The price of Build A Fire Corp. stock will be either $65 or $92 at the end of th

Question

The price of Build A Fire Corp. stock will be either $65 or $92 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 3 percent.

Suppose the current price of the company's stock is $72. What is the value of the call option if the exercise price is $60 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Suppose the exercise price is $85 and the current price of the company's stock is $72. What is the value of the call option now? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

The price of Build A Fire Corp. stock will be either $65 or $92 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 3 percent.

Explanation / Answer

Hi there,

A) The value of the call is the stock price minus the present value of the exercise price

Value = 72 - 60/1.03 = 72 - 58.2524 = $13.75

B) Delta = Swing of the Call/Swing of the Stock = [$7 - $0]/[$92 - $65] =7/27 If we purchase 7/27 of the stock we get either $16.85 [$65 x 7/27] or $23.85[$92 x 7/27] worth of value which is exactly $7 more than the payoffs of the call options of 0 [$16.85-$0] and $7 [$23.85-$7] respectively.

Therefore the amount to borrowed = $7/1.05 = $6.67.

Value of the Call = Stock Price x Delta – Amount Borrowed C0 = $72 x 7/27 - $6.67 = $12

Kindly rate my answer and give feedback in the comments section.

Cheers!!!

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