Question

Decision Inputs (Data)	Cost Structure Alternative #1	Cost Structure Alternative #2
Delivery price (i.e., revenue) per package	$60	$60
Variable cost per package delivered	$48	$30
Contribution margin per unit	$12	$30
Fixed costs (per year)	$600,000	$3,000,000

(8) Assume an average income-tax rate of 40%. What volume (number of deliveries) would be needed to generate an after-tax profit, ?A, of 5% of sales for each alternative?

Answer 1

• All working forms part of the answer
• Let volume under both the alternative be ‘x’, then:

Working		Alternative #1	Alternative #2
A = Let the volume be 'x'	No. of deliveries	x'	x'
B	Contribution margin per delivery	12	30
C	Delivery Price per delivery	60	60
D = A x C	Total Sales	60x	60x
E = D x 5%	5% of Sales = After Tax Profits	3x	3x
F = E/60%	Before Tax profits	5x	5x
G =A x B	Total Contribution margin	12x	30x
H	Fixed Cost cost	600000	3000000
I = G - H = F	Equation	12x - 600000 = 5x	30x - 3000000 = 5x
		12x - 5x = 600000	30x - 5x = 3000000
		7x = 600000	25x = 3000000
		x = 85714 deliveries	x = 120000 deliveries

• Answer:

No. of deliveries to earn an after tax profit of 5% of sales revenue:

For Alternative #1 = 85,714
For Alternative #2 = 120,000