1. Equity Valuation Dividend Discount Method with constant earnings growth rate 1

2. Balance Sheet 2

3. 3

4. Equity Value  For a simple firm  Liabilities + Equities = Debt Capital + Equity Capital + “Non-Capital”  Capital = Debt Capital + Equity Capital  C = DB + EB  Fair value of firm = Fair value of firm’s capital  V = D + E  Fair value of equity, E, is computed from the discounted cash flow to the equity holders discounted at the rate cost of equity capital  Assume that the cash flow to equity holders is only dividends 4

5. Firm Value 5

6. Constant Growth Rate Equity Value  The value of an financial entity is the present value of future cash flows discounted at the rate cost of the cash flows  Now assume that the dividend is growing at a constant rate, g DIV  Write as a infinite sum as follow 6

7. Constant Growth Value  As the spread between the rate cost, k, and cash flow growth, g, narrows, the convergence slows considerably  As cash flow growth rate approaches the rate cost, the series does not converge 7 k=10%

8. Equity Value Management  Explore the relationships between  Earnings growth  Dividend payouts  Cost of equity (rate)  Fair value of equity  Based on the Dividend Discount Method with dividends growing at a constant rate)  Gordon Growth Formula Gordon Growth Formula 8

9. Equity Value Per Share 9

10. Share price v. Dividend Growth Rate d 1 = $0.50, k E = 10% p 0 = pvcy + pvgo 10

11. Price/Earnings Ratio: pe 11  C =  EB +  DB =  RE +  PAR +  APC +  DB  C = additional capital  DB= additional debt  EB= additional equity  RE= additional retained earnings (=NP 1 – DIV 1 )  PAR= additional common equity at par  APC= additional paid in common equity i=-1 Previous period i=0 Next period i=1

12. Price/Earnings Ratio, pe i=-1 i=0 i=1 e 0 e 1 d 0 d 1 eb -1 eb 0 eb 1 b = plowback ratio (assume constant) thus g e = g d (1-b) = dividend payout ratio 12  RE = NP – DIV = NP∙ b RE NP  RE DIV

13. Price/Earnings Ratio: pe  In the case of no additional (external) investor financing   DB = 0,  APC =  PAR = 0   C =  EB =  RE  And a scalable firm with a constant plowback, b 13 b= plowback ratio reinvestment of earnings (1-b) = dividend payout ratio eb = equity book value per share Long run assumption g e =g eb

14. Price/Earnings Ratio: pe 14 Note: With this input, after ~40 years g eb -> g e

15. 15 Source

16. PEG Ratio  The peg is a price measure normalized for earnings (e 1 ) and earnings growth rate (g e )  3 to 5 years estimated growth rate  Typical heuristic  > 2 relatively high valuation  = 1 pe ratio = earnings growth (converting ratio to percent)  < 1 relatively low valuation  Morningstar Table Morningstar Table 16

17. Valuation Ratios 17

18. Forward PE Ratio 18

19. Critical Growth Rates  Internal growth rate, g int : the maximum growth rate that does not require additional external financing  Sustainable growth rate, g sus : the maximum growth rate that maintains the current capital structure,, with additional investor contributed debt 19 NA -1 NA 0 NA 1 IC -1 IC 0 IC 1 i=-1 i=0 i=1 DIV 0 = NP 0 ∙(1-b) DIV 1 = NP 0 ∙(1-b)∙(1+g)  RE 0 = NP 0 ∙b  RE 1 =NP 0 ∙b∙(1+g) Critical growth rate derivations for core business operations So use NA not TA and IC not C or LE NA  IC roa is return on net book assets roe is return on book equity

20. Critical Growth Rates 20  NA=  IC = IC 1 – IC 0 =  DB +  EB =  DB +  APC +  PAR +  RE  NA= g∙NA 0  NA =  RE  DB = NP 0 ∙b∙(1+g) +  DB NA -1 NA 0 NA 1 i=-1 i=0 i=1  RE 0 = NP 0 ∙b  RE=NP 0 ∙b∙(1+g)  NA =  RE  DB 

21. Internal Growth Rate, g int 21 NA -1 NA 0 NA 1 i=-1 i=0 i=1  RE 0 = NP 0 ∙b  RE 1 =NP 0 ∙b∙(1+g)  NA 1 =  RE 1  DB 1 

22. Sustainable Growth Rate, g sus 22 NA -1 NA 0 NA 1 i=-1 i=0 i=1  RE 0 = NP 0 ∙b  RE 1 =NP 0 ∙b∙(1+g)  NA 1 =  RE 1  DB 1 