ABC Ltd is considering adding a new product line. Adding the product line would require additional investment of $0\mathrm{.}5$ million today and would return cash flow of $0\mathrm{.}6$ million in one year$$s time.

ABC$$s assets consist of $0\mathrm{.}5$ million in cash, as well as production facilities to produce its existing products. Next year these facilities will return cash flows of $5$ million if the demand is high and $2$ million if the demand is low. The probability of high demand is $70\%.$

The firm$$s discount rate is $0\%$ and you can ignore all cash flows extending beyond one year.

Assume that ABC has no debt.

$($a$)$ What is the expected net worth of ABC$$s owners if they do not add the new product line and instead pay the cash out as dividends?

$($b$)$ What is the expected net worth of ABC$$s owners if they choose to add the new product line instead of paying out dividends?

$($c$)$ Now redo assuming the company has debt with face value $$2\mathrm{.}5$ million due in one year. What is the expected net worth of ABC$$s owners if they do not add the new product line but rather pay the dividend?

$($d$)$ Continue to assume that the company has debt of $$2\mathrm{.}5$ million due in one year. What is the expected net worth of ABC$$s owners if they choose to add the new product line and not pay the dividend?

$($e$)$ Do your answers in parts $($a$)$ to $($d$)$ show that the value of the company is not optimized when the firm has debt? Use figures to support your conclusions.

Use the table format to present your answers.