Question

Gilmore, Inc., had equity of $155,000 at the beginning of the year. At the end of the year, the company had total assets of $310,000. During the year, the company sold no new equity. Net income for the year was $33,000 and dividends were $4,200.

a. 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.)

b. Calculate the internal growth rate using ROA × b for beginning of period total assets. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

c. Calculate the internal growth rate using ROA × b for end of period total assets. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a. 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.)

Let’s first calculate return on equity (ROA)

Return on Asset (ROA) = Net income / Total Assets   

Where,

Net income = $33,000

Total Asset at the end of period = $310,000

Dividend paid = $4,200

Retained earnings = Net income - Dividend paid = $33,000 - $4,200

= $28,800

Total Asset at the beginning of period = Total Asset at the end of period - retained earnings

= $310,000 - $28,800

= $281,200

Therefore, Average asset = (Total Asset at the end of period +Total Asset at the beginning of period)/2

= ($310,000 + $281,200)/2

= $295,600

Therefore,

Return on Asset (ROA) = $33,000 / $295,600 = 0.1116 or 11.16%

Now,

Internal Growth rate = Retention rate * ROA

Retention rate (b) = (1- payout ratio)

Where, Payout ratio = dividend paid / net income = $4,200 / $33,000 = 0.1273 or 12.73%

Therefore, retention rate = (1- payout ratio) = (1-0.1273) = 0.8727

Therefore, Internal Growth rate by using average asset

Internal Growth rate =0.8727 * 11.16% = 0.0974 or 9.74%

b. Calculate the internal growth rate using ROA × b for beginning of period total assets. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Return on Asset (ROA) = Net income / beginning of period total assets

Total Asset at the end of period = $310,000

Dividend paid = $4,200

Retained earnings = Net income - Dividend paid = $33,000 - $4,200

= $28,800

Total Asset at the beginning of period = Total Asset at the end of period - retained earnings

= $310,000 - $28,800

= $281,200

Return on Asset (ROA) = $33,000 / $281,200 = 0.1174 or 11.74%

Now,

Internal Growth rate = Retention rate * ROA

Retention rate (b) = (1- payout ratio)

Where, Payout ratio = dividend paid / net income = $4,200 / $33,000 = 0.1273 or 12.73%

Therefore, retention rate = (1- payout ratio) = (1-0.1273) = 0.8727

Therefore, Internal Growth rate by using average asset

Internal Growth rate =0.8727 * 11.74% = 0.1024 or 10.24%

c. Calculate the internal growth rate using ROA × b for end of period total assets. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Return on Asset (ROA) = Net income / end of period total assets

Where,

Total Asset at the end of period = $310,000

Return on Asset (ROA) = $33,000 / $310,000 = 0.1065 or 10.65%

Now,

Internal Growth rate = Retention rate * ROA

Retention rate (b) = (1- payout ratio)

Where, Payout ratio = dividend paid / net income = $4,200 / $33,000 = 0.1273 or 12.73%

Therefore, retention rate = (1- payout ratio) = (1-0.1273) = 0.8727

Therefore, Internal Growth rate by using average asset

Internal Growth rate =0.8727 * 10.65% = 0.0929 or 9.29%