ABC, Inc., had equity of $180,000 at the beginning of the year. At the end of th

Question

ABC, Inc., had equity of $180,000 at the beginning of the year. At the end of the year, the company had total assets of $335,000. During the year, the company sold no new equity. Net income for the year was $38,000 and dividends were $5,200.

The answer to a is 10.85%. I cannot get b or c.

Calculate the internal growth rate for the company. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

ABC, Inc., had equity of $180,000 at the beginning of the year. At the end of the year, the company had total assets of $335,000. During the year, the company sold no new equity. Net income for the year was $38,000 and dividends were $5,200.

Explanation / Answer

The ROA using end of period assets is: ROA = $38,000 / $335,000

ROA = 0.1134, or 11.34%

The addition to retained earnings is computed as:

Addition to retained earnings = NI - Dividends paid

Addition to retained earnings = $38,000 – 5,200

Addition to retained earnings = $32,800

The beginning of period assets had to have been the ending assets minus the addition to retained earnings, so:

Beginning assets = Ending assets – Addition to retained earnings Beginning assets

= $335,000 – 32,800

Beginning assets = $302,200

And the ROA using beginning of period assets is: ROA = $38,000 / $302200

ROA = 0.1257 or 12.57%

the plowback ratio is:

Plowback ratio = Addition to retained earnings/NI

Plowback ratio = $32,800 / $38,000

Plowback ratio = 0.8632 or 86.32%

a Calculate the internal growth rate for the company.

Using the internal growth rate equation

Internal growth rate = (ROA × b ) / [1 – (ROA × b )]

Internal growth rate = [0.1134*(0.8632)] / [1 – 0.1134*(0.8632)]

Internal growth rate =10.85%

b

Calculate the internal growth rate using ROA × b for beginning of period total assets

0.1257*0.8632=10.85%

c

Calculate the internal growth rate using ROA × b for end of period total assets.

Using the formula ROA × b , and end of period assets

=[0.1134*(0.8632)]

=9.79%

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