Corporate applications Flashcards
(39 cards)
What is the main idea in this chapter?
Common debt and equity can be regarded as as options where the assets are the underlying.
elaborate on the various kinds of derivatives firms issue
The key distinction is made on “explicit” vs “implicit” derivatives.
Explicit are things like warrants, convertible bonds etc.
Implicit refers to the ordinary debt and equity.
What is the ourpose of the chapter?
Understand how options and derivatives affect corporate finance
introduce the capital structure we are working with
We assume in the beggining at least, that we have:
Non dividend paying equity.
A single zero coupon bond. This bond represent the debt and has maturity value B_bar.
We use terminology:
A_t : assets at time t
E_t : Equity value at time t
B_t : Value of the debt at time t
Naturally, the value of the debt will sneak in towards the B-bar value, which is the debt value at maturity.
what does the value of the debt and equity depend on?
the value of the assets.
what must equity holders do to be 100% possession owners of hte firm?
Pay the debt at maturity. Meaning, pay B_bar at time T.
if A_t > B_bar, equity holders will pay B_bar to debt holders.
If A_t < B_bar, equity holder would have to inject additional funds or bankrupt. In such a case, the equity holders lose the posession, and the firms assets A_t is now fully owned by the debt holders.
elaborate on the value of equity
equity is equal to assets less debt.
We can say that the equity value at time T, E_T, is given by:
E_T = max[0, A_t - B_bar]
This is the expression of the payoff of a call option that has B_bar as the strike price and A_t as the underlying assets.
elaborate on the value of debt
bond holders will always receive the smallest amount possible.
if the firm manage to pay the debt, bond holders receive B_bar.
If the firm is not able to pay the debt, bond holders receive A_t.
Therefore, the value of the debt is given by:
B_T = min (A_t, B_bar).
This expression can be changed.
B_T = A_t - max(0, A_t - B_bar)
this also can be understood as “debt = assets - equity).
B_T = A_T - max(0, A_T - B_bar)
What is the interpretation of this?
Bond holders own all the assets of the firm, but they have written a call option to the equity holders.
these max equations are nice etc. but how to use them?
we need to assume that assets are log normally distributed. then we can use black scholes to value them.
how to find the value of a firms equity?
We use a call option, black scholes. Strike price is the debt value at maturity, or the principal.
The underlying is the vlaue of the assets.
how do we find the debt value at maturity?
We use the fact that “B_t = A_t - E_t” and use black scholes to find the value of the equity. Since BS requires A_t, we can easily sole for the debt.
elaborate on YTM, the concepts
firstly, yield to maturity is the interest rate that equates a bond’s price with its face value (present value).
for a zero coupon bond, this is:
FaceValue x e^(-yt) = Price
FaceValue/Price = e^(yt)
yt = ln(FV/P)
y = 1/t ln(FV/P)
relate YTM to the debt of the firm
the firm has a current debt level B_t, and the maturity face value B_bar.
y = 1/t ln(B_bar / B_t)
equity and debt are
options
what happens to the debt if the assets increase by one unit
Equity is given by BS. The equity delta tell us how much the equity change in value from a change in the total assets.
Then we use “B_t = A_t - E_t”.
if assets increase by one unit, the debt will change by:
1 - ∆_equity
Interpretation: I suspect equity will change the most, perhaps 0.9 or something, and leave the little rest for the debt.
why does debt increase in value from an increase in assets?
It is the same as OTM vs ITM options. The probability of expiring ITM for deep OTM options is very low. Therefore the added asset value is more likely to remain in the hands of the debt holders, or the option holder.
The debt holders own the assets, and write a call. Therefore, if the option is already deep OTM, an increase in asset value is equivalent to seeing a little increase in the stock price. However, the option will still most likely expire worthless. If it expire worthless, the added asset value translate into positional value, because debt holders already hold the assets.
Debt can be written as “B_t = A_t - max(0, A_t - B_bar)”
What is the alternative way
B_T = B_bar - max(0, B_bar - A_T)
why would YTM exceed risk free rate?
because there is a probability of default, associated with the volatility of the assets.
Bond holders, debt holders, want to be compensated for this risk. Therefore, they are not willing to lend out risk free.
elaborate on finding return on equity
We need the elasticity of the option. we know that the elascitiyy of the option is given by “delta S / C”, and represent “percentage change in call option that results from a percentage change in the underlying”. It gives a a number that say “if the underlying moves 1 percent, the option will move X percent”.
If we take the excess return on the assets, and multiply it by the option elasticity, and add the risk free return, we basically say that “the assets will have this expected return, and therefore hte option will have something else because of the elasticity multiplier. then we add risk free rate to seal the deal”.
give the formula for return on equity
how do we find the equity option elasticity
we need to have asset value, the equity option delta, and the option price. elasticity = A_t ∆ / E_t, where E_t is the option value.
how do we find the return on the debt?
same procedure as with return on equity, but now everything is changed to be debt.
how do we find the elasticity of debt?
this is slightly more complicated. Why? because we compute debt as:
B_t = A_t - E_t
Therefore, we find elasticity as the weighted average elasticity. this assumes that we have the elasticity of the assets - which we always have because it is always equal to 1!
The weighted average is the classical case.
