Your ﬁrm needs a computerized line-boring machine which costs $80,000, and requires $20,000 in maintenance for each year of its three year life. After three years, the salvage value will be zero.
The machine falls into the Class 10 equipment category (CCA rate 30%). Assume a tax rate of 34%
And a discount rate of 10%.
Compute the depreciation tax shield for year 3.

Question

Quizplus · Accepted Answer

To find the depreciation tax shield for year 3, we need to first calculate the capital cost allowance (CCA) for year 3 using the declining balance method:
Year 1: $80,000 x 0.3 = $24,000
Year 2: ($80,000 - $24,000) x 0.3 = $16,800
Year 3: ($80,000 - $24,000 - $16,800) x 0.3 = $8,760

The tax shield for year 3 is the CCA for year 3 multiplied by the tax rate of 34%:
$8,760 x 0.34 = $2,978.40

However, we need to discount this tax shield back to present value using the discount rate of 10%. Using the formula for present value of a single amount, we get:
PV = FV / (1 + r)^n
where PV is present value, FV is future value, r is the discount rate, and n is the number of years.

PV = $2,978.40 / (1 + 0.1)^3 = $2,392.01

Therefore, the depreciation tax shield for year 3 is $2,392.01, which is closest to option C: $4,855.

Your ﬁRm Needs a Computerized Line-Boring Machine Which Costs $80,000