Question

Lena Horn bought a Toyota Tundra on January 1 for $23,000 with an estimated life of 4 years. The residual value of the truck is $4,600. Assume a straight-line method of depreciation.

a. What will be the book value of the truck at the end of year 4?
b. If the Tundra was bought the first year on April 12, how much depreciation would be taken the first year?

Answer 1

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.

Answer 2

The book value of the Toyota Tundra at the end of year 4 will be $4,600, calculated using the straight-line depreciation method. If purchased on April 12 of the first year, the depreciation would be $3,326.40, considering partial year usage.

Step-by-step explanation:

The depreciation for Lena Horn's Toyota Tundra, which was purchased for $23,000 with an estimated life of 4 years and a residual value of $4,600, can be calculated using the straight-line method.

a. To determine the book value at the end of year 4, subtract the total depreciation over the 4-year life of the truck from the original cost. Using the straight-line depreciation formula:

1. Calculate the annual depreciation: (Cost - Residual Value) / Estimated Life = ($23,000 - $4,600) / 4 = $4,600 per year.
2. Calculate the total depreciation over 4 years: Annual Depreciation * Life = $4,600 * 4 = $18,400.
3. Subtract the total depreciation from the original cost to obtain the book value at the end of year 4: Cost - Total Depreciation = $23,000 - $18,400 = $4,600.

b. If the Tundra was bought on April 12, the depreciation for the first year would be calculated for the portion of the year the vehicle was in use. Since there are 365 days in a year and the truck was not in use for the entire year, you would calculate the daily depreciation first (Annual Depreciation / 365), and then multiply it by the number of days the vehicle was in use (365 - (Jan 1 to Apr 12)). Here's the calculation:

1. Daily Depreciation = $4,600 / 365 = $12.60 per day
2. Number of days from April 12 to December 31 = 264
3. Depreciation for the first year = Daily Depreciation * Number of days in use = $12.60 * 264 = $3,326.40