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# In Merton model, why isn't V = E + L ??

#### daquity37

##### New Member
In the Merton model, we assume from the outset that
V = E + L
Firm(Asset) = Equity + Debt

However, in Merton calculation examples, we are given V and L(face value of debt) and asked to calculate E,by using the BSM formula. This ends up vastly different from being V - L (and I also don't see the point in using this formula if E is simply V - L ?)
?????

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#### ShaktiRathore

##### Well-Known Member
Subscriber
Hi,
In Merton model its the other way around i think you get present value of equity E first through BSM then get the value of debt by using the equation Firm(Asset) = Equity + Debt, as V-E(different from face value of Debt L with maturity T,V being the present value of the firm).
You can understand this by drawing analogy with the stock we calculate the value of call option on equity(maturity T) from BSM with S-PV(X) being present intrinsic value of the equity where S is the current value of the equity and X is the exercise price(PV(X)=X*exp(-rT) where r is the risk free rate),similarly you get to calculate call option on Firms Assets(equity value) from the BSM formula with V - PV(L) being present intrinsic value of the Firms Assets where V is the current value of the Firms Assets and L is the exercise price .Therefore V - PV(L) is the present intrinsic value of the Firms Assets not the value of equity that is being calculated for a specific period of time T. Like a call option on equity has Intrinsic value(S-PV(X))+Time value ,call option on firms assets(equity value) has Intrinsic value(V-PV(L)+Time value ,Therefore finally what you get as the equity value is the intrinsic value of firms assets (V - PV(L))+Time value of the Firms assets being greater than L.
Thanks

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#### daquity37

##### New Member
What do you mean that the value of debt is different from face value of debt L?
By "value of debt", do you mean the present value of the debt (rather than face value) ?

Also, you said "you get present value of equity E through BSM and get value of debt by V-E" but don't you need, in the first place, the value of debt as an input to the BSM ?

#### ShaktiRathore

##### Well-Known Member
Subscriber
Hi
Yes i mean value of debt as the present value of the debt rather than face value,its not same as PV(L) which is the present value of the Face Value L discounted at risk free rate.
Value of debt is the present value of the debt which we get after subtracting value of equity(BSM calculated) from the present value of the Firms Assets its not same as PV(L),the present value of Face Value of Debt or L the Face Value of Debt.
thanks

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#### daquity37

##### New Member
Thanks man. I get it now! Thanks for all your help