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Chapter 24 - Options and Corporate Finance
1. Valuing a Call Option
A. A Simple Model: Part II
The option may, however, finish out-of-the money. So, adjust your
second portfolio as follows: instead of loaning the PV(E), loan the
PV(lowest possible S1) at the risk-free rate and buy enough calls to have
the difference between the lowest and highest possible prices.
Example: Suppose a stock is currently selling for $67 and can have
a price of $60 or $80 in one period. There is a call option with a strike
price of $70. The risk-free rate is 9%.
Loan PV(60) = 55.05 at the risk-free rate. The loan proceeds will
be $60 at expiration, by design.
Difference between 80 and 60 = $20. If the stock price is $80, then
the payoff on one call is 80 – 70 = $10. Therefore, it takes 2 calls to make
up the difference between the two possible prices.
So, your two possible portfolios are:
1. Buy the stock
2. Buy 2 calls and loan $55.05 at 9%
At expiration:
Stock = 60; Portfolio 2 = 0 + 60 = 60
Stock = 80; Portfolio 2 = 2(80 – 70) + 60 = 80
Since the two portfolios have the same ending value, they must sell
for the same amount today.
S0 = 2C0 + 55.05
C0 = (67 – 55.05)/2 = $5.98
B. The Fifth Factor
Variance of return – the greater the variability in return (price), the
more a call option is worth. Greater variability increases the probability of
finishing in-the-money; whereas, finishing deep-out-of-the-money versus
just out-of-the-money doesn’t cost any more money.
Consider the same example as in part A, only the stock can end up
at 55 or 85. The replicating portfolio becomes buy 2 calls and loan $50.46.
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Chapter 24 - Options and Corporate Finance
C0 = (67 – 50.46)/2 = 8.27.
C. A Closer Look
Let S equal the difference in the possible stock prices, and let C
be the difference in option values at expiration. Then the number of
options needed to replicate the possible stock prices is S/C.
2. Employee Stock Options
Employee Stock Options (ESOs) allow employees to purchase company stock at a
fixed price for a fixed amount of time.
A. ESO Features
Features differ from company to company, but here are some
common ones.
-Typical expiration of 10 years
-Cannot be sold or transferred unless the employee dies, then the
options transfer to the estate
-Vesting period during which they cannot be exercised and the
employee loses the options if s/he leaves the company
ESOs are granted for two basic reasons:
-Align employee interests with owner interests
-Cheaper form of compensation for cash-strapped companies
Lecture Tip: The idea behind using stock options to align
management interests with stockholder interests is a noble one. Many
companies have embraced it wholeheartedly because it seems so logical.
However, overusing ESOs and other employee stock grants may backfire.
We saw in previous chapters that holding a diversified portfolio is
important because we are only rewarded for bearing non-diversifiable
risk. If a substantial portion of an employee’s portfolio is tied up in
company stock, then s/he may have difficulty diversifying fully. This lack
of diversification leads to a higher required return by employee-owners
than outside owners. The higher required return leads employees to place
a lower value on the stock than outside stockholders. Recent research
indicates that this does tend to be the case. Therefore, stock options may
not provide as much incentive as it would appear at first glance.
Employers need to be careful about overusing this incentive or it loses its
value.
B. ESO Repricing
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Chapter 24 - Options and Corporate Finance
When the stock price falls well below the strike price on an
employee stock option, the option is said to be underwater. Companies
have been known to “reprice” underwater options so that they are once
again at-the-money. This practice is controversial. If the purpose of issuing
stock options is to incentivize employees to increase the value of the
stock, then repricing effectively removes the incentive.
C. ESO Backdating
In 2006, a scandal erupted because it was found that companies had a
practice of looking back in time to select the grant date (and therefore the
exercise price) of the option. They picked a date where the price was low,
meaning the options were immediately in-the-money.
3. Equity as a Call Option on the Firm’s Assets
The underlying asset is the value of the firm (the value of its assets). The
stockholders have a call on this value with a strike price equal to the face value of
the firm’s debt. If the firm’s assets are worth more than the debt, the option is in-
the-money and stockholders exercise the option by paying off the debt. If,
however, the face value of the debt is greater than the value of the firm’s assets,
the option expires unexercised (i.e., the company defaults on its debt). Thus, the
bondholders can be viewed as owning the firm’s assets and having written a call
against them.
A. Case I: The Debt is Risk-Free
The option will be in-the-money: Suppose the assets are worth
$1,000 (= S0) and the firm has a pure discount bond outstanding with a
face value of $1,000 (=E). Assume the assets will be worth either $1,200
or $1,400 in one period and the risk-free rate is 11%. What is the value of
the firm’s equity?
C0 = 1,000 – PV(1,000) = 99.10
Value of the debt = 1,000 – 99.10 = 900.90 (Remember that Assets =
Liabilities + Equity)
B. Case II: The Debt is Risky
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Chapter 24 - Options and Corporate Finance
Suppose all circumstances are the same as above except that the
firm’s assets will be worth either $900 or $1,700 in one period. How much
are the debt and the equity worth?
The present value of 900 at 11% is 810.81.
S = 1,700 – 900 = 800
C = 700 – 0 = 700
So, we need to “buy” 8/7 options.
S0 = 1000 = (8/7)C0 + 810.81
C0 = 165.54 = equity
Debt = 1,000 – 165.54 = 834.46 (which implies a discount rate of 19.84%)
Lecture Tip: Option valuation can explain why companies may
have incentive to take on projects with negative NPV. Consider the
following example:
Market value of assets = 1,000
Bond value = 1500
Equity value = ?
The company has the following two investments that it could invest
in:
1. Project A has an expected payoff of $1,000, is extremely risky,
and has a NPV of -$50
2. Project B has an expected payoff of $400, is very safe, and has a
NPV of $200.
Project B, with the higher NPV, would normally be preferred, but if
accepted, its payoff when combined with the current $1000 value of assets
would still fall short of the $1500 required to payoff the creditors. The
only project which may save the company is the high risk project, with the
low NPV, but possibly high payoff. If project A fails, stockholders aren’t
any worse off.
4. Options and Capital Budgeting
Real options provide the right to buy or sell real assets. These options often apply
in capital budgeting situations and can be very valuable.
Explicit options – contracts giving the holder the right to buy or sell the asset
Implicit options – options that exist in many capital budgeting situations, but are
often “hidden”
A. The Investment Timing Decision
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Chapter 24 - Options and Corporate Finance
Virtually all projects can be viewed as real options if you think of the
initial investment as the strike price and the project as the asset.
Timing – if we take a project today, we can’t take it later. Consequently,
even though a project has a positive NPV, it doesn’t mean we should take
it now. It may be worth more to us if we wait one year, or two, or three …
Investment Timing Decision – deciding when to take a project
The option to wait is particularly valuable when the economy or market is
expected to be bigger in the future. It is not valuable when trying to
capitalize on current fads.
The option to wait may actually turn a bad project into a good project –
waiting a year or two may allow the firm to capture higher cash flows.
B. Managerial Options
Managerial options are options to modify a project once it has been
implemented.
Contingency Planning – what do we do if …?
Option to expand – ability to make the project bigger if it is a successful.
We underestimate the NPV if we ignore this option.
Option to abandon - ability to shut down the project if things don’t go as
planned. We underestimate the NPV if we ignore this option.
Option to suspend or contract – ability to downscale when the market is
weaker than expected.
Strategic options – using a project to explore possible new ventures or
strategies. These projects open up a wide number of future opportunities
but are more difficult to analyze with traditional DCF analysis.
5. Options and Corporate Securities
A. Warrants
Warrant – security issued by firms that gives the holder the right, but not
the obligation, to purchase the common stock directly from the company
at a fixed price for a given period.
Sweeteners or equity kickers – warrants issued in combination with
privately placed loans or bonds, public issues of bonds, and new stock
issues.
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Chapter 24 - Options and Corporate Finance
The exercise of warrants causes an increase in the number of outstanding
shares, whereas the exercise of “normal” calls does not. When the number
of shares increases, the EPS will decrease, all else equal. Because of the
dilution impact of warrants, firms with a large number of warrants or
convertible securities outstanding report earnings on a diluted basis.
B. Convertible Bonds
Convertible bond – a bond that may be converted into a fixed number of
shares of common stock on or before the maturity date.
Terminology
-Conversion ratio – number of shares per $1000 bond received if
converted
-Conversion price – bond’s (or preferred’s) par value divided by
conversion ratio
-Conversion premium – difference between the conversion price and the
current stock price divided by the current stock price
Value of a convertible bond
-Straight bond value – what the bond would sell for if it didn’t have a
conversion feature, i.e., the discounted coupons and face value at maturity
-Conversion value – what a convertible bond would be worth if converted
now
-Floor value – Max(straight-bond value, conversion value)
-Option value – the value of the bond over and above the floor value. The
conversion option is essentially a call option on the company’s stock with
the strike price equal to the face value of the bond.
C. Other Options
Callable bond – many corporate bonds are callable, meaning that the
company can retire the bonds early for a specified call price. The company
pays for the call by receiving a lower bond price (paying a higher yield)
than they would have for a comparable non-callable bond.
Put bonds – a combination of a straight bond and a put option. The put
option allows the bondholder to require the firm to buy the bond back
prior to maturity for a specified price.
Insurance and loan guarantees – insurance and loan guarantees can be
viewed as combinations of the underlying asset plus a put option. If the
asset declines in value, the put holder exercises the option and “sells” the
underlying asset to the put writer.
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Chapter 24 - Options and Corporate Finance
6. Summary and Conclusions
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