Question

In​ 2016, the Allen Corporation had sales of $62 ​million, total assets of $45 ​million, and total liabilities of $25 million. The interest rate on the​ company's debt is

5.6 ​percent, and its tax rate is 35 percent. The operating profit margin is 14 percent.

Calculate the​ firm's operating return on assets AND return on equity.​ (Hint: You can assume that interest must be paid on all of the​ firm's liabilities.) (round answer to 2 decimal places)

Answer 1

Solution:

Calculation of operating return on firm’s assets :

As per the information given in the question we have

Operating profit margin is 14 percent = 14 % = 0.14 ; sales = $ 62 million = $ 62,000,000

The formula for calculating the operating margin is = Operating profit / sales

Applying the above information in the formula we have

0.14 = Operating profit / $ 62,000,000

0.14 * $ 62,000,000 = Operating profit

Operating profit = 0.14 * $ 62,000,000

Operating profit = $ 8,680,000

The formula for calculating the operating return on firm’s assets is

= Operating profit / Total assets

As per the information given in the question we have

Operating profit = $ 8,680,000 ; Total assets = $ 45,000,000

Applying the above information in the formula we have the operating return on the assets as

= $ 8,680,000 / $ 45,000,000

= 0.192889

= 19.2889 %

= 19.29 % ( when rounded off to two decimal places )

Thus the operating return on the assets is = 19.29 %

Calculation of return on equity :

The formula for calculating the return on equity is

= Net Income / Total Equity

The Net income is calculated as follows

= ( Operating profit – Interest payment on liabilities ) * ( 1 – Tax rate )

= ( Operating profit – ( Total liabilities * interest rate on debt )) * ( 1 – Tax rate )

As per the information given in the question we have

Operating profit = $ 8,680,000 ;   Total liabilities = $ 25,000,000 ; Interest rate on debt = 5.6 % = 0.056 ;

Tax rate = 35 % = 0.35

Applying the above values in the formula we have net income as

= ( $ 8,680,000 – ( $ 25,000,000 * 0.056 ) ) * ( 1 – 0.35 )

= ( $ 8,680,000 – $ 1,400,000 ) * ( 1 – 0.35 )

= $ 7,280,000 * 0.65

= $ 4,732,000

Thus the Net Income = $ 4,732,000

The total Equity = Total assets – Total liabilities

As per the information given in the question we have

Total assets = $ 45,000,000 ;   Total liabilities = $ 25,000,000   ;

Thus the Total equity = $ 45,000,000 - $ 25,000,000

= $ 20,000,000

Thus the Net income = $ 4,732,000 ; Total equity = $ 20,000,000

Thus the return on equity = $ 4,732,000 / $ 20,000,000

= 0.2366000

= 23.6600 %

= 23.66 % ( when rounded off to two decimal places )

Thus the Return on equity = 23.66 %