Debbie Chon, CFA, is evaluating a put option on Lincoln Industrial. Lincoln's current stock price is $64 per share and the company will pay a $0.56 dividend. The
90-day U.S. Treasury bill is yielding 5.3%. Lincoln's 3-month European call option with a strike price of $70 has a premium of $3.50. Based on the put-call parity, calculate the value of the associated Lincoln put option.
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A. B. C.C
To calculate the value of the associated Lincoln put option using put-call parity, we need to understand the relationship between put and call options. Put-call parity states that the value of a European call option minus the present value of the strike price is equal to the value of a European put option plus the current stock price minus the present value of any dividends.
The formula for put-call parity is as follows:
C - Xe^(-rt) = P + S - D
Where: C = Value of the call option X = Strike price e = Base of the natural logarithm (approximately 2.71828) r = Risk-free interest rate t = Time to expiration (in years) P = Value of the put option S = Current stock price D = Present value of any dividends
Let's calculate each component of the formula:
C = $3.50 (given premium for the call option) X = $70 (strike price) r = 5.3% (annualized risk-free interest rate) t = 90/365 = 0.2466 (converting 90 days to years) S = $64 (current stock price) D = $0.56 (dividend)
First, let's calculate the present value of the dividend using the risk-free interest rate:
Present value of dividend = $0.56 * e^(-rt)
Present value of dividend = $0.56 * e^(-0.053 * 0.2466)
Present value of dividend = $0.56 * e^(-0.013)
Present value of dividend ≈ $0.56 * 0.987
Present value of dividend ≈ $0.55272
Now, we can rearrange the put-call parity formula to solve for P:
P = C - Xe^(-rt) - S + D
P = $3.50 - $70 * e^(-0.053 * 0.2466) - $64 + $0.55272
P = $3.50 - $70 * e^(-0.013) - $64 + $0.55272
P = $3.50 - $70 * 0.987 - $64 + $0.55272
P = $3.50 - $68.97 - $64 + $0.55272
P ≈ -$129.91528
Since the value of a put option cannot be negative, we can assume there's an error in the calculations or data provided.
Based on the available answers, none of them accurately represents the value of the associated Lincoln put option. It's recommended to double-check the calculations or review the question and data provided for any inconsistencies.