Page - Stevenson, Chapter 5, Strategic Capacity Planning

Evaluating Capacity Alternatives (Problems 1 & 3, in class; problems 4 & 5 HW)

Fixed Costs (FC): Rent, insurance, utilities,

Variable Costs (VC): costs to produce

Total Costs (TC) = FC + (VC * Quantity)

Total Revenue (TR) = Revenue * Q

Profit (P) = TR - TC

P= (R * Q) – ((FC +(VC * Q))

## P= Q (R – VC) – FC

Quantity for Breakeven Point (QBEP)

QBEP is where TR=TC

QBEP = FC

R - VC

In a capacity decision, would you want to purchase a machine with a capacity less than QBEP? Why or why not?

Quantity Needed for a specified level of profitability

Q = P + FC

R - VC

How does this relate to capacity decisions?

## Example

Page 192, Number 3

FC = \$9,200/month

VC = \$.70/unit

Price (Revenue) = \$.90/unit

1. determine the volume/month required to breakeven

QBEP = FC

R – VC

= \$ 9,200

.90 -.70

= \$9,200

.20

= 46,000 pieces of pottery per month

What if the property being considered has a maximum capacity of 40,000 pieces of pottery/month. What is your recommendation?

1. What profit would be realized on a monthly volume of 61,000 pieces? Of 87,000 pieces?

P = Q ( R – VC) – FC

P = 61, 000 (.90-.70) – 9,200

P = 61,000(.20) – 9,200

P = 12,200 – 9,200

P= \$3,000

Profit for a volume of 87,000 pieces of pottery

P = Q ( R – VC) – FC

P = 87,000 (.90-.70) – 9,200

P = 87,000 (.20) – 9,200

P = \$17,400 - \$9,200

P = \$8,200

C. what volume is needed to obtain a profit of \$16,000/month

Q = P + FC

R - VC

Q = 16, 000 + 9,200

.90 - .70

Q = 25,200

.20

Q= 126, 000 Units

D. what volume is needed to provide revenue of \$23,000 per month?

TR = R * Q

\$23,000 = .90 * Q

23,000 = .90Q

.90 .90

Q= 25, 555.5

E. Plot TC and TR. Where do you get your values for TC and TR? Pick quantities above and below the breakeven point (46, 000 pieces), such as 10,000, 15,000, 20,000, 50,000 and 60,000 and solve TC and TR for those quantities. Plot both TC and TR with quantity on the x-axis and \$ on the y-axis.

## TC = FC + (VC * Q)TR = R * Q

TC 10,000 pieces = 9,200 + (.70 * 10,000) TR10,000pieces = .90 * 10,000

TC 10,000 pieces = \$16,200 TR10,000pieces = \$9,000

At a production quantity of 10,000 pieces, are we making money? How much?

TC 20,000 pieces = 9,200 + (.70 *20,000)TR 20,000 pieces = .90 * 20,000

TC 20,000 pieces = \$23,200 TR 20,000 pieces = \$18,000

TC 60,000 pieces = 9,200 + (.70 *60,000)TR 60,000 pieces = .90 * 60,000

TC 60,000 pieces = \$51,200 TR 60,000 pieces = \$54,000

## Total Cost and Total Revenue Plot

\$

70,000 |

|

60,000|

|

50,000|

|

40,000|

|

30,000|

|

20,000|

|

10,000|

|

0|______

5101520253035404550

Quantity (in thousands)

Problem 1

1. Determine the utilization and efficiency for each situation:

Utilization = Actual Output

Design capacity

Efficiency =Actual Output

Effective capacity

a. a loan processing operation that processes an average of 7 loans/day. The operation has a design capacity of 10 loans per day and an effective capacity of 8 loans/day.

Utilization = 7 loans/day = .70 or 70%

10 loans/day

What could cause the utilization to be less than 100%?

Efficiency = 7 loans/day = .875 or 87.5%

8 loans/day

b. a furnace repair team that services an average of four furnaces a day if the design capacity is six furnaces a day and the effective capacity is five furnaces per day.

Utilization = 4 furnaces/day = .6666 or 66.67%

6 furnaces/day

Efficiency = 4 furnaces/day = .80 or 80%

6 furnaces/day

c. Would you say that systems that have higher efficiency ratios than other systems will always have higher utilization ratios than other systems? Explain.

Problem 4

A small firm intends to increase the capacity of a bottleneck operation by adding a new machine. Two alternatives A & B have been identified and the costs and revenues associated with each have been estimated. Annual fixed costs for A would be \$40,000 and \$30,000 for B; Variable costs per unit would be \$10 for A and \$11 for B; and revenue per unit would be \$15.

Machine AMachine B

FC = \$40,000FC=\$30,000

v=\$10v=\$11

R=\$15R=\$15

(a) Determine each alternative’s Break-even point in units.

QBEP = FC

R – VC

Machine AMachine B

QBEP = FC QBEP = FC

R – VC R – VC

QBEP = 40,000 QBEP = 30,000

15-10 15 – 11

QBEP = 40,000 QBEP = 30,000

5 4

QBEP = 8,000 unitsQBEP = 7,500 units

If demand was 7800 units what should you do?

(b) at what volume of output would the two alternatives yield the same profit?

Profit = Q ( R - v) - FC

Profit A = Profit B

Q ( R - v) - FC = Q ( R - v) - FC

Q(15-10) - 40,000 = Q(15-11) - 30,000

Q(5) - 40,000 = Q(4) - 30,000

Q =10,000 units

(c) If your expected annual demand is 12,000 units, which alternative yields higher profit?

Profit A

Profit A = Q ( R - v) - FC

## Profit A = 12, 000 ( 15 -10) - 40,000

Profit A = 12,000 (5) - 40,000

Profit A = \$20,000

Profit B

Profit B = Q ( R - v) - FC

Profit B = 12,000 (15 - 11) - 30,000

Profit B = 12,000 (4) - 30,000

Profit B = \$18,000

Problem 5

D= 30,000 pens

FC = \$25,000

v = \$.37

(a). Find the breakeven quantity if pens sell for \$1.

R=\$1

QBEP = FC

R – VC

QBEP = 25,000

1 – .37

QBEP = 25,000

.63

QBEP = 39,682.53 Can you have .53 of a pen? Which direction should you round?

(b) At what price must pens be sold to obtain a monthly profit of \$15,000 assuming estimated demand materializes? (What variable are you going to solve for?)

## Profit = Q ( R - v) - FC

\$15,000 = 30,000 ( R -\$.37) - \$25,000

\$15,000 = 30,000R - 11,100 - 25,000

\$15,000 = 30,000R - 36,100

\$51,100 = 30,000R

51,100 = 30,000R

30,000 30,000

1.70333=R

How do you handle the decimal places? If you charged \$1.70 per pen would you yield a monthly profit of \$15,000? What should the selling price be?

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