Question

Q.7. Suppose that an oil well is expected to produce 1,200,000 barrels of oil during its first production year. However, its subsequent production (yield) is expected to decrease by 9% over the previous year's production. (a) Suppose that the price of oil is expected to be $120 per barrel for the next five years. What would be the present worth of the anticipated revenue trim at an interest rate of 10% compounded annually over the next five years? (b) Suppose that the price of oil is expected to start at $120 per barrel during the first year, but to increase at the rate of 5% over the previous year's price. What would be the present worth of the anticipated revenue stream at an interest rate of 10% compounded annually over the next five years? Q.8. From the following cash flow diagram, find the value of C that will establish economic equivalence between the deposit series and the withdrawal series at an interest rate of 8% compounded annually. $6,000 $6,000 $6,000 0 1 Years 5 2 3 4 --- с с с с с с с с Q.9. It is said that a lump-sum amount of $40,000 at the end of five years is equivalent to an equal-payment series of $4,000 per year for 10 years, where the first payment occurs at the end of year 1. What earning interest is assumed in this calculation?

Answer 1

1) The production is 1200000 barrels of oil in 1st year and that is decreasing by 9% per year.
a) Price of the barrel is $120
Production 1st year = 1200000
Production 2nd year = 1092000

5th year = 822899.53
PV = PMT / ( 1 + Discount Rate )^Year
PV of 1st year
( 1200000 * 120 ) / ( 1.10 ) = 130909090.9
2nd Year
( 1092000 * 120 ) / ( 1.10² ) = 108297520.7

Year	Production	Revenue	PV @ 10%
1	1200000	144000000	130909090.9
2	1092000	131040000	108297520.7
3	993720	119246400	89591585.27
4	904285.2	108514224	74116675.09
5	822899.53	98747943.84	61314703.94
		NPV	464229575.87

b) Now the price is rising 5% each year
Revenue = Price * Production
PV = PMT / ( 1+Discount Rate )^Year
1st Year
( 1200000 * 120 ) / ( 1.10 ) = 130909090.9
2nd Year
( 1200000 * 0.91 ) * ( 120 * 1.05 ) / ( 1.10² ) = 113712396.7

Year	Production	Price	Revenue	PV @ 10%
1	1200000	120	144000000	130909090.9
2	1092000	126.00	137592000	113712396.7
3	993720	132.30	131469156	98774722.76
4	904285.2	138.92	125618778.6	85799316
5	822899.53	145.86	120028742.9	74528405.85
			NPV	503723932.22

2) The cashflow in the diagram indicates an outflow of $6000 at the end of years 8, 9 and 10.
The value of the outflow is equal to $18000.

PV at the beginning of the outflow
PV = PMT / ( 1+Interest Rate )^Years
18000 / (1.08)^2 = 15432.10

This is the FV of the series of cash inflows with a total duration of 8 years.
FV = PMT * ( 1+Interest Rate )^Years

=PMT(8%,8,,-15432.1)
= 1450.85

The payment has a value of $1450.85

3) A lump-sum payment of $40000 is made after 5 years.
While a series of $4000 payment is made each year for 10 years.

Each has the same value that means the FV of a series of payments made for 10 years is $40000.
We will have to use trial and error method to calculate the interest rate

=FV(1%,10,-4000)
= 41848.85
This is higher than our required result

=FV(0.5%,10,-4000)
= 40912.11
This also higher so we need to move closer to the zero.

=FV(0%,10,-4000)
= 40000
This is our required amount and so that the interest rate here is zero.