Question

Q3 A package service company offers overnight package delivery to its business cus- tomers. It has recently decided to expand its facilities to better satisfy current and pro- jected demand. Current volume totals two million packages per week at a price of $12 each, and average variable costs are constant at all output levels. Fixed costs are $3 million per week, and profit contribution averages one-third of revenues on each delivery (profit contribution=(p–AV C)Q). After completion of the expansion project, fixed costs will double, but variable costs will decline by 25%.

(1). Calculate the change in the company’s weekly breakeven output level that is due to expansion. (10 points)

(2). Assuming that volume remains at 2 million packages per week, calculate the change in the degree of operating leverage that is due to expansion. (10 points)

(3). Again assuming that volume remains at two million packages per week, what is the effect of expansion on weekly profit? (10 points)

there is the question and the answer but i'm lost how we get 8$ as AVC

  Solution 3

1. (P - AVC) Q = 1/3P(Q)

P - AVC = 1/3P

AVC = 2/3($12)

AVC = $8

So, Average variable costs are $8

Answer 1

Given Price=P=$12

Fixed Cost=FC=$3,000,000

We know that

Contribution margin =Price-Average Variable Cost=P-AVC

We are given profit contribution is 1/3 of revenue i.e. price. So,

P-AVC=1/3P

(12-AVC)=1/3*12=4

AVC=$8

a)

Initial BEP (Break even point)=FC/(P-V)=3000000/(12-8)=750,000

New fixed Cost=FC1=2*3000000=$6000000

New AVC=AVC1=8*(1-25%)=$6

Price=P=$12

BEP in case of expansion=FC1/(P-AVC1)=6000000/(12-6)=1000000 or 1 million

Increase in weekly break even output level=1000000-750000=250,000

b)

Let us consider the weekly volume=Q=2,000,000

Degree of operating leverage is given by

DOL before expansion

DOL after expansion

Increase in DOL after expansion=6-1.60=4.40

c)

Let us calculate the weekly profit before expansion.

Total Revenue=TR=P*Q=12*2000000=$24,000,000

Total Cost=TC=FC+AVC*Q=3000000+8*2000000=$19,000,000

Weekly Profit=TR-TC=24,000,000-19,000,000=$5,000,000

Now we calculate weekly profit after expansion

Total Revenue=TR=P*Q=12*2000000=$24,000,000

Total Cost=TC=FC1+AVC1*Q=6000000+6*2000000=$18,000,000

Weekly Profit =TR-TC=24,000,000-18,000,000=$6,000,000

Increase in weekly profit=6,000,000-5,000,000=$1,000,000