Debt Overhang

[Ankur S]

Hi David,

In Q44: Debt overhang - you have an example of Stulz Firm HLG which has debt of $1Bln maturing in 1 yr. HLG will sell 1 Mln oz of gold at the end of year either @ 1400 or 800 / oz each with 50% prob. Price of Gold is not a systematic risk, Risk free is 4%. HLG can invest $100 Mln with a payoff of $200 Mln at the end of year

What is HLG Debt to equity ratio @ the beginning and end of year?

You have a spreadsheet which explains very clearly. The point where i am confused is where you calc 50% prob of debt when price at the end of year is 800. You have taken that as Min(HLG debt of $1bln, $800Mln). Why? let say HLG makes $800 Mio at the end of year and paysoff the debt the net debt still remains of $400 Mio in that case..no? why take minimum?

Pls advise. I have attached your calc as well.

Many thanks!!

 

[Ankur S]

errata: pls read- net debt remains $200Mln instead of $400mln

 

[David Harper CFA FRM]

Hi ankur,

Hey thanks for referring to the XLS! Hopefully you understand I'm not creative: I adapted Stulz's example of debt overhang. (it's not like i would ever value this way. Um, never)

So the idea, his logic reflected here, is not from the perspective of the company's obligation, but just the value of the debt if you are the debt(bond) holder. So, if the par value of the bond is $1,000 (i.e., at the end of the year, the bondholder expects to be repaid $1,000), then the value of the debt is just a weighted average of the two future outcomes:

• 50%* 1,000+ ; i.e., if gold goes up, we are whole
• 50% * 800; if gold goes down, the most the company can repay is 800. Bond repayment is capped by value of the firm.

This is essential Merton, just like treating value of debt as sum of riskless debt + put option on firm with strike equal to debt. In this case, debt of $1,000 is the strike price. If you are the bondholder, the Merton view is that you have written (sold) a put option with K = $1,000. So if firm value (S) goes to $800, you have lost $200. I hope this explains, thanks, David

 

[Ankur S]

Very clear..Thanks!!