Return on Equity (ROE) – How to Learn it

ROE can be a bit of a maze to understand because of all the little parts (the details). Every detail matters and it takes
practice to understand ROE, and become comfortable with it because of the math. Each time you calculate ROE,
ALWAYS interpret the answer. Ask yourself - What does this answer mean? As you interpret the answer, be sure to see
if it makes sense with what is happening with the company, based on the information provided. If it doesn’t make
sense, you may not have calculated it correctly.

Step 1: Start by reading about ROE in your etext. Study the topic thoroughly in the etext, including any videos that may
be included with the course material. Before digging into ROE (or any of the financial ratio), it is critical that you
understand the nuts and bolts of each of the four financial statements. Ratio analysis is pointless without a clear and
indepth understanding of the components of the financial statements.

Step 2: To help understand the topic (to go hand in hand with the etext), you can also read the below explanation of
what ROE is, how it is calculated, and what to do with the calculatoin answer, and read these articles, and/or watch
these YouTube Videos. Sometimes it helps to read the topic from another perspective to help learn it.

1. https://investinganswers.com/dictionary/r/return-equity-roe
2. https://investinganswers.com/dictionary/d/dupont-analysis
3. https://www.investopedia.com/terms/r/returnonequity.asp
4. https://corporatefinanceinstitute.com/resources/knowledge/finance/what-is-return-on-equity-roe/
5. Watch these short videos (video 1, video 2, video 3)
6. ROE Example

Step 3: Practice calculating and interpreting ROE by doing these practice problems (link). Note: to access the practice
problems, you must be fully logged out of any other accounts (i.e. Google, Microsoft, etc) in order for access to work.

What is ROE?
We know that ROE is a financial ratio. Financial ratios are ways (calculations) to help us learn new information about a
company by “reading between the lines” of the financial statements that have been given to the financial professionals
by the accounting professionals. ROE, more specifically is a Profitability financial ratio. Profitability is one of the 5 major
categories that the financial ratios in the etext can be placed within. Profitability ratios, such as ROE, help us understand
how efficient a business is at producing a profit. We also want to remember that the term “Profit” is the same as “Net
Income” and also the same as “Earnings” – which is found at the bottom of the income statement. Some people call this
the “Bottom line”. So, ROE is one way of evaluating the profitability of a business. It helps the business and/or investors
see how much profit is being produced for each dollar invested into the business.

How is ROE calculated?

ROE has two formulas that can be used. There is an “easy formula” and there is a harder formula (known as “Dupont”).
Regardless of which formula you use, if you calculate them both correctly for a given business, you should get the same
answer with both formulas. Anytime you are asked to work a problem to solve for ROE, first try the easy formula since it
can save you time and headache. If you are unable to use the easy formula, then go to the Dupont formula. Note:
Sometimes a problem will specifically want you to use the Dupont formula. In that case, use the Dupont formula.

The “easy” formula is ROE = Net Income divided by Equity or ROE = NI/E

It is “easy” because you are simiply just dividing one number over another – a very easy formula.
The Net Income (NI) comes from the income statement (Sales Revenue – Expenses = Net Income) and equity comes
from the balance sheet (A – L = E). You can see that we are pulling numbers from different financial statements in order
to run the calculation. For this reason, it is critical that you understand the composition of each of the financial
statements very well. Not understanding the financial statements often times leads to confusion and frustration with
financial ratios.

IMPORTANT TIP: Any time you come across a question about ROE. Always see if you can try to solve it using the shorter
version of the formula first BEFORE trying the Dupont equation.

Let’s look at an example…

Let’s suppose a company has Sales Revenue of $2 million and total Expenses of $1.2 million. The income statement
would tell us that the company’s Net Income is $800k. That is subtracting the expenses from the revenue (R – E = NI).
Let’s also suppose that the company has $5 million in total Assets and $3 million in total liabilities. The Balance sheet
would tell us that the companies Equity is $2 million. That is subtracting the liabilities form the assets (A – L = E). Using
the easy formula of ROE we would get $800,000 / $2,000,000 = 0.4. What does “0.4” mean? The answer of 0.4 means
that for every dollar that is invested in the business, the business makes $0.40 (40 cents) in profit. In other words, ROE =
40%.

The higher the ROE the better. Investors look for companies that having increasing ROE numbers because they are
looking to invest their money in companies that are improving/increasing the efficiency of making a profit.

We don’t always have the luxury of solving an ROE problem using the easy formula. Sometimes we have to use the
Dupont formula.

The Dupont formula is more complex but remember that you should get the same answer as the easy formula.

The Dupont equation is…

ROE = (Net Income / Sales) x (Sale / Assets) x (Assets / Equity) Or

ROE = Net Income Margin x Asset Turnover x Leverage Multiplier

Each of the three division parts of the Dupont equation have a name, hence the second way I wrote the Dupont
equation.

Net Income Margin = Net Income / Sales

Asset Turnover = Sales / Assets
Leverage Multiplier = Assets / Equity

To simplify the complexity of the Dupont formula, we can see that all we are doing is multiplying three numbers. We are
multiplying the Net Income Margin by the Asset Turnover by the Leverage Multiplier.

Let’s take the example from above and put some numbers to the Dupont equation now…

ROE = Net Income Margin x Asset Turnover x Leverage Multiplier

ROE = (Net Income / Sales) x (Sale / Assets) x (Assets / Equity)
ROE = ($800,000 / $2,000,000) x ($2,000,000 / $5,000,000) x ($5,000,000 / $$2,000,000)
ROE = 0.4 x 0.4 x 2.5  in other words…Net Income Margin = 0.4, Asset Turnover = 0.4, and Leverage Multiplier = 2.5.
ROE = 0.4 or 40% or $0.40 (40 cents)
By solving with the Dupont equation, we got the exact same answer as using the easy formula.

What do we do with the answer of financial ratios?

Whenever you calculate the answer of a financial ratio, you cannot rely just on the answer alone. Ratio analysis is a
process that helps “standardize” the ability to compare companies. The process of comparing company financial ratios
is called “Benchmarking”. We always have to benchmark our ratio answers to a competitor or industry levels. Here is
an example, using the given table of information:

Industry Biggest
2019 2020
Average Competitor
ROE 0.35 0.4 0.5 0.37

Let’s suppose the company in our previous example had an ROE of 0.35 or 35% in 2019 and we just calculated the ROE
for 2020, which came to 0.4 or 40%. We calculated this with both the easy formula and the Dupont formula. We see
that the company improved their efficiency and ability to make a profit from 2019 to 2020 because their ROE increased
from 2019 to 2020, but we also see that the ROE for the company’s industry is 0.5 or 50%. Since the company in our
example has an ROE lower than the industry average, this means that the company is less efficient at being profitable
than the average company in their industry. We also see that the closest/biggest competitor to our company has an
ROE of 0.37 or 37%. This would tell us that our company was less profitable than our biggest competitor in 2019, but
improved its profitability and is more profitable than the biggest competitor in 2020 (a good thing).
 FINANCE
PRACTICE PROBLEMS

This document contains practice problems for students learning Finance at WGU. These practice problems are not to
substitute for watching/participating in unit cohorts, reading the etext, or working the practice problems within the
etext (module and unit problems). Distribution (or sharing) of these questions (and answers), in any way, shape, or
form, without written consent, is prohibited. The below practice problems do not guarantee passing of any
assessments and problems are organized as follows:

✓ Time Value of Money (Questions 1-21)

✓ Perpetuities (Questions 22-24)
✓ ROE & SGR (Questions 24-32)
✓ Expected Return and Return on Investment (Question 33)

IMPORTANT NOTE: All of the Time Value of Money (TVM) practice problems (questions 1-21) are best worked with a
financial calculator (C708) or Excel (D076), not by hand using TVM formulas. If you do not have a financial calculator
(C708), it is recommended that you get one as quickly as possible.

C708 Students: Before starting on these questions be sure you have done the following:
• Obtained a Financial Calculator (TI BA II Plus is recommended)
• Viewed the Unit 3 and Unit 4 Cohort
• Read the etext regarding Time Value of Money, Perpetuities, ROE, and SGR, Expected Return, and ROI
• Work all practice problems within the etext (module and unit summary quizzes)
• Need additional help, see www.tvmcalcs.com.

D076 Students: Before starting on these questions be sure that you have done the following:
• Have the MyEducator Excel Add-in properly installed.
• Read the etext regarding Time Value of Money, Perpetuities, ROE, SGR, Expected Return, and ROI
• Worked all the lesson, module, and unit questions
• Need additional help with TVM, see www.tvmcalcs.com.

Remember your CI can help you with these problems. Don’t hesitate to make an appointment.

Time Value of Money

1. Determine how much $1,000 deposited in a savings account paying 8% (compounded annually) will be worth
after 5 years.

a. $5,526
b. $ 784
c. $1,400
d. $1,469

2. The earnings of Omega Supply Company have grown from $2.00 per share to $4.00 per share over a nine-year
time period. Determine the compound annual growth rate.

a. 11.1%
b. 8%
c. 22.2%
d. 100%
3. Comet Powder Company has purchased a piece of equipment costing $100,000. It is expected to generate a ten-
year stream of benefits amounting to $16,273 per year. Determine the rate of return Comet expects to earn
from this equipment.

a. 16.3%
b. 62.7%
c. 10%
d. 20%

4. Air Atlantic (AA) has been offered a 3-year old jet airliner under a 12-year lease arrangement. The lease requires
AA to make annual lease payments of $500,000 at the end of each of the next 12 years. Determine the present
value of the lease payments if the opportunity cost of funds is 14 percent.

a. $2,830,145
b. $13,635,500
c. $6,000,000
d. $3,226,367

5. If you invest $10,000 in a 4-year certificate of deposit (CD) paying 10 percent interest compounded annually,
determine how much the CD will be worth at the end of 4 years.

a. $13,600
b. $45,730
c. $14,641
d. $15,958

6. Your grandparents put $1,000 into a savings account for you when you were born 20 years ago. This account has
been earning interest at a compound rate of 7 percent. What is its value today?

a. $3,870
b. $1,967
c. $3,026
d. $3,583

7. Baggos has seen their EPS increase from $0.30 to $3.16 in seven years. What has been the growth rate of
Baggos's EPS?

a. about 30%
b. about 40%
c. about 20%
d. about 10%

8. You have just won a $50,000 bond that pays no interest and matures in 20 years. If the discount rate is 10%,
what is the present value of your bond?

a. $7,432
b. $8,175
c. $8,900
d. $1,490
9. BB&C bank has agreed to lend you $30,000 today, but you must repay $42,135 in 3 years. What rate is the bank
charging you?

a. 10%
b. 11%
c. 12%
d. 13%

10. The Florida lottery agrees to pay the winner $250,000 at the end of each year for the next 20 years. What is the
future value of this lottery if you plan to put each payment in an account earning 9 percent?

a. $2.28 million
b. $12.79 million
c. $14.32 million
d. $ 5.00 million

11. Billy Bob has decided to put $2,400 a year (at the end of each year) into an IRA over his 40 year working life and
then retire. What will Billy have if the account will earn 10 percent compounded annually?

a. $394,786
b. $ 23,470
c. $1,062,222
d. $810,917

12. Jane wants to have $200,000 in an account in 20 years. If her account earns 11 percent per annum over the
accumulation period, how much must she save per year (end of year) to have the $200,000?

a. $25,116
b. $3,115
c. $10,000
d. $3,492

13. An insurance company offers you an end of year annuity of $48,000 per year for the next 20 years. They claim
your return on the annuity is 9 percent. What should you be willing to pay today for this annuity?

a. $429,600
b. $438,170
c. $408,672
d. $398,144
14. New Jersey Mutual has offered you a single premium annuity that will pay you $12,000 per year (end of year) for
the next 15 years. If you must pay $109,296 today for this annuity, what is your expected rate of return?

a. 8%
b. 9%
c. 7%
d. 10%
15. Suppose that you have $10,000 in a retirement account right now. You think you can get an annual return of 7%
on your money by investing in the stock market. Additionally, you put $100 into the account each month for 20
years. How much will you have at the end of the 20 years.

What would you have if you compound annually? What about compounding monthly, quarterly, or
semiannually?

Compounding Periods
Annual Monthly Quarterly Semiannual
N 20 240 80 40
I/Y 7.0000% 0.5833% 1.7500% 3.5000%
PV -$10,000 -$10,000 -$10,000 -$10,000
PMT -$1,200 -$100 -$300 -$600
FV $87,891.44 $92,480.05 $91,602.07 $90,322.76

16. Suppose that a restaurant owner is looking to expand his restaurant building. His bank will lend him $40,000 at an
interest rate of 8%. If the monthly loan payments are $325.50, approximately how long with it take the borrower to pay
the loan off?
a. 10-12 years
b. 15-17 years
c. 20-22 years
d. 25-27 years

17. How much do you need to save per month, at 9% interest, to have $1 million at the end of 12 years?
a. $3,880
b. $11,782
c. $49,651
d. $148,878
18. How much do you need to save per month, at 6% interest, to have $1 million at the end of 10 years?
a. $6,322.33
b. $75,867.96
c. $6,102.05
d. $73,224.60

19. How much do you need to save per month, at 8% interest, to have $500k at the end of 5 years?
a. $8,333.33
b. $6,804.79
c. $398.97
d. $2,195.63

20. What is the present value of $500k that will be received in 10 years from today if there is an 8% compounding
interest rate?
a. $231,596.74
b. $1,079,462.50
c. $500,000.00
d. $352,474.12
TVM with ANNUITY DUE:

21. Assuming an annual rate of 5%, what is the present value of a 25-year annuity due if you were to receive annual
payments of $8,000?

a. $112,751.56
b. $118,389.13
c. $189,561,35
d. $190,351.19

Perpetuities:

The next set of questions (21-23) will focus on practicing the calculation of the Present Value of a Perpetuity (or Growing
Perpetuity). Before working these practice problems, review page 129 of the eText which teaches about Perpetuities.
The formula for calculating the Present Value of a Perpetuity (PVGP) is not on the formula sheet. This is a formula that
students WILL need to memorize for the pre-assessment and the objective assessment.

22. Suppose you would like to find the current value of a company stock price so that you can decide whether or not to
buy it. The company pays an annual dividend of $5 for each share and expects to pay this dividend indefinitely. How
much would the stock price be if you required your investment return to be 5%?
a. $100 per share
b. $200 per share
c. $300 per share
d. $400 per share

23. Suppose you would like to find the current value of a company stock price. The company pays an annual dividend of
$3 for each share. The company expects to pay this dividend indefinitely but intends to grow it at 1% per year. How
much would the stock price be if you required your investment return to be 4%?
a. $100 per share
b. $200 per share
c. $300 per share
d. $400 per share

24. Jill is considering buying a house and using it as a rental property for investment income. How much should Jill pay
for the property if she intends to make $1,000 per month in rental income, faces a 7% interest rate, and anticipates
increasing the rent by 2% each year?
a. $20,000.00
b. $133,333.33
c. $171,428.57
d. $240,000.00
Return on Equity (ROE) and Sustainable Growth Rate (SGR):

25. Suppose a company has sales of $33 million, net income of $8 million, a total asset turnover of 1.35, and a
leverage multiplier of 0.95. What is the company’s return on equity?

a. 31.09%
b. 37.70%
c. 32.73%
d. 24.24%

26. Greg is interested in investing in a small company, and he thinks Good Buy Co. might be a good investment. He
has been given the following information and would like to know the return on stockholder's equity. Assume
Good Buy’s marginal tax rate is 40%.

Earning before taxes $3 million

Net profit margin 3.6%
Total liabilities $15.0 million
Total stockholder's equity $10.0 million

ANS: 18%
27. What is the return on stockholders' equity for a firm with a net profit margin of 5.2 percent, sales of $620,000, a
leverage multiplier of 1.8, and total assets of $380,000?

ANS: 15.27%
28. Given the following information, calculate the return on equity for Regrets Only Dating Services, Inc.:

Net Profit margin = 5%

Total asset turnover = 2
Total Debt = $730,000
Total Assets = $1,000,000

a. 14%
b. 7.3%
c. 37%
d. 21%

29. Sally’s Retailers and Joe’s Retailers both operate in the same apparel industry and have the same return on
equity ratio of 45 percent. Each company has the following ratios:

Ratio Sally Joe

Profit Margin 30% N/A
Total Asset Turnover 0.50 6.0
Leverage Multiplier N/A 0.50

Using the information above, determine the Profit Margin for Joe’s Retailers and the Leverage Multiplier for
Sally’s retailers.

ANS: Joe’s Profit Margin = 15%; Sally’s Leverage Multiplier = 3.0

30. A company has a return on equity of 16%, a total asset turnover of 0.93, and a net margin of 21%. What is the
company’s leverage multiplier?

a. 1.9300
b. 0.1963
c. 0.8193
d. 1.2095

31. Suppose a firm has a net profit margin of 14%, sales of $143 million, assets of $201 million, and a leverage
multiplier of 1.2. If the dividend payout ratio is 0%, what is the firm’s sustainable growth rate?

a. 14.00%
b. 11.95%
c. 10.77%
d. 18.24%

32. A firm has net income of $20 million and pays out $2 million in dividends. If the firm has total assets of $ $450
million and total liabilities of $300 million, what is the firm’s sustainable growth rate?

a. 12%
b. 4%
c. 7%
d. 10%

Expected Return and Return on Investment

33. Suppose you have an investment portfolio that has $150,000 in it ($100,000 in stocks and $50,000 in bonds).
Half of your stocks have expected to earn 15% and the other half of your stocks expect to earn 8%. 70% of your bonds
expect to earn 4% and the other 30% of your bonds expect to earn 7%. What is your overall expected return for your
entire investment portfolio?

A. 11.5%
B. 4.9%
C. 9.3%
D. 8.5%