Merton model B(T) and L

[Alfie]

Hi,

I am struggling with the difference between B(T) and L in the merton model - particularly knowing when the value they have given us in the question is L or if it is B(T). EG in april 2022 question 9, it gives "debt with current outstanding amount of 20m" so the solutions say L is 20 accumulated to time 7. so is B(t)=20m?
part iv then goes on to ask for the implied value of the companies debt. So in both parts we are looking for the company's debt, i am struggling to differentiate between knowing when we are given L as the companys debt or given B(T) as the companys debt as B(T)=min(F(T),L) and so we would get different answers depending on which we use.

Thank you

 

[msm]

As far as I understand, B(T) = L if the company has enough to pay the debtholders back.
Debt at the current time is B(t) hence yes B(t)= 20m
in the aprill 22 qn, they have mentioned "(where the total value of the company is the value of the equity plus the value of the debt)" which I would take as a big hint that they want the value from Total Assets=Debt+ Equity, and not get into what the debtholders would actually receive.
If they had asked for the value of debt and not qualified it with anything, I would have answered that L the accumulated value of 20m, and B(T) = min(F(T),L) hence B(T)= whatever.
I think mainly, I understand it as L is the ideally paid out debt ie nominal value owed, and B(T) is the debt they will actually be able to pay. B(T) allows for the risk of default, and L is the objective value.
Hope that helps. Maybe I could understand the confusion better if you gave another example?

 

[Alfie]

As far as I understand, B(T) = L if the company has enough to pay the debtholders back.
Debt at the current time is B(t) hence yes B(t)= 20m
in the aprill 22 qn, they have mentioned "(where the total value of the company is the value of the equity plus the value of the debt)" which I would take as a big hint that they want the value from Total Assets=Debt+ Equity, and not get into what the debtholders would actually receive.
If they had asked for the value of debt and not qualified it with anything, I would have answered that L the accumulated value of 20m, and B(T) = min(F(T),L) hence B(T)= whatever.
I think mainly, I understand it as L is the ideally paid out debt ie nominal value owed, and B(T) is the debt they will actually be able to pay. B(T) allows for the risk of default, and L is the objective value.
Hope that helps. Maybe I could understand the confusion better if you gave another example?

Hi,
Ah thank you so much that's really cleared it up! Thanks for explaining that so clearly
Good luck!