You are considering investing in a piece of equipment to implement a cost-cutting proposal. The pre-tax cost reduction is expected to equal $41.67 for each of the three years of the project's life.
The equipment has an initial cost of $125 and belongs in a 20% CCA class. Assume a 34% tax
Bracket, a discount rate of 15%, and a salvage value of zero.
What is the annual after-tax cost reduction for the project?

Question

Quizplus · Accepted Answer

Step 1: Calculate the CCA deduction for the first year:
CCA rate = 20%
CCA deduction = $125 x 20% = $25

Step 2: Calculate the tax shield for the first year:
Tax shield = $25 x 34% = $8.50

Step 3: Calculate the cash inflow for the first year:
Cash inflow = $41.67 - $8.50 = $33.17

Step 4: Calculate the present value of the cash inflows:
PV = $33.17 / (1 + 15%) = $28.80

Step 5: Calculate the annuity factor for three years at 15%:
Annuity factor = (1 - 1 / (1 + 15%)^3) / 15% = 2.2838
(The annuity factor can also be taken from financial tables.)

Step 6: Calculate the present value of the cost:
PV of cost = -$125

Step 7: Calculate the net present value:
NPV = PV of cash inflows + PV of tax shield + PV of CCA deduction + PV of salvage value + PV of cost
NPV = $28.80 + $8.50 / (1 + 15%) + $25 / (1 + 15%) + $0 + (-$125) = -$72.52

Since the NPV is negative, the project should not be undertaken. Therefore, the best choice is not to invest in the piece of equipment.

You Are Considering Investing in a Piece of Equipment to Implement