Question

The Solar Calculator Company proposes to invest $15 million in a new calculator-making plant. Fixed costs are $4 million per year. A solar calculator costs $20 per unit to manufacture and sells for $75 per unit. If the plant lasts for three years and the cost of capital is 5%, what is the break-even level (i.e., NPV = 0) of annual sales? Assume that revenues and costs occur at the end of each year. Assume no taxes and no depreciation.

	A.	133,000 units
	B.	172,875 units
	C.	175,500 units
	D.	244,000 units

Answer 1

Let the annual production is "P" units per annum.

Annual inflow: P* ( sale price- cost) - Fixed cost

Annual inflow: P* (75-20) - 4 million

For break- even point;

15 million = [P* (75-20) - 4 million] * PVAF@5%,3 year

15 million = [P* (75-20) - 4 million] * 2.7232

P* (75-20) - 4 million = 15 million / 2.7232

P* (75-20) - 4 million = 5.5082 million

P* (75-20) = 5.5082 million + 4 million

P* (75-20) = 9.5082 million

P = 9.5082 million / 55

P = 172,875 units

Hence, break even point is 172,875 units