a oe year long forward contract on a non dividend paying stock is entered Ito when the stock price is €150 and the risk free rate of interest is 4% per annum with contiuios compounding . A) what are the forward price and theinital value of the.forward contract? B) six months later the price of the stock is €160 and the risk free interest rate.is still 4% what are the forward price and thee value of the forward contract ?

To solve this problem, we'll need to use the standard formulas for calculating the forward price and the value of the forward contract. Let's break it down step by step.

### Part A: Initial Forward Price and Initial Value of the Forward Contract

#### 1. **Forward Price Calculation**
The formula for the forward price \( F_0 \) of a non-dividend-paying stock is:

\[
F_0 = S_0 \times e^{rT}
\]

Where:
- \( S_0 \) is the current stock price
- \( r \) is the risk-free rate of interest (continuous compounding)
- \( T \) is the time to maturity of the forward contract (in years)

Given:
- \( S_0 = €150 \)
- \( r = 0.04 \) (4% per annum)
- \( T = 1 \) year

Substitute the values:

\[
F_0 = 150 \times e^{0.04 \times 1}
\]

\[
F_0 = 150 \times e^{0.04}
\]

Let's calculate the forward price.

\[
F_0 \approx 150 \times 1.0408 \approx €156.12
\]

So, the forward price is approximately **€156.12**.

#### 2. **Initial Value of the Forward Contract**
The initial value of the forward contract at inception is always **zero** because there is no initial payment when entering into a forward contract.

### Part B: Forward Price and Value of the Forward Contract After Six Months

#### 1. **New Forward Price Calculation**
Six months later, the time remaining to maturity \( T \) is 0.5 years, and the stock price \( S_t \) is now €160.

The new forward price \( F_t \) is calculated using the same formula, but with the updated time to maturity:

\[
F_t = S_t \times e^{r(T-t)}
\]

Where:
- \( S_t = €160 \)
- \( T - t = 0.5 \) years

Substitute the values:

\[
F_t = 160 \times e^{0.04 \times 0.5}
\]

\[
F_t = 160 \times e^{0.02} \approx 160 \times 1.0202 \approx €163.23
\]

So, the new forward price is approximately **€163.23**.

#### 2. **Value of the Forward Contract**
The value of the forward contract \( V_t \) six months later can be calculated using the formula:

\[
V_t = S_t - F_0 \times e^{-r(T-t)}
\]

Substitute the known values:

\[
V_t = 160 - 156.12 \times e^{-0.04 \times 0.5}
\]

\[
V_t = 160 - 156.12 \times e^{-0.02} \approx 160 - 156.12 \times 0.9802 \approx 160 - 152.99 \approx €7.01
\]

So, the value of the forward contract is approximately **€7.01**.

### Summary of Results
1. **Initial Forward Price (Part A):** €156.12
2. **Initial Value of the Forward Contract (Part A):** €0
3. **New Forward Price after 6 months (Part B):** €163.23
4. **Value of the Forward Contract after 6 months (Part B):** €7.01

Do you want more details or have any questions?

Here are some relative questions:
1. How would the forward price change if the risk-free rate increases?
2. What happens to the value of a forward contract if the stock price drops instead?
3. How does the introduction of dividends affect the forward price calculation?
4. What if the contract was entered with a different maturity date, say 2 years instead of 1?
5. Can you explain the difference between a forward contract and a futures contract?

**Tip:** Continuous compounding gives you the most accurate measure of how interest accrues over time, especially for financial derivatives like forwards and options.

Learn how to calculate the forward price and value of a forward contract for a non-dividend paying stock using continuous compounding and interest rate principles. Solve the problem step-by-step with detailed formulas and calculations.

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