Using the annual unit sales and the probabilities given for each possible sales volume, we first calculate the expected sales as a weighted average: (80,000 × .10) + (85,000 × .20) + (90,000 × .30) + (95,000 × .20) + (100,000 × .10) + (110,000 × .10) = 92,000 units. Expected sales of 92,000 units × $5 per unit contribution margin = $460,000 net annual cash flow before tax. $460,000 × (1 ? .40) = $276,000 net annual cash flow after tax. The depreciation tax shield is $1,000,000 / 5 = annual depreciation of $200,000, and $200,000 × .40 = the depreciation tax shield of $80,000 per year. So the net annual after-tax cash flow for each of the 5 years is $276,000 + $80,000, which is $356,000. Discounting $356,000 using the PV of an annuity factor for 12% for 5 years, we have $356,000 × 3.605, which is $1,283,380. $1,283,380 – the initial investment of $1,000,000 = NPV of $283,380.
This answer results from using a simple average of the various possible annual unit sales as the expected sales used in calculating the net present value of the project. The expected sales should be a weighted average of the possible annual unit sales, weighted according to probabilities.
This answer results from using the annual unit sales with the highest probability of occurring (90,000) as the expected sales used in calculating the net present value of the project. The expected sales should be a weighted average of the possible annual unit sales, weighted according to probabilities.
This answer results from multiplying the annual projected depreciation ($200,000) by 1 ? the tax rate to calculate the annual depreciation tax shield. To calculate the depreciation tax shield, the annual depreciation should be multiplied by the tax rate, not 1 ? the tax rate.
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If Long utilizes a 12% hurdle rate and is subject to a 40% effective income tax rate, the expected net present value of the project would be