1. CHAPTER 8
Basic Stock Valuation

2. Topics in Chapter Valuing preferred stock Valuing common stock
Dividend growth model
Free cash flow valuation model 1

3. Preferred Stock Hybrid security.
Similar to bonds in that preferred stockholders receive a fixed dividend which must be paid before dividends can be paid on common stock. 33

4. Value of Preferred Stock (Dividend = $2.10; rps = 7%)
V ps = Dividend r ps = $2.10 7% = $30

5. Different Approaches for Valuing Common Stock
Dividend growth model
Constant growth
Nonconstant growth
Free cash flow model

6. Value of dividend-paying stock = PV of dividends discounted at required return^
(1 + rs)1 (1 + rs)2 (1 + rs) (1 + rs)∞
D D D D∞ +
+ … +
Conceptually correct, but how do you find the present value of an infinite stream?

7. Suppose dividends are expected to grow at a constant rate, gL, forever.
D1 = D0(1 + gL)1
D2 = D0(1 + gL)2
Dt = D0(1 + gL)t
What is the present value of a constant growth Dt when discounted at the stock’s required return, rs?

8. Constant Dividend Growth Model (gL<rs)
If gL is constant and less than rs, then
P 0 = D 1 r s − g L = D g L r s − g L

9. Estimated Intrinsic Stock Value: D0 = $2.00, rs = 13%, gL = 6%
D1 = D0(1+gL)
D1 = $2.00(1.06) = $2.12
P 0 = D g L r s − g L = D 1 r s − g L
P 0 = $ −0.06 = $30.29

10. Expected Stock Price in 1 Year
In general: P t = D t+1 r s − g L
D2 = D1(1+gL)
D1 = $2.12(1.06) = $2.2472
P 1 = D 2 r s − g L
P 0 = $ −0.06 = $32.10

11. Expected Dividend Yield and Capital Gains Yield
$2.12
$30.29 D1 P0
CG Yield = =
P1 – P0 ^
$32.10 – $30.29
= 6.0%. 14

12. Total Return at Year 1
Total return = Dividend yield + Capital gains yield.
Total return = 7% + 6% = 13%.
Total return = 13% = rs.
For constant growth stock:
Capital gains yield = 6% = gL.

13. Rearrange model to rate of return form
Then, rs = $2.12/$
= = 13%. ^
P0 = D1
rs – g to P0 rs =
+ g.

14. Nonconstant Growth Stock
Nonconstant growth of 30% for Year 0 to Year 1, 25% for Year 1 to Year 2, 15% for Year 2 to Year 3, and then long-run constant gL = 6%.
Can no longer use constant growth model.
However, growth becomes constant after 3 years. 17

15. Example of Estimating Current Stock Value (D0 = $2.00, rs = 13%)
gL = 6%
Year 1 2 3 4
Dividends
D0(1+g0,1) ↓
$2.600
D1(1+g1,2)
$3.250
D2(1+g2,3)
$3.7375
$2.301
← $2.600/(1+rs)1
PVs of divs.
$2.545
← $3.250/(1+rs)2
$2.590
← $3.7375/(1+rs)3
$39.224
$56.596/(1+rs)3 ←
$46.661

16. The Free Cash Flow Valuation Model: FCF and WACC
Free cash flow (FCF) is:
The cash flow available for distribution to all of a company’s investors.
Generated by a company’s operations.
The weighted average cost of capital (WACC)

17. Sources of Corporate Value
Value of operations
Nonoperating assets
Short-term investments and other marketable securities
Ownership of non-controlling interest in another company

18. Claims on Corporate Value
Debtholders have first claim.
Preferred stockholders have the next claim.
Any remaining value belongs to common stockholders.

19. Estimated Intrinsic Value of Equity (VEquity)
Voperations
+ ST Inv.
+ Ownership in other co.
VTotal
−Debt
− Preferred Stk.
VEquity

20. Value of Operations (Vop)
The PV of expected future FCF, discounted at the WACC, is the value of a company’s operations (Vop):
Vop = Σ ∞
t = 1
FCFt
(1 + WACC)t

21. Value of Operations (Vop)
V op = FCF 1 (1+WACC) FCF 2 (1+WACC) 2
+ FCF 3 (1+WACC) 3 +…+ FCF ∞ (1+WACC) ∞
Conceptually correct, but how do you find the present value of an infinite stream?

22. Suppose FCFs are expected to grow at a constant rate, gL, starting at t=1, and continue forever.
FCF2 = FCF1(1 + gL)1
FCF3 = FCF1(1 + gL)2
FCFt = FCF1(1 + gL)t-1

23. Constant Growth Formula for Value of Operations
If FCF are expected to grow at a constant rate of gL from Time 1 and afterwards, and gL<WACC:
Vop,0 =
FCF1
(WACC - gL)

24. Constant Growth Formula for Value of Operations
Vop,0 =
FCF0 (1+gL)
(WACC - gL)

25. Data for FCF Valuation FCF0 = $24 million WACC = 11%
FCF is expected to grow at a constant rate of gL = 5%
Short-term investments = $100 million
Debt = $200 million
Preferred stock = $50 million
Number of shares =n = 10 million

26. Find Value of Operations
Vop =
FCF0 (1 + gL)
(WACC - gL)
$24(1+0.05)
(0.11 – 0.05)
= $420

27. Total Value of Company (VTotal)
Voperations
$420.00
+ ST Inv.
100.00
VTotal
$520.00

28. Intrinsic Value of Equity (VEquity)
Voperations
$420.00
+ ST Inv.
100.00
VTotal
$520.00
−Debt
200.00
− Preferred Stk.
50.00
VEquity
$270.00

29. Intrinsic Stock Price per Share, P 0
Voperations
$420.00
+ ST Inv.
100.00
VTotal
$520.00
−Debt
200.00
− Preferred Stk.
50.00
VEquity
$270.00
÷ n 10
P 0
$27.00

30. Expansion Plan: Nonconstant Growth
Finance expansion financed by owners.
Projected free cash flows (FCF):
Year 1 FCF = −$10 million.
Year 2 FCF = $20 million.
Year 3 FCF = $35 million
FCF grows at constant rate of 5% after year 3.
No change in WACC, marketable securities, debt, preferred stock, or number of shares of stock.

31. Estimating the Value of Operations
Free cash flows are forecast for three years in this example, so the forecast horizon is three years.
Growth in free cash flows is not constant during the forecast, so we can’t use the constant growth formula to find the value of operations at time 0.

32. Time Line of FCF
Year 1 2 3 4 5
… t
FCF
−$10
$20
$35
FCF3(1+gL)
FCF4(1+gL)
FCFt(1+gL)
Growth is constant after the horizon (Year 3), so we can modify the constant growth formula to find the value of all free cash flows beyond the horizon, discounted back to the horizon. This is called the “horizon” value.

33. Vop at time t = HV = FCFt(1+g) (WACC - g) Horizon Value
Year 1 2 3 4 5
… t
FCF
FCF3(1+gL)
FCF4(1+gL)
FCFt(1+gL)
HV3 ←↵
Horizon value is also called terminal value, or continuing value.
Vop at time t =
FCFt(1+g)
(WACC - g)
HV =

34. Horizon Value Application (FCF3 = $35, WACC = 11%, gL = 5%)
HV3 = Vop,3 =
FCF3(1+g)
(WACC - g)
HV3 =
$35(1+0.05)
(0.11 – 0.05)
=$612.50
This is the value of FCF from Year 4 and beyond discounted back to Year 3.

35. Current Value of Operations
gL = 5%
Year 1 2 3 4
FCF
−$10
$20
$35 ↓
FCF 4 WACC− g L
−$9.009
← −$10/(1+WACC)1
PVs of FCF
$16.232
← $20/(1+WACC)2
FCF 3 (1+ g L ) WACC− g L
$25.592
← $35/(1+WACC)3
PV of Vop,3 $
$612.5/(1+WACC)3 ←
Vop,3= $612.5
← $  
 Vop =
$480.67

36. Intrinsic Stock Price, P 0
Voperations
$480.67
+ ST Inv.
100.00
VTotal
$580.67
−Debt
200.00
− Preferred Stk.
50.00
VEquity
$330.67
÷ n 10
P 0
$33.07

37. Comparing the FCF Model and Dividend Growth Model
Can apply FCF model in more situations:
Privately held companies
Divisions of companies
Companies that pay zero (or very low) dividends
FCF model requires forecasted financial statements to estimate FCF

38. ROIC vs. WACC
If ROIC<WACC/(1+g), then operation value will be less than the investment in total net operating capital (NOWC+net PP&E)
If ROIC<WACC/((1+WACC), the any growth makes the company less valuable.

39. Assignment Review slides of chapter 9 in FINC3131.
Chapter 8 problems: 1,2,4,6,7,17,18.