Question

James Kelvin just completed an Engineering Management degree program, main reason is to enhance his investment capability. Now, he wants to take advantage of the falling prices of crude oil to invest in the oil business, with an anticipation that the prices will rise again. He has been offered an oil well with a proven reserve of 1800000 barrels. From his feasibility study, he will be able to produce 80,000 barrels of oil during the first year of operations. He believes that as the production capacity increases, he will increase the oil production by 10% annually, starting from the second year. A financial institution has offered to finance this investment at 9% interest rate compounded annually. From historical data, the price of oil is expected to remain steady at $30 per barrel over the next three years and start to increase thereafter at the rate of 8% annually for the next 5 years. When the price is peaked at the end of the 8th year, it stays steady for the next 4 years. He hopes to sell the oil well at the end of 10 years of operations for $5,000,000. What is maximum price (to break even) that James should buy the oil well now? (in order words, in other words, what will be the present worth of this investment).

Answer 1

The capacity utilization grows at 10% each year

Year 1 = 80000, Year 2 = 80000 x (1+10%), Year 3 = 80000 x (1+10%) x (1+10%),....

Oil Price in a year = Previous year Price X (1+growth rate)

For Example Oil price in year 5 = Price in Year4 x (1+ price growth rate) = $32.40 x (1+8%) = $34.99. Similarly for other years

Sales Value = Capacity used in the year x Oil price in the year

Present Worth of Sales Value = Sales Value / (1+9%)^t

In 10th Year, oil well will be sold for $5,000,000. This value is added in the sales value

Total Present Worth (including present worth of proceeds from sale of well in year 10)

= $30,395,294

The maximum price James should buy this well for is $30,395,294

Time 'T'	Capacity used 'C'	Utilization growth rate	Oil Price 'P'	Oil Price growth rate	Sales value = C x P	Present Worth @9% = Sales Value/ (1+9%)^t
1	80,000.00		30.00		2,400,000	2,201,835
2	88,000.00	10%	30.00	0%	2,640,000	2,222,035
3	96,800.00	10%	30.00	0%	2,904,000	2,242,421
4	106,480.00	10%	32.40	8%	3,449,952	2,444,033
5	117,128.00	10%	34.99	8%	4,098,543	2,663,772
6	128,840.80	10%	37.79	8%	4,869,069	2,903,267
7	141,724.88	10%	40.81	8%	5,784,454	3,164,294
8	155,897.37	10%	44.08	8%	6,871,931	3,448,790
9	171,487.10	10%	44.08	0%	7,559,125	3,480,431
10	188,635.82	10%	44.08	0%	13,315,037	5,624,416
Total						30,395,294