Chapter 3, Problem 3.15E

To determine

To calculate: The balance of retained earnings each year for the given companies.

Answer to Problem 3.15E

The balance of retained earnings each year for the given companies is as follows:

			($ in millions)
Year	Company V		Company R
	Net income (loss)	Retained earnings	Net income (loss)	Retained earnings
2009	0	$0	$35	$11
2010	$30	30	-43	-32
2011	-7	23	63	31
2012	41	64	63	94
2013	135	199	102	196
2014	30	229	135	331
2015	-131	98	-42	289
2016	577	675	74	363
2017	359	1,034	110	473
2018	360	1,394	162	635

Table (1)

Explanation of Solution

Retained earnings:

Retained earnings are the portion of earnings kept by the business for the purpose of reinvestments, payment of debts, or for future growth.

Working note:

1. Calculate the retained earnings Company V.

Year 2010:

Opening retained earnings = $0

Net income = $30 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings}=\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{+ Net income – Dividends}\end{array}\right)\\ =\text{\$0 }\text{}+\$30\text{million}-\$0\\ =\boxed{\$30\text{million}}\end{array}$ (1)

Year 2011:

Opening retained earnings = $30 million

Net loss = $7 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings}=\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{– Net loss – Dividends}\end{array}\right)\\ \text{= \$30 million }\text{}–\$7\text{million}-\$0\\ =\boxed{\$23\text{million}}\end{array}$ (2)

Year 2012:

Opening retained earnings = $23 million

Net income = $41 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{+ Net income – Dividends}\end{array}\right)\\ \text{= \$23 million }\text{}+\$41million-\$0\\ =\boxed{\$64million}\end{array}$ (3)

Year 2013:

Opening retained earnings = $64 million

Net income = $135 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{+ Net income – Dividends}\end{array}\right)\\ \text{= \$64 million }\text{}+\$135million-\$0\\ =\boxed{\$199million}\end{array}$ (4)

Year 2014:

Opening retained earnings = $199 million

Net income = $30 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{+ Net income – Dividends}\end{array}\right)\\ \text{= \$199 million }\text{}+\$30million-\$0\\ =\boxed{\$229million}\end{array}$ (5)

Year 2015:

Opening retained earnings = $229 million

Net loss = $131 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{– Net loss – Dividends}\end{array}\right)\\ \text{= \$229 million }\text{}–\$131\text{million}-\$0\\ =\boxed{\$98\text{million}}\end{array}$ (6)

Year 2016:

Opening retained earnings = $98 million

Net income = $577 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{+ Net income – Dividends}\end{array}\right)\\ \text{= \$98 million }\text{}+\$577million-\$0\\ =\boxed{\$675million}\end{array}$ (7)

Year 2017:

Opening retained earnings = $675 million

Net income = $359 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{+ Net income – Dividends}\end{array}\right)\\ \text{= \$675 million }\text{}+\$359million-\$0\\ =\boxed{\$1,034million}\end{array}$ (8)

Year 2018:

Opening retained earnings = $1,034 million

Net income = $360 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{+ Net income – Dividends}\end{array}\right)\\ \text{= \$1,034 million }\text{}+\$360million-\$0\\ =\boxed{\$1,394million}\end{array}$ (9)

2. Calculate the retained earnings Company R.

Year 2010:

Opening retained earnings = $11 million

Net loss = $43 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{– Net loss – Dividends}\end{array}\right)\\ \text{= \$11 million }\text{}–\$43\text{million}-\$0\\ =\boxed{\$(32\text{million)}}\end{array}$ (10)

Year 2011:

Opening retained earnings = $(32 million)

Net income = $63 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{+ Net income – Dividends}\end{array}\right)\\ \text{= \$(32 million ) }\text{}+\$63million-\$0\\ =\boxed{\$31million}\end{array}$ (11)

Year 2012:

Opening retained earnings = $31 million

Net income = $63 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{+ Net income – Dividends}\end{array}\right)\\ \text{= \$31 million }\text{}+\$63million-\$0\\ =\boxed{\$94million}\end{array}$ (12)

Year 2013:

Opening retained earnings = $94 million

Net income = $102 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{+ Net income – Dividends}\end{array}\right)\\ \text{= \$94 million }\text{}+\$102million-\$0\\ =\boxed{\$196million}\end{array}$ (13)

Year 2014:

Opening retained earnings = $196 million

Net income = $135 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{+ Net income – Dividends}\end{array}\right)\\ \text{= \$196 million }\text{}+\$135million-\$0\\ =\boxed{\$331million}\end{array}$ (14)

Year 2015:

Opening retained earnings = $331 million

Net loss = $42 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{– Net loss – Dividends}\end{array}\right)\\ \text{= \$331 million }\text{}–\$42\text{million}-\$0\\ =\boxed{\$289\text{million}}\end{array}$ (15)

Year 2016:

Opening retained earnings = $289 million

Net income = $74 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{+ Net income – Dividends}\end{array}\right)\\ \text{= \$289 million }\text{}+\$74million-\$0\\ =\boxed{\$363million}\end{array}$ (16)

Year 2017:

Opening retained earnings = $363 million

Net income = $110 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{+ Net income – Dividends}\end{array}\right)\\ \text{= \$363 million }\text{}+\$110million-\$0\\ =\boxed{\$473million}\end{array}$ (17)

Year 2018:

Opening retained earnings = $473 million

Net income = $162 million

Dividends = $0

$\begin{array}{c}\text{Ending retained earnings = }\left(\begin{array}{l}\text{Beginning retained earnings }\\ \text{+ Net income – Dividends}\end{array}\right)\\ \text{= \$473 million }\text{}+\$162million-\$0\\ =\boxed{\$635million}\end{array}$ (18)