Question

The cash flows of a firm next year will be $100, $200 and $300 in (equally probable) bad, normal and good states, respectively. The firm dissolves at the end of the year and discount rates are zero. Shareholders decide to issue bonds with face value $100 and distribute the proceeds as dividends. Shareholders decide to issue additional debt, according to the existing covenants, with face value $100 and pocket the proceeds as dividends.

1. What is the change in shareholder and bondholder wealth, if the new issue is of equal seniority to the old one? Answer: Shareholders: +16.67 Bondholders: -16.67

2. What is the change in shareholder wealth, if the new issue is of higher seniority to the old one? S: +33.33 B: -33.33

3. What is the change in shareholder wealth, if the new issue is of lower seniority (junior debt) to the old one? Both $0

This is about covenants, I have the answers but please show work!

Answer 1

Shareholders only take whatever is left out after paying the bondholders. The cash flows to existing bondholders and shareholders before the new issue is as follows

State	CF	Existing Bondholders	Shareholders
Bad	100	100	0
Normal	200	100	100
Good	300	100	200
Expected Values	200	100	100

1. In case, new debt is of same seniority as Existing debt , cash flows are as presented below

State	CF	Existing Bondholders	Shareholders
Bad	100	50	50
Normal	200	100	100
Good	300	100	200
Expected Values	200	83.33333333	116.6666667

In case of Bad State , $100 cashflow will be equally shared between the existing bondholders and new issue holders (shareholders)

So, Expected shareholder wealth will increase by 16.66 (+16.66) and that of Bondholders will decrease by 16.66 (-16.66)

2.

In case, new debt is of higher seniority than Existing debt , cash flows are as presented below

State	CF	Existing Bondholders	Shareholders
Bad	100	0	100
Normal	200	100	100
Good	300	100	200
Expected Values	200	66.66666667	133.3333333

In case of Bad State, senior debtholders will have first claim on cashflow and hence, there will be nothing left for existing bondholders in this state.

So, Expected shareholder wealth will increase by 33.33 (+33.33) and that of Bondholders will decrease by 33.33 (-33.33)

3. In case, new debt is of lower seniority than Existing debt , cash flows are as presented below

State	CF	Existing Bondholders	Shareholders
Bad	100	100	0
Normal	200	100	100
Good	300	100	200
Expected Values	200	100	100

In case of Bad State, senior (existing) debtholders will have first claim on cashflow and hence, there will be nothing left for new bondholders in this state.

So, Expected shareholder wealth will not change. There is no change from the original state