CP

Tying the Ratios Together: The Du Pont Chart and Equation 393

MicroDrive made 3.8 percent, or 3.8 cents, on each dollar of sales, and its assets were

“turned over” 1.5 times during the year. Therefore, the company earned a return of

5.7 percent on its assets.

If the company were financed only with common equity, the rate of return on as-

sets (ROA) and the return on equity (ROE) would be the same because the total assets

would equal the common equity:

This equality holds if and only if Total assets 
Common equity, that is, if the com-

pany uses no debt. MicroDrive does use debt, so its common equity is less than total

assets. Therefore, the return to the common stockholders (ROE) must be greater than

the ROA of 5.7 percent. To find the ROE, multiply the rate of return on assets (ROA)

by the equity multiplier,which is the ratio of assets to common equity:

Firms that use a large amount of debt financing (a lot of leverage) will necessarily have

a high equity multiplier—the more the debt, the less the equity, hence the higher the

equity multiplier. For example, if a firm has $1,000 of assets and is financed with $800,

or 80 percent debt, then its equity will be $200, and its equity multiplier will be

$1,000/$200 
5. Had it used only $200 of debt, then its equity would have been

$800, and its equity multiplier would have been only $1,000/$800 
1.25.^11

MicroDrive’s return on equity (ROE) depends on its ROA and its use of

leverage:^12

(10-2)

Now we can combine Equations 10-1 and 10-2 to form the extended Du Pont equa-

tion,which shows how the profit margin, the assets turnover ratio, and the equity mul-

tiplier combine to determine the ROE:

 (10-3)

Net income

Sales



Sales

Total assets



Total assets

Common equity

.

ROE
(Profit margin)(Total assets turnover)(Equity multiplier)

12.7%.

5.7%2.23

5.7%$2,000/$896

Net income

Total assets



Total assets

Common equity

ROE
ROAEquity multiplier

Equity multiplier

Total assets

Common equity

.

ROA

Net income

Total assets

Net income

Common equity

ROE.

(^11) Expressed algebraically,
Here D is debt, E is equity, A is total assets, and A/E is the equity multiplier. This equation ignores pre-
ferred stock.
(^12) Note that we could also find the ROE by “grossing up” the ROA, that is, by dividing the ROA by the
common equity fraction: ROE
ROA/Equity fraction
5.7%/0.448
12.7%. The two procedures are
algebraically equivalent.
Debt ratio
D
A

AE
A

A
A
E
A

1 ^1
Equity multiplier
.

Analysis of Financial Statements 389