Question

You are the sole bondholder in a firm that will be liquidated next year. Your main concern is that you will not be paid back the $200M you are owed at that time. The current market value of the firm is $225M, although it is unknown what the market value will be next year.

a)Provide the payoff diagram for the bondholder with the final market value of the firm on the x-axis.

b)The financial manager of the firm is currently considering a project that will cause the market value of the firm to be equal to either $450M or nothing next year with equal probability.Assume that the bondholders and shareholders have to maintain their positions until firm liquidation next year. What is the expected payoff to bondholders and shareholders next year under this project? (Hint:Use the table below.)

Firm value next year	Bondholder payoff	Stockholder payoff
$450M
$0M
Expected payoff next year

c)If you were to completely protect yourself against the state of the world where the firm does not pay you back, would you buy a (call or put)option on the final market value of the assets of the firm, and at what strike price?

d)This option youpurchase has a price of only $40M. You decide to borrow the $40M, in order to pay for the option, at a 10% interest rate. The loan plus interest must be repaid in one year. What is your total expected payoff (bond + option –loan repayment) in one year?(Hint:Use the table below.)

Firm value next year	Payoff from bond	Payoff from option	loan repayment	Total payoff
$450M
$0M
Expected payoff next year

Firms that go bankrupt are typically unable to fully repay all bondholders. Bondholders can protect themselves from this by entering into “Credit Default Swaps”, in which they pay a third counterparty a fee (or a sequence of fees over time), and in exchange the third counterparty will repay the bondholders instead in the event that the firm goes bankrupt (you also hand over the bond to that third counterparty). “Credit Default Swaps” are, in essence, the option that you purchased in part (c).

Answer 1

B) Payoff to the bondholder = Amount of face value being paid back to bondholder

Payoff to shareholder = Total market value of the firm - Payoff to the bondholder

The Expected payoff is as per the below :

Firm value next year	Bondholder payoff	Stockholder payoff
$450M	$200 M	$250 M
$0M	0	0
Expected payoff next year	200*.5+0*.5=$100 M	250*.5+0*.5 =$125 M

c) If I were to completely protect myself against the state of the world where the firm does not pay me back, I would buy a put option on the final market value of the assets of the firm. The strike price shall be $200 M. The put option gives a right to exercise the option if the underlying price goes below the strike price. So if the final market value of the assets goes below 200 M the payoff to the bondholder shall be 200 - new final market value.

d) The total loan repayment = Loan + Interest amount

=40 + 10%*40

=$ 44 M

Payoff from the option = Strike price - Final Market Value of the assets

Firm value next year	Payoff from bond	Payoff from option	loan repayment	Total payoff
$450M	$200 M	0	$44 M	200-44= $156 M
$0M	0	$200	$44M	200-44=$156 M
Expected payoff next year				156*.5+ 156*.5=   $156M