Suppose we hold a forward contract on a stock with expiration 66
months from now. We entered into this contract 66 months ago so that when we entered into the contract, the expiration was T = 1T=1 year. The stock price$ 66 months ago was S_0 = 100S
0
=100, the
current stock price is 125125 and the current interest rate is r = 10\%r=10%
compounded semi-annually. (This is the same rate that prevailed 66 months ago.) What is the current value of our forward contract?
Please submit your answer in dollars rounded to one decimal place so if your answer is 42.67842.678 then you should submit an answer of 42.742.7.
Can you please show work for some of the questions you posted, or at least let us know where you are getting stuck? Thanks.
To calculate the current value of a forward contract, we need to consider the following factors:
1. The current price of the underlying asset (stock price)
2. The price of the underlying asset at the time of entering the contract
3. The interest rate
4. The time remaining until expiration of the contract
In this case, we have the following information:
- Stock price at the time of entering the contract (66 months ago): S₀ = 100
- Current stock price: S = 125
- Interest rate: r = 10% compounded semi-annually (same as 66 months ago)
- Time remaining until expiration: T = 66 months
To calculate the current value of the forward contract, we can use the formula:
Value of a Forward Contract = (S - S₀)e^(rT)
where e is the mathematical constant approximately equal to 2.71828.
Let's plug in the given values and calculate the current value of the forward contract:
Value of a Forward Contract = (125 - 100)e^(0.1 * (66/12))
First, let's calculate the exponent:
0.1 * (66/12) = 0.55
Next, let's calculate the exponential part:
e^(0.55) ≈ 1.73325
Now, let's calculate the current value of the forward contract:
Value of a Forward Contract = (125 - 100) * 1.73325
Value of a Forward Contract ≈ 43.33 (rounded to two decimal places)
Therefore, the current value of the forward contract is approximately $43.3.
To calculate the current value of the forward contract, we need to consider the formula:
Forward Contract Value = (S - K) * e^(-r * T)
Where:
S = Current stock price = $125
K = Forward price (not given, assuming it equals the initial stock price) = $100
r = Interest rate = 10% compounded semi-annually = 0.10 / 2 = 0.05
T = Time in years = 66 months / 12 months/year = 5.5 years
Plugging in the values into the formula:
Forward Contract Value = (125 - 100) * e^(-0.05 * 5.5)
Calculating the exponential term:
Forward Contract Value = 25 * e^(-0.275)
Using a calculator to calculate e^(-0.275), we get:
Forward Contract Value ≈ 25 * 0.759488
Forward Contract Value ≈ $18.987
Rounding to one decimal place, the current value of the forward contract is approximately $19.0.