Question

You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1,320,000. Over the past five years, the price of land in the area has increased 6 percent per year, with an annual standard deviation of 32 percent. A buyer has recently approached you and wants an option to buy the land in the next 12 months for $1,470,000. The risk-free rate of interest is 4 percent per year, compounded continuously.

How much should you charge for the option? (Enter your answer in dollars, not millions of dollars. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 1,234,567.89.)

Call price           $

Answer 1

The final answer is call price of $ 131,316.67

Methodology:

This can be seen and valued as a call option

We are using Black Scholes Formula to value this call option.

The formula is:

I have done it using the excel. A snapshot is shown below. The inputs are highlighted in yell colored cells. The outputs are in the blue colored cells. Against each output, the formula used is also produced so that you understand the mathematics.

Hence, you charge for the option a call price of $ 131,316.67

Please enter 131,316.67 in the answer box.