經濟,財務,統計學,數理科學與政治評論

Hello there:

  這裡要談企業的FCFF(Free Cash Flow to the Firm)與FCFE(Free Cash Flow to Equity),以及他們各自與CFO, CFI和CFF的關係!!!

(1) FCFF with I/S (Income Statement)

  FCFF(Free Cash flow to the Firm)

     = Net Income + Non-Cash Charge(NCC) + Interest Expense*(1- tax rate) - FCInv - Diff NWCInv

 其中

   Non-Cash Charge包含兩個部分,一個是Depreciation for the tangible assets與amortization for the intangible assets,因其並沒有實際的現金流入與流出,另一個是Deferred income taxes Asset/Liability的部分,Deferred item的減項(增項)就是FCFF的增項(減項),特別值得注意的是這些項目短期不會調整回到equity的科目,,因為如果為短期,則目前記入之後再過來又必須回沖,如此就失去了FCFF的穩定性,因此主要的考量點就在於這個項目是否為the persistent component of FCFF,如果短期會回沖回equity科目,則不記入FCFF,若否,方才記入;而FCInv則為新購買的PP&E (Property, plan and equipment).這個部分Capital expenditure的增項(因其為逐年累積的科目);NWCInv則等於Non-cash assets扣除Non-Cash,non-Debt Liabilities,Non-Cash,non-debt liabilities必須扣除notes payable與其他長短期的debt item,因其為financing item而非operating item!!所以一般Diff NWCInv = Diff Accounts receibles + Diff Inventory - Diff Accounts payables + Diff Accrued taxes or expenses (expense上升表示現金未付,因此得到保存!!); 所有內涵均為增量(incremental value)!! Also note that,If these cash flows are not expected to persistent in the near future, then we should not include them in the FCFF. (e.g. Employee stock options,as we receive the money, it is treated as Cash Flow from Financing instead of Cash flow from operating!!)

  因此FCFF簡單可寫為

    FCFF = Net Income

         + Depreciation and Amortization

         +/- Deferred taxes liability (asset)

         +/- Loss(gain) from assets sales <infequent and usual items>

         + Asset impairments <infrequent and usual items>

         + Int. Exp.*(1 - TR)

         - FCInv

         - (Diff A.R. + Diff Inv. - Diff A.P. + Diff Accrued taxes and expenses)

  p.s.要注意Accrued items與Deferred items在概念上是不同的,Accrued item 是NWCInv, Deferred item 是屬於NCC!!!

 (2) FCFF with CFO (Cash Flow from operations)

  Cash flow from operations 傳統上面包含幾個項目:

   CFO = Net Income + Depreciation - Diff Accounts receivable - Diff Inventory + Diff Accounts payable

  而Cash flow from investing(一般將CFO是為短期投資所需資金流,將CFI是為長期投資所需資金流),一般包含著Purchase of PP&E,而這個部分為FCInv item,i.e., FCInv = Purchase of PP&E,所以我們知道FCInv主要為CFI的item

  至於CFF在這裡談的主要是短期借款(notes payable)與長期債務(long-term debt),因此這兩個部分必須被排除在NWCInv當中(為Financing 項目,而非operating項目)...只是我們知道這些每年增量的部份(net borrowing)還是會包含在FCFE裡面!!

  也因為如此我們知道

     FCFF = (NI + Dep. - Diff NWCInc) + Int. exp.* (1- tax rate) - FCInv

          = CFO + interest expense*(1 - tax rate) - FCInv

  值得注意的是infrequent and unusual items,比如 Asset impairments與losses on asset sales,這些部分同樣屬於non-cash charges,因此必須add back回到CFO上面!!

 (3) FCFF與FCFE

   FCFE = FCFF - interest expense * (1- tax rate) + Net Borrowing

  這裡的Net Borrowing主要指的是CFF的items,Diff Notes payable與Diff Long-term debt financing(both are B/S items, we focus on their incremental number increased in a year)所收到的錢!!

 (4)FCFF or FCFE 與EBITDA or EBIT

  Recall that

   Net Income = (EBIT - Interest Expense)*(1- Tax rate)

   EBITDA = EBIT + Depreciation + Amortization

   i.e., Net Income = (EBITDA - Dep. - Int. Exp.)*(1- tax rate)

 因此

  FCFF

  = NI + NCC + Int. Exp.*(1 - TR) - FCInv - NWCInv

  = EBIT*(1 - TR) + NCC - FCInv - NWCInv

  = EBITDA*(1- TR) + Dep.*(Tax Rate) -FCInv - NWCInv

  and

  FCFE

  = EBIT*(1 - TR) + NCC - FCInv - NWCInv - Int. Exp.*(1 - TR) + Net Borrowing

  = EBITDA*(1- TR) + Dep.*(Tax Rate) -FCInv - NWCInv - Int. Exp.*(1 - TR) + Net Borrowing

  (5) Forecasting FCFF與FCFE with target debt ratio (DR)

 Recall that

  FCFF = NI + NCC + IntExp.* (1 - TR) - FCInv - NWCInv

       = EBIT * (1 - TR) + Dep. - FCInv - NWCInv

       = EBITDA * (1 - TR) + Dep. * TR  - FCInv - NWCInv

 與

   FCFE = FCFF - IntExp.* (1 - TR) + Net Borrowing

        = NI - (FCInv - Dep.) - NWCInv + Net Borrowing

  當我們預期NCC部分只有折舊(depreciation),而且我們知道 (Capital expenditure - Depreciation expense)/(Increase in Sales)為一個定值,這個背後的概念是capital expenditore包含兩個部分,一個是fixed asset replenish,一個是fixed assets investment for future growth!!同樣地,Increase in Working Capital/(Increase in Sales) 也是假定為另一個定值,此處是將operating中常用的現金流與過往的變動銷售量的關係展現為一個固定比例,以彰顯企業的成長動能來自於等比例的銷售量變動增量!!

  因此...我們可以利用這個數值將其轉化成為Debt Ratio (DR) 去.....

   Net Borrowing = DR * (FCInv - Dep.) + DR * NWCInv

所以我們知道

   FCFE

   = NI - (FCInv - Dep.) - NWCInc + DR * (FCInv - Dep.) + DR * NWCInv

   = NI - (1 - DR) * (FCInv - Dep.) - (1 - DR) * NWCInv

  DR is the target debt-to-asset ratio !!!

 (6) Preferred Stocks and preferred dividends

   對於FCFF而言,因為preferred dividends已經在紀錄Net Income時被扣除了,但FCFF應該包含preferred shareholders...因此

      FCFF = NI + NCC + Int.exp. * ( 1- tax rate) + Preferred dividends - FCInv - NWCInv

  但對於FCFE來說,因為preferred dividends已在Net Income計算出來時被扣除,因此不必包含於其中...

      FCFE = NI + NCC  - FCInv - NWCInv + Net Borrowing [Diff ST loan + Diff LT Bond]