Toronto Skates Corp.is considering a five-year project that requires an initial investment of $250,000.The project is expected to generate operating incomes of $60,000 in year 1, $90,000 in year 2, $150,000 in year 3, $100,000 in year 4, and $80,000 in year 5.The asset belongs to asset class 7, which has a CCA rate of 15%.The firm's marginal tax rate is 35% and cost of capital is 10%.Ignoring CCA, what is the present value of the after-tax operating cash flows?

Question

Quizplus · Accepted Answer

We need to calculate the present value of after-tax operating cash flows. To do that, we need to calculate the after-tax operating cash flow for each year first:
Year 1: $60,000 x (1 - 0.35) = $39,000
Year 2: $90,000 x (1 - 0.35) = $58,500
Year 3: $150,000 x (1 - 0.35) = $97,500
Year 4: $100,000 x (1 - 0.35) = $65,000
Year 5: $80,000 x (1 - 0.35) = $52,000

Next, we need to discount each of these cash flows to the present using the cost of capital of 10%. Using the present value formula for annuity, we get:

PV = CF x [(1 - (1 / (1 + r)t )) / r]

PV of Year 1 = $39,000 x [(1 - (1 / (1 + 0.1)1 )) / 0.1] = $35,455
PV of Year 2 = $58,500 x [(1 - (1 / (1 + 0.1)2 )) / 0.1] = $46,418
PV of Year 3 = $97,500 x [(1 - (1 / (1 + 0.1)3 )) / 0.1] = $70,999
PV of Year 4 = $65,000 x [(1 - (1 / (1 + 0.1)4 )) / 0.1] = $43,121
PV of Year 5 = $52,000 x [(1 - (1 / (1 + 0.1)5 )) / 0.1] = $32,745

Finally, we add up all the present values to get the total PV of after-tax operating cash flows:

Total PV = $35,455 + $46,418 + $70,999 + $43,121 + $32,745 = $228,738

However, since the asset belongs to asset class 7, we also need to consider the effect of CCA. The CCA rate is 15%, which means in the first year, we can claim CCA of $37,500 ($250,000 x 15%). This will reduce our taxable income and hence reduce the amount of taxes we need to pay. The tax savings from CCA can be calculated as:

Tax savings = CCA x tax rate = $37,500 x 0.35 = $13,125

Adding this tax savings to the after-tax operating cash flow of Year 1, we get:

Revised after-tax operating cash flow of Year 1 = $39,000 + $13,125 = $52,125

Now, we can recalculate the present value of after-tax cash flows using this revised cash flow for Year 1. Using the same formula as above, we get:

Revised PV of Year 1 = $52,125 x [(1 - (1 / (1 + 0.1)1 )) / 0.1] = $47,730

The total present value of after-tax operating cash flows with the effects of CCA is:

Total PV = $47,730 + $46,418 + $70,999 + $43,121 + $32,745 = $241,013

Therefore, the best choice is B.