Question

A farm machine cost ₦300000 with a salvage value of ₦50000 at the end of its life for 10 years. If money is worth 6% annually, use sinking fund method and determine the annual depreciation of the asset, the total depreciation and the book value

Answer 1

First, we need to calculate the sinking fund factor (SFF) using the formula:

SFF = (i * (1 + i)^n) / ((1 + i)^n - 1)

Where:
i = annual interest rate = 6% or 0.06
n = number of years = 10

SFF = (0.06 * (1 + 0.06)^10) / ((1 + 0.06)^10 - 1)
SFF = (0.06 * (1.06)^10) / ((1.06)^10 - 1)
SFF = (0.06 * 1.790847) / (2.673012 - 1)
SFF = 0.10745 / 1.673012
SFF = 0.064235

Next, we can calculate the annual sinking fund depreciation using the formula:

Annual sinking fund depreciation = (Cost - Salvage Value) * SFF

Annual sinking fund depreciation = (₦300,000 - ₦50,000) * 0.064235
Annual sinking fund depreciation = ₦250,000 * 0.064235
Annual sinking fund depreciation = ₦16,087.5

The total depreciation over 10 years will be:
Total depreciation = Annual sinking fund depreciation * number of years
Total depreciation = ₦16,087.5 * 10
Total depreciation = ₦160,875

Finally, we calculate the book value each year:
Book value = Cost - Total depreciation for that year

Year 1:
Book value = ₦300,000 - ₦16,087.5
Book value = ₦283,912.5

Year 2:
Book value = ₦283,912.5 - ₦16,087.5
Book value = ₦267,825

Continue this calculation for each year up to year 10 to determine the book value at the end of each year.