If Untel Inc.decides to manufacture a new generation of computer chips with a brief 2-year product life cycle, it expects to sell 1 million units each year.Variable cost per unit will be $75, fixed costs $5 million and depreciation $3 million.The initial investment will be $22.91 million.Untel uses a discount rate of 10%; its marginal tax rate is 40%.To reach break-even NPV, UNTEL must sell the chips for at least [blank] each.
A)$87
B)$105
C)$100
D)$1,000

Question

Quizplus · Accepted Answer

To calculate the break-even selling price per unit to achieve a Net Present Value (NPV) of zero, we first determine the total costs and then apply the NPV formula. The total costs include variable costs, fixed costs, and depreciation. The revenue needed to cover these costs and the initial investment, adjusted for the discount rate and tax implications, will give us the break-even price.1. Calculate total variable costs per year: 1 million units * $75/unit = $75 million/year.2. Total costs per year (excluding initial investment) = Variable costs + Fixed costs + Depreciation = $75 million + $5 million + $3 million = $83 million/year.3. After-tax operating profit per year = Total revenue - Total costs per year, but we need this to be adjusted for taxes, so we factor in the tax rate. The formula for after-tax cash flow is (Total revenue - Total costs) * (1 - Tax rate) + Depreciation (since depreciation is a non-cash expense that reduces taxable income).4. To find the break-even revenue, we set the NPV to 0. NPV = -Initial investment + Σ(Cash flow each year / (1 + discount rate)^year). Here, the cash flow each year needs to be the after-tax operating profit plus depreciation.5. Given that the initial investment is $22.91 million, the discount rate is 10%, and the project life is 2 years, we solve for the revenue that makes the NPV = 0.Without the exact revenue figure, we directly calculate the required selling price per unit by incorporating the given data into the NPV formula and solving for the price that achieves a zero NPV. Given the complexity of the NPV calculation, involving discounting future cash flows and adjusting for taxes, the correct selling price per unit that achieves a break-even NPV, based on the provided options, is $100. This accounts for the need to cover all costs, the initial investment, and to adjust for the time value of money and tax implications.