Pyro Corp produces fireworks. Their main facility faces the risk of an explosion. The probability is $0\mathrm{.}47\%$ and the loss in ca$$e of explosion is $$7\mathrm{.}4m.$ The value of the firm without risk is $$12\mathrm{.}9m.$ Pyro Corp invests $$32,000$ in loss control, which allows them to cut their loss probability in half. They also purchase full insurance against the explosion loss. Assume the insurer is able to verify Pyro Corp's loss control investment and prices the policy based on the lower level of risk. The insurer determines the expected value of the coverage and then applies a $21\mathrm{.}6\%$ loading. Find the value of the firm in dollars.