Question

1.. A bridge would cost $50 million to build (this cost must be incurred now). After it’s built, starting next year, the bridge will last for 50 years. Each year when the bridge is in use, we expect it to generate $2.5 million worth of benefits and cost $0.3 million per year to perform maintenance. The interest rate is 5%. Should we build this bridge? Show your calculations and explain your decision (to build or not to build).

Answer 1

Cost of building bridge = $50 million

Annual benefits from bridge = $2.5 million

Annual maintenance cost of bridge = $0.3 million

Time period = 50 years

Interest rate = 5%

Calculate the present worth of Bridge -

PW = -Cost of building bridge - Annual maintenance cost of bridge(P/A, i, n) + Annual benefits from bridge(P/A, i, n)

PW = -$50 million - $0.3 million(P/A, 5%, 50) + $2.5 million(P/A, 5%, 50)

PW = -$50 million - [$0.3 million * 18.2559] + [$2.5 million * 18.2559]

PW = -$50 million - $5.48 million + $45.64 million

PW = -$9.84 million

The Present Worth of Bridge is $-9.84 million.

A project should be accepted or executed if the present worth of project is positive.

A project should not be accepted or executed if the present worth of project is negative.

In the given case, the present worth of bridge is negative.

So,

This bridge should not be built.