会计学得太糟糕了,以至于现在老被一些细节困扰。在近来这个重新学习DCF进行公司估值的过程中,我发现很多公式中的Tax很搞。
计算FCF的公式虽然换汤不换药,但没有彻底搞清每个零部件之间关系的情况下,还是让人觉得挺烦的,看过最精简的一个是这样的:FCF = NOPAT— Net Investment in operating assets, 不错不错,一个NOPAT一下合并了好多项。(参考中文第十章:企业价值评估,实体现金流量=息前税后利润-净投资)
但我一直不很懂这么一个Net Operating Profit After Tax是如何被创造出来的,因为它并不是在利润表可以现成数据表现出来的,当然它在计算EVA时功不可没,现在似乎有所感悟:之所以要计算这个NOPAT,是因为在给公司估值时,我们关心的只是经营活动,所以税收我们也只考虑经营活动产生收益部分所需缴税,至于非经营活动产生税收跟企业持久的发展是没有必然联系的,所以不予考虑。因此便有了这么一个公式:
NOPAT = Operating Profit - Taxes on Operating Profit,用EBIT来简单等价Operating Profit的话,就得到NOPAT = EBIT*(1-tax rate),
这还不够准确,因为还有递延税款等在税上面的影响。所以精确的说法应该是:
If OP=EBIT, NOPAT = EBIT*(1-t) + change in deferred taxes.
首先值得高兴的是,今天纠正了一个小错误,根本来说,Operating Income/Profit ≠ EBIT
Operating income is sales minus COGS, SGA and depreciation. This sounds like EBIT but isn't always EBIT: companies often include nonoperating income in EBIT. 看一下间接计算EBIT的公式就清楚了:
EBIT = 销售收入-成本-营业费用-管理费用+营业外收支净额+投资净收益,而确切定义的OP是不包括最后两项的,这就是两者的差别所在。也就是说
OP=EBIT- nonoperating income当然,我们常常可以看到把EBIT和OP近似处理的情形,但是定义上一定要搞清!另外,我也知道为什么一直处于混沌状态的原因了,因为西方报表自上而下读下来,看起来似乎OP就是EBIT嘛,但这只是简化了的报表,由此也得到一个教训:学东西还是一步到位,从最复杂的看起,这样起码不会犯以偏概全的错误了。
GROSS SALES
– (SALES) DISCOUNTS, RETURNS, AND ALLOWANCES
= NET SALES
– COST OF GOODS SOLD
= GROSS PROFIT or "GROSS MARGIN"
- OPERATING EXPENSES (Selling, Gen. & Adm.) [*excluding Dep. & Amort.]
= EARNINGS BEFORE INTEREST, TAXES, DEP., & AMORT. (EBITDA)
- DEPRECIATION & AMORTIZATION
= NET OPERATING INCOME (NOI) or EARNINGS BEFORE INTEREST AND TAXES (EBIT)
- INTEREST EXPENSE
= EARNINGS BEFORE TAXES (EBT)
- TAX EXPENSE
= NET INCOME BEFORE PREFERRED DIVIDENDS or NET INCOME AFTER TAXES
- PREFERRED DIVIDENDS
= NET INCOME AVAILABLE TO COMMON STOCKHOLDERS (NIACS)
下面是微软的IS,这个就比较全面了:
Total Revenue
Cost of Revenue
Gross Profit
Operating Expenses
Research and Development
Selling General and Administrative Expense
Non Recurring Other Operating Expenses Operating Income
Total Other Income and Expenses Net
EBIT
Interest Expense
Income Before Tax
Income Tax Expense
Equity Earnings or Loss
Unconsolidated Subsidiary
Minority Interest
Net Income From Continuing Operations
Nonrecurring Events
Discontinued Operations
Extraordinary Items
Effect Of Accounting Changes
Other Items
Net Income Preferred Stock And Other Adjustments
Net Income Applicable To Common Shares 区别就在蓝色标注地方啦,简单的IS中都没列出nonrecurring events,另外这里的nonrecurring events,似乎还不纯粹就是我们中国IS中的营业外收支
,真是烦人啊...
搞清了OP和EBIT的区别,接下来就要分析这个NOPAT与Tax之间的关系了,还是举个例子吧。假设条件:
BS: Future income taxes今年比去年增加了325,也就是说change in deferred tax=325
IS: Taxes=(434)
IS: Interest Expense=(675)
IS: Foreign exchange gain=14 (nonoperating gain)
OP=2056
Marginal tax rate=31.16%
Effective tax rate = 31.1%
方法一: 从OP开始计算,NOPAT= Operating income - taxes on operating income, 重点关注taxes on operating income如何一步一步计算的
(1) 我们可以得出Actual Taxes Paid = Reported Taxes - Change in Def.Taxes
= 434-325
=109
(2)
We must take care of the taxes paid on the foreign exchange gain (nonoperating income) and the taxes saved due to the interest expense. 根据上面的假设条件,
the taxes saved because of interest expense is 31.16%*675 = 210
the taxes it paid on its foreign exchange gain is 31.16% *14=4
(3) Taxes on operating income is then
Actual Taxes + Taxes Saved because of Interest Expense - Taxes Paid on Nonoperating Income = 109 + 210 -14 = 315.
(4) NOPAT = Operating income - taxes on Operating Income
= 2056 - 315
= 1714
这是最基本的方法,完全从NOPAT的定义一步一步推导得出,关键需要注意的是这里的NOPAT不能只是简单的用OP*(1-tax rate),也就是2056*(1-31.16%)=1415,
这样算的问题在于:this method
understates company's actual NOPAT due to
the taxes it deferred and other tax savings. 但如果把degferred taxes加上去的话,我们得到1415+325 = 1740,这就跟前面计算的NOPAT非常接近了,但要完全一致的话,需要用实际税率来计算,也就是说
NOPAT=Operating Income*(1-effective tax rate) + change in Def.tax, 即
NOPAT = 2056 *(1-31.1%) + 325 = 1741, 就是方法一中一步一步推导来的结果。
这种方法计算的关键是先一步步把taxes on OP求出,然后从OP中减去即可,详细公式可以这样表示:NOPAT = OP - [(reported tax - change in Def.tax) + I*(1-t) - Nonoperating income*(1-t)] 方法二: 从EBIT开始计算,很简单,利用OP = EBIT - nonoperating income这个关系代入方法一的简化公式可得:NOPAT = (EBIT - Nonoperating income) * (1-t) + change in Def.tax。
方法三: 从NI开始计算,也很简单,利用EBIT = NI/(1-t) + Interest Expense这个关系, 简化得到为:NOPAT=NI + change in Def.tax + I*(1-t) - Nonoperating income*(1-t).
总结:抓住一点,记住NOPAT的最初定义,和近似处理NOPAT=OP(1-t)+change in Def.tax, 以及NOPAT、EBIT和NI之间的关系,然后视情况而定。基本就是这样啦,累死了。
晚上回家继续研究,才发现原来几乎所有的教材中都是直接用EBIT(1-T)作为NOPAT,也就是息前税后利润来计算FCF,那岂不是把一些非经营活动产生收入也都算进来了?
另外看到J.O'Hanlon的讲义里边讲FCF也是从NOPAT出发计算,其中他特别引用了Mckinsey那本Valuation: Measuring and Nanaging the Value of Campanies中的一段话(看来经典教材就那么几本了,我是最近才知道这本书,当当还老缺货,那时可是毫无意识的):Free cash flow is equal to the after-tax operating earnings of the company, plus non-cash charges, less investment in operating working capital, property, plant and equipment and other assets.
It does not incorporate any financing-related cash flows such as interest expense or dividends. THe tax should relect the tax relating to the operating entity and should not reflect the interest deduction.强调了息前的概念,因为这里估的是整个企业的价值,而不是股权价值,前者比后者多了一个I*(1-T).
老头的公式是FCF=NOPAT - Increase in operating capital
= NOPAT + DA - △WC - Capital Expenditure
顺便把CFA II中FCFF的四种方法一并给出吧:首先说明
NCC: includes non-cash items such as Depreciation and Def.tax
FCInv : Fixed capital investment equals forecasted increase in the net PP&E account plus depreciation
FCFF = NI + NCC + I*(1-T) - WCInv - FCInv FCFF = EBIT*(1-T) + Dep - WCInv - FCInv, 本来就有NI+I*(1-T) = EBIT*(1-T)成立
FCFF = EBITDA*(1-T) + Dep*T- WCInv - FCInv, 只要把EBIT=EBITDA-DA代如即可
FCFF = CFO - FCInv + I*(1-T)
*******************************************************************
FCFE = FCFF - I*(1-T) + net borrowing (net borrowing = long and short term new debt issues - long and short term debt repayments)
FCFE = NI + NCC - WCInv - FCInv + net borrowing
FCFE = CFO - FCInv + net borrowing
如此看来,再总结一下: 上面说了那么多关于NOPAT的东西,还是以CFA为准吧,要不真正晕头了。这样,也就不用把Def.tax作为NOPAT的一项,直接放置NCC里,如此分类似乎更为清晰;当然把Def.tax放进去的话,在税后这个概念上也许可以表述得更加准确一些。反正一个原则就是用纯经营活动产生收益operating profit来扣税,一般来说,也就是EBIT了。至于EBIT包含有非经营活动收益的情况,也就是说EBIT≠ OP的情形(这个在中国的利润表里倒是很容易理解),以后慢慢再琢磨吧。一句话,计算FCF从NOPAT开始,也就是从EBIT(1-T)开始。结束。