By Elaine Kub

DTN Contributing Analyst

I have always loved taking tests. Full days of filling out long bubble sheets with a No. 2 yellow pencil ... those were some of my favorite moments at school. However, I got the impression that my preference was freakishly unusual.

Well, in the last Kub's Den column, I posted half of a little grain market math test and invited readers to send in their answers to win a prize (a signed copy of "Mastering the Grain Markets: How Profits Are Really Made"). It wasn't until I opened my email inbox to see the flood of responses that I realized I was not alone in my strange attraction to math quizzes.

Granted, it was a rainy week in the Midwest and there were probably many farmers who were desperate for something to distract them from how late the 2014 harvest is stretching along. One winner said he thought the number of responses was because people like any chance for a prize, but it probably takes a half hour or more to do the calculations, and depending on what your time is worth, the book isn't even that expensive.

There is an overall point to the grain market math test, though, and one reader picked up on it and included this comment with his test answers: "A very thought provoking little exercise you put together. There is a lot more math involved in crop farming than we realize, or maybe we do and rarely acknowledge it. Definitely going to be some math going on this winter trying to find something to plant next year."

So without further ado, here is the second half of the math test for you to try. Again, there are some easy arithmetic questions (which tend to be the ones that trip people up the most), there are some deliberately confusing word problems, and there are a few which require some advance knowledge of how the markets work. Good luck!

6. What will it cost per bushel to move wheat (which weighs 60 pounds per bushel) from Scott City, Kan., to Salina, Kan.? A trucking company quotes you $1.45 per mile and can haul 57,000 pounds of bulk dry matter per truck. The truck has a backhaul opportunity, so you only need to pay for one leg of the trip. Be careful and find the shortest mileage!

7. Your truck arrives at the elevator and finds eight trucks already in line. The elevator's average throughput is 10 trucks per hour. How long will your truck be at the elevator?

8. Let's say you hedge 50,000 bushels of your 2015 corn production via at-the-money December 2015 put options with a strike price of $4.10. The current price of the put options is $0.38. Assuming zero commission and transaction fees, and assuming a delta of -0.44, what do you assume the hedge profit in your brokerage account will be if the December 2015 futures contract price moves from $4.11 to $3.61?

9. As of Oct. 1, 2014, there were at least 10.1 million head of cattle on feed and it's estimated that 5.325 billion bushels of corn will be used as livestock feed (and "residual," but let's ignore the "residual" piece for now). Assume corn consumption by the entire livestock industry grows continually at the fastest-ever recorded pace of growth in the U.S. beef cattle inventory, which was an increase of 7% from 1973 to 1974. How many years will it take for us to feed a new record-high quantity of corn, beating the previous maximum of 6.135 billion bushels in 2004?

10. For 2014 soybean crop insurance policies, the Projected Price from February was $11.36. First calculate the Harvest Price (using the November contract's daily closes only up through 10/29/14, the publication date of this test). Say a farmer purchased basic Revenue Protection crop insurance at a 75% coverage level for a soybean field with an APH of 42 bpa, and has harvested exactly 42 bpa from that field this year. What will his insurance payout be? What if he had purchased the crop insurance at an 85% coverage level? What if he had purchased the crop insurance at an 85% coverage level but harvested 44 bpa this year?

Extra Credit: If the Projected Price and Harvest Price are exactly the same next year (2015) for soybeans, what payment would a land-owning farmer receive from the new ARC-CO program, assuming he has a yield history of 42 bpa on his soybean base acres?

Send your responses to mathtest@masteringthegrainmarkets.com before Nov. 12, when the answers will be posted in the next Kub's Den column, just like the Part 1 answers are posted below.

1. Your grain cart presently contains 21,500 pounds of grain. A truck's main trailer holds 51,000 pounds of grain and its pup trailer holds 33,000 pounds. You previously dumped 38,900 pounds from your grain cart into the main trailer. How much more grain do you need to get the truck full and headed down the road? How much volume is that, in bushels of soybeans?

ANSWER: 23,600 lbs, or 393.33 bushels.

2. You've been combining soybeans that were planted at a 30-degree angle in a field that is half a mile wide. At the point where your long pass ends exactly at the corner of the field, how many acres remain to be harvested in that field? See the illustration at www.masteringthegrainmarkets.com/mathtest.html.

ANSWER: 46.2 acres (1/2 mile is 2,640 feet. Use the tangent of 30 degrees to find the length of the opposite side is 1,523.28 feet. The area is base times height divided by 2, or 2,010,729.6 square feet. There are 43,560 square feet in an acre.)

3. You could get the whole series of annual U.S. corn yields from nass.usda.gov, but let's say all you know is that average yield was 127.1 bpa in 1996, 142.2 in 2003, and is now estimated at 174.2 in 2014. Assume the yield trend is linear and give an estimate for what U.S. average corn yields will be in 2015.

ANSWER: 176.9 bpa (Use the equation y = mx + b to find the slope of the linear trend line, then solve for y when x is 2015.)

4. You've added up what it costs to operate, insure, and finance your grain storage bins and decided your cost of carry is 4 1/2 cents per bushel per month. Today you see the March '15 corn futures contract closed at $3.57 and the May '15 contract closed at $3.65, and your local ethanol plant is bidding -24H for March delivery, -27K for April delivery, and -23K for May delivery. You want to sell some grain this afternoon with a forward contract for spring delivery, but which month offers you the best opportunity to capture the market's carry structure?

ANSWER: Sell cash corn in April. (There is only 4 cents of carry between April and May, which is less than the 4 1/2 cents it would cost you to store it for another month.)

5. Pretend we live in a world where the global stocks-to-use ratio of the corn market is a perfect predictor of price (CAUTION: THE MARKETS DON'T ACTUALLY WORK THIS WAY!). For each 0.01 increase in that ratio, this relationship suggests the corn price should fall $0.63 per bushel. Lately the price of corn has been consolidating around $3.25 per bushel, but today the USDA released a fresh monthly supply and demand report. They left global total use constant at 973 million metric tons, but lowered the global ending stocks from 190 mmt to 185 mmt. Estimate what you think the corn price will be after the report.

ANSWER: $3.57 (The price is expected to move up $0.32 because the ratio tightened by 0.005.)

Extra Credit: By how many bushels did the USDA reduce its global ending stocks estimate in Question 5?

ANSWER: 5 million metric tons is 196.8 million bushels.

Elaine Kub is the author of "Mastering the Grain Markets: How Profits Are Really Made" and can be reached at elaine@masteringthegrainmarkets.com or on Twitter @elainekub.

(CZ/AG)

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