Wyatt Oil owns a major oil refinery in Channelview, Texas. The refinery processes crude oil into valuable

Question:

Wyatt Oil owns a major oil refinery in Channelview, Texas. The refinery processes crude oil into valuable outputs in a two-stage process. First, it distills a barrel of crude oil at a variable cost of $2 per barrel into two types of outputs: light distillates (such as gasoline, jet fuel, diesel fuel, and kerosene) and heavy distillates. The light distillates are sold for $48 per barrel. The heavy distillates can either be sold for $30 per barrel or fed into a catalytic cracking unit ("cat cracker") at a variable cost of $3 per barrel to be converted into light distillates and sold, for $48 per barrel. The diagram in Figure 1 illustrates the refining process.
Wyatt's Channelview refinery can distill 60 million barrels of oil per year and feed 30 million barrels of heavy distillate a year into the cat cracker. It can process either light, sweet crude from Texas (such as West Texas Intermediate) or heavy, sour crude from the Middle East (such as Kuwait Export), depending on the market prices of the two types of crude. More valuable products are distilled from a barrel of light, sweet crude than from a barrel of heavy, sour crude (see Figure 2). Light, sweet crude currently costs $34 per barrel and heavy, sour crude costs $30; however, the price
FIGURE 1
Crude oil distillation:

Product Recovered: Unit Use Temp (°F): Sent to: Gas Butane & lighter <90° processing Light straight naphtha Gasoline 9

FIGURE 2
Product yield from simple distillation

100% 80% LPG Naphtha 60%- Kerosene 40%- O Light gas oil Intermediate gas oil 20%- Residue 0%- Arab WTI Light

FIGURE 3
Price difference between light crude oil and heavy crude oil, 1988-2001

Table 1:

Table 2:

differential is volatile, as noted in Figure 3. The output from 60 million barrels of West Texas Intermediate and 60 million barrels of Kuwait Export is shown in Table 1.
The fixed and variable costs and capacities associated with distilling crude and cracking the heavy distillates are shown in Table 2.
Until recently, Wyatt's Channelview refinery processed West Texas Intermediate, but it switched to Kuwait Export when the price differential between the two reached $3.50 per barrel. Kim Quillen, manager of the refinery, is concerned because the switch to heavy, sour crude has resulted in the refinery selling only 50 million barrels of light distillates instead of 60 million- because the refinery has capacity to crack only 30 million barrels of heavy distillates. The refinery's projected accounting income for the year is shown next.
Revenue from light distillates ................................... $960,000,000
Revenue from processed heavy distillates .................... 1,440,000,000
Revenue from sold heavy distillates ............................. 300,000,000
Cost of crude oil ................................................ (1,800,000,000)
Variable distilling costs .......................................... (120,000,000)
Variable cracking costs ........................................... (90,000,000)
Fixed distilling costs ............................................. (180,000,000)
Fixed cracking costs ............................................... (90,000,000)
Net income ....................................................... $ 420,000,000
Buying an additional cat cracker to increase cracking capacity by 10 million barrels would cost $900 million. It would last for 20 years, increasing the refinery's annual fixed costs by $45 million per year. Quillen has asked his accountant, John Hanks, to evaluate the investment, and Hanks has contemptuously dismissed the project. His analysis appears next.
Sales value of light distillates ...................................... $48.00 per bbl.
Cost of heavy distillates* .......................................... (35.00) per bbl.
Additional cat cracker accounting costs** ........................ (7.50) per bbl.
Capital charge*** ................................................... (13.50) per bbl.
Residual income (loss) ............................................... $(8.00) per bbl.

Hank concludes his evaluation by saying, "What an awful project! Our residual income decreases by $8 on every barrel. Not to mention the possibility that we might switch back to using West Texas Intermediate sometime. Then we would have excess cat cracker capacity, which would just rust away over time since expanding our distilling capacity is not feasible. There is no way we should pursue this project."
Quillen is puzzled, for he knows that many other refineries have been installing additional cat cracker capacity in response to the growing price differential between sweet, light crude and sour, heavy crude. Fortunately, he has just hired you to evaluate the capital investment.
Required:
a. Allocate the projected $420 million accounting income of the Channelview refinery among its three activities-light distillates, processed heavy distillates, and sold heavy distillates-by allocating joint costs on the basis of (1) physical volume and (2) net realizable value. Compare the ratio of accounting profit to net realizable value of the three activities under both methods.
b. Did Quillen make the right decision to switch from West Texas Intermediate to Kuwait Export when the price differential reached $3.50 per barrel? Assuming there are no switching costs, find the optimal decision rule as a function of the price differential.
c. Would your decision rule be different if you were to expand the cracker capacity to 40 million barrels? Find the optimal switching rule if the refinery can crack 40 million barrels of heavy distillates each year.
d. Assume the price differential between West Texas Intermediate crude and Kuwait Export crude remains the same at $4 per barrel. Should Quillen expand the refinery's cat cracking capacity?
e. Now consider the possibility of changes in the price differential. Suppose that this year's price differential is $4, but next year's price differential could be anywhere between 75 percent and 125 percent of the current year differential (equally likely, so next year's price differential can be thought of as a random variable uniformly distributed on the interval [$3, $5]). Each succeeding year, the price differential follows the same pattern: between 75 percent and 125 percent of the prior year price differential. Should Quillen expand capacity? Why or why not?