Questions: Two oil wells are for sale. The first will yield payments of 10,900 at the end of each of the next 14 years, while the second will yield 7,000 at the end of each of the next 29 years. Interest rates are assumed to hold steady at 4.1% per year over the next 29 years. Which has the higher present value? the first oil well the second oil well they are the same cannot be determined

Two oil wells are for sale. The first will yield payments of 10,900 at the end of each of the next 14 years, while the second will yield 7,000 at the end of each of the next 29 years. Interest rates are assumed to hold steady at 4.1% per year over the next 29 years. Which has the higher present value?
the first oil well
the second oil well
they are the same
cannot be determined

Transcript text: Two oil wells are for sale. The first will yield payments of $10,900 at the end of each of the next 14 years, while the second will yield $7,000 at the end of each of the next 29 years. Interest rates are assumed to hold steady at 4.1% per year over the next 29 years. Which has the higher present value? the first oil well the second oil well they are the same cannot be determined

Solution

Solution Steps

To determine which oil well has the higher present value, we need to calculate the present value of each annuity. The present value of an annuity can be calculated using the formula for the present value of an annuity:

\[ PV = P \times \left(1 - (1 + r)^{-n}\right) / r \]

where $ P $ is the payment per period, $ r $ is the interest rate per period, and $ n $ is the number of periods. We will calculate the present value for both oil wells and compare them.

Step 1: Calculate Present Value of the First Oil Well

The present value $ PV_1 $ of the first oil well, which yields payments of $ \$10,900 $ at the end of each of the next $ 14 $ years, is calculated using the formula:

\[ PV_1 = 10900 \times \left(1 - (1 + 0.041)^{-14}\right) / 0.041 \]

After performing the calculation, we find:

\[ PV_1 \approx 114381.6347 \]

Step 2: Calculate Present Value of the Second Oil Well

The present value $ PV_2 $ of the second oil well, which yields payments of $ \$7,000 $ at the end of each of the next $ 29 $ years, is calculated using the same formula:

\[ PV_2 = 7000 \times \left(1 - (1 + 0.041)^{-29}\right) / 0.041 \]

After performing the calculation, we find:

\[ PV_2 \approx 117491.0967 \]

Step 3: Compare Present Values

Now, we compare the two present values:

\[ PV_1 \approx 114381.6347 \quad \text{and} \quad PV_2 \approx 117491.0967 \]

Since $ PV_2 > PV_1 $, the second oil well has a higher present value.