Math Snap

STEP 1

What is this asking?
We've got a big, expensive piece of equipment and we need to figure out how its value goes down over time, then something happens and we need to recalculate!
Watch out!
Don't mix up the initial cost with the book value later on.
Also, remember that a change in estimate only affects future depreciation, not past.

STEP 2

1. Calculate Annual Depreciation
2. Calculate Book Value after 10 Years
3. Calculate Revised Annual Depreciation

STEP 3

Alright, let's start by figuring out how much the equipment depreciates each year initially.
This is called straight-line depreciation, which means the value decreases by the same amount every year.
It's like a steady, predictable decline.

STEP 4

The formula for straight-line depreciation is:
$$\text{Annual Depreciation} = \frac{\text{Cost} - \text{Residual Value}}{\text{Useful Life}}$$

STEP 5

Let's plug in the numbers we know.
The initial cost is $\$304,000$, the residual value (what it's worth at the end) is $\$41,600$, and the useful life is 16 years.

STEP 6

$$\text{Annual Depreciation} = \frac{\$304,000 - \$41,600}{16}$$

STEP 7

$$\text{Annual Depreciation} = \frac{\$262,400}{16}$$

STEP 8

$$\text{Annual Depreciation} = \$16,400$$

STEP 9

Great! Now we know the equipment loses $\$16,400$ in value each year.
So, after 10 years, how much value is left?
This is called the book value.

STEP 10

The formula for book value is:
$$\text{Book Value} = \text{Cost} - (\text{Annual Depreciation} \cdot \text{Years of Use})$$

STEP 11

Let's plug in our numbers:
$$\text{Book Value} = \$304,000 - (\$16,400 \cdot 10)$$

STEP 12

$$\text{Book Value} = \$304,000 - \$164,000$$

STEP 13

$$\text{Book Value} = \$140,000$$

STEP 14

Hold on!
At the start of the eleventh year, things change.
We now think the equipment will only last another 8 years and its final value will be $\$16,800$.
We need to recalculate the depreciation for these remaining years.

STEP 15

The book value at the end of year 10 becomes the new cost basis for the remaining life of the equipment.

STEP 16

The formula for the revised annual depreciation is:
$$\text{Revised Annual Depreciation} = \frac{\text{Book Value at End of Year 10} - \text{New Residual Value}}{\text{Remaining Useful Life}}$$

STEP 17

Let's plug in the new numbers.
The book value at the end of year 10 is $\$140,000$, the new residual value is $\$16,800$, and the remaining useful life is 8 years.

STEP 18

$$\text{Revised Annual Depreciation} = \frac{\$140,000 - \$16,800}{8}$$

STEP 19

$$\text{Revised Annual Depreciation} = \frac{\$123,200}{8}$$

STEP 20

$$\text{Revised Annual Depreciation} = \$15,400$$

a. The annual depreciation is $\$16,400$.
b. The book value at the end of the tenth year is $\$140,000$.
c. The depreciation expense for each of the remaining eight years is $\$15,400$.