Your ﬁrm needs to either buy or lease $230,000 worth of vehicles. These vehicles have a life of 4 years after which time they are worthless. The vehicles belong in CCA class 10 (a 30% class) and
Can be leased at a cost of $68,000 a year for the 4 years. The corporate tax rate is 34% and the
Cost of debt is 10%.
What is the present value of the depreciation tax shield?

Question

Quizplus · Accepted Answer

To calculate the present value of the depreciation tax shield, we need to calculate the depreciation expense for each year and the tax savings from the depreciation expense.

For CCA class 10, the annual depreciation rate is 30%, so the annual depreciation expense is $69,000 ($230,000 x 30%).

The tax savings from the depreciation expense is equal to the depreciation expense multiplied by the corporate tax rate, so the annual tax savings is $23,460 ($69,000 x 34%).

To calculate the present value of the tax shield, we need to discount each year's tax savings to its present value using the cost of debt.

PV of Year 1 tax savings = $23,460 / (1 + 10%)^1 = $21,327.27

PV of Year 2 tax savings = $23,460 / (1 + 10%)^2 = $18,479.34

PV of Year 3 tax savings = $23,460 / (1 + 10%)^3 = $15,957.69

PV of Year 4 tax savings = $23,460 / (1 + 10%)^4 = $13,743.11

Total present value of the tax shield = $69,507.41

Comparing the present values of leasing versus buying, we can see that leasing provides a tax shield of $69,507.41 over the four-year period. However, if we buy the vehicles, we will have an initial tax shield of $79,200 ($230,000 x 34% x 30%), but we will also have to factor in the opportunity cost of using the $230,000 for the purchase versus investing it elsewhere.

Therefore, based solely on the calculation of the present value of the depreciation tax shield, the best choice is to lease the vehicles.

Your ﬁRm Needs to Either Buy or Lease $230,000 Worth