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Ivana 🍭 · 2023年05月12日

能解释一下为什么要NI/Asset这个吗?不是很懂解析

NO.PZ2022090807000007

问题如下:

A company is considering a switch from an all-equity capital structure to a structure with equal amounts of equity and debt without increasing assets. This change will reduce the net income by 30%. If the current return on equity (ROE) is 10%, the ROE under the proposed capital structure will be closest to:

选项:

A.6%.

B.20%.

C.14%.

解释:

Solution

C is correct.

Alternatively, looking at the effects of the changes in sequence:

When equity decreases by half, ROE would become 10%/0.50 = 20%.

When net income decreases by 30%, the adjusted ROE would become = 20% × (1 – 0.30) = 14%.

A is incorrect because it uses (Net Income × 30%) instead of (Net Income × [1 – 30%]) in the solution. (Net Income/Assets) × (30%/50%) = 10% × 0.6 = 6%.

B is incorrect because it does not adjust net income in the solution.

(Net Income/Assets)/50% = 20%

能解释一下为什么要NI/Asset这个吗?不是很懂解析

1 个答案

王琛_品职助教 · 2023年05月15日

嗨,努力学习的PZer你好:


1

因为题干涉及 ROE,公式为 NI / Equity

变化前,公司的资本结构为 all-equity,即资产负债表右边,全是 equity,没有 debt

所以 equity_0 等于 asset

2

变化后,asset 总量不变,但是 equity 和 debt 占比各 50%,参考题干 "equal amounts of equity and debt without increasing assets."

所以 equity_1 等于 asset / 2

3

其实题目考查的是 ROE 的公式

相当于,分子 NI 变成原来的 70%,分母 Equity 变成原来的 50%,问:分数的结果 ROE,相当于原来的多少

即 70% / 50% = 1.4,变成原来的 1.4 倍

因为变化前的 ROE_0 = 10%,所以变化后的 ROE_1 = 10% x 1.4 = 14%

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