Question

The University is considering a four-year promotional campaign to sell a new brand of hot dog at home football games. The campaign requires an up-front investment of $1,000,000 and will generate sales over four years.

If the marginal cost of each sale is constant at $1, and the price is $3, how many sales must be made each year for the University to break-even? (Assume a discount rate of 5%).

If the University can sell 300,000 units per year, what is the break-even price? (Assume a discount rate of 5%).

Answer 1

There is a four-year promotional campaign that requires an initial investment of $1,000,000. The marginal cost of each sale is constant at $1, and the price is $3. Let the sales that must be made each year for the University to break-even be X. Break even implies that annual equivalent value of the cost and revenues are same. This implies that

3X = 1000,000(A/P, 5%, 4) + X

2X = 1000,000*0.28201

This gives required annual sales to be X = 141006.

If the University can sell 300,000 units per year, the break-even price is

300,000P = 1000,000(A/P, 5%, 4) + 300,000

300,000P = 1000,000*0.28201 + 300,000

P* = 1.94.