Problem 3:  CBA Inc

Subject:FinancePrice: Bought3

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Problem 3: 

CBA Inc. is a publicly traded all-equity firm on which options are traded. The current price of CBA Inc. is $30 and the standard deviation of its annual return is .20. The current annual risk-free rate is 2 percent. 

You are on the compensation committee for CBA Inc. and have recommended that the top management of the firm be given European call options, in addition to a fixed salary, as part of their compensation. The option contract is for 10,000 shares with an exercise price of $40. The option contract expires exactly in one year. 

You understand that options can give managers adverse incentives when selecting projects. You think that management might have to choose between the following two mutually exclusive potential projects:

 

                        Effect on Firm's                   Standard Deviation of the Stock Price

                    Current Stock Price                         with the new project

           

Project 1                  up $1                                                    .20

 

Project 2                down $1                                                 .45

Note: Once a particular project is taken, the market will recognize that project's NPV and will adjust the stock price to reflect that NPV. Thus, if the management picks Project 1, the NPV is such that the stock price will rise by $1 while if they choose Project 2, Project 2's NPV is such that the stock price will drop by $1. 

 1. Use the Black-Scholes formula to calculate the total market value of the call contract if the management picks Project 1. 

2. If, instead of Project 1, the managers pick Project 2, what is the total market value of the option contract under Project 2?    

3. Which project would the management want to take given the proposed option contract? Why?