08/15 mdm(cs 8)
John Carter was afarmer in NorthernMassachusetts. John,like all of the farmersaround him, grewapples and alien hisharvest to Boston for auction at the prevailing marketprice. The acreage had been in John’s ancestors for threegenerations; from his bequest and prudentmanagement, John had congenital his net account to$300,000. Like abounding of his neighbors, John was beingpressed by accretion costs and by the abortion ofrevenues to accumulate up with this increase. John worriedthat a absolutely bad year could clean him out and he mightlose the farm.
John approved to activity the bulk of autumn and theprice that it would accompany at market. This year hebelieved the acreage would acquire revenues in the around of$310,000. John’s assay of accomplished costs adumbrated thatthe acreage would acquire $220,000 this year in anchored costsand that capricious costs would be $0.03 per batter ofapples produced. The tax agenda for farmers meantthat John did not pay any taxes unless he becoming over$25,000 in a year. Amid $25,000 and $50,000, hewould accept to pay a bordering bulk of 24 percent, sothat his absolute taxes on $50,000 would be 12 percent.Over $50,000, the bordering tax bulk added to45.6 percent on earnings.
During the accomplished few years, John had belted hisrevenues application advanced contracts. When he entered aforward contract, John had to agreement the commitment ofthe apprenticed bulk of apples at harvest. If John’sown crop fell beneath the bulk of apples that he hadsold forward, he would accept to buy abundant apples onthe accessible bazaar to accomplish up the difference. Any applesthat John’s acreage produced aloft the bulk specifiedin the arrangement would be awash at the prevailing marketprice. All transactions, including any acquittal receivedby John from the advanced arrangement and any affairs orbuying of apples on the atom bazaar at autumn wouldbe acclimatized at the aforementioned time in the fall
John believed the bulk at autumn would best beapproximated by a accustomed administration with a meanof $0.2079 per batter and a accepted aberration of$0.0247 per pound. Advanced affairs were onlyavailable in increments of 100 tons, and the accepted advanced bulk was $0.2079 per pound. In the past, Johnhad affected that he could adumbrate with authoritativeness whathis acreage would produce, and he had usually hedgedroughly bisected that amount. John sometimes wondered ifthat was the best action for how abundant to hedge, givenhis anticipation of what his acreage would produce.
John Junior, home from academy for springvacation, had absitively to advice his father. He hadproduced a worksheet that modeled the approaching bulk ofapples in an @RISK simulation. John Junior initially bureaucracy the archetypal so that the autumn was absolutely his father’sforecast—743 bags of apples—and he agreed to helphis ancestor bulk out what the ideal bulk was to sellforward, accustomed the acceptance that angel productionwas accepted with certainty.
However, John Junior was anxious that hisfather’s assumptions about the autumn did not captureall of the risks that the acreage faced. Afterwards someprodding, John Junior was able to get his ancestor toadmit that his forecasts were not consistently right, andJohn Senior provided John Junior with abstracts aboutactual bazaar prices and autumn yields in the past(Exhibit 1). John Junior acclaimed with some affair thathis father’s anticipation for the accessible autumn wassimply the beggarly of the accomplished ten years’harvests. Inaddition to the simple assay his dad had asked himto do, John Junior absitively to archetypal the farm’sprofitability, factoring in ambiguity about how manytons of apples would absolutely be produced. He decidedthat assembly abundance was best approximated by anormal administration with a beggarly of 743 bags (hisfather’s forecast) and accepted aberration of 87 tons.
After commutual his basal archetypal for his ancestor andhis“improved”model with the ambiguity about thesize of the harvest, John Junior knew he could helpdecide how abounding bags of apples to advertise forward. Butsomething was acrimonious him. He doubtable there wastypically a accord amid the abundance of applesharvested and the bulk at market. Afterwards all, if his fatherhad a bad year, alternative farmers ability additionally accept bady ears, and this could affect price. As a result, he absitively to add a alternation capricious to his archetypal to bigger abduction the alternation amid the autumn and bazaar price. To assay what alternation did for the accommodation of how abundant to advertise forward, he absitively to assay how abounding bags his ancestor should advertise advanced bold 0 alternation amid bulk and quantity,þ0.99 correlation, and0.99 correlation. He wondered whether the variables would be that awful correlated.
John Junior concluded, from talking over banquet with his ancestor about accident preference, that his ancestor was decreasingly accident afraid and a logarithmic account action would be an adapted archetypal of his accident preference. John Junior appropriately modeled the account of the accumulation afterwards tax of anniversary ambiguity scenario. Based on the after-effects of the altered simulations, John Junior hoped to explain to his ancestor what the risks and implications were for the accommodation about advanced contracts.
1.Assume that the achievement abundance of John Carter’s acreage is accepted with certainty. Is it a acceptable abstraction to barrier bisected the production? How abundant should Carter hedge? Note: There are 2000 pounds in a ton.
2.Now accept that the achievement abundance is uncertain. How does the alternation amid achievement and prices affect Carter’s accommodation on how abundant to hedge? Prepare your assay bold ambiguity decisions for correlations of -.99, 0, and .99.
3.Assuming achievement abundance is uncertain, which alternation would you use to accomplish a ambiguity decision? How abundant should Carter barrier bold that correlation
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