Problem $12$ Under risk neutrality, a factory can be worth $$500,000$ or $$1,000,000$ in two years,

depending on product demand, each with equal probability. The appropriate cost of capital is $6\%$

per year. The factory can be financed with proceeds of $$500,000$ from loans today. What are the

promised and expected cash flows and rates of return for the factory $($without a loan$),$ the loan,

and the levered factory owner?