This comes into all the fun that is "Holding Out". Look up AC 120-12A discussing Common Carriage vs Private Carriage. In this case, I think it would be ultimately safe to argue that the farmer came to your company because you had airplanes and pilots and not because you offer cow-finding flights. The farmer is not asking for a charter flight and you don't "hold out" your cattle search services. Therefore you could consider this flight private-carriage-for-hire. Something that can be done without being on a commercial operators certificate and something any commercial pilot with a commercially capable aircraft (100-hour, etc) can do.
The AC defines common carriage as: (1) a holding out of a willingness to (2) transport persons or property (3) from place to place (4) for compensation. This scenario does not meet (1) or (3).
Extremely common misconception - that so-called "private carriage" does not require an operator's certificate. It does. AC 120-12A is both misleading and antiquated.
Aside from that, so far anyway, I have not seen the FAA ever apply the supposed "test" in 120-12A to say that a specific passenger-carrying operation did not require an operating certiicate unless it's one of the exceptions in 119.1.
Or, as FSIMS says in para 2-127,
==============================
B. Not Common Carriage. An applicant is not engaged in common carriage if he does not meet the above requirement. Operations not involving common carriage include the following definitions or exceptions. These definitions or exceptions are contained in part 119 and in sections of 14 CFR Part 91 , General Operating and Flight Rules.
1) Non-common carriage involves the carriage of persons or property for compensation or hire but there is no holding out.
Non common carriage operations require the issuance of an operating certificate. Operations would be conducted under part 125 , Certification and Operations: Airplanes Having a Seating Capacity of 20 or More Passengers or a Maximum Payload Capacity of 6,000 Pounds or More; and Rules Governing Persons on Board Such Aircraft; or part 135 , depending on the type of aircraft, seating configuration, and payload capacity.
2) Private carriage involves the carriage of persons or property for compensation or hire with limitations on the number of contracts. The carriage of persons or property for compensation or hire under a contractual business arrangement between the operator and another person or organization, which did not result from the operator’s holding out or offering service is considered to be private carriage. (In this situation, the customer seeks an operator to perform the desired service and enters into an exclusive, mutual agreement as opposed to the operator seeking customers).
Private carriage operations require the issuance of an operating certificate. Operations would be conducted under part 125 or part 135 , depending on the type of aircraft, seating configuration, and payload capacity.
Go to the last page of this PDF for an example of a private carriage operating certificate.
http://fsims.faa.gov/wdocs/8900.1/v02 air op & agency cert/chapter 04/02_004_005.pdf
