British Petroleum Company Case

Assumptions and Approaches

To calculate the value of the repurchase plan, we used the Black-Scholes option pricing model. Since anyone who owned partly paid BP shares could sell them at any time from 30 Oct, 1987 to 6 Jan, 1988 to the Bank of England for £0.70 regardless of the prevailing market price, we consider the repurchase plan as an american put option.

Using the Black-Scholes model, however has one major limitation: it cannot be used to accurately price options with an American-style exercise as it only calculates the option price based on exercise at expiration. It does not consider the steps along the way where there could be the possibility of early exercise of an American option. This will generate an option value lower than it really is but for the purpose of our analysis, it produces a good indication of it’s true value as you will see in the comparison of the value of the repurchase plan and the change in equity value of the underwriters later in this discussion.

The key inputs that have been used are as follows:

1) Volatility (σ) : From Exhibit 7, we can observe BP ordinary shares price from 10/01/87 to 10/30/87. The standard deviation of daily return during that period is 3.79%, and we can obtain historical volatility of 61.06% from annualizing standard deviation. (assumption : 260 trading days in a year)

2) Time to maturity (T) : The offer to repurchase shares would start on Oct 30, 1987 and expire on Jan 6, 1988. So the time to maturity is 68days/365days = 0.1863.

3) Stock price (S) : According to Exhibit 7, BP shares price on Oct 30, 1987 is 2.65(£).

4) Strike price (X) : The Bank of England agreed to buy for £0.70 any and all partly paid BP shares(first installment of £1.20 which underwriters were also committed to pay) regardless of the market price, and those who sold their shares to the Bank of England would be relieved of their obligation to pay the second and third installments which is £1.05+£1.05 = £2.10. In...