given these answers, answer c: In January, Rankine Company paid $10,200,000 for land and a building. An appraisal estimated that the land had a fair value of $3,000,000 and the building was worth $7,200,000. Rankine estimated that the useful life of the building was 30 years, with no residual value.


a. Calculate annual depreciation expense using the straight-line method.

$240000
b. Calculate depreciation for the ﬁrst and second year using the double-declining-balance method. Round to the nearest whole dollar amount.  Use rounded answers in subsequestion calculations.  

Year 1 $480000

Year 2 $448000

c. Assume that in the third year, Rankine changed its estimate of the useful life of the building to 25 years. If the company is using the double-declining-balance method of depreciation, what amount of depreciation expense would Rankine record in the third year?

Do not round until your final answer. Round answer to the nearest whole number.


Let's solve this step by step.

### Information we know:
- **Cost of the building**: $7,200,000 (based on the appraisal).
- **Original useful life**: 30 years.
- **Double-declining-balance method** is being used for depreciation.
- Depreciation for Year 1: $480,000.
- Depreciation for Year 2: $448,000.
- In the **third year**, the estimated useful life was changed to **25 years** (instead of 30).

### Step 1: Calculate the book value at the beginning of Year 3.
- Book value after Year 1 = $7,200,000 − $480,000 = **$6,720,000**.
- Book value after Year 2 = $6,720,000 − $448,000 = **$6,272,000**.

### Step 2: Determine the new depreciation rate for Year 3.
With the change in estimated useful life to 25 years, the **remaining useful life** at the beginning of Year 3 is now **23 years** (25 years minus 2 years of prior depreciation).

- The double-declining-balance method uses a rate that is **double** the straight-line rate.
- New straight-line rate = $ \frac{1}{25} $ = 4%.
- New double-declining rate = 4% × 2 = **8%**.

### Step 3: Calculate the depreciation expense for Year 3.
Now, apply the new double-declining rate (8%) to the book value at the beginning of Year 3:

\[
\text{Depreciation for Year 3} = 8\% \times 6,272,000 = 0.08 \times 6,272,000 = 501,760
\]

So, the depreciation expense for the third year is **$501,760** (rounded to the nearest whole number).

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Would you like more details or have any questions? 

Here are 5 related questions:
1. How is the straight-line method different from the double-declining-balance method?
2. How does changing the useful life affect depreciation calculations?
3. What would be the depreciation for Year 4 using the new useful life estimate?
4. What are some advantages of using the double-declining-balance method over other depreciation methods?
5. How do residual values impact depreciation in various methods?

**Tip**: When switching depreciation methods or changing estimates, always ensure that the accumulated depreciation doesn't exceed the asset's original cost.

In January, Rankine Company paid $10,200,000 for land and a building. An appraisal estimated that the land had a fair value of $3,000,000 and the building was worth $7,200,000. Rankine estimated that the useful life of the building was 30 years, with no residual value. Calculate annual depreciation expense using the straight-line method. Calculate depreciation for the first and second year using the double-declining-balance method. In the third year, Rankine changed its estimate of the useful life of the building to 25 years. What amount of depreciation expense would Rankine record in the third year using the double-declining-balance method?

Learn how to calculate the depreciation expense for Rankine Company's building using both the straight-line and double-declining-balance methods. This example covers calculating depreciation for the first two years and adjusting for a change in useful life in the third year, including detailed steps and formulas. Suitable for college-level accounting students.

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