Question

A firm with annual sales of $60 million pays out 50% of its sales as cost of goods sold. Overhead amounts to $10 million. Labour and salaries are $14 million. Thus, a profit of $6 million is realised. Assets are $20 million, of which 20% are in inventories. a) If the firm can (1) increase sales volume, (2) raise price, (3) reduce labour and salaries, (4) decrease overhead, or (5) reduce the costs of goods sold, how much change (in percent) in each category would be required to increase the profit to $8 million? b) If prices of purchased materials (i.e. costs of goods sold) can be reduced by 6% percent, what return on assets can be realised? How does this compare with the current ROA?

Answer 1

Current case

Sales	A	60
COGS	B	30
Gross Profit	C=A-B	30
Overhead	D	10
Labour &salaries	E	14
Other costs	F=D+E	24
Profit	G=C-F	6

a) 1) Increase sales volume by 6.67% from 60 to 64
Sales	A	64
COGS	B	32
Gross Profit	C=A-B	32
Overhead	D	10
Labour &salaries	E	14
Other costs	F=D+E	24
Profit	G=C-F	8
a) 2) Increase sales price by 3.33% from 60 to 62. As price increases only not volume, COGS does not change
Sales	A	62
COGS	B	30
Gross Profit	C=A-B	32
Overhead	D	10
Labour &salaries	E	14
Other costs	F=D+E	24
Profit	G=C-F	8
a) 3) reduce labour and salaries by 14.28% from 14 to 12
Sales	A	60
COGS	B	30
Gross Profit	C=A-B	30
Overhead	D	10
Labour &salaries	E	12
Other costs	F=D+E	22
Profit	G=C-F	8
a) 4) decrease overhead by20% from 10 to 8
Sales	A	60
COGS	B	30
Gross Profit	C=A-B	30
Overhead	D	8
Labour &salaries	E	14
Other costs	F=D+E	22
Profit	G=C-F	8
a) 5) reduce COGS by 6.67% from 30 to 28
Sales	A	60
COGS	B	28
Gross Profit	C=A-B	32
Overhead	D	8
Labour &salaries	E	14
Other costs	F=D+E	22
Profit	G=C-F	10

B)

Original			b) reduce COGS by 6%
Sales	60		Sales	60
COGS	30		COGS	28.2
Gross Profit	30		Gross Profit	31.8
Overhead	10		Overhead	8
Labour &salaries	14		Labour &salaries	14
Other costs	24		Other costs	22
Profit	6		Profit	9.8
ROA = Profit/Assets	30%		ROA = Profit/Assets	49%

ROA will increase from 30% to 49%