Here is the step-by-step decomposition of the Return on Equity (ROE) for Universal Store Holding Ltd. into its two components: Return on Assets (ROA) and Equity Multiplier (EM).

Step 1: Calculate ROA (Return on Assets)

The formula for ROA is:

[ ROA = \frac{\text{Net Income}}{\text{Average Total Assets}} \times 100 ]

We already know the Net Income for 2023 is $23,571,000.

To calculate Average Total Assets:

• Total assets at the beginning of 2023 (end of 2022): $203,553,000
• Total assets at the end of 2023: $264,845,000

[ \text{Average Total Assets} = \frac{203,553 + 264,845}{2} = 234,199 ]

Now, calculate ROA:

[ ROA = \frac{23,571}{234,199} \times 100 \approx 10.06% ]

Step 2: Calculate the Equity Multiplier (EM)

The formula for Equity Multiplier (EM) is:

[ EM = \frac{\text{Average Total Assets}}{\text{Average Shareholders' Equity}} ]

We already know Average Shareholders' Equity is $123,976,000. Now, calculate EM:

[ EM = \frac{234,199}{123,976} \approx 1.89 ]

Step 3: Verify ROE

To verify that the decomposition of ROE holds true:

[ ROE = ROA \times EM ]

Substitute the values for ROA and EM:

[ ROE = 10.06% \times 1.89 \approx 19.02% ]

This matches the previously calculated ROE.

Conclusion:

• Return on Assets (ROA): 10.06%
• Equity Multiplier (EM): 1.89
• Return on Equity (ROE): 19.02% (as verified)

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