be $2,500,000 in its first year of operation, with a projected annual rate of increase of 2.25% per year due to the anticipated annual increase in traffic across the bridge. Assuming zero market (salvage) value for the bridge at the end of 30 years and MARR 10% per year, should the toll bridge be constructed?

Answer 1

The student's question involves calculating the present worth of benefits and costs for a proposed toll bridge as part of an economic feasibility study using the benefit-cost (B-C) ratio with a 10% MARR over 30 years, considering both revenue and maintenance alongside historical infrastructure reliability and demand elasticity issues.

Step-by-step explanation:

The question relates to the economic feasibility of constructing a toll bridge that would become part of the U.S. Interstate Highway system, using the benefit-cost (B-C) ratio method. This involves calculating the present worth of all benefits and costs over the 30-year life of the bridge. The initial investment cost is $17,000,000, with yearly operating and maintenance costs of $325,000, and resurfacing costs of $1,250,000 every fifth year (except the final year). The revenue is anticipated to start at $2,500,000 in the first year, with a projected increase of 2.25% annually. With a minimum attractive rate of return (MARR) of 10%, these cash flows must be brought to a present value and compared to determine if the B-C ratio is greater than 1, which would suggest a favorable investment. Considering aspects of infrastructure reliability and safety is essential, as seen in historical cases like the Silver Bridge collapse due to corrosion and the Tacoma Narrows Bridge collapse due to resonance failures. Moreover, understanding the elasticity of demand is crucial in setting toll prices to maximize revenue without exceeding consumers' willingness to pay.

Answer 2

The question asks whether the construction of a toll bridge is justified financially using the B-C ratio method, considering initial investment, ongoing costs, periodic resurfacing, and anticipated toll revenues over a 30-year period with a 10% MARR.

Step-by-step explanation:

The financial viability is determined by comparing the present value of costs to the present value of escalating revenues, and maximizing revenues by charging tolls in the inelastic portion of the demand curve.

The question involves the evaluation of a proposed toll bridge's viability using the benefit-cost (B-C) ratio method. This financial assessment includes considering the initial investment costs, operational and maintenance expenses, periodic resurfacing costs, and the projected toll revenues with an annual increase.

To determine if the toll bridge should be constructed, one needs to calculate the present value (PV) of all costs and compare it to the PV of the anticipated revenues over the 30-year projected life of the bridge, considering the Minimum Acceptable Rate of Return (MARR) which is 10% in this case.

If the PV of revenues is greater than the PV of costs, the B-C ratio will be greater than 1, indicating that the project is financially viable.

Calculating the PV of costs involves summing the initial investment, the annual operating and maintenance costs, and the discounted cost of resurfacing every fifth year—excluding the 30th year.

To find the PV of revenues, the anticipated revenue in the first year should be grown by 2.25% annually, and each year's revenue should be discounted back to the present value using the MARR of 10%.

Should the resulting B-C ratio be greater than 1, it would support the construction of the toll bridge. If it is less than 1, the project would not be justified financially.

Another financial aspect to consider is the demand elasticity, which affects the optimal pricing strategy to maximize toll revenues.

Charging tolls in the inelastic portion of the demand curve would be the most beneficial strategy, as changes in price have a smaller impact on the quantity of demand; hence, revenue can be maximized even if prices are increased.