財務筆記: Equity valuation - Residual Income Valuation (part 21) @ 經濟,財務,統計學,數理科學與政治評論

寫在前面:Residual Income與Eccnomic Value Added(EVA)起源於1920年代General Motor希望評估自身部門的獲利能力!!RIM適用於越到後期的現金流量與價值越難估計以及現金股利發放少或現金流量會隨著各種總體情況變動大的企業!!

Hello there:

這裡從P/B開始談residual income對於企業價值的評價!!Residual Income Method相對於傳統的Discounted Dividend Method,期初的資金流入認列是比較多的,因此越到後面的terminal value對於RIM遠以DDM來得小!!相對上RIM適用於不發現金股利或將大部份的現金做為營運資本中的企業!!

the value of firm = Sum of (Residual Income for each period discounted at required return on equity)

The imprtant concept and implement principle behind RIM:

RIM適用於(a)不發放現金股利或企業現金流量波動度大的企業(e.g.,高科技半導體產業等等),(b)預期未來Free Cash Flows為負值,(c)企業的終值(the terminal value)具有相當程度的不確定性,因此使得相當依賴終值估計的DDM與FCFM Mehthods相當難以使用!!而RIM的缺點在於當企業的B/S上帳面價值變動並非完全來自於I/S中Earnings的增長時,必須進行相當程度的調整!這與另一個類似的估計方法EVA=NOPAT-$WACC = EBIT*(1-tax rate)-WACC* Total Capital是相同的!!RIM適用於有實質資產且有其成長動能必須保留大量現金來發展的企業,因此RIM法在某些程度上面確實可以視為是DDM的延伸,意即在某些情境之下可以得到與DDM相同的結論!!而RIM是以企業股東為主的思考,但也可以延伸從公司所有利益相關者去思考,那時其所連結的折現率就是WACC (Stern company所發展出來的EVA即為一例!!)!!

所需調整的項目包含(a) Capiatalize important R&D or amortize Goodwill將其加回類似EBIT(1-TR)項目,因其對於未來企業的Residual imcome與ROE均有相當正面的影響,(b)Operating leases一律改回成Capital leases,(c)將Deferred tax部分刪除只考慮cash taxes部分,以降低其估算造成的不確定性,(d)Inventory因為採用LIFO的調整必須改成FIFO並去掉LIFO reserve科目,(e)PBO的部分必須進行調整已反映future status of the plan(特別是IAS smoothing所造成的估計差異),(f)nonrecurrung items應被排除在Residual income之外,應其並非常駐項目!!(g)加入the cost of Strategic investment,因其對未來的residual income有正面幫助!!等等.....都是因為RIM法相當程度上面是擁有Dirty Surplus relation而非Clean Surplus relation的!!(詳見後面!!)

Important issues:

1. Po/Bo = (ROE - g)/(r - g)

<=> Vo= Bo + [(ROE - r)/(r - g)]* Bo

2. RIM最傳統的定義為:

Vo = Bo + Sum of (t=1,2,3,4,....., RI(t) discounted at the required rate of return on equity r)

= Bo + Sum of (t=1,2,3,4,....., [E(t) - r * B(t-1)] discounted at the required return on equity r)

其中 E(t) = the EPS in the period t

B(t-1) = the BVPS in the period t-1

= Bo + Sum of (t=1,2,3,4,....., [E(t) - r * B(t-1)] discounted at the required return on equity r)

= Bo + Sum of (t=1,2,3,4,....., ([ROE(t) - r] * B(t-1)) discounted at the required return on equity r)

因為 EPS = ROE * BVPS

值得注意的地方是,我們需要每一期帳面價值的資訊,與每期EPS與配發現金股利的資訊,對此我們稱之為Clean Surplus Relation

B(t) = B(t-1) + E(t) - D(t)

這裡帳面價值的增加(B(t)-B(t-1), the B/S item)完全來自於Earnings(E(t), the I/S item)的增加!!

3.RIM與DDM的關係

DDM:

Vo = Sum of (t=1,2,3,4,..... D(t) discounted at required return on equity)

= Sum of (t=1,2,3,4,..... (E(t) - [B(t) - B(t-1)]) discounted at required return on equity)

= Bo + Sum of (t=1,2,3,4,..... [E(t) - r * B(t-1)] discounted at required return on equity)

最後透過Clean Surplus Relation轉化成為RIM的關係.....

值得一提的是所謂的Clean Surplus Relation談的是企業B/S的項目完全都是透過I/S的累積所產生出來的,而所謂的Dirty Surplus Relation則是指B/S裡面的科目並非透過I/S相對應的科目累積出來,而是直接在B/S項目中展現,e.g.,Other Comprehensive Income, Cumulative Translation Adjustmet等等!!

另外,當我們知道目前的帳面價值,與未來企業每年將賺得相同的Earnings直到永遠,且將所有的Earning都配發為dividend,此時我們將知道the value of the firm using the DDM = the value of the firm using the RIM!!

4. The Market-to-Book Value relation for the RIM

Vo = Bo + Bo * (ROE - r)/(r - g)

= Bo + Sum of (t=1,2,3,4,....., ([ROE(t) - r] * B(t-1)) discounted at the required return on equity r)

i.e., (ROE - r) * Bo/(r - g)

= Sum of (t=1,2,3,4,....., ([ROE(t) - r] * B(t-1)) discounted at the required return on equity r)

這裡透露了一個重要的觀念,當ROE = r時,我們知道P/B = 1與RI = 0!!!

5.The Multistage RIM valuation with persistent factor omega (between zero and one)

概念為 Vo = Bo + PV of interim high-growth RI + PV of continuing RI,所以我們知道

Vo = Bo + Sum of (t=1,2,..T, ([ROE(t) - r] * B(t-1)) discounted at r) + [P(T) - B(T)]/(1 + r)**T

= Bo + Sum of (t=1,2,...T, [E(t) - r * B(t-1)] discounted at r) + [E(T) - r * B(T-1)]/[(1 + r - omega)*(1 + r)**(T - 1)]

(a) RI persists forever, then we set omega to be 1!

PV of contimuing RI in the period T-1

= Residual Income of time T/requird return on equity (r)

(b) RI suddenly stops and to be zero after time T, we set omega to be zero!

PV of contimuing RI in the period T-1

= Residual Income of time T/(1 + r)

PV of contimuing RI in the period T-1

= Residual Income of time T/(1 + r - omega)

(d) We have further information (like P/B ratio estimate or something else) for the terminal period T, then we have

PV of contimuing RI in the period T-1

= [(P(T) - B(T)) + RI(T)]/(1 + r)

where

P(T) may be B(T)* (P/B estimate) or other information given

B(T) is the book value we calculate in the period T

RI(T) is the residual income of the period T

(小結) omega可以為一,也可以為零,也可以介於零與一之間!!當企業追求成長保有大量現金來發展時,omega就非常接近一,因其成長動能得以維繫,所以RI的數值不會太小!!同樣地,當企業的ROE太高,可能造成其他人的加入,因此預期omega將越來越低,最後導致ROE=r,最後使得omega=0與RI=0!!