Explaining equity being analogous to a call option and bonds being equivalent to a short put

Question

I read this:

Equity in a corporation is essentially a call option on the enterprise value (the sum of all the firm’s assets) with a strike price equal to the firm’s debt. The firm’s bonds are a risk-free bond with a short put option where the strike price again equals the debt face value.

Which later mentioned the Merton Model, which I think is over my head, but can someone explain to me the intuition behind this? The short-put kind of makes sense, since if the assets fall behind the debt a business is likely to go bankrupt, but I don't really understand the equity being like a call option at all.

Answer 1

Let A = assets (enterprise value) and D = debt.

If A > D, then the firm is solvent: Bonds have the full value D, and equity has the value A - D.

If A < D, then the firm is bankrupt: Bondholders receive A (a loss of D - A), and equity is wiped out.

So the value of equity = max(A - D, 0), which corresponds to a call option with strike D.

And the loss by bondholders = max(D - A, 0), which corresponds to a put option with strike D.