Question

violet corporation has the following data for the past 2 years

	year1	year 2
sales	1000	500
ROI	40%	12.5%
residual Income	160	10
requires rate of return	?

the sales margin in year 2 is half of the margin in year 1, what is the required rate of return in year 1

Explain Please!!

Answer 1

REQUIRED RATE OF RETURN

	YEAR 1	YEAR 2
SALES	1000$	500$
ROI	40%	12.5%
residual income	160$	10$
REQUIRED RATE OF RETURN	?	10%
sales margin	2Z	Z

RESIDUAL INCOME IS ACTUAL INCOME ABOVE THE REQUIRED INCOME.

RESIDUAL INCOME = OPERATING INCOME - MINIMUM REQUIRED RETURN ON INVESTMENT

STEP 1

FIND OUT INVESTMENT IN YEAR 2

SUPPOSE THE INVESTMENT IN YEAR 2 IS X.

RESIDUAL INCOME = ACTUAL RETURN ON INVESTMENT - MINIMUM RETURN IN INVESTMENT

10 = 0.125X - 0.10X

10 = 0.025X

X= 400$ IS THE INVESTMENT FOR YEAR 2.

ROI = RETURN / INVESTMENT *100

12.5% = RETURN /400

ACTUAL RETURN (OPERATING INCOME) = 400*12.5%

ACTUAL RETURN = 50$

STEP 2

FIND SALES MARGIN IN YEAR 2

OPERATING INCOME/ SALES *100

=50/500 *100

=10%

STEP 3

FIND SALES MARGIN IN YEAR 1 (SALES MARGIN IN YEAR 2 IS HALF OF THE SALES MARGIN IN YEAR 1)

= 2* SALES MARGIN IN YEAR 2

=20%

ACTUAL OPERATING INCOME = SALES * SALES MARGIN

1000*20%

=200$

STEP 4

FIND INVESTMENT IN YEAR 1

ROI = ACTUAL RETURN / INVESTMENT

40% = 200$/ INVESTMENT

INVESTMENT =500$

STEP 5

RESIDUAL INCOME = ACTUAL INCOME - (INVESTMENT *MINIMUM REQUIRED RETURN)

160 = 200 - (500*X%)

500*X% = 200-160

X = 40/500 *100

= 8%