Final answer:
The accounting break-even point is approximately 40,601 units. The degree of operating leverage at this point is undefined because fixed costs are zero at the break-even point. To analyze the base-case cash flow, sensitivity of NPV, and sensitivity of OCF, we need to carry out further calculations, including NPV using the discounted cash flows method.
Step-by-step explanation:
To solve the business scenario provided for evaluating a project, we must first calculate various financial metrics starting with the accounting break-even point. The accounting break-even point is the level of sales at which the project will make zero accounting profit, and is calculated by dividing the fixed costs plus depreciation by the contribution margin per unit, where the contribution margin per unit equals the price per unit minus the variable cost per unit. For this case, the depreciation is $845,000 divided by 8 years, or $105,625 per year. So fixed costs including depreciation are $950,000 + $105,625 = $1,055,625. With a price per unit of $53 and a variable cost per unit of $27, the contribution margin per unit is $53 - $27 = $26. Therefore, the accounting break-even point in units is $1,055,625 / $26 ≈ 40,601 units.
The degree of operating leverage at the break-even point is defined as the percentage change in operating income that results from a given percentage change in sales at the break-even level of sales. It can be calculated by taking the quantity at the break-even point multiplied by the contribution margin, divided by the quantity at the break-even point multiplied by the contribution margin minus the fixed costs (which are zero at the break-even point), which gives an indeterminate form. In practice, the degree of operating leverage can be found using alternative methods beyond the scope of this calculation.
To calculate the base-case cash flow, we subtract the fixed costs and depreciation from the total revenue and adjust for taxes. Total revenue is 51,000 units multiplied by the price of $53 per unit, equating to $2,703,000. Therefore, the base-case operating cash flow before taxes is $2,703,000 - $950,000 - $105,625 = $1,647,375. After applying the tax rate of 22%, the after-tax operating cash flow is $1,647,375 * (1-0.22) = $1,284,953. The net present value (NPV) can then be calculated using the discounted cash flows method, but the required cash flows for each year and the discount rate provided of 10% would be needed for complete calculation, which are not provided in this scenario.
The sensitivity of NPV to changes in the quantity sold can be examined by recalculating the NPV using different quantities sold and observing the change in NPV compared to the change in quantity. Similarly, the sensitivity of operating cash flow (OCF) to changes in the variable cost can be investigated by adjusting the variable cost per unit and recalculating the operating cash flow to see how it is affected.