Questions: UNIT 4 - CHALLENGE 4.1: Depreciation Using double declining balance depreciation, the book value of the machine at the end of year two will be a.) 360,000 b.) 486,000 c.) 540,000 d.) 426,000

Solution Steps

The double declining balance (DDB) method is an accelerated depreciation method. It calculates depreciation at twice the straight-line rate. The formula for the DDB method is:

$$\text{Depreciation Expense} = 2 \times \text{Straight-Line Rate} \times \text{Book Value at Beginning of Year}$$

Assuming the machine has a useful life of $n$ years, the straight-line rate is:

$$\text{Straight-Line Rate} = \frac{1}{n}$$

For this problem, we need the useful life of the machine to proceed. However, since it is not provided, we will assume a typical useful life for machinery, such as 5 years, for demonstration purposes.

$$\text{Straight-Line Rate} = \frac{1}{5} = 0.2$$

The double declining rate is twice the straight-line rate:

$$\text{Double Declining Rate} = 2 \times 0.2 = 0.4$$

Assuming the initial cost of the machine is $C$, the depreciation for the first year is:

$$\text{Depreciation Year 1} = 0.4 \times C$$

The book value at the end of year 1 is:

$$\text{Book Value Year 1} = C - 0.4 \times C = 0.6 \times C$$

The depreciation for the second year is based on the book value at the end of year 1:

$$\text{Depreciation Year 2} = 0.4 \times (0.6 \times C) = 0.24 \times C$$

The book value at the end of year 2 is:

$$\text{Book Value Year 2} = 0.6 \times C - 0.24 \times C = 0.36 \times C$$

To find the book value at the end of year 2, we need the initial cost $C$. Since the options are given, we can assume the initial cost is such that one of the options matches the calculated book value.

Final Answer