Corporate Valuation Equations & Procedures
(1) Constant Growth Model: ‫معدل النمو الثابت‬
P
D0 * (1  g )
kg
(2) Two Growth Model: ‫ أحدهما مؤقت و اآلخر دائم‬،‫معدلين نمو‬
  1  g1  1  g1  N
P  D0  

  k  g1   1  k 

 1  g1   1  g 2  
*


 k  g1   k  g 2  
(3) Multiple Growth Model: ‫عدة معدالت نمو اخرها دائم‬
D1  D0 (1  g1 )
D2  D0 (1  g1 )(1  g 2 )
.
.
Dn  D0 (1  g1 )(1  g 2 )...(1  g n )
Stochastics ‫العشوائيات‬
(4) Additive ‫عشوائي بإضافة ثابتة‬
D0
1 1 
C* p*  2 
k
k k 
P: Price
C: constant increase in dividends
p: probability (such as paying out dividends 5 times in 9 years)
k: cost of equity
‫العائد على حقوق المالكين‬
: Dividends D0
P
(5) Additive with BR ‫عشوائي بإضافة ثابتة مع احتمال إفالس‬
 1

D0 * (1  BR )
1
C* p*

2
k
 k  BR (k  BR ) 
BR: Bankruptcy
P
(6) Geometric ‫عشوائي بنمو نسبي‬
P
D0 (1  p * g )
k  p*g
(7) Geometric with BR ‫عشوائي بنمو نسبي مع احتمال إفالس‬
P
D0 * (1  ( p * g )  BR )
k  ( p * g )  BR
1
Corporate Valuation Equations & Procedures
(8) Additive with Dividend Cuts ‫عشوائي إضافي ثابت مع تنزيل‬
P
D0
1 1
 (  2 ) * C * ( pu  p d )
k
k k
(9) Additive with cuts and BR ‫عشوائي إضافي ثابت مع تنزيل و إفالس‬
P

D0 * (1  BR )  1
1


* C * ( pu  p d )
2
k  BR
 k  BR (k  BR ) 
(10) Geometric with cuts ‫عشوائي بنمو مع تنزيل‬
P
D0 1  ( pu  pd )* g
k  ( pu  p d ) * g
(11) Geometric with cuts and BR ‫عشوائي بنمو مع تنزيل مع احتمال إفالس‬
P
D0 (1  ( pu  p d ) * g  BR )
k  ( pu  pd ) * g  BR
Projecting the FCF:
1.
2.
3.
4.
5.
6.
7.
8.
9.
NOPAT = Operating Profit – Tax on Operating Profit
Operating Current Assets (OCA) = Cash + Inventory + Accounts Receivable
Operating Current Liabilities (OCL) = Accounts Payable + Accrued Expenses
Net Operating Working Capital (NOWC) = OCA – OCL
Total Net Operating Capital (Total Operating Current Assets) = NOWC + Net PPE (Net
Operating Long Term Assets)
Investment in Total Net Operating Capital = (Total Net Operating Capital)n – (Total Net
Operating Capital)n-1
FCF = NOPAT – Investment in Total Net Operating Capital
ROIC = NOPAT / (Total Net Operating Capital)n-1
Tax Rate = Taxes / Earnings before Taxes
Estimating the Weighted Average Cost of Capital:
WACC = Rd * Wd (1 – t) + Re * We
a. Rd: cost of debt = YTM (annual)
b. Wd: weight of debt
c. T: tax
d. Re: cost of equity = rf + B * Risk Premium = rf + B * (rm – rf)
e. We: weight of equity
2
Corporate Valuation Equations & Procedures
Estimating the Per Share Value:
FCFn 1
FCFn (1  g )

WACC  g
WACC  g
Debt = Long Term Debt at MV + Short Term Debt at BV
PV = Value of Operations = NPV
Value of Equity = PV of Operations – Debt
Price Per Share = Value of Equity / # of Shares
1. HV n 
2.
3.
4.
5.
Projections of Financials and Valuation:
1. Interest Income = Interest Rate on Short Term Investment * (Short Term
Investments)n-1
2. Interest Expense = Interest Rate on Debt * (ST Debt + LT Debt)n-1
3. Additions to Retained Earnings = Net Income – Dividends
4. (Retained Earnings)n = (Retained Earnings)n-1 + Additions to RE
5. Total Common Equity = Common Stock + Retained Earnings
6. Specified Assets = OCA + Net PPE
7. Specified Liabilities = OCL + LT Debt + Total Common Equity
8. Total Value of Firm = PV of Operations + Value of Investments
9. PV of Operations = NPV(WACC,FCF1, ….., FCFN). FCFN includes HV.
10. Value of all Debt, preferred stock, and other non-operation liabilities = ST Debt + LT
Debt (in the class example; might be changed in other examples)
Ratios & Equations:
1. ROE = NI / Equity
EPS  Dividends
EPS
3. Growth Rate = ROE * RR ‫معدل النمو لتوسع الشركة‬
4. Growth in Dividends = (D1 – D0) / D0
5. Growth in Sales = (S1 – S0) / S0
6. PE = PPS / EPS; PE ‫هو مضاعف الربحية و عكسه هو معدل العائد المطلوب مقابل كل دينار يتم دفعه‬
When PE increase, stability decrease.
7. SPS = Sales / # of Shares
8. PS = PPS / SPS (‫)كم دينار أنا مستعد أن أدفع مقابل كل دينار تحصله الشركة للسهم الواحد‬
9. Value of Operations (Vop) = VD + VE
10. Book Value Per Share (BVPS) = VE / # of Shares
11. Price to Book Ratio (PB) = P / BVPS; P is the MV (‫)القيمة السوقية‬
12. PPS = PE * EPS = VE / # of Shares; VE is the MV capitalization
13. BVPS = Equity (from the B/S) / # of Shares
14. g = RR * ROE = (1-payout) * ROE
2. Re tentionRate( RR ) 
3