The current price of a stock is $400 per share and it pays no dividends. Assuming a constant interest rate of 8% per year compounded quarterly, what is the stock's theoretical forward price for delivery in 9 months?
Please submit your answer rounded to two decimal places so for example, if your answer is 567.1234 then you should submit an answer of 567.12
To calculate the theoretical forward price of a stock, we can use the formula:
Forward Price = Spot Price * (1 + i)^n
Where:
Spot Price = $400 per share (given)
i = interest rate per compounding period = 8% / 4 = 2% per quarter
n = number of compounding periods = 9 months / 3 months (quarterly) = 3 quarters
Now let's substitute the values into the formula:
Forward Price = $400 * (1 + 0.02)^3
Calculating the exponential term:
(1 + 0.02)^3 = (1.02)^3 = 1.060896
Multiplying by the spot price:
Forward Price = $400 * 1.060896
Calculating the forward price:
Forward Price = $424.36 (rounded to two decimal places)
Therefore, the theoretical forward price for the stock, with delivery in 9 months, is $424.36 per share.
To find the theoretical forward price of a stock, you can use the formula:
Forward Price = Spot Price * e^(r*t)
Where:
Spot Price = Current price of the stock
e = Mathematical constant approximately equal to 2.71828
r = Interest rate
t = Time period in years
In this case:
Spot Price = $400 (given)
r = 8% per year compounded quarterly, so we need to calculate the quarterly interest rate, which is 8% / 4 = 2% = 0.02
t = 9 months = 9/12 = 0.75 years
Now, we can substitute these values into the formula:
Forward Price = $400 * e^(0.02 * 0.75)
To calculate e^(0.02 * 0.75), we use the exponential function on a calculator or a spreadsheet software. This gives us the result:
Forward Price = $400 * 1.0150605
Rounding to two decimal places, the theoretical forward price for delivery in 9 months is:
Forward Price = $400 * 1.02 = $408.02