Questin $5$: Wealth redistribution via capital structure changes

Firm currently has debt with face value $D=120.$ Again there are two, equally likely, states of nature. The firm starts out with asset values as given in the first table below.

$\backslash$table$[[$Table $1,$Bad $(1/2),$Good $(1/2)],[$Total Payoff,$100,200],[$Payoff to Debt,,$],[$Payoff to Equity,,$]]$

$($a$)$ Fill in the tables and find the payoffs to debt and equity. Assuming discount rate $=0,$ calculate enterprise value $V_{\text{f}\text{i}\text{r}\text{m}},$ debt value $V_{\text{d}\text{e}\text{b}\text{t}},$ and equity value $V_{\text{e}\text{q}\text{u}\text{i}\text{t}\text{y}}.$

$($b$)$ Now, the firm issues additional debt, with same priority as existing debt, with a face value $D=30,$ and uses the funds to pay a dividend.

$\backslash$table$[[$Table $2,$Bad $(1/2),$Good $(1/2)],[$Total Payoff,$100,200],[$Payoff to Old Debt,,$],[$Payoff to New Debt,,$],[$Payoff to Equity,,$]]$

Fill in the tables and find the payoffs to old debt, new debt, and equity. Assuming discount rate $=0,$ calculate $V_{\text{f}\text{i}\text{r}\text{m}},V_{\text{o}\text{l}\text{d}\text{d}\text{e}\text{b}\text{t}},V_{\text{n}\text{e}\text{w}\text{d}\text{e}\text{b}\text{t}\text{,}},$ and $V_{\text{e}\text{q}\text{u}\text{i}\text{t}\text{y}}.$

$($c$)$ If in an efficient market, the investors of new debt receive a zero$-$NPV deal. Zero$-$NPV means the proceeds from issuing the debt is equal to the present value of the future payoff for the debts. How much money the firm can receive from issuing the debt? If the proceeds from issuing the debt are used to pay the dividend, what is the maximum amount that can be paid as a dividend?

$($d$)$ Compare Table $1$ and Table $2,$ what happen to $V_{\text{f}\text{i}\text{r}\text{m}\text{,}},V_{\text{o}\text{l}\text{d}\text{d}\text{e}\text{b}\text{t}\text{,}}$ and $V_{\text{e}\text{q}\text{u}\text{i}\text{t}\text{y}}?$ How do you interpret the results?

$5$