​(Using **DuPont**​ analysis)**** 

GarwrykGarwryk​, 

​Inc., which is financed with debt and​ equity, presently has a debt ratio of 

8484 

percent. What is the​ firm's equity​ multiplier? How is the equity multiplier related to the​ firm's use of debt financing​ (i.e., if the firm increased its use of debt financing would this increase or decrease its equity​ multiplier)? Explain.

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Part 1

What is the​ firm's equity​ multiplier?

The equity multiplier is given​ by:

Equity Multiplier equals StartFraction 1 Over 1 minus Debt Ratio EndFractionEquity Multiplier=11−Debt Ratio

The equity multiplier is 

enter your response here. 

 ​(Round to two decimal​ places.)

To calculate the equity multiplier using DuPont analysis, we apply the formula:

\[
\text{Equity Multiplier} = \frac{1}{1 - \text{Debt Ratio}}
\]

Given that the debt ratio is 84%, or 0.84, we can substitute it into the formula:

\[
\text{Equity Multiplier} = \frac{1}{1 - 0.84} = \frac{1}{0.16}
\]

Now, let's compute the result:

\[
\text{Equity Multiplier} \approx 6.25
\]

### Part 2: Explanation of the Relationship Between Debt Financing and the Equity Multiplier
The equity multiplier reflects how much of the firm's assets are financed by equity. A higher equity multiplier indicates more leverage, meaning the company is using more debt to finance its assets.

If the firm increases its use of debt financing, the equity multiplier will **increase**, as the debt ratio increases. This is because the denominator in the formula \( (1 - \text{Debt Ratio}) \) will decrease, making the overall multiplier larger. Higher debt increases financial leverage, raising the risk and potential return for equity holders.

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### Related Questions:
1. What is the DuPont analysis, and how does it work?
2. How does a higher equity multiplier affect a company's Return on Equity (ROE)?
3. What risks are associated with a high equity multiplier?
4. How does a firm's debt ratio affect its overall financial stability?
5. How can a company reduce its equity multiplier while maintaining profitability?

**Tip:** A higher equity multiplier indicates higher financial leverage, but also higher financial risk.

Garwryk Inc., which is financed with debt and equity, presently has a debt ratio of 84 percent. What is the firm's equity multiplier? How is the equity multiplier related to the firm's use of debt financing (i.e., if the firm increased its use of debt financing would this increase or decrease its equity multiplier)? Explain.

This problem explores how to calculate the equity multiplier using DuPont analysis, given a debt ratio of 84%. The solution involves applying the equity multiplier formula and explains the relationship between debt financing and the equity multiplier, highlighting how an increase in debt impacts financial leverage. Suitable for undergraduate finance students.

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