Show work done in steps. *Use benefit-cost ratio* 1. ) The Townsville City Counc

Question

Show work done in steps. *Use benefit-cost ratio*

1. ) The Townsville City Council is considering a proposal by the mayor to construct a recreational facility at a cost of $1.0 million. The facility is expected to have a useful life of 30 years during which operating costs are expected to average $100,000 per year. It is anticipated that one-time renovations costing $500,000 will be carried out after 18 years. Overall benefits to the community are expected to average $220,000 per year. The facility will have no salvage value. Assuming an interest rate of 5% per year, determine the benefit-cost ratio for the proposed facility. Should the Council approve the proposal?

Explanation / Answer

Benefit-cost ratio (BCR) = Present value (PV) of all benefits / PV of all costs

PV of benefits ($) = 220,000 x PVIFA(5%, 30) = 220,000 x 15.3725 [From PVIFA table]

= 3,381,950

PV of costs ($) = 1,000,000 + [100,000 x PVIFA(5%, 30)] + [500,000 x PVIF(5%, 18)]

= 1,000,000 + [100,000 x 15.3725] + [500,000 x 0.4155 (From PVIF table)]

= 1,000,000 + 1,537,250 + 207,750

= 2,745,000

BCR = $3,381,950 / $2,745,000 = 1.23

Since BCR > 1, Council should approve the proposal.

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