Using relevant examples, discuss the various elements of a valid contract with case law.

A valid contract is a legally binding agreement between two or more parties, and it is enforceable by law. There are several key elements that a contract must have to be considered legally valid.

1. Offer and Acceptance: An offer is a promise to act or refrain from acting, which is made in exchange for a return promise to do the same. For example, in the case of Carlill v Carbolic Smoke Ball Company (1893), the company offered £100 to anyone who could, having used their product, contract influenza. Mrs. Carlill used the smoke ball and contracted influenza, so she claimed the £100. The court held that there was a valid contract between the parties.

2. Intention to Create Legal Relations: Both parties must intend the agreement to be legally binding. In the case of Balfour v Balfour (1919), a husband promised to pay his wife £30 per month while he was abroad. The court held that there was no contract as there was no intention to create legal relations.

3. Consideration: This is something of value given by both parties to a contract that induces them to enter into the agreement to exchange mutual performances. In the case of Thomas v Thomas (1842), the court held that a peppercorn rent of £1 per year was good consideration.

4. Capacity: The parties must have the capacity to legally enter into the contract. For example, minors, mentally impaired individuals, and intoxicated individuals may lack the capacity to enter into a contract.

5. Consent: The agreement must be made of the free will of both parties and not under duress, undue influence, or misrepresentation. In the case of Barton v Armstrong (1976), a contract was set aside because it was made under duress.

6. Legality of Purpose: The contract's purpose must not be illegal or against public policy. In the case of Pearce v Brooks (1866), a contract for the hire of a carriage to a prostitute was held to be void as it was against public policy.

In conclusion, a valid contract requires an offer and acceptance, intention to create legal relations, consideration, capacity, consent, and legality of purpose. Case law provides numerous examples of these elements in action.