Final answer:
To determine the break-even level of annual sales for the Solar Calculator Company, we calculate the quantity of units sold that results in a zero NPV over 3 years. The calculation takes into account the initial investment, fixed and variable costs, sale price per unit, and the 12% cost of capital. The break-even level is found to be 228,000 units.
Step-by-step explanation:
Break-Even Analysis for Solar Calculator Company
To find out the break-even level of annual sales for the Solar Calculator Company, we will calculate the quantity of units that need to be sold such that the Net Present Value (NPV) is zero. The company's initial investment is $5 million, fixed costs are $2 million per year, variable costs are $5 per unit, and each calculator sells for $20. Using a cost of capital of 12%, we can use the formula for NPV and set it to zero to find the break-even level of sales over the plant's 3-year life span.
The formula for NPV is:
NPV = R - C - (Fixed Costs + Variable Costs) / (1 + r)^n
Where R represents the revenue, C is the initial cost, r is the discount rate (cost of capital), and n is the number of years.
The revenue (R) per year can be calculated as the sale price per unit ($20) times the number of units sold (X), i.e., 20X. The variable costs can be calculated as the cost per unit ($5) times the number of units sold (X), i.e., 5X. The fixed costs are $2 million each year, and these do not change with the number of units sold.
To find the break-even level of sales, we set the NPV equal to zero:
0 = [20X - (5X + 2,000,000)] / 1.12 + [20X - (5X + 2,000,000)] / 1.12^2 + [20X - (5X + 2,000,000)] / 1.12^3 - $5,000,000
By solving this equation, we find that X, the number of units needed to break-even rounded to the nearest thousand, is 228,000 units.
Therefore, the correct answer is (d) 228,000 units.