1. Equity Valuation
Chapter 13

2. Book Value
Historical Values recorded on the firm’s financial statements
BV Equity = Total Assets – Total Liabilities
The values are historical and may not reflect current market conditions/values
Limits the informativeness of these values

3. Valuing Stock: Intrinsic v Price
An investors purchasing a share is acquiring the cash flows associated with that share
The present value of these cash flows is the Intrinsic Value
For now assume intrinsic value is the same as market value, we will relax this assumption later in the semester

4. Expected HPR
When the market price = intrinsic value the E(r) = Div Yield + Capital Gain
Div Yield = D1 / P0
Capital Gain = (P1 - P0) / P0
E(r) = D1 / P0 + (P1 - P0) / P0
Also known as the market capitalization rate

5. Valuing Common Stock
The price should reflect the PV of future cash flows
So will an investor planning on selling his share in a year be willing to pay today?
The investor buying the share next year plans on selling it a year later so he is only willing to pay?

6. Keep Going Using summation: P0 = H Dh / (1 + k)h + PH / (1 + k)H
This process can be repeated into the future
Using summation:
P0 = H Dh / (1 + k)h + PH / (1 + k)H
What happens to PH as H approaches infinity?
ASIDE: Will an investor’s expected holding period affect the price they are willing to pay today?

7. Constant Dividend
How do you value a stock that will pay a constant dividend?
Hint: what does the cash flow stream look similar to?

8. Constant Dividend Example
What is the value of a stock that is expected to pay a constant dividend of $2 per share?
The required rate of return is 10%

9. Constant Dividend Example
What is the market capitalization rate of a stock that is selling for $60, that is expected to pay a constant dividend of $2 per share?

10. When Dividends Grow
Now lets assume that the firm and its dividend will grow at g forever
Dividends now:

11. DDM with Constant Growth
V0 = D1 / (k-g)
V0 = {D0*(1+g) }/ (k-g)
Is a stock more or less valuable when dividends grow?

12. Growing Dividend Example
Geneva steel just paid a dividend of $2.10. Dividend payments are expected to grow at a constant rate of 6%. The appropriate discount rate is 12%. What is the price of Geneva stock?

13. Firm Life Cycles
Firms generally grow faster when they are young, then growth slows as the firm matures
Two-Stage DDM (Multistage Growth Models)
Allow dividends to grow at different rates as firm matures

14. Differential Growth Rates
Dividends will grow at g1 for T years and g2 thereafter
Step 1: An T-year annuity growing at rate g1
Step 2: A growing perpetuity at rate g2
PN = DivN+1 / (k-g2)
Step 3: PB = PN / (1+k)T
Step 4: P0 = PA + PB

15. Non-Constant Growth Example (Given)
Websurfers Inc, a new internet firm is expected to do very well during its initial growth period. Investors expect its dividends to grow at 25% for the next 3 years. Obviously one cannot expect such extraordinary growth to continue forever, and it is expected that dividends will grow at 5% after year 3 in perpetuity. Its current dividend is $1/share. Required rate of return on the stock = 10%. Calculate what the current price should be.

16. Websurfer Inc, Example (Given)
1*1.253
*1.052
= 2.15
PA=[(1.25)/( )]*[1-{1.25/1.10}3] = 3.90
PN ={2.05}/( ) = 41.00
PB =41.00/(1.103) = 30.80
P0 = PA + PB = = $34.70
1*1.253*1.05 = 2.05
1*1.25 = 1.25
1*1.252 =1.56
1*1.253 = 1.95

17. A Differential Growth Example
A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity. R=12%
What is the stock’s intrinsic value?
PA =
PN =
PB =
P0 = PA + PB =

18. Problem 1 (Given)
A firm is expected to grow at 25% for the next 3 years. Its growth is expected to decline to 15% for the following 4 years. It is then expected to grow at 5% in perpetuity. Find the current share price if the current dividend is $1 and the discount rate is 10%. 
Phase 1 – Year 1-3 (Growth is 25% for 3 years)
DIV1 = 1.00 * 1.25 = 1.25
P0 = DIV1/(r-g) * [1 – (1+g)3/(1+r)3]
= 1.25/( ) * [ /1.13]
= 3.89
Phase 2 – Year 4-7 (Growth is 15% for 4 years)
First cash flow of this growing annuity is DIV4
DIV4 = 1 * * 1.15 = 2.25
P3 = DIV4/(r-g) * [1 – (1+g)4/(1+r)4]
= 2.25/( ) * [ /1.14]
= 8.76
P0 = P3 * D(10%, 3)
= 8.76 * 1/1.13
= 6.58 
Phase 3 – Year 8- (Growth is 5% for perpetuity)
First cash flow of this growing perpetuity is DIV8
DIV8 = 1 * * 1.154* 1.05 = 3.59
P7 = DIV8/(r-g)
= 3.59 / (0.10 – 0.05)
= 71.8
 P0 = P7 * D(10%, 7)
= 71.8 * 1/1.17
= 36.83
 P0 =
= 47.30

19. Problem 1 (Given) PA=[(1.25)/(0.10-0.25)]*[1-{1.25/1.10}3]=3.89
A firm is expected to grow at 25% for the next 3 years. Its growth is expected to decline to 15% for the following 4 years. It is then expected to grow at 5% in perpetuity. Find the current share price if the current dividend is $1 and the discount rate is 10%.
PA=[(1.25)/( )]*[1-{1.25/1.10}3]=3.89
PN1 ={1*1.253*1.15}/( )]*
[1-{1.15/1.10}4]=8.76
PB =8.76/(1.103) = 6.58
PN2 ={1*1.253*1.154*1.05}/( )] = 71.80
PC =71.80/(1.107) = 36.83
P0 = PA + PB + Pc = = $47.30
Phase 1 – Year 1-3 (Growth is 25% for 3 years)
DIV1 = 1.00 * 1.25 = 1.25
P0 = DIV1/(r-g) * [1 – (1+g)3/(1+r)3]
= 1.25/( ) * [ /1.13]
= 3.89
Phase 2 – Year 4-7 (Growth is 15% for 4 years)
First cash flow of this growing annuity is DIV4
DIV4 = 1 * * 1.15 = 2.25
P3 = DIV4/(r-g) * [1 – (1+g)4/(1+r)4]
= 2.25/( ) * [ /1.14]
= 8.76
P0 = P3 * D(10%, 3)
= 8.76 * 1/1.13
= 6.58 
Phase 3 – Year 8- (Growth is 5% for perpetuity)
First cash flow of this growing perpetuity is DIV8
DIV8 = 1 * * 1.154* 1.05 = 3.59
P7 = DIV8/(r-g)
= 3.59 / (0.10 – 0.05)
= 71.8
 P0 = P7 * D(10%, 7)
= 71.8 * 1/1.17
= 36.83
 P0 =
= 47.30

20. Problem 2 (Given)
Consider a firm whose dividend growth is expected to decline gradually. For the next two years, the growth is expected to be 20%. In the following years, it is expected to grow at 18%, 13% and 10%. From year 6 onwards, dividends are expected to grow at 5% for perpetuity. Assume the current dividend is $1 and the required rate of return is 10%. What is the current price?
DIV0 = 1.00
DIV1 = 1.00 * 1.20 = 1.20
DIV2 = 1.20 * 1.20 = 1.44
DIV3 = 1.44 * 1.18 = 1.70
DIV4 = 1.70 * 1.13 = 1.92
DIV5 = 1.90 * 1.10 = 2.11
DIV6 = 2.11 * 1.05 = 2.22
Phase 1 – Years 1-5
P0 = 1.2/ / / / /1.15
= 6.18
Phase 2 – Years 6-
P5 = DIV6 / (r-g)
= 2.22/( )
= 44.4
P0 = P5 * D(10%, 5)
= 44.4 * 1/1.15
= 27.57
Current Price = = 33.75

21. Problem 2: Phase 1 – Years 1-5 (Given)
DIV1 = 1.00 * 1.20 = 1.20
DIV2 = 1.20 * 1.20 = 1.44
DIV3 = 1.44 * 1.18 = 1.70
DIV4 = 1.70 * 1.13 = 1.92
DIV5 = 1.92 * 1.10 = 2.11
PA = 1.2/ / / / /1.15 = 6.18

22. Problem 2 Phase 2 – Years 6- (Given)
DIV6 = 2.11 * 1.05 = 2.22
PN = DIV6 / (r-g) = 2.22/( ) = 44.4
PB = 44.4 * 1/1.15 = 27.57
Current Price = = $33.75

23. What to do with Cash
Once a firm has paid everyone, it has two chooses with what to do with any remaining money
Give it to shareholders
Who can invest it themselves
Reinvest it in the company
Growth the firm
When should the firm give the cash to investors? Reinvest?

24. How Fast Can a Firm Grow? g = plowback ratio * ROE
The firm’s growth is determined by how much it re-invests (plowback ratio) & the return on its re-investment
Plowback (b)how much of every dollar is re-invest
Earnings Retention Ratio
REMEMBER: Plowback + Payout = 1
Return on investment is the firm’s ROE
g = plowback ratio * ROE

25. Calculating Growth Rates (g)
Consider two firms with earnings of $5 & k=12.5%
Cash Cow pays out all earnings as dividends
CC’s growth rate is _______
CC’s share price is _______
Growth Prospects wants to grow → Div Payout = 40% & ROE is 15%
GP’s growth rate is _______
GP’s share price is _______

26. Alternative Growth Valuation
Price is composed of:
The value of the current operations (100% Div Payout)
EPS1 / k
Growth opportunities
PVGO
P0 = EPS1 / k + PVGO

27. Who cares about PVGO?
For what type of stock is the PVGO more important?
Growth or Value stocks
For a growth stock PVGO is a big component of price.
For an income stock, PVGO is a very small component.

28. PVGO Example
A firm reinvests 60% of its earnings in projects with ROE of 10%, capitalization rate is 15%. Expected year-end dividend is $2/share, paid out of earnings of $5/share.
Compute the firm’s share price?
What is the per share value of the firm’s current assets?
What is the per share PVGO?

29. Price-Earnings Ratio
The price-earnings ratio is calculated as the current stock price divided by annual EPS.
The Wall Street Journal uses last 4 quarter’s earnings
Many analysts use this to determine how the market feels about a company

30. Price-Earnings Ratio Breakdown
P0 = EPS1 / k + PVGO ↓
P/E can be thought of as a ratio of growth options to current assets

31. Price-Earnings Ratio and Growth
When PVGO=0, P0=E1 / k. The stock is valued like a constant perpetuity.
P/E rises dramatically with PVGO.
High P/E indicates that the firm has ample growth opportunities.

32. Price Earnings Ratio 2nd Breakdown
P0 = Div1 / (k –g)
Div1: is E1 * (1+b)
g is ROE * b
P0 = {E1 * (1+b) }/ {k –(ROE * b)}

33. Price-Earnings Ratio Implications
Since riskier stocks have higher k (rates of returns) this implies they will also have lower P-E multiples
P/E increases:
As ROE increases
As plowback increases IF ROE>k

34. ROE & Plowback on Growth and the P/E Ratio, k=12%

35. Issues With P/E Analysis
Uses accounting earnings
Earnings Management
Choices on GAAP
Inflation
Reported earnings fluctuate around the business cycle

36. Figure 13.4 Earnings Growth for Two Companies

37. Figure 13.5 Price-Earnings Ratios

38. Industrial P/E Ratios

39. Other Comparative Valuation Ratios
Price-to-book: Indicates how aggressively the market values the firm
Price-to-cash-flow: Cash flow less affected by accounting decisions than earnings
Price-to-sales: For start-ups with no earnings

40. Free Cash Flow to the Firm
Value the firm by discounting its free cash flows by WACC
Free cash flow to the firm, FCFF, equals:
After tax EBIT
Plus depreciation
Minus capital expenditures
Minus increase in net working capital
FCFF= EBIT(1-tc) + Dep - Cap Ex - Inc. NWC

41. Using FCFF to Value the Firm
FCFF= EBIT(1-tc) + Dep - Cap Ex - Inc. NWC

42. Free Cash Flow to Equityholders
Two ways to determine the value of Equity
Firm Value minus Debt
Discounting free cash flows to equity by cost of equity
Free cash flow to equity, FCFE, equals:
FCFF
Minus Interest Expense After Tax
Plus Increase in Net Debt
FCFE= FCFF – Int Exp * (1-tc) + Inc. net Debt

43. Finding the Value of Equity
Equity = Firm Value – Debt Or
FCFE= FCFF – Int Exp * (1-tc) + Inc. net Debt

44. Stock Value Represents:
Present value of expected future dividends,
Present value of free cash flow,
Present value of average future earnings under a no-growth policy plus the present value of growth opportunities
Value of the firm
We found that the value of an equity share is the present value of all dividends ever to be paid to the share.
Does it imply that the total value of the firm’s equity is the present value of all dividends the firm will ever pay.
In general, the answer is “NO”.
 Let nt –the number of equity shares at time t.
DIVt – dividend per share in period t
 The total value of the equity in the firm is given by
V0 = n0 * P0
= n0*DIV1/(1+r) + n0*DIV2/(1+r)2 + ….
Now, total dividends paid out by the firm in period t,
Dt = DIVt * nt
 But what do we have in the above valuation equation: DIVt * n0.
 In general, this is not equal to Dt. Only when the firm sells no more stock in the future will the above condition be true.
 In general, it is not correct to say that the total value of a firm’s equity is the present value of all dividends to be ever paid by the firm.

45. Free Cash Flow to the Firm
Eagle Products’ EBIT is $400, its tax rate is 30%, depreciation is $16, capital expenditures are $56, and the planned increase in net working capital is $25.
What is the free cash flow to the firm?

46. What is the value of MoMi? What is the value of MoMi’s equity?
MoMi Corp’s operating cash flows before interest and taxes was $2M last year
MoMi expects this to grow by 5% per year forever
To make this happen, MoMi will have to invest 20% of pretax cash flow each year.
Depreciation last year was $200K and is expected to grow at the same rate as OCF
Market capitalization rate for unleveraged CF is 12%
WACC
Firm has $4M in debt outstanding
The tax rate is 35%
What is the value of MoMi?
What is the value of MoMi’s equity?
2m * = 2.1m
-.2m * 1.05 = .21m
1.89m
Taxes *.65
EBIAT m
Dep +.21m
1.4385m
Cap Ex -.42m
NWC 0
FCFF
MoMi = / ( ) = 14.55m
MoMi’s Equity = 14.55m – 4m = 10.55m

47. FCFE Example
Acme reports free cash flow to the firm of $205 million. The interest expense to the firm is $22 million. If the tax rate is 35% and the net debt of the firm increased by $25 million, what is the approximate market value of equity if the FCFE grows at 2% and the cost of equity is 11%? 
FCFE = ( ) + 25 = Value = (215.7×1.02)/( ) = 2,445

48. Different Models Different Values
In practice
Values from these models differ
Analysts are always forced to make simplifying assumptions
Problems with DCF
Calculations are sensitive to small changes in inputs
Growth opportunities and growth rates are hard to pin down