Max runs a car yard and needs to lodge depreciation records with the tax office, tonight. His asset management system has crashed and the gate padlock is electronic. Solve each asset calculation to restore the system and unlock the lot.
Progress
0%0 / 6 solved
1
Annual Depreciation, the first record
The first vehicle on the lot: a ute purchased for $20,000. Its useful life is 5 years and its scrap value is $5,000.
Use the straight-line formula to find the annual depreciation D in dollars.
D = (P − S) ÷ n = (20,000 − 5,000) ÷ 5 = ?
✓ Correct, D = $3,000 per year
2
Value after 4 years, the ute's current worth
The same ute (P = $20,000, D = $3,000/year) was purchased 4 years ago.
What is the ute's current value in dollars?
V = P − D × n = 20,000 − 3,000 × 4 = ?
✓ Correct, V = $8,000
3
End of life, when does the ute reach scrap value?
Max needs to flag when assets reach their scrap value. The same ute: P = $20,000, D = $3,000/year, S = $5,000.
After how many years does the ute reach its scrap value of $5,000?
Set V = S: 20,000 − 3,000 × n = 5,000. Solve for n.
✓ Correct, n = 5 years
4
Missing purchase price, the mystery sedan
The records for one sedan are incomplete. What's known: it has been depreciating for 3 years at $2,000 per year, and its current value is $11,000.
What was the sedan's original purchase price P?
Rearrange V = P − D × n → P = V + D × n
✓ Correct, P = $17,000
5
End-of-life value, the work truck
A work truck was purchased for $42,000 with a scrap value of $6,000 and a useful life of 6 years.
What is the truck's value at the end of its useful life (after 6 years)?
First find D = (P − S) ÷ n. Then V = P − D × 6. (This should equal the scrap value!)
✓ Correct, $6,000 (the scrap value, as expected!)
6
Tax threshold, below $10,000
Max needs to flag any vehicle once its book value falls below $10,000 for tax purposes. A vehicle was purchased for $28,000 with a scrap value of $4,000 and a useful life of 6 years.
After how many complete years does its value first fall below $10,000?
Find D = (28,000 − 4,000) ÷ 6 = 4,000. Then find the first n where 28,000 − 4,000 × n < 10,000.
✓ Correct, after 5 years (value = $8,000)
🔓 LOT UNLOCKED!
Max's system is restored, every depreciation record filed, every asset valued. The gate swings open and the tax deadline is met. Nailed it.