Problem $5.$ A biotech firm is considering abandoning its old plant, built $23$ years ago, and constructing a new facility that has $50\%$ more square footage. The original cost of the old facility was $$300,000,$ and its capacity in terms of standardized production units is $250,000$ units per year. The capacity of the new laboratory is to be $400,000$ units per year. During the past $23$ years, costs of laboratory construction have risen by an average of $5\%$ per year. If the cost$-$capacity factor, based on square footage, is $0\mathrm{.}80,$ what is the estimated cost of the new laboratory?