Question

3. Page’s firm is starting out, and he is not sure how much of the firm’s product he will be able to sell. He can begin with three alternative levels of capacity: 0-20,000 units (low), 0-40,000 units (medium), or 0-60,000 units (high). The total fixed costs depend on the capacity level chosen: $50,000 (low), $80,000 (medium), or $100,000 (high). Page is sure that at all levels of production and sales, the sales price, unit variable manufacturing and unit variable selling costs will be $10, $5, and $1, respectively. Also, Page only produces units as demanded by customers.

1. For each level of capacity, what is the break-even point in units?

2. Suppose Page can sell as much as he wants within each capacity level. Which level of capacity leads to highest profits?

3. As discussed in class, the choice of capacity level is not a trivial task. If Page chooses too low a capacity level, then he risks losing out on potential sales. But, if Page chooses too high a capacity level, then he risks incurring a loss if demand is low. Over what range of demand is the low capacity level optimal? What about the medium capacity level? Finally, what about the high capacity level?

Answer 1

Ans.   a) Calculation of Breakeven point at each level of productions

  

BEP = Fixed cost /contribution per unit

Contribution per unit = Sales -Variable cost per unit

   = 10-4-1 = 4 per unit

BEP at 0-20000 unit capacity = 50000/4 = 12500 units

BEP at 0-40000 unit capacity = 80000/4 = 20000 units

BEP at 0-60000 unit capacity = 100000/4 =25000 units

b) Calculation of highest profit level capacity

Step: 1 calculation of contribution at each capacity level

0-20000 unit capacity = 20000X4 = 80000

0-40000 unit capacity = 40000X4 = 160000

0-60000 unit capacity = 60000X4 = 240000

Step :2 profit at each capacity level (contribution -fixed cost)

0-20000 unit capacity = 80000 -50000 = 30000

0-40000 unit capacity = 160000-80000 = 80000

0-60000 unit capacity = 240000-100000= 140000

Highest profit capacity level is 0-60000

c) Optimal Range of demand at low risk level = 12500-20000 units

Optimal range of demand at medium risk level = 20000-40000 units

Optimal range of demand at high risk level = 25000 to 60000 units