Question

Two map printing systems are being compared by the State Highway Department. The system I have a fixed cost of $1,000/year and a variable cost of $0.90/map. System II has a fixed cost of $5,000/year and a variable cost of $0.10/map.

a. What is the breakeven point per year of System I, in number of maps and in USD?

b. What is the breakeven point per year of System II, in number of maps and in USD?

c. What System must be chosen if the estimated number of maps to print per year is 3,000? Why?

d. What System must be chosen if the estimated number of maps to print per year is 6,000? Why?

e. At what volume (number of maps printed per year), the decision shifts to choose one system over the other?

NOTE: You can sell each map at $1.25

Answer 1

Given

Price=P=$1.25

a)

In case of system A,

Fixed Cost=F=$1000

Variable cost per map=V=$0.90

Breakeven point=BEP=F/(P-V)=1000/(1.25-0.90)=2857.143 or say 2858 maps

Breakeven volume in dollars=P*BEP=1.25*2857.143=$3571.43

b)

In case of system B,

Fixed Cost=F=$5000

Variable cost per map=V=$0.10

Breakeven point=BEP=F/(P-V)=5000/(1.25-0.10)=4347.826 or say 4348 maps

Breakeven volume in dollars=P*BEP=1.25*4347.826=$5434.78

c)

At a volume of 3000 maps (i.e. Q=3000)

Profit of system A =(P-V)*Q-F=(1.25-0.90)*3000-1000=$50

Profit of system B =(P-V)*Q-F=(1.25-0.10)*3000-5000=-$1550

Profit is higher in case of system A. It should be chosen.

d)

At a volume of 6000 maps (i.e. Q=6000)

Profit of system A =(P-V)*Q-F=(1.25-0.90)*6000-1000=$1100

Profit of system B =(P-V)*Q-F=(1.25-0.10)*6000-5000=-$1900

Profit is higher in case of system B. It should be chosen.

e)

Let the volume be Q

We know that Profit=(P-V)*Q-F

Set Profit from system A=Profit from system B

(1.25-0.90)*Q-1000=(1.25-0.10)*Q-5000

0.35Q-1.15Q=1000-5000

0.80Q=4000

Q=5000

At a volume of 5000 maps or higher we can switch over from system A to system B.