b Assuming that the proceeds from the new debt issue are use

(b)    Assuming that the proceeds from the new debt issue are used to pay a special dividend to shareholders, after the debt is issued what will be the value of (i) the old debt, (ii) the new debt, and (iii) equity?  Has total firm value changed?  Who is made better off or worse off from the transaction? (interest rates are zero)

A firm is currently partially financed with zero-coupon debt that promises to repay bondholders S200 at maturity. These bonds mature one year from today at t-1. The fim is in a very risky industry, so its assets will be worth S400 next year with probability 1/3, $200 next year with probability 1/3, and S100 next year with probability 1/3. The existing debtholders were very trustful of management, so they did not insist on any clauses governing issuance of additional debt. It turns out that this was a mistake. The firm is planning on issuing new debt that is senior to the old debt (i.e., in bankruptcy the new debtholders are first in line to get their cash back) This new debt promises to pay these new debtholders $100 at maturity. Assume for simplicity that interest rates are zero and thus that the value of a claim today at t=0 is equal to the expected payoff to the claimholder att-1. The firm operates in a world with no taxes.

Solution

The old debt value (maturity payment) is $200 and firm value will be probability adjusted firm value as below: (400 * 1/3 + 200 * 1/3 + 100 * 1/3) = $233.33. Out of this $200 is the claim of old debt holders and residual $33.33 will go to equity holders.

The new debt value (maturity payment) is $100 and it shall be used to pay special dividend to equity holders. Now the firm value remains $233.33 - since the new debt was raised and disbursed immediately. However now the first claim is of new debt holders who will get their $100 first and then $133.33 will go to old debt holders and nothing left from expected vaue of 233.33 for equity holders. Thus with the issuance of new debt: