Correct Option: A. Purchased at a certain price Explanation of Why Option A is Correct: Goodwill is an intangible asset that represents the excess value of a business over its identifiable net assets (assets minus liabilities). It typically arises when a company is acquired for more than the fair value of its net identifiable assets. This excess payment is often due to factors such as brand reputation, customer relationships, or proprietary technology that are not separately identifiable.

1. Acquisition Context: When a business is purchased, the buyer often pays a premium over the fair value of the identifiable assets and liabilities. This premium is recorded as goodwill on the balance sheet. For example, if a company is valued at $1 million based on its tangible assets and liabilities, but it is purchased for $1.2 million, the $200,000 difference is recorded as goodwill.
2. Accounting Standards: According to accounting standards (such as IFRS and GAAP), goodwill is recognized only when it is acquired in a business combination. This means that goodwill is not self-generated or created internally; it must be a result of a transaction where a business is bought.
3. Impairment Testing: Goodwill is not amortized but is subject to annual impairment tests. If the carrying amount of goodwill exceeds its recoverable amount, an impairment loss must be recognized.

Why the Other Options are Wrong or Weaker:

• Option B: Raised in connection with the admission of a new partner
• This option refers to goodwill that may arise in partnerships when a new partner is admitted. However, this type of goodwill is not recognized in the same way as purchased goodwill. In partnerships, goodwill can be calculated and shared among partners, but it does not appear on the balance sheet as an intangible asset in the same manner as purchased goodwill. Therefore, it does not meet the criteria for recognition under accounting standards.
• Option C: Raised to account for the true value of a business on the death of a partner
• Similar to Option B, this option pertains to the internal calculation of goodwill in a partnership context. When a partner dies, the remaining partners may need to value the business, which could include goodwill. However, this is not recognized as an intangible asset on the balance sheet. Instead, it is a valuation method used for settling the deceased partner's share, and it does not reflect the acquisition of goodwill in the context of business combinations.
• Option D: Raised in order to prevent the balance sheet showing that the business is insolvent
• This option suggests that goodwill could be artificially created to improve the appearance of a company's financial position. However, this is not permissible under accounting standards. Goodwill must be based on actual transactions and cannot be used to manipulate financial statements. Creating goodwill to mask insolvency would be considered fraudulent and is not an acceptable accounting practice.

Summary of Key Points:

• Goodwill is recognized only when a business is purchased for more than the fair value of its identifiable net assets.
• It represents intangible factors like brand reputation and customer loyalty.
• Goodwill is subject to annual impairment testing and is not amortized.
• Goodwill cannot be self-generated or created through internal means, such as in partnerships or to manipulate financial statements.

This understanding of goodwill is crucial for financial accounting, especially when analyzing business acquisitions and their impact on financial statements.