Return on Equity (ROE)

The shareholders point of view !

ROE =	Profit
	Equity

Click here to see the source of data

Starworld Group	2021	2022	2023
Profit After Taxes (PAT)	305	450	715
Common Stock	900	1100	1100
Retained Earnings	300	405	550
Total Owners' Equity	1200	1505	1650
ROE	25.43 %	29.91 %	43.32 %

ROE is a basic measure of the efficiency with which the firm employs the owners' capital and estimates the earnings per € 100 of invested equity capital.

It incorporates the consequences of the financing policy of the firm, that is the way the assets are financed. This is called the "financial leverage".

ROE ratio can be decomposed into 3 elements :

ROE =	Profit	x	Sales	x	Assets
	Sales		Assets		Equity

Click here to see the source of data

Starworld Group	2021	2022	2023
Profit After Taxes (PAT)	305	450	715
Total Owners' Equity	1200	1505	1650
Sales	2784	3341	4343
Assets	2250	2605	2700
Return on sales [ Profit / Sales ]	10.96 %	13.47 %	16.46 %
Asset Turnover [ Sales / Assets ]	1.237	1.283	1.609
Financial Leverage [ Assets / Equity ]	1.875	1.731	1.636
ROE	25.43 %	29.91	43.32 %

This decomposition shows the 3 levels for managerial control of ROE. It also demonstrates that two companies may have the same ROE, but resulting from very different cocktails or strategies.

Example :

	Profit margin	x	Asset Turnover	x	Financial leverage	=	ROE
Firm A	6 %	x	0,5	x	4	=	12 %
Firm B	2 %	x	1,5	x	4	=	12 %

A ROE may be based on high operating margins combined with a rather poor asset turnover and a low indebtedness but it may very well be the combination of low operating margins capitalized by high productivity of assets and a high financial leverage

Why do we want to maximize ROE ?

Because we want to make our shareholders happy : fundamental objective of the firm.

How can we expect to raise additional funds from our shareholders if we do not provide them with a return with the risk they are accepting to take in investing their money in our firm ?

If you do not make your shareholders happy, somebody is going to make them happy for you.

There is a second fundamental reason why we want to maximize ROE : it is to maximize our Self-Sustainable Growth (SSG).

What is SSG ? It is the rate of growth that a company can maintain (can sustain) internally without changing its financial structure (D/E).

The basic question is therefore : given the firm's characteristics how large a growth rate can it support without distorting its D/E ratio and without raising additional outside equity capital ?

The fundamental relation between ROA and ROE : the concept of "financial leverage"

Profit Equation :

ROE =	ROA	+	[ ROA - i ]	.	D
					E

Example

Click here to see the source of data

Income Statement

Starworld Group	2021	2022	2023
EBIT	478	676	1042
Interest expense	42	33	21
EBT	436	643	1021
Tax 30 %	131	193	306
PAT	305	450	715

Click here to see the source of data

Financial structure

Starworld Group	End of year
	2021	2022	2023
L-T Debt	1050	1100	1050
Equity	1200	1505	1650
Total of financing (= net Asset)	2250	2605	2700

Calculation on a pre-tax basis

Starworld Group	2021	2022	2023
Pre-tax ROA	21.24 %	25.95 %	38.59 %
Interest rate	4.00 %	3,00 %	2.00 %
D/E ratio	0,875	0,731	0,636
Financial Leverage	15.08 %	16.77 %	23.28 %
ROE	31.49 %	42.72 %	61.87 %

Calculation on an after-tax basis

Starworld Group	2021	2022	2023
EBIT - Tax rate	335	473	729
After-tax ROA	14.89 %	18.16 %	27.00 %
Interest rate - Tax rate	2.80 %	2.10 %	1.40 %
D/E ratio	0,875	0,731	0,636
Financial Leverage	10.58 %	11.74 %	16.28 %
ROE	25.46 %	29.90 %	43.28 %

Financial Leverage :

Financial Leverage =	[ ROA - i ]	x	D
			E

 

What is this formula telling us ?

ROE = ROA + Leverage factor

"Leverage factor" dependent upon 2 elements :

1. ROA - Interest rate
2. D / E (gearing ratio)

If a firm has no debt, Leverage factor = 0, ROE = ROA

If a firm has debts, 3 possible situations exist :

ROA > i : invest borrowed money at the rate > cost of interest ; (ROA - i) > 0 Leverage factor > 0

ROA = i : shareholders are not benefiting from the use of borrowed money. (ROA - i) = 0, Leverage factor = 0, ROA = ROE

ROA < i : Leverage factor < 0, ROE < ROA, Return to the shareholders is deteriorated by the use of borrowed funds.

Reasons of negative financial leverage :

• High levels of interest rates and depressed ROA caused by rising costs
• increased competition
• price controls, etc...

Example :

D / E	0,0	0,11	0,25	0,43	0,67	1,00	1,50	2,33
ROA	15 %	15 %	15 %	15 %	15 %	15 %	15 %	15 %
i	9 %	10 %	11 %	12 %	13 %	14 %	15 %	16 %
ROA - i	6 %	5 %	4 %	3 %	2 %	1 %	0 %	-1 %
Leverage	0,00%	0.55 %	1.00 %	1.29 %	1.34 %	1.00 %	0.00 %	-2.33 %
ROE	15 %	15,55%	16,00%	16,29%	16,34%	16,00%	15,00%	12,67%

The ROE is maximum with a D/E ratio of 0,67.

Comments

Financial leverage can be used on a pre-tax or on an after-tax basis.

Low interest rate = Competitive advantage for the firm

Be very careful in interpreting the leverage formula !

An easy conclusion : (ROA-i) > 0 : borrow as much as possible ! but Debts interest rate increases financial risk.

 

Sources :

Interpreting and using financial statements, 1999, Marc Bertonèche, Ph. D. in Finance from the Northwestern University, Professor at the Bordeaux University and at Sciences-PO Paris, Visiting Professor at Harvard Business School and Oxford University.

© ECOFINE.COM, Bernard Jaquier, Professor Emeritus & Dr Honoris Causa, Lausanne, Switzerland, 2024