A call option on Hartco stock with an exercise price of S50 and an expiration date one year from now is worth $4.00 today. A put option on Hartco stock with an exercise price of $50 and an expiration date one year from now is worth $2.25 today. U.S. Treasury notes maturing in one year are yielding 2.0%. Hartco does not pay a dividend. The value of Hartco*s stock is closest to:
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A. B. C.C
To determine the value of Hartco's stock, we need to use the concept of put-call parity. Put-call parity states that the sum of a call option's price and the present value of the exercise price is equal to the sum of a put option's price and the stock price.
Mathematically, the put-call parity equation is as follows:
C + PV(X) = P + S
Where: C = Call option price PV(X) = Present value of the exercise price P = Put option price S = Stock price
We are given that the call option price is $4.00, the put option price is $2.25, and the exercise price (X) is $50. We also know that the risk-free rate (U.S. Treasury notes yield) is 2.0%, which we can use as the discount rate to calculate the present value of the exercise price.
PV(X) = X / (1 + r)
Where: r = Risk-free rate
Plugging in the values, we get:
PV(X) = $50 / (1 + 0.02) = $50 / 1.02 = $49.02
Substituting the values into the put-call parity equation:
$4.00 + $49.02 = $2.25 + S
Simplifying the equation:
S = $4.00 + $49.02 - $2.25 = $50.77
Therefore, the value of Hartco's stock is closest to $50.77 per share. However, none of the provided answer choices match this value exactly. The closest option is option B, which states $47 per share. Please note that there may be an error in the given answer choices or the calculations provided in the question.