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 dis-tilled 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 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 .

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 whynot?

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Unit Use Sent to: Product Recovered: Butane & lighter Temp CF): Gas processing Light straight → blending 200 350 Naphtha reforming Crude oil- → 350-450K Kerosene Dist. fuel blending 450°-650_ _Distillate Heavy cracking gas oil 00-1 Fluid catalytic → 1,000+Residuum Coking TABLE 1 West Texas Intermediate Kuwait Export Light distillates Heavy distillates Total 30 million bbls./year 30 million bbls/year 60 million bbls/year 20 million bbls./year 40 million bbls./year 60 million bbls./year TABLE 2 Distilling Crude Oil Cracking Heary Distillates Variable cost Annual fixed cost Annual capacity $2 per bbl. $180 million 60 million bbls. 3 per bbl. $90 million 30 million bbls.