The Knight Corporation faces the need to raise external funds to undertake a new investment opportunity. By investing $$100$M$,$ the project will generate $$140$M for sure in the next period and the market knows that. Thus, the NPV of the project is $$40$M$.$ Unfortunately, Knight has no internal funds and, because of the nature of the business, has to raise funds by issuing equity. The problem is that the market does not know whether the current value of Knight assets is $$100$M or $$20$M$,$ and regards both outcomes as equally likely. Assume that the discount rate is zero and Knight's managers are loyal agents of the existing shareholders.

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a$.$ If the market expects Knight to issue equity and undertake the investment independent of the true value of the company, what is the fraction of the company that new investors will ask for to invest $$100$M in the company?

b$.$ If Knight's managers know that the true value of Knight's existing assets is $100$M$,$ what is the true equity value $($in millions$)$ of the old investors after new project is undertaken?

c$.$ If Knight's managers know that the true value of Knight's existing assets is $20$M$,$ what is the true equity value $($in millions$)$ of the old investors after the new project is undertaken?$$

d$.$ Suppose instead that the market expects that Knight's managers will issue equity and undertake the investment only when they know that the true value of the company is $$20$M$.$ What is the fraction of the company that new investors will ask for to invest $$100$M in the company?

e$.$ Under the assumption in $($d$),$ if Knight's managers know that the true value of Knight's existing assets is $$20$M$,$ what is the true equity value $($in millions$)$ of the old investors after the new project is undertaken?

f$.$ Which of the following statements is true?$$

Group of answer choices

Under the assumption in $($a$),$ the Knight will forgo the project if the manager knows that the firm's existing assets is worth $$20$M$.$

Under the assumption in $($a$),$ the Knight will forgo the project if the manager knows that the firm's existing assets is worth $$100$M$.$

Under the assumption in $($d$),$ the Knight will forgo the project if the manager knows that the firm's existing assets is worth $$20$M$.$

Under the assumption in $($d$),$ the Knight will forgo the project if the manager knows that the firm's existing assets is worth $$100$M$.$