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Expert-verified Found in: Page 481 ### Essentials Of Investments

Book edition 9th
Author(s) Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus
Pages 748 pages
ISBN 9780078034695

# The DuPont formula defines the net return on shareholders’ equity as a function of thefollowing components: • Operating margin• Asset turnover• Interest burden• Financial leverage• Income tax rateUsing only the data in Table 14.20: a. Calculate each of the five components listed above for 2010 and 2013, andcalculate the return on equity (ROE) for 2010 and 2013, using all of the fivecomponents.b. Briefly discuss the impact of the changes in asset turnover and financial leverage onthe change in ROE from 2010 to 2013.

1. 11.9 and 13.6
2. Increased ROE
See the step by step solution

## Step 1: Given information

 Income statement Particulars 2010 2013 Revenues $542$979 Operating income 38 76 Depreciation and amortization -3 -9 EBIT 35 67 Interest expense -3 0 Pre-tax income 32 67 Taxes -13 -37 Net income 19 30

## Step 2: Calculation of operating margin ‘a’

Operating margin = EBIT / Sales

For 2010 = $35 /$542 = 0.065

For 2013 =$67 /$979 = 0.068

Step 2: Calculation of Asset turnover

Asset turn-over = Sales / Total Assets

For 2010 = $542 /$245 = 2.21

For 2013 =$979 /$291 = 3.96

## Step 3: Calculation of Interest burden

Interest burden = Pre-tax profit / EBIT

For 2010 = $32 /$35 = 0.914

For 2013 =$67 /$67 = 1

## Step 4: Calculation of financial leverage

Financial leverage = Total Assets / Total Equity

For 2010 = $245 /$159 = 1.54

For 2013 =$291 /$220 = 1.32

## Step 5: Calculation of Income tax rate

Income tax rate = Net income after tax / Pre-tax income

For 2010 = $13 /$32 = 40.63%

For 2013 =$37 /$67 = 55.22%

## Step6 : Explanation on impact of changes ‘b’

Using the DuPont formula:

ROE(2010) = (1 - .4063) x .9143 x .0645 x 2.2122 x 1.5409

= .119

=11.9%

ROE(2013)= (1 - .5522) x 1.0 x 0.684 x 3.3643 x 1.3227

= .136

= 13.6%

This implies that the asset turnover increased substantially over the period thus increasing the ROE.

This also implies that the financial leverage declined over the period thereby adversely affecting the ROE. Since asset turnover increased more than financial leverage declined the net effect was an increase in ROE.

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