XYZ LLC$,$ a manufacturing firm specializing in innovative electronic kitchen appliances, has an estimated firm value of USD $200,000$ based on expected net cashflows, excluding risk costs. However, XYZ also faces potential risks. Specifically, there is a $10\%$ chance that manufacturing defects could result in a total loss of USD $60,000$ due to warranty payments and recalls.

As a risk management consultant, your role is to assist XYZ in selecting the most suitable risk management strategy. You have recommended a risk control technology that involves AI$-$based testing of the appliances before their market launch. Below are details on some risk management options.

Answer the following questions based on this information:

$1)$ Option $1$: Take no action. The residual cost of risk remains at USD $18,000.$Calculate XYZ$\text{'}$s firm value net of the total cost of risk.

$2)$ Option $2$: Invest $$4,000$ in risk control, reducing the loss probability to $5\%.$ The residual risk cost is $$13,000.$Calculate XYZ$\text{'}$s firm value net of the total cost of risk under option $2.$