Calculating bankruptcy cost

CFA Level III
#1

Hi. Currently working on some problem sets and I’m having a hard time with this question.

A company has an outstanding bond that will mature in two years. After two years the company will terminate all activity. The company unlevered equity value in two years can be $25 million with a 50% probability, or $12 million with probability 50%. The bond is a zero-coupon bond with face value $15 million. Everyone is risk-neutral, and the risk-free rate is 5%. The market price of the bond is 75% of the face value. Assume perfect capital markets and no taxation.

What is the value of bankruptcy costs at year two?

The answer should be $2.19million, but I don’t see the reasoning behind it. Can someone please explain?

#2

How did you get 2.19 mln?

#3

I didn’t get it. I have it because the answers are included with the problem sets, but the calculations are not! :frowning:

#4

Where are these problem sets from?

#5

You see, i noted a contradiction in the problem - if “…Everyone is risk-neutral,…” then it cannot be that “…The market price of the bond is 75% of the face value.”. And the face value of the bond should be discounted at a 5% risk-free rate for the two periods to have the market price today.

Then, the market value of the firm is the sum of Equity Market Price and Debt Market Price less Bankruptcy Cost. We need to consider two states of the world each one has probability 50% of occurence, Success and Failure.

  1. Success. Year 2. The firm value is 25 mln + 11.25 mln x 1.05>2 = 37.4 mln. Less 15 mln to the bondholders and there are 22.4 mln left to equityholders. The difference is 25 - 22.4 = 2.6 mln the equityholders to lose, where 11.25 mln = 0.75 x 15 mln.

  2. Failure. Year 2. The firm value is 12 + 11.25 mln x 1.05>2 = 24.4 mln. Less 15 mln and the equityholders are left with 9.4 mln. The difference is the same, 12 - 9.4 mln = 2.6 mln.

This is the bankruptcy explicit cost for the equityholders. It should be the same in the both states.

I dont think i’m correct though.

#6

Thank you. Yeah, that’s what I tried to do too. 2.6 is not among the 4 alternatives. Let’s just forget about the whole thing unless someone comes to the rescue. Probably poorly written due to the contradiction.

#7

State G: bondholder gets 15, State B - bondholder gets 12-x, where x is the cost of bankruptcy (wasted money).

Bondholder in risk neutral, which means that the price of the bond is the expected value of discounted payoffs:

0.75*15=(1/1.05)^2*[15/2+(12-x)/2] then x = 15+12-2*0.75*15*(1.05)^2=2.19375.

does it help?

#8

Haven’t started studying yet, but above answer is correct.

If bank does well debt holder gets everything back in return. so 15/1.05^2

If bank does bad and goes bankrupt (12-x)/1.05^2. Since there is cost to bankruptcy (legal, less cusomters, blah blah blah).

-((15*.75)*(1.05^2)/.5-15 -12)= 2.19375.

There is nothing to do with equity value at all… Just debt payback

#9

It is just the debtholders expected payoff discounted at the risk-free rate provided the company total value is either 25 or 12 at year 2. However, the problems provides us with “The company unlevered equity value” which means “…the stock of a company that is financing operations with all equity and no debt…” - but our company is still levered (total assets = debt + equity) at year 2.

I would agree with the shown above calculations if the firm value were considered under the Modigliani and Miller assumptions - you might know this as the M&M Proposition 1: “The market value of any firm is independent of its capital structure…”, i.e.

Value Levered = Value Unlevered + Tax Rate x Debt, and since Tax=0, the both firm’s values are equal, provided:

  1. NO bankruptcy costs,

  2. Perfect markets,

  3. Cash flows are RERPETUITIES, etc.

However, the assumptions (1 & 3) are relaxed and therefore it is not our case. Then, an optimal capital structure exists which makes the value of a levered firm to differ from the value of the unlevered one.