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timberly construction makes a lump - sum purchase of several assets on january 1 at a total cash price of $810,000. the estimated market values of the purchased assets are building, $444,150; land, $292,950; land improvements, $28,350; and four vehicles, $179,550.
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compute the first - year depreciation expense on the building using the straight - line method, assuming a 15 - year life and a $30,000 salvage value.
note: round your answer to the nearest whole dollar.

Explanation:

Step1: Calculate total market value

First, we need to find the total market value of all the assets. The market values are: building (\$444,150), land (\$292,950), land improvements (\$28,350), and four vehicles (\$179,550). So we sum these up:
$$444150 + 292950 + 28350 + 179550$$
$$= (444150 + 292950) + (28350 + 179550)$$
$$= 737100 + 207900$$
$$= 945000$$

Step2: Allocate cost to building

The total cash price is \$810,000. We allocate the cost to the building based on its proportion of the total market value. The proportion of the building's market value to the total market value is $\frac{444150}{945000}$. Then the cost of the building is this proportion times the total cash price:
$$\text{Building Cost} = 810000 \times \frac{444150}{945000}$$
Simplify the fraction $\frac{444150}{945000}$: divide numerator and denominator by 150, we get $\frac{2961}{6300}$, then divide by 3, we get $\frac{987}{2100}$, then divide by 3 again, we get $\frac{329}{700}$. So:
$$810000 \times \frac{329}{700} = \frac{810000 \times 329}{700}$$
Calculate 810000 ÷ 700 ≈ 1157.1429, then multiply by 329: 1157.1429 × 329 ≈ 380,700 (let's check: 444150/945000 = 0.47, 810000 × 0.47 = 380700. Yes, that's correct. Because 444150 ÷ 945000 = 0.47, since 945000 × 0.47 = 945000 × 0.4 + 945000 × 0.07 = 378000 + 66150 = 444150. So the building cost is 810000 × 0.47 = 380700.

Step3: Calculate annual depreciation

Using the straight-line depreciation formula: $\text{Depreciation Expense} = \frac{\text{Cost} - \text{Salvage Value}}{\text{Useful Life}}$. The cost of the building is \$380,700, salvage value is \$30,000, useful life is 15 years. So:
$$\text{Depreciation Expense} = \frac{380700 - 30000}{15}$$
$$= \frac{350700}{15}$$
$$= 23380$$

Answer:

23380