Final answer:
A write-down of goodwill is required in the case of a decline in the fair value of a reporting unit, indicating potential impairment of the goodwill.
Step-by-step explanation:
The circumstance that would require a write-down of goodwill is a decline in the fair value of a reporting unit. Goodwill is an intangible asset that represents the excess of purchase price over the fair value of the net identifiable assets of a business when acquired.
According to accounting principles, if the fair value of a reporting unit, including its goodwill, drops below its carrying value, this indicates that the goodwill may be impaired and a write-down is required. An increase in market value of identifiable assets, normal fluctuations in foreign exchange rates, or an increase in future cash flows would not necessitate a write-down of goodwill.