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Call option/stock price/annual risk free rate

1. Suppose you believe that Sherwin Williams Co.'s stock price is going to increase from its current level of $22.50 sometime during the next 5 months. For $435.75 you can buy a 5-month call option giving you the right to buy 100 shares at a price of $25 per share. If you buy this option for $435.75 and Sherwin Williams Co.'s stock price actually rises to $50, what would your pre-tax net profit be?

2. The current price of Samsung Electronics' stock is $22, and at the end of one year its price will be either $27 or $17. The annual risk-free rate is 4.5%, based on daily compounding. A 1-year call option on the stock, with an exercise price of $22, is available. Based on the binominal model, what is the option's value?

3. The current price of PPG Industries' stock is $45, the annual risk-free rate is 5.5%, and a 1-year call option with a strike price of $65 sells for $7.00. What is the value of a put option, assuming the same strike price and expiration date as for the call option?

4. Suppose you believe that Renesas Electronics Corp's stock price is going to decline from its current level of $82.50 sometime during the next 5 months. For $463.63 you could buy a 5-month put option giving you the right to sell 100 shares at a price of $85 per share. If you bought this option for $463.00 and Renesas Electronics Corp's stock price actually dropped to $48, what would your pre-tax net profit be?

5. An analyst wants to use the Black-Scholes model to value call options on the stock of Kia Motors when the price of the stock is $45, the strike price of the option is $30 and the option matures in 3 months (t = 0.25). The standard deviation of the stock's returns is 0.40 and the variance is 0.16 while the risk-free rate is 4.5%.

What is the value of the call option if, when given this information, the analyst then calculated the following necessary components of the Black-Scholes model and N(d1) and N(d2) represent areas under a standard normal distribution function:

• d1 = 1.613
• d2 = 1.413
• N(d1) = 0.94667
• N(d2) = 0.92123

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Solution Summary

The call option/stock price/annual risk free rates are examined.

$2.19