Question

Problem 5-4

A small firm intends to increase the capacity of a bottleneck operation by adding a new machine. Two alternatives, A and B, have been identified, and the associated costs and revenues have been estimated. Annual fixed costs would be $37,000 for A and $31,000 for B; variable costs per unit would be $9 for A and $11 for B; and revenue per unit would be $19.

    

a.	Determine each alternative’s break-even point in units. (Round your answer to the nearest whole amount.)

    

QBEP,A	units
QBEP,B	units

   

b.	At what volume of output would the two alternatives yield the same profit? (Round your answer to thenearest whole amount.)

    

Profit

units

   

c.	If expected annual demand is 15,000 units, which alternative would yield the higher profit?

    

Higher profit

(Click to select)BA

Answer 1

Given values:

Annual fixed costs for A = $37,000

Annual fixed costs for B = $31,000

Variable cost for A = $9 per unit

Variable cost for B = $11 per unit

Revenue = $19 per unit

Solution:

(a) At Break-even point (BEP), total revenue is equal to total costs.

Total Revenue = Total Costs

Alternative A:

Let the number of units = x

Total Revenue = Total Costs

$19x = $37,000 + $9x

x = 3,700

QBEP(A) = 3700 units

Alternative B:

Let the number of units = x

Total Revenue = Total Costs

$19x = $31,000 + $11x

x = 3,875

QBEP(B) = 3875 units

(b) Profit is calculated as;

Profit = Total Revenue - Total Costs

Let the volume of output at which both the alternatives yield the same profit = x

Profit (A) = Profit (B)

Total Revenue (A) - Total Costs (A) = Total Revenue (B) - Total Costs (B)

$19x - ($37,000 + $9x) = $19x - ($31,000 + $11x)

$37,000 + $9x = $31,000 + $11x

x = 3000

Volume of output at which the two alternatives would yield the same Profit = 3000 units

(c) Expected annual demand = 15,000 units

Profit of Alternative A:

Profit = Total Revenue (A) - Total Costs (A)

Profit = $19x - ($37,000 + $9x)

Profit = ($19 x 15000) - [$37,000 + ($9 x 15000)]

Profit = $113,000

Profit of Alternative B:

Profit = Total Revenue (B) - Total Costs (B)

Profit = $$19x - ($31,000 + $11x)

Profit = ($19 x 15000) - [$31,000 + ($11 x 15000)]

Profit = $89,000

At 15,000 units, Higher profit = Alternative A