Question

We are evaluating a project that costs $844,764, has an eight-year life, and has no salvage value. Assume that depreciation is straight-line to zero over the life of the project. Sales are projected at 63,149 units per year. Price per unit is $40, variable cost per unit is $21, and fixed costs are $415,308 per year. The tax rate is 35%, and we require a return of 20% on this project. In dollar terms, what is the sensitivity of NPV to changes in the units sold projection? The sensitivity is just the first order condition in the calculus. For example, in our question, the sensitivity of NPV changes associate change in the units sold as an example. The sensitivity means the NPV changes associate 1% change in units sold. Thus, the change starting points and ending points will not affect the question. (Round answer to 0 decimal places. Do not round

Answer 1

The sensitivity of NPV to changes in the units sold projection for a business project can be calculated by analyzing the impact of a 1% change in sales volume, considering the price per unit, variable costs, fixed costs, tax rate, and required rate of return.

Step-by-step explanation:

We are tasked with evaluating the sensitivity of the Net Present Value (NPV) to changes in the projection of units sold for a particular project. The calculation of NPV sensitivity to sales volume provides insights into the project's risk profile, especially if revenue projections do not go as planned. Considering the provided information, with sales projected at 63,149 units per year, a price per unit of $40, variable cost per unit of $21, and fixed costs of $415,308 per year, the NPV sensitivity can be found by analyzing the impact of a 1% change in units sold on the overall NPV of the project.

Given that the project has an eight-year life and employs straight-line depreciation, the annual depreciation expense would be $844,764 / 8 years = $105,595. With the provided details, we can calculate the project's revenue, expenses, taxable income, and ultimately NPV. The sensitivity of NPV to unit changes involves the derivative of NPV with respect to sales volume, taking into account the unit contribution margin (price per unit minus variable cost per unit) and marginal tax rate, among other factors.To apply this to the change in NPV per unit sold, we must understand the contribution margin, which is the price per unit minus variable cost per unit, and then determine its impact post-tax. To do so, we calculate the incremental pre-tax profit from selling one additional unit, which is $(40 - $21), and then adjust it for the tax rate. After taxes, the profit per additional unit would be $(19 × 0.65). We multiply this amount by the number of units for which we want to determine the sensitivity (1% of 63,149 units is 631.49 units) and discount this value back over the life of the project to calculate the effect on NPV.