Options to Buy Stock

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					Chrysler Warrants

In 1980, Chrysler, then on the verge of bankruptcy, received loan guarantees from the
government. As partial payment for the guarantees, Chrysler gave the U.S. government
options to buy Chrysler stock for $13 a share until 1990. At the time these options
(technically known as “warrants”) were issued, Chrysler stock was trading at about $7.50
per share. By mid-1983, however, Chrysler stock had risen to well over $30 a share and
in July of that year, Chrysler repaid the guaranteed loans in full.

Lee Iacocca, Chrysler’s CEO at the time, argued that the government had not shelled out
a dime to provide the loan guarantees and asked that the warrants be returned to Chrysler
at little or no cost. However, many congressmen felt that the government had taken a risk
by providing the guarantees and if the warrants were to be returned to Chrysler, they
should be returned at their full market value. Ultimately, the government decided to hold
an auction for the warrants. Determined to recover its warrants, Chrysler participated in
the auction, which occurred when Chrysler stock was trading at about $28 a share.
Chrysler’s bid, about $22 per warrant, was the winning bid in the auction.

Computing the Black-Scholes warrant values for Chrysler

Stock price = $28 a share

Volatility = 30% per year

The annual risk-free rate = 10%

The warrants were American options, with no dividends to be paid over the life of the
option, and there is no dilution effect, so it is possible to value the warrants as European
options.

The options had an expiration date exactly in 7 years

The strike price was $13

       ln( S / X )  (r   2 / 2)T       ln( 28 / 13)  (0.1  0.3 2 / 2)7
d1                                                                           2.246
                  T                                  0.3 7

d 2  d1   T  2.246  0.3 x 2.646  1.452

N (d1 )  0.9878

N (d 2 )  0.9265

c  SN (d1 )  Xe  rT N (d 2 )

c  28x0.9878  6.67x0.9222  21.51

				
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