Final answer:
a. The book value of the truck at the end of year 4 would be $4,600. b. The depreciation taken in the first year would be $1,450.
Step-by-step explanation:
a. The book value of the truck at the end of year 4 can be calculated using the formula: Book Value = Initial Cost - (Depreciation per year x Number of years). In this case, the initial cost is $23,000 and the depreciation per year can be calculated by subtracting the residual value ($4,600) from the initial cost and dividing it by the estimated life (4 years). So, the depreciation per year is ($23,000 - $4,600) / 4 = $4,350. Therefore, the book value at the end of year 4 would be $23,000 - ($4,350 x 4) = $4,600.
b. To calculate the depreciation taken in the first year, we need to determine the number of months from January 1 to April 12, and then divide it by 12 (months in a year) to get the fraction of the year. The number of months is 4 (January to April), so the fraction of the year is 4/12 = 1/3. Using this fraction, the depreciation taken in the first year can be calculated by multiplying the depreciation per year ($4,350) by the fraction of the year (1/3). Therefore, the depreciation taken in the first year would be $4,350 x 1/3 = $1,450.