If Apple costs $130 today, interest rates are 10%, and Apple pays a $3 dividend
ID: 2789669 • Letter: I
Question
If Apple costs $130 today, interest rates are 10%, and Apple pays a $3 dividend every year, what is the fair forward price of a five-year forward?
What would the fair forward price be if Apple’s stock price goes up to $150?
For the IBM example: ($100 IBM price today, 2 year forward, 10% interest rates, $5 dividend per year), suppose you bought the forward at the fair forward price of $110.5. Now IBM falls to $80. You want to get out. What is the most you would pay to get out of your forward contract struck at $110.5?
Explanation / Answer
When price is 130: Five year forward=(130-3/1.1-3/1.1^2-3/1.1^3-3/1.1^4-3/1.1^5)*1.1^5=191.051
When price is 150: Five year forward=(150-3/1.1-3/1.1^2-3/1.1^3-3/1.1^4-3/1.1^5)*1.1^5=223.2612
IBM fair price at stock=100=(100-5/1.1-5/1.1^2)*1.1^2=110.5
For price at 80=(80-5/1.1-5/1.1^2)*1.1^2=86.3
This is the most I will receive or I will pay max 110.5-86.3=24.2 to get out of the contract