Question

Two oil wells are for sale. The first will yield payments of $9,300 at the end of each of the next 15 years, while the second will yield $7,000 at the end of each of the next 28 years. Interest rates are assumed to hold steady at 3.5% per year over the next 28 years. Which has the higher present value?

Answer 1

Answer:

The first oil well has a higher present value of $83,266.24 as compared to the present value of the second oil well of $74,804.25

Explanation:

Step 1: Determine the total yield for both oil wells

Total yield of the first oil wells=Yield payments per year×number of yield years

where;

Yield payments per year=$9,300

Number of yield years=15

replacing;

Total yield of the first oil wells=(9,300×15)=$139,500

The future value of the first oil well=$139,500

Total yield of the second oil well=Yield payment per year×number of yield  years

where;

Yield payments per year=$7,000

Number of payment years=28

replacing;

Total yield of the second oil well=(7,000×28)=$196,000

The future value of the second oil well=$196,000

Step 2: Determine the present value of the two oil wells

First oil well present value=Future value/(1+r)^15

r=3.5%=3.5/100=0.035

First oil well present value=$139,500/(1+0.035)^15

=139,500/(1.035^15)=83,266.24

The present value of the first oil well=$83,266.24

Second oil well present value=Future value/(1+r)^28

r=3.5%=3.5/100=0.035

Second oil well present value=$196,000/(1+0.035)^28

=196,000/(1.035^28)=74,804.25

The present value of the second oil well=$74,804.25

The first oil well has a higher present value of $83,266.24 as compared to the present value of the second oil well of $74,804.25