Final answer:
The amount of amortization expense for the franchise by the end of the first year is $50,000, calculated using partial year straight-line amortization.
Step-by-step explanation:
To calculate the amortization expense for the franchise, we use the straight-line amortization method. This method spreads the cost of the franchise evenly over its useful life. In this case, the franchise has a cost of $2,000,000 and a useful life of 10 years, so the annual amortization expense would be $2,000,000 ÷ 10 years = $200,000 per year.
Since the purchase was made on October 1 and the year ends on December 31, we only need to calculate the expense for the fraction of the year that the franchise was in use, which is 3 months out of 12. Therefore, the amortization expense for the first year is $200,000 × (3/12) = $50,000.