Question

You are considering a new product launch. The project will cost $2,075,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 220 units per year; price per unit will be $18,800, variable cost per unit will be $12,350, and fixed costs will be $610,000 per year. The required return on the project is 11 percent, and the relevant tax rate is 25 percent.

a. Based on your experience, you think the unit sales, variable cost, and fixed cost projections given here are probably accurate to within ±10 percent. What are the upper and lower bounds for these projections? What is the base-case NPV? What are the best-case and worst-case scenarios? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round your NPV answers to 2 decimal places, e.g., 32.16. Round your other answers to the nearest whole number, e.g. 32.)
b. Evaluate the sensitivity of your base-case NPV to changes in fixed costs. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c. What is the cash break-even level of output for this project (ignoring taxes)? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
d-1. What is the accounting break-even level of output for this project? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
d-2. What is the degree of operating leverage at the accounting break-even point? (Do not round intermediate calculations and round your answer to 3 decimal places, e.g., 32.161.)

Answer 1

Total costs combine fixed and variable costs, as shown in the example of a barbershop. The total cost curve starts with fixed costs at zero production, with variable costs added as production increases. Average variable costs get closer to average total costs as output grows because fixed costs distribute over more units.

Step-by-step explanation:

Total costs include both fixed costs and variable costs. To compute total costs at a barbershop as an example, if the fixed costs for space and equipment are $160 per day, and each barber hired incurs an additional $80 in variable costs, hiring two barbers would lead to variable costs of $160 (2 × $80). Therefore, the total cost with two barbers would be $320 ($160 fixed + $160 variable).

At zero production, the fixed cost remains the same, while variable costs increase with output level. The total cost curve will always start at the fixed cost value when output is zero. The curve for average total costs will always be above the curve of average variable costs because it includes both average variable and fixed costs.

As more goods are produced, the average variable cost may approach the average total cost, due to fixed costs spreading over a larger output, thereby decreasing its significance per unit. For instance, if the cost for 80 haircuts is $400 in variable costs, the average variable cost is $5 per haircut. If the total cost at that output level is $640, then the average total cost is $8 per haircut.