compay's profit margin is 4%
sales-to-asset ratio of 3
a. what is its ROA?
b. if debt-equity ratio is 1.00 taxes 10,000 interest 10,000 and EBIT
40,000 what is the ROE?

Hi!!

a. what is its ROA?

ROA = Net Income/Total Assets =
    = Net Income/Total Assets * Sales/Sales =
    = Net Income/Sales * Sales/Total Assets =
    = Profit Margin * sales-to-asset ratio =
    = 0.04 * 3 =
    = 0.12 or 12%


b. if debt-equity ratio is 1.00, taxes 10,000, interest 10,000 and EBIT
40,000 what is the ROE?

EBT = EBIT - I 

ROE = Net Income/Equity =
    = Net Income/Sales * Sales/Assets * Assets/Equity =
    = Profit Margin * sales-to-asset ratio * Assets/Equity 

Since it is:
Assets = Equity + Debt , 
then:
Assets/Equity = 1 + Debt/Equity 

Then:
ROE = Profit Margin * sales-to-asset ratio * (1 + Debt/Equity) =
    = ROA * (1 + Debt/Equity) =
    = 0.12 * (1+1) =
    = 0.12 * 2 =
    = 0.24 or 24%


See for references:
"Du Pont Identity":
http://www.investopedia.com/terms/d/dupontidentity.asp


------------------------------------------------

I hope that this helps you. Feel free to request for a clarification
if you need it.

Regards.
livioflores-ga

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Request for Answer Clarification by nolig81-ga on 17 Jun 2005 18:49 PDT

livioflores-ga
Thanks for the quick answer. My book answer is a).12 and for b).16
would you say the book answer is wrong for part b.

thanks for you help

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Clarification of Answer by livioflores-ga on 17 Jun 2005 23:44 PDT

Hi!!

I used the most common formula for ROE, I can also use the info
provided by the problem's statement and get the same result:

Assets = Equity + Debt ==> Debt = Assets - Equity ==>

==> Debt * Equity/Equity = Assets - Equity ==>

==> (Debt/Equity)*Equity + Equity = Assets ==>

==> Equity * (1 + Debt/Equity) = Assets ==>

==> Equity = Assets/(1 + Debt/Equity)

On thew other hand we got ROA, and also know that ROA is:
ROA = Net Income/Total Assets 

Then:
Assets = Net Income / ROA =
       = (EBIT - I - T) / ROA

Joining both results we get:
Equity = (EBIT - I - T) / [ROA * (1 + Debt/Equity)] =
       = (40000 - 10000 - 10000) / (0.12 * 2) =
       = 20000 / 0.24 =
       = 83333.333


ROE = Net Income/Equity =
    = (EBIT - I - T)/Equity =
    = 20000 / 83333.33 =
    = 0.24 

This is the same result that we got before. please take a look into
the book to see if something different to the above is used and/or
token into account that can give us a clue to clarify why the results
are differents.

REgards.
livioflores-ga

i do not

Good job thanks