Question $6$

Grandma's Peanut Butter, Ltd$.$ has debt outstanding $25$ million due next year $($Year $1).$ The firm owns an old$-$fashioned product line. If the firm does not improve this old product line, its cash flow next year will be $20$ million. However, by investing $5$ million today $($Year $0),$ the firm can improve the productivity of the old line. In this case, the updated product line will be able to generate a cash flow of $30$ million in Year $1.$ Assume that the product line in isolation has no value. Additionally, assume neither taxes nor uncertainties in the firm's cash flows. The risk$-$free rate is $10\%.$

a$)$ If the firm chooses not to improve the existing product line, what would the value of the firm's equity and the value of debt, respectively, be$?$

b$)$ Determine the NPV of the investment that makes the existing line more productive.