Answer:
Residual Value = $5,400
Explanation:
At first, we have to calculate the cost of equipment.
Using double-declining method,
The depreciation as per 2023 = $30,000.
The depreciation rate to use the double-declining method = (100%/Useful life) x 2 = (100%/8) x 2 = 25%
Therefore, the beginning balance of equipment in 2023 (or, the ending balance in 2022) = [tex]\frac{30,000}{0.25}[/tex]
The beginning balance of equipment in 2023 = $120,000
Using the same approach,
The beginning balance of equipment in 2022 (Or, the purchasing price) =
Depreciation = Purchase price x 25%
since the purchase price and depreciation are unknown, therefore, we use,
Ending value in 2022 = Purchase price x (100% - 25%) (Depreciation rate is 100%)
or, $120,000 = Purchase price x 75%
or, Purchase price = $120,000/0.75 = $160,000
Now, using the straight-line method,
Useful life = 8 years
Purchase price = $160,000
Book value after 4 years (As of December 2025, the equipment was purchased in January 2022) = $82,700
Therefore, accumulated depreciation = $160,000 - 82,700 = $77,300 for 4 years.
As the straight-line method depreciation is same for each year,
the depreciation for the first year = [tex]\frac{77,300}{4}[/tex] = $19,325
According to the straight-line method,
Depreciation = [tex]\frac{Purchase price - Residual value}{Useful life}[/tex]
or, $19,325 = [tex]\frac{160,000 - Residual Value}{8}[/tex]
or, $19,325 x 8 = $160,000 - Residual value
or, Residual Value = $160,000 - $154,600
Hence, Residual value = $5,400
