Merton Model - de Servigny Page 69

[fuzzyaces]

All,

I am trying to follow the 6.c.1 Merton worksheet. Specifically, I am trying to tie the numbers back to the de Servigny book p. 69, which is the first column in the worksheet.

In the book, they describe equity value as $3bn, threshold at $10bn, mu is 5%, and sigma is 9.6%. Most of these values are the same in the worksheet, but how do they arrive at the firm value of $12.75? I understood Vt to be simply St (equity value) + Pt (principal of bonds).

A related question is they show a value of A0 of $12.511bn, but I can't find anywhere in the preceding pages for what that number is meant to represent.

Any input is greatly appreciated!!

 

[David Harper CFA FRM]

Hi fuzzyyaces

I've never been able to reconcile the $12.511 in the source De Servigny. I could be wrong; but you'll notice i lined it up next to the Stulz column, which matches his, so I have some confidence in, at least, the internal consistency of the 6.c.1. Merton.

I solved for the firm value of $12.75, at time 0, because that current firm value produces a DD of 3.0. You'll notice that, in the lower rows, this parses into equity and debt values.

In my opinion, the De Servigny has a mistake, or at the least, misses something. If A(0) = 12.511 is the asset value, then as asset = debt + equity, it should be the V(t). But the V(t) is not solved for. And, it should be the present value (at time 0, if you will) because the drift term (mu) is already in the formula elsewhere. But, if you use 12.511, you don't get DD =3.0. In which case, A(0) is not equal to V(t). I did consider the implied LN(12.75/12.511) = 1.96%, but we don't want to grow the current firm value. In this way, on my own, I just assume that V(t) must be 12.75.

Thanks, David

 

[fuzzyaces]

David,

Thank you!! I absolutely agree with 100% with what you said. I tried all of the exact same things trying to tie back to what he said. I had noticed that you tied the DD, so I assumed that you backed into V(t), but didn't want to go too far before I got myself in trouble.

I have been trying to read up on the Merton model in other books (primarily because, until the FRM, I had never heard of it). I was going crazy, because I was starting to get worried I was fundamentally missing something in the application of this model - especially since I can see it's applications to my work.

Again, thank you for your help.

 

[neveo]

Can someone tell me how to locate the 6.c.1 spreadsheet - I cant find it posted anywhere.

 

[neveo]

...sorry, found it in the Topics Review.