ANSWERS TO BEGINNING-OF-CHAPTER QUESTIONS
See the BOC model.
Based on the Black-Scholes model, we see that the value of the
option increases with the stock price, time to expiration, variance, and the risk-free rate.
The option value declines with increases in the strike price.
As discussed in the chapter, options are compensation, compensation is an expense, and
expenses should be deducted from revenues when calculating income.
should be deducted on the income statement.
However, if options are to be expensed,
their values must be estimated.
Although it may not provide an exactly precise estimate
of the “true” value of an option, the Black-Scholes model can give us a reasonably good
estimate of the option’s value, and that estimate can be used both to let employees know
what they are getting when they are granted options and also for purposes of expensing
Companies need to provide some specific level of compensation, and total
compensation might consist of regular salary, a cash bonus for targeted performance
levels, and stock options.
The value of the options must be estimated if a rational
compensation package is to be established.
High tech companies have made the greatest use of options.
The companies benefited
from reduced cash requirements during their rapid growth phase, and many employees of
successful companies became millionaires.
However, options produced problems in the
period 2000-2002, when stock prices fell sharply, driving down the values of options
awarded in earlier years.
The stock collapses were due primarily to a general decline in
the market from its “bubble” high, not by poor employee performance.
If an employee
had received options whose value was based on an unrealistically high stock price, and if
that price later declined sharply, then it could be argued that his or her “true” past
compensation was too low.
Should the company now re-price its outstanding options,
lowering the strike price so as to make the options valuable and thus provide the expected
level of total compensation?
And, if options are re-priced, is this fair to stockholders,
who don’t get any comparable treatment?
This is an issue that many companies are
currently struggling with today.
It’s interesting to note that in 2003 Warren Buffett had Berkshire Hathaway expense
options, and he hired two Wall Street firms to find a value of the options.
It turned out
that their values were consistent with Black-Scholes, indicating that even investment
banking firms value options with Black-Scholes.
It appears that Buffet will give up on
trying to improve on Black-Scholes and will simply use it.
Answers and Solutions: