$100 stock pays out $3 dividend in 6 months. At 5% annual interest, that dividend is "worth" $2.82 now. Subtract that from the stock price to get the forward price: $100 - $2.82 = $97.18.
Here's how to calculate the 1-year forward price for the stock:
Present Value of Dividend: We need to determine the present value of the $3 dividend paid after 6 months. Using the continuous compounding formula for present value:
Present Value = Future Value / exp(Interest Rate * Time)
In this case:
- Future Value = $3 dividend
- Interest Rate = 5% per annum (0.05/2 for 6 months)
- Time = 6 months (0.5 years)
Therefore, the present value of the dividend is:
Present Value = $3 / exp(0.05/2 * 0.5) ≈ $2.821
2. Forward Price: The forward price is calculated by subtracting the present value of the dividend from the spot price:
Forward Price = Spot Price - Present Value of Dividend
Plugging in the values:
Forward Price = $100 - $2.821 ≈ $97.18
Therefore, the 1-year forward price of the stock is approximately $97.18.
Remember, this is an approximation due to rounding in the present value calculation.