An oil well now produces 100,000 barrels per year. The well will produce for 18 years more, but
production will decline by 4% per year. Oil prices, however, will increase by 2% per year. The
discount rate is 8%. What is the PV of the well’s production if today’s price is $14 per barrel

To calculate the present value (PV) of the well’s production, we need to account for the changing oil production, increasing oil prices, and the time value of money due to the discount rate. Here’s how we can approach this problem:

### Variables
- **Initial annual production (P₀):** 100,000 barrels
- **Decline rate of production (d):** 4% per year
- **Annual increase in oil prices (i):** 2% per year
- **Discount rate (r):** 8%
- **Current oil price (C₀):** $14 per barrel
- **Number of years (n):** 18 years

### Formula Setup
The present value (PV) of each year's production is calculated as:

\[
\text{PV}_t = \frac{P_t \times C_t}{(1 + r)^t}
\]

Where:
- $ P_t $ is the oil production in year $ t $ after the decline.
- $ C_t $ is the price per barrel in year $ t $ after the increase.
- $ r $ is the discount rate (8%).

We need to sum this over 18 years, where $ P_t $ and $ C_t $ change as follows:
- $ P_t = P_0 \times (1 - d)^t $
- $ C_t = C_0 \times (1 + i)^t $

### Step-by-Step Calculation:
The total present value (PV) of the well’s production is:

\[
\text{PV} = \sum_{t=0}^{17} \frac{P_0 \times (1 - d)^t \times C_0 \times (1 + i)^t}{(1 + r)^t}
\]

We can calculate this step-by-step for each year $ t $ from 0 to 17, summing the discounted cash flows for each year. Let's compute this.The present value (PV) of the well's production over the next 18 years, given the declining production, increasing oil prices, and the discount rate, is approximately **$12,428,723**.

Would you like more details on any part of this calculation or further explanation?

Here are 5 related questions to expand your understanding:
1. How does changing the discount rate affect the present value?
2. What happens to the present value if oil prices increase faster than 2%?
3. How does a smaller decline rate in production impact the total value?
4. How is the formula for present value derived in financial mathematics?
5. What is the significance of discounting future cash flows?

**Tip:** When calculating the present value of future cash flows, higher discount rates reduce the present value, emphasizing the time value of money.

An oil well now produces 100,000 barrels per year. The well will produce for 18 years more, but production will decline by 4% per year. Oil prices, however, will increase by 2% per year. The discount rate is 8%. What is the PV of the well’s production if today’s price is $14 per barrel?

Learn how to calculate the present value (PV) of an oil well's production over 18 years, accounting for a 4% decline in production, a 2% increase in oil prices per year, and an 8% discount rate. Understand key financial concepts such as present value, net present value (NPV), and the time value of money.

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