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whbyry
equity_as_an_option.pptxValuing equity as an option – distressed firms
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Valuing Equity as an option
The equity in a firm is a residual claim, i.e., equity holders lay claim to all cashflows left over after other financial claim-holders (debt, preferred stock etc.) have been satisfied.
If a firm is liquidated, the same principle applies, with equity investors receiving whatever is left over in the firm after all outstanding debts and other financial claims are paid off.
The principle of limited liability, however, protects equity investors in publicly traded firms if the value of the firm is less than the value of the outstanding debt, and they cannot lose more than their investment in the firm.
4/9/2016
FIN 461 - Portfolio Management - Prof. Krause
2
It is limited liability that creates the optionality. Thus, this may not hold for private businesses, where lenders can come after the owners’ assets….
Payoff Diagram for Liquidation Option
4/9/2016
FIN 461 - Portfolio Management - Prof. Krause
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The option revolves around the outstanding debt; the face value of the debt is the strike price and the remaining life of the debt is the life of the option. The value of the assets in liquidation becomes the stock price.
Application to valuation: A simple example
Assume that you have a firm whose assets are currently valued at $100 million and that the standard deviation in this asset value is 40%.
Further, assume that the face value of debt is $80 million (It is zero coupon debt with 10 years left to maturity).
If the ten-year treasury bond rate is 10%,
how much is the equity worth?
What should the interest rate on debt be?
4/9/2016
FIN 461 - Portfolio Management - Prof. Krause
4
I am assuming that if this firm is liquidated, I will get the $ 100 million as my sales proceeds.
Looks like there is insufficient information to answer either question.
Options Valuation Software - Derivagem
http://www-2.rotman.utoronto.ca/~ hull/software/index.html
4/9/2016
FIN 461 - Portfolio Management - Prof. Krause
5
It is limited liability that creates the optionality. Thus, this may not hold for private businesses, where lenders can come after the owners’ assets….
Model Parameters
Value of the underlying asset = S
Value of the firm = $ 100 million
Exercise price = K
Face Value of outstanding debt = $ 80 million
Life of the option = t
Life of zero-coupon debt = 10 years
Variance in the value of the underlying asset = 2
Variance in firm value = 0.16
Riskless rate = r
Treasury bond rate corresponding to option life = 10%
4/9/2016
FIN 461 - Portfolio Management - Prof. Krause
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The reason why I chose a zero coupon bond now should be clear. Because it is a zero coupon bond (with no covenants), I as the equity investors get complete unfettered power for the next 9 years and 364 days, since I have no contractual payments to make.
If it were a coupon bond, the logic for treating equity as an option will still hold, but I will then have a series of options that build on top of each other, since I have to make coupon payments every 6 months or a year.
Valuing Equity as a Call Option
Based upon these inputs, the Black-Scholes model provides the following value for the call:
d1 = 1.5994 N(d1) = 0.9451
d2 = 0.3345 N(d2) = 0.6310
Value of the call = 100 (0.9451) - 80 exp(-0.10)(10) (0.6310) = $75.94 million
Value of the outstanding debt = $100 - $75.94 = $24.06 million
Interest rate on debt = ($ 80 / $24.06)1/10 -1 = 12.77%
4/9/2016
FIN 461 - Portfolio Management - Prof. Krause
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Not only can I value the equity and give you the correct default spread for the company, I can also estimate the probability that the firm will go bankrupt as 37% (1- N(d2) =1- Probability that the value of assets > Face value of debt)
There are services such as KMV that use this approach to assess the likelihood of default for clients and their portfolios.
I. The Effect of Catastrophic Drops in Value
Assume now that a catastrophe wipes out half the value of this firm (the value drops to $ 50 million), while the face value of the debt remains at $ 80 million. What will happen to the equity value of this firm?
It will drop in value to $ 25.94 million [ $ 50 million - market value of debt from previous page]
It will be worth nothing since debt outstanding > Firm Value
It will be worth more than $ 25.94 million
4/9/2016
FIN 461 - Portfolio Management - Prof. Krause
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While the value of the firm drops by $ 50 million, the value of equity will drop by less because the bondholders will bear (reluctantly) some of the loss
Valuing Equity in the Troubled Firm
Value of the underlying asset = S
Value of the firm = $ 50 million
Exercise price = K
Face Value of outstanding debt = $ 80 million
Life of the option = t
Life of zero-coupon debt = 10 years
Variance in the value of the underlying asset = 2
Variance in firm value = 0.16
Riskless rate = r
Treasury bond rate corresponding to option life = 10%
4/9/2016
FIN 461 - Portfolio Management - Prof. Krause
9
I changed only S… All of the other inputs are unchanged. (Half the firm disappeared but the standard deviation should not change… )
The Value of Equity as an Option
Based upon these inputs, the Black-Scholes model provides the following value for the call:
d1 = 1.0515 N(d1) = 0.8534
d2 = -0.2135 N(d2) = 0.4155
Value of the call = 50 (0.8534) - 80 exp(-0.10)(10) (0.4155) = $30.44 million
Value of the bond= $50 - $30.44 = $19.56 million
The equity in this firm drops by $45.50 million, less than the overall drop in value of $50 million, because of the option characteristics of equity.
This might explain why stock in firms, which are in Chapter 11 and essentially bankrupt, still has value.
4/9/2016
FIN 461 - Portfolio Management - Prof. Krause
10
The probability of bankruptcy has shot up to 58.45%... Debt holders bear $4.5 million of the loss. Equity investors bear the rest..
Equity value persists ..
4/9/2016
FIN 461 - Portfolio Management - Prof. Krause
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Equity is an incredibly stubborn instrument. Its value remains, at least in this case, even as firm value drops to a fraction of the outstanding debt. That is because, as an option, it has time value and you get to play (as the equity investor) for the next 10 years… maybe, something good will happen.
II. The conflict between stockholders and bondholders
Consider again the firm described in the earlier example , with a value of assets of $100 million, a face value of zero-coupon ten-year debt of $80 million, a standard deviation in the value of the firm of 40%. The equity and debt in this firm were valued as follows:
Value of Equity = $75.94 million
Value of Debt = $24.06 million
Value of Firm == $100 million
Now assume that the stockholders have the opportunity to take a project with a negative net present value of -$2 million, but assume that this project is a very risky project that will push up the standard deviation in firm value to 50%. Would you invest in this project?
Yes
No
4/9/2016
FIN 461 - Portfolio Management - Prof. Krause
12
Everything that we have been taught in corporate finance and capital budgeting suggests that a negative net present value project is bad, and a risky, negative net present value project may be even worse…
Valuing Equity after the Project
Value of the underlying asset = S
Value of the firm = $ 100 million - $2 million = $ 98 million (The value of the firm is lowered because of the negative net present value project)
Exercise price = K
Face Value of outstanding debt = $ 80 million
Life of the option = t
Life of zero-coupon debt = 10 years
Variance in the value of the underlying asset = s2
Variance in firm value = 0.25
Riskless rate = r
Treasury bond rate corresponding to option life = 10%
4/9/2016
FIN 461 - Portfolio Management - Prof. Krause
13
Looks at equity as an option… Note the drop in S and the increase in variance…
Option Valuation
Option Pricing Results for Equity and Debt Value
Value of Equity = $77.71
Value of Debt = $20.29
Value of Firm = $98.00
The value of equity rises from $75.94 million to $ 77.71 million , even though the firm value declines by $2 million. The increase in equity value comes at the expense of bondholders, who find their wealth decline from $24.06 million to $20.19 million.
4/9/2016
FIN 461 - Portfolio Management - Prof. Krause
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Some value magic or is it? Equity as an optilon gains more from the increase in risk than it loses in firm value.. The real losers are the bondholders.
What lessons can bondholders draw from this?
Take an equity stake in deeply troubled firms.
Take an active role in the way the companies are run.
Write in restrictive covenants on new investments and monitor existing investments to prevent risk shifting.
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