Suppose a five-year project requires an initial capital investment of $600,000 and an initial net working capital investment of $30,000.The project is expected to provide operating revenue of $400,000 per year.The associated operating costs are expected to be $175,000 per year.The capital asset belongs to Class 7 and has a CCA rate of 15%.The asset is expected to sell for $168,000 when the project terminates.Assume the asset class remains open after the project ends and that the half-year rule applies in the first year.The firm's marginal tax rate is 40% and cost of capital is 10%.What impact would it have on the project's NPV if the operating revenue falls by 5%?

Question

Quizplus · Accepted Answer

First, let's calculate the initial investment outflow:
Initial investment = Initial capital investment + Initial net working capital investment
Initial investment = $600,000 + $30,000
Initial investment = $630,000

Next, let's calculate the annual operating cash flows:
Operating cash inflow = Operating revenue - Operating costs
Operating cash inflow = $400,000 - $175,000
Operating cash inflow = $225,000

Now, let's calculate the CCA tax shield:
CCA tax shield = CCA rate x Capital asset value
CCA tax shield = 0.15 x ($600,000 - $30,000)
CCA tax shield = $82,500

Using these values, we can calculate the project's NPV:
NPV = -Initial investment + PV of annual operating cash flows + PV of terminal cash flow + PV of CCA tax shield
NPV = -$630,000 + ($225,000 / 0.1) x [1 - (1 / (1 + 0.1)^5)] + ($168,000 / (1 + 0.1)^5) + ($82,500 / (1 + 0.4))
NPV = -$630,000 + $658,730.65 + $90,123.41 + $31,250
NPV = $149,104.06

If the operating revenue falls by 5%, the new operating revenue will be $380,000 per year. Recalculating the NPV with this new value, we get:
NPV = -$630,000 + ($205,000 / 0.1) x [1 - (1 / (1 + 0.1)^5)] + ($168,000 / (1 + 0.1)^5) + ($82,500 / (1 + 0.4))
NPV = -$630,000 + $500,063.09 + $90,123.41 + $31,250
NPV = $-8,563.50

The decrease in NPV is calculated as follows:
Decrease in NPV = (New NPV - Original NPV) / Original NPV
Decrease in NPV = (-$8,563.50 - $149,104.06) / $149,104.06
Decrease in NPV = 38.84%

Therefore, the correct answer is B. The NPV decreases by 38.84% if the operating revenue falls by 5%.

Suppose a Five-Year Project Requires an Initial Capital Investment of $600,000