请问如何理解 Assets to Shareholders' Equity ？

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书上的解释是： “Leverage provides the ability to control more assets than an owner would otherwise have the right to control. This ratio tells us precisely how many more assets an owner can control relative to their own equity capital. As a consequence, it also measures how returns are magnified through the use of leverage”

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关键词：Shareholders shareholder Holder Assets equity

非常感谢来自外国朋友h2h2的私信回复，我把他给我的回答详细po在这里，和大家一起学习

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h2h2:

Total Assets=TA, Total Liabilities=TL, Total Equity=TE, Return=R, Return On Assets=ROA, Return On Equity=ROE, Assets To Equity=ATE.

1. TA=TL(if any leverage)+TE
2. ROA=R/TA, R=ROA*TA
3. ROE=R/TE
4. ATE=TA/TE

Assumed: ROA = 0.3 (0.3 Return for each 1 Total Assets employed)

Case 1:
TE=1, TL=0, so TA=1 and ATE=1.
Since ROA=0.3, so R=0.3, then ROE=0.3.

Case 2:
TE=1, TL=9 (loan to buy assets), so TA=10
"Leverage provides the ability to control more assets(9) than an owner would otherwise have the right to control."

and ATE=10. (Case 1 of ATE=1 vs. case 2 of ATE=10)
"This ratio tells us precisely how many more assets(9) an owner can control relative to their own equity capital."

Since ROA=0.3, so R=3, then ROE=3.
(Case 1 of ROE=0.3 vs. case 2 of ROE=3)
"As a consequence, it also measures how returns are magnified through the use of leverage.”

Thank you for your reply ! 再次感谢