Finance Question: A firm wishes to maintain a growth rate of 12.4 percent and...

[jackson1245]

A firm wishes to maintain a growth rate of 12.4 percent and a dividend payout ratio of 28 percent. The ratio of total assets to sales is constant at 0.60 and the profit margin is 7.1 percent. If the firm wishes to maintain a constant debt to equity ratio what must it be?
Could you please answer using these formulas?

Sustainable growth rate (SGR) = (ROE*R) / (1-(ROE*R))

ROE = p(S/A) (1+D/E)

 

[jackson1245]

Finance Question

Sorry for not showing how for I got.

For Sustainable Grow Rate equation I got:

Retention Ratio R= 1-0.28=0.72

0.124=(ROE * 0.72) / ((1-(ROE * 0.72)) For this equation I do not know how to algebraically re-arrange it to solve for ROE ?

Once I get ROE then I could put into the below equation but with it I do not know how to re-arrange the equation to solve for D/E ? I need help on how to re-arrange to solve for D/E.

What I have so for I believe is : ROE = 0.071(1/0.6) (1+D/E)

Thanks for your help

 

[ksdhart2]

Okay, so rearranging equations to solve for a specific variable is pretty easy. It's just a matter of moving terms around until you isolate the variable you want to solve for. One key thing to remember is that you can always perform any operation, so long as you perform the same operation to both sides of the equation. Let's look at your first equation that you want to solve for ROE.

\(\displaystyle 0.124=\dfrac{ROE \cdot 0.72}{1-(ROE \cdot 0.72)}\)

What if you multiplied both sides by 1 - (ROE * 0.72) to "clear" the fraction?

\(\displaystyle 0.124 \cdot (1-(ROE \cdot 0.72)) =\dfrac{ROE \cdot 0.72}{1-(ROE \cdot 0.72)} \cdot \dfrac{1-(ROE * 0.72)}{1}\)

Where does that lead you? Similarly for the second equation, except here we'll want to run the process "in reverse" to "create" a fraction. Start with the given:

\(\displaystyle ROE = 0.071 \cdot \dfrac{1}{0.6} \cdot \left(1+\dfrac{D}{E} \right)\)

What if you divided both sides by 0.071?

\(\displaystyle \dfrac{ROE}{0.071} = \dfrac{0.071}{0.071} \cdot \dfrac{1}{0.6} \cdot \left(1+\dfrac{D}{E} \right)\)

Where does that lead you?

 

[jackson1245]

Finance

For the first part would it be as follows ?

ROE = (1-0.72) / 0.124

Thanks for your help.

 

[jackson1245]

Finance Question

Thanks Dennis

If I re-write the formula.

G = (E*R) / ((1-(E*R))

0.124 = (E*0.72) / (1-(E*0.72))

If I wish to solve for E would the following be correct I am still have trouble with the algebra I think ?

E = (1-0.72) / 0.124

 

[Otis]

0.124 = (E*0.72) / (1-(E*0.72))

If I wish to solve for E would the following be correct ...

E = (1-0.72) / 0.124

You can determine this is not correct by evaluating.

Your value for E is 2.25 (rounded).

If you replace E with 2.25, in the first equation above, followed by evaluating the right-hand side, you'll get:

0.124 = -2.598 (rounded)

Your value of E does not lead to a true statement.

---

As an example, here's an equation of similar form. Try to follow these steps, and then apply them to your equation.

6 = E*2 / (1 - E*2)

Start by multiplying both sides by (1 - E*2). This will clear the denominator, on the right.

6*(1 - E*2) = E*2

Use the Distributive Property to expand the left side.

6 - E*12 = E*2

Combine the E-terms, by adding E*12 to both sides.

6 = E*14

Divide both sides by 14, to solve for E.

3/7 = E

 

[jackson1245]

Finance Question

Thanks Otis for helping. Can someone have a look at what I have got now.

Formula: G = (E*R) / (1-(E*R))

Variables:
G=0.124
R=0.72
E= Unknown

0.124=(E*0.72)/(1 - E*0.72))

0.124*(1 - E*0.72) = E*0.72

0.124 - E*0.08928 = E*0.72

0.124 = E*0.80928

E=0.1532

Therefore could it have been written as follows:

E = 0.124 / ((0.124*0.72)+0.72)
E = 0.1532

Therefore could the formula G = (E*R) / (1-(E*R)) be written as follows to solve for E:

E = G / ((G*R)+R)

If someone could check greatly appreciate it.