SOLUTION: The forward price of a forward contract on a stock maturing in 3 years is $70. The stock is expected to pay a dividend of $1 twice: in 6 months and in a year from now. Solve for th

Question 1191944: The forward price of a forward contract on a stock maturing in 3 years is $70. The stock is expected to pay a dividend of $1 twice: in 6 months and in a year from now. Solve for the current stock price if the continuous compounding interest rate is 6%.
Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
Here's how to solve for the current stock price:
**1. Understand the Formula:**
The forward price (F) of a stock with dividends is calculated as:
F = (S - PV of dividends) * e^(rT)
Where:
* F = Forward price
* S = Current stock price (what we want to find)
* PV of dividends = Present value of all dividends paid during the life of the forward contract
* r = Continuously compounded interest rate
* T = Time to maturity of the forward contract (in years)
**2. Calculate the Present Value of Dividends:**
* **Dividend 1 (in 6 months):** PV1 = $1 * e^(-0.06 * 0.5) = $1 * e^(-0.03) ≈ $0.9704
* **Dividend 2 (in 1 year):** PV2 = $1 * e^(-0.06 * 1) = $1 * e^(-0.06) ≈ $0.9418
Total PV of dividends = PV1 + PV2 ≈ $0.9704 + $0.9418 ≈ $1.9122
**3. Plug Values into the Formula and Solve for S:**
We know:
* F = $70
* r = 0.06
* T = 3 years
* PV of dividends ≈ $1.9122
Now, plug these values into the formula:
$70 = (S - $1.9122) * e^(0.06 * 3)
$70 = (S - $1.9122) * e^(0.18)
$70 = (S - $1.9122) * 1.1972
$70 / 1.1972 = S - $1.9122
$58.47 = S - $1.9122
S = $58.47 + $1.9122
S ≈ $60.38
**Therefore, the current stock price is approximately $60.38.**

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