Larson Manufacturing is considering purchasing a new injection$-$molding machine for $$250,000$ to expand its production capacity. It will cost an additional $$20,000$ to do the site preparation. With the new injection$-$molding machine installed, Larson Manufacturing expects to increase its annual revenue by $$90,000.$ The machine will be used for five years, with an expected salvage value of $$75,000.$ At an interest rate of $12\%,$ would the purchase be justified using the present worth $($PW$)$ method?

A newly constructed bridge costs $$15,000,000.$ The bridge is estimated to need renovation every $15$ years at a cost of $$3,000,000.$ Annual repairs and maintenance are estimated to be $$1,000,000$ per year. If the interest rate is $6\%$ per year, determine the capitalized equivalent cost of the bridge, assuming service life is indefinitely long.