978-0077861704 Chapter 24 Lecture Note Part 2

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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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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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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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