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卓娅 · 2023年07月06日

计算

NO.PZ2017102901000052

问题如下:

Companies X and Z have the same beginning-of-the-year book value of equity and the same tax rate. The companies have identical transactions throughout the year and report all transactions similarly except for one. Both companies acquire a £300,000 printer with a three-year useful life and a salvage value of £0 on 1 January of the new year. Company X capitalizes the printer and depreciates it on a straight-line basis, and Company Z expenses the printer. The following year-end information is gathered for Company X.

Ÿ Ending shareholders’ equity: £10,000,000

Ÿ Tax rate: 25%

Ÿ Dividends: £0.00

Ÿ Net income: £750,000

Based on the information given, Company Z’s return on equity using year-end equity will be closest to:

选项:

A.

5.4%.

B.

6.1%.

C.

7.5%.

解释:

B is correct.

Company Z’s return on equity based on year-end equity value will be 6.1%. Company Z will have an additional £200,000 of expenses compared with Company X. Company Z expensed the printer for £300,000 rather than capitalizing the printer and having a depreciation expense of £100,000 like Company X. Company Z’s net income and shareholders’ equity will be £150,000 lower (= £200,000 × 0.75) than that of Company X.

ROE=NI/equity=(750,000-150,000)/(10,000,000-150,000)=600,000/9,850,000=0.

题目假设X公司和Z公司财务数据都是一样的,除了对一笔printer采购支出的处理之外。X公司是资本化,而Z公司是费用化,题目给了X公司的财务数据,让计算Z公司的ROE。我们根据题目给的数据可以计算出来X公司的ROE,在此基础上进行调整就可以得到Z公司的ROE。调整的时候就要考虑资本化和费用化导致的两个公司NI和Equity的不同。

看NI的不同,我们就要看损益表:X公司资本化,printer被当做资产处理,损益表中会有一笔100,000的折旧费用。Z公司费用化,printer的全部成本都算作expense,因此Z公司损益表中会有一笔300,000的expense。两个公司损益表中费用的差额为200,000,由于有税收的影响,最终NI的差异是200,000*(1-25%)=150,000,也就是Z公司的NI比X公司的NI少150,000。

再比较equity的不同,因为其他条件都相同,两个公司equity受到的影响就只有retained earning的影响,这个也是跟NI相关联,Z公司NI比X公司少150,000,那么Z公司的equity也会比X公司的equity少150,000。

最后再调整X公司的ROE以得到Z公司的ROE:

(750,000-150,000)/(10,000,000-150,000)=600,000/9,850,000=0.61

文字的解题明白,但是计算中的数字是怎么一个个计算出来的呢?麻烦老师一步步解题解释一下,谢谢

1 个答案
已采纳答案

lynn_品职助教 · 2023年07月07日

嗨,从没放弃的小努力你好:


return on equity 


这道题说难也难,说简单也简单,其实就是考了ROE的计算,但是因为给的条件是X公司的。


所以真正考的是资本化和费用化导致的两个公司NI和Equity的不同。


首先我们需要理解税盾的意义——折旧和费用在I/S表中都是在税前扣除的,所以虽然这些费用会使NI下降,但是同时也使公司要交的税下降了,所以实际对于公司的NI的下降程度就没有那么高,实际对NI的减少就变成:折旧或费用*(1-t)


X 公司对打印机资本化,那就是期初确认30万资产,同时减少30万现金。使用一年后,折旧费用发生30/3=10万,资产减少10万,同时利润表减少10万折旧。由于折旧有税盾的作用,所以最后由于产生了折旧,所以少交了10*tax rate的税费——即实际这笔折旧值减少了10*(1-tax rate)的现金(B/S表)以及10*(1-tax rate)的利润(NI)


Z公司费用化,就是减少30万现金,同时确认30万费用。到年底由于费用也具有税盾的作用,实际可以少交30*tax rate的税费,也就节省了30*tax rate的现金支出——所以这笔费用化减少了30*(1-tax rate)的现金(B/S表)和50*(1-tax rate)的利润(NI)


两者做差就会发现,Z公司相对X公司,无论NI还是equity都下降了30*(1-tax rate)-10*(1-tax rate) = 20*(1-tax rate) ,所以最后计算Z公司的ROE的时候,就是分子分母同时减去 20*(1-tax rate) =150,000

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