write one essay on finance topic about 600 words
stepheny
07EquityValuation.pptxTopic 7 Equity Valuation
Fundamentals of Finance
Fall 2017
Zhun Liu
10/19/2017
1
Outline
Types of equity securities
Fundamental value aka intrinsic value
Dividend Discount Model (DDM)
Zero dividend growth
Constant dividend growth
Two-stage dividend growth
Valuation ratios
The kind of arbitrage opportunities we just talked about are exceedingly rare. In general, stock analysts have a much more difficult task than, say, comparing the price of a stock on 2 markets and checking whether they trade for a different price. They have to come up with a systematic method of valuing the firm.
We will discuss alternative measures of the value of a firm, starting with balance sheet valuation models, and moving to fundamental or intrinsic value.
From there we progress to quantitative tools, called dividend discount models that security analysts commonly use to measure the value of the firm as an ongoing concern. A special case of the general DDM is the Gordon Growth model.
We will then talk about valuation ratios, such as the price-earnings ratio and talk about why they are so often used by analysts.
2mins
Remember
The corporation differs from other forms of business organization in 3 important ways:
Ownership is usually widely dispersed;
Shareholders have no right to be involved in the daily running of the corporation; and,
Shareholders have limited or no liability for the liabilities incurred by the corporation.
Equity Securities
Basic Facts
Stocks are equity securities - certificates of ownership in a corporation
Households hold the largest share of equity securities, more than 36% of corporate equity
Pension funds are largest institutional investors in equities (21%), followed by mutual funds (20%), and foreign investors (10%)
4
The Market for Equity Securities
Equity Securities
Common Stock and Preferred Stock
Represent ownership interest in a corporation
Are the two most frequently used types of equity securities.
Dividend payments do not affect a firm’s taxes and are not “guaranteed” but are “promised” to preferred stockholders.
Have limited liability so claims made against the corporation cannot include a stockholder’s personal assets.
Are generally viewed as perpetuities because they do not have maturity dates.
5
Equity Securities
Common stock
Is the basic ownership claim in a corporation
Has the right to vote on matters such as electing a board of directors, setting a capital budget, and proposed mergers or acquisitions
Has the right to a firm’s residual assets after creditors, preferred stockholders, and others with higher priority claims have been satisfied
Warren Buffett
“Intrinsic value (or fundamental value) is an all-important concept that offers the only logical approach to evaluating the relative attractiveness of investments and businesses. Intrinsic value can be defined simply: It is the discounted value of the cash that can be taken out of a business during its remaining life.”
Example: Book value / intrinsic value of a college education
A second, and more popular way to value firms is to calculate the expected present discounted value of the firm’s cash flows. This is called fundamental value or intrinsic value.
Upon graduation, the book value of education is what you paid for it plus lost income.
The intrinsic value is the present value of future earnings in excess of what would be earned without the education. (Also, there is precious experience of college life.)
3mins/28mins
Fundamental/Intrinsic Value
Consider the distribution of next year’s dividend, D1, and price, P1
Assuming the required rate of return
Fundamental-value of the stock at time 0 is V0:
Suppose that there is a mispricing, P0≠V0, then expected HPR:
Q: What is a stock?
A: It’s a claim to future dividends. So, then the market value of a firm’s equity must have to do with the future dividends it will pay.
This is the risk-adjusted discount rate or the required rate of return.
The fundamental or intrinsic value of the stock is the discounted value of the cash-flows, discounted by the CAPM rate of return (which properly accounts for the risk in the stock).
Another way to put this is that the fundamental value is such that the expected holding period return of the stock equals the rate of return given by the CAPM.
4mins
One-year Case
A One Year Investor
Two potential sources of cash flows from owning a stock:
Dividends
Selling Shares
9
One-year Case
A One Year Investor
Since the cash flows are not risk-less, they must be discounted at the equity cost of capital
more precisely, the P0 should be V0, the intrinsic value, since rE, the required rate of return, is used here
(Eq. 7.1)
10
One-year Case - Summary
Dividend Yields, Capital Gains, and Total Returns
Dividend Yield
Capital Gain
Capital Gains Rate
Total Return
(Eq. 7.2)
11
One-year Case – Summary (Cont.)
Dividend Yields, Capital Gains, and Total Returns
The expected total return of the stock should equal the expected return of other investments available in the market with equivalent risk
12
DIY: Fundamental vs Actual Value
Suppose the current stock price is $48. We expect next year’s price and dividend to be $52 and $4. The required rate of return by investors is 12%.
Compute the expected holding period return.
Is the stock over- or undervalued?
Compute the fundamental value of the stock.
Is the stock over- or undervalued?
Let us start with thinking about a 1-year holding period return on a dividend paying stock. Suppose the current price is $48. We want to know whether this stock is attractively priced, given today’s expectation over next year’s price and dividend. Suppose you know the expected value of the dividend and the price of the stock at the end of the year. Where do you know them from? From God or nature (meaning we never really know that), the best forecaster or from your favorite stock analyst, the second best thing to God. You can calculate the expected div (=$4) and price tomorrow ($52). Your expected HPR = 4+52-48/48 = 0.167. It is the sum of the expected dividend yield (4/48=0.0835) and expected capital gain yield (52-48/48=0.0835).
Expected HPR = (52+4)/48-1 = 16.67%
In our example, the expected HPR exceeds the required return. The investor will want to include more of this asset in her portfolio because she expects that the return will be higher than what she is entitled to according to the systematic risk in the stock. We said that the stock was undervalued.
Another way to see this is to compare the fundamental or intrinsic value of the stock to its market price. The fundamental value is the present value of the cash payments to the investor, dividends and proceeds from the sale of the stock, discounted at the required rate of return given by the CAPM. The intrinsic value is the investor’s own estimate of what the stock is really worth. Because the current market price at time zero P_0=48 > intrinsic value V_0=50, the stock is under-priced.
V0=(4+52)/1.12=50, so undervalued.
5mins
What About Two-year (or longer) Case
A Multiyear Investor
Suppose we planned to hold the stock for two years
Then we would receive dividends in both year 1 and year 2 before selling the stock, as shown in the following timeline:
What if we don’t sell it in the 1st year, instead, we keep it until the 2nd year? What price the stock should be?
14
What About Two-year (or longer) Case
A Multiyear Investor
As a two-year investor, we care about the dividend and stock price in year 2
(Eq. 7.3)
How we get this equation? What is the logic? (Derive on whiteboard by substituting P1 with P0’s formula)
Because multiyear, make sure time is correct – which cash flow occurs at what time
D1 and D2 not necessarily the same, all of the future cash flows are expected values
To do this substitution, there is an implicit assumption: the market price equals to the intrinsic value – no arbitrage
We could insert more periods
15
If It Is Longer,
Dividend-Discount Model Equation
The price of the stock is equal to the present value of all of the expected future dividends it will pay, along with the cash flow from the sale in year N
(Eq. 7.4)
Take this equation to infinite periods, we get…
16
Dividend Discount Model (DDM)
Assume that the market is efficient so that the price P0 equals the fundamental value V0.
Use the fundamental-value equation repeatedly:
If the market is efficient, the stock is priced correctly and the market price equals the fundamental value: P0=V0.
Next year, the stock is also selling for its intrinsic value: P1=V1= E[D2]+E[P2]/(1+R).
Repeatedly substitute in, then you get that the fundamental value of a stock is the expected present discounted value of future dividends. This is the price of a stock. This formula is called the dividend discount model. The intrinsic value of the firm per share, which equals the price of a stock, is equal to the present discounted value of all future expected dividends (= expected cash flows). The discount rate R is given by the CAPM.
Note that this looks similar to pricing a bond. Q: What are the two key differences?
A: we have expected dividends because we don’t know what the actual dividends will be. Second, R not only discounts future CF for the TVM but also for risk – systematic risk.
Q: Who cares about dividends. Capital gains is what we all worry about. This formula doesn’t have any capital gains?
A: no, that is not true. Future prices start disappearing in this formula because they are farther and farther in the future. The thing that determines prices tomorrow, and hence the capital gain, is the price in the period thereafter and that ultimately depends on the firm’s dividends.
Q: What about non-dividend paying stocks?
A: it’s cash flows that count, not necessarily only dividends. A firm could be reinvesting all its profits year after year and not pay out any dividend. But the company would still be worth something. An example of such other sort of cash flow is a big cash-flow, big dividend, upon liquidation that you can get your hands on, e.g. upon a take-over. Company valuation comes from cash-flows: dividends or final liquidation value.
7mins/43mins
DDM Case 1: Zero Dividend Growth
Suppose that dividends are constant
E(D1)=D0, E(D2)=D0, etc.
Use the Dividend-Discount Model:
We will discuss three special cases of this general DDM in this class.
A first special case of the formula obtains if we assume that all dividends are constant: constant expected future cash-flows. D = E[D_1]= E[D_2]=…
Q: What does this formula remind you of?
A: The value of a perpetuity, with cash flow D and discount rate R.
Q: What is the intrinsic value of the firm then?
A: V_0 = D/R. For example, D= $10, R = 20% => P = $50. Preferred stock that pays a fixed dividend can be valued using this formula.
Q: What can cause the stock price to go up?
A: D = $20 => P = $100. Higher D, higher P.
A: R = 10% => P = $100. Lower R, higher P.
5min/48mins
What Is Dividends (in the Dividend Discount Model)
Dividends Versus Investment and Growth
A Simple Model of Growth
The dividend each year is equal to the firm’s earnings per share (EPS) multiplied by its dividend payout rate
(Eq. 7.8)
Firms make earnings through operation, but what do they do with the earnings? In general, 2 ways: investment/reinvestment, payout as dividend.
19
Dividends Versus Investment and Growth
A Simple Model of Growth
The firm can increase its dividend in three ways:
It can increase its earnings
It can increase its dividend payout rate
It can decrease its number of shares outstanding
Where Does Growth Come From? (in the Dividend Discount Model)
20
Assumption: all increases in future earnings result exclusively from new investment made with retained earnings.
Increase in Earnings (in the Dividend Discount Model)
(Eq. 7.9)
We call this “Retained earnings of this year” investment. ROI (on whiteboard)
10/19/2017
21
Dividends Versus Investment and Growth
A Simple Model of Growth
New investment equals the firm’s earnings multiplied by its retention rate - the fraction of current earnings that the firm retains:
(Eq. 7.10)
What Is Investment (in the Dividend Discount Model)
22
Dividends Versus Investment and Growth
A Simple Model of Growth
Substituting Eq. 7.10 into Eq. 7.9 and dividing by earnings gives an expression for the growth rate of earnings:
(Eq. 7.11)
What Is Growth (in the Dividend Discount Model)
23
Dividends Versus Investment and Growth
A Simple Model of Growth
If the firm chooses to keep its dividend payout rate constant, then the growth in its dividends will equal the growth in its earnings:
(Eq. 7.12)
What Is Growth (in the Dividend Discount Model)
24
Where does growth come from?
Growth comes from earning a high return on reinvested earnings
b is the percentage of earnings that are not paid as dividends – reinvestment rate
ROI is the return on (re-)investment
Growth rate g = b x ROI
I cheated a bit here. I picked the right growth rate to make the P/E ratio in data the same as the model. The point of my cheating though is to show you that you can use the formula in two ways:
Given g, R, b, calculate the P/E ratio (use your own estimate or the analysts’ forecast of g)
Given P/E ratio, b and R find expected growth rate g that is consistent with P/E ratio.
Now, let’s understand where that growth rate on the previous slide came from. How does a company grow? It is not enough for a company to simply retain earnings, it also needs to use them productively. It matters what you do with the earnings. I.e. how productive are you at using your retained earnings for generating future profits. That will ultimately determine the growth rate of earnings.
A company’s Return on Equity (ROE) measures how productive the internal investment projects are at that company. You can think of this ROE as the Internal Rate of Return on all the company’s projects.
8mins/30mins
Have a think after class:
Prove that firm’s earnings per share , dividends per share , and share price all grow at the same rate
Prove that forward price-earnings ratio equals:
DDM Case 2: Constant Dividend Growth
Suppose that expected dividends grow at a rate g, that is,
E(D1)=(1+g)D0, E(D2)=(1+g)2D0, etc.
Use the Dividend-Discount Model:
This is sometimes called the Gordon Growth Model (GGM)
A second special case of the general DDM is a case where expected future dividends are not constant, but grow at a constant rate g forever. This model is called the constant growth dividend discount model or also the Gordon growth model.
Explain the math + geometric series. Explain that our previous example of constant dividends is the case where g = 0. Explain that the two formulations are identical.
Example on next slide.
This is a good formula for companies that have achieved a stage of maturity; they grow at about a constant rate.
One other implication of the Gordon growth model: the stock price is expected to grow at the same rate as the dividends. E[P_1]/P_0={E[D_1]*(1+g)/(R-g)}/{E[D_1]/(R-g)} = (1+g). In other words, your capital gain yield is equal to the growth rate of dividends.
Remark
The formula for geometric progressions can be used provided that R>g. If R<g term in geometric series goes to infinity. So we suspect that something is at work that pushes g<R as an equilibrium phenomenon. g = growth rate forever. Sure, some companies will start out growing 50% per year, but they will later slow down. From microeconomics we know that more firms come into a fast growing market. As more firms enter, each firm’s share of the pie decreases, profits are competed away. So, it’s growth rate goes down. As an equilibrium phenomenon R>g makes sense.
10mins/58mins
Example GGM
Suppose E(D1)=$4, rE =12%, g=4%, then
P0 = V0 = E(D1) / (rE - g) = 4 / (0.12 - 0.04) = $50.00
Sensitivity analysis, 50% increase of one variable:
Suppose E(D1)=$6, then P0 = $75.00
Suppose RE =16%, then P0 = $36.36
Suppose g=6%, then P0 = $66.67
We find that the stock price depends on:
Expected dividend level (+)
Growth rate of dividend (+)
Discount factor (-)
DDM Case 3: Two-Stage DDM
A company can grow exceptionally for a while, but at some point the company matures and its growth normalizes.
Suppose that you estimate that a company’s growth will reach its “long-run” level of g after, say, 3 years.
Then, in 3 years its price is
Based on estimates of the next 3 years dividends, the earnings after 4 years, the long-run earnings growth and retention rate, today’s value is:
Instead of estimating future growth rate, one can estimate future P/D ratio, or P/E ratio and earnings retention ratio.
The Gordon growth model assumed that the growth rate of earnings is constant forever. This is a serious simplification. It seems important to incorporate a stage of fast growth, in which pay-out ratio is low, and a stage of slower growth, when the pay-out ratio is high. This is how we often think of the life-cycle of a company. The company starts out as a fast growing, dynamic enterprise, and as it grows, it matures and the growth rate slows down.
A good example is Microsoft, for 18 years Microsoft decided not to pay out any dividend. It grew very fast plowed back all of its earnings. But in Feb 2003 year, Microsoft started distributing dividends. It now pays $0.44 per share. In the future its dividend level will likely further increase, maybe because the company has fewer growth opportunities. This has already happening: MSFT’s revenue growth was 28% per year between 1992-99 and only 12% between 2000-07. Analysts currently forecast that Microsoft will grow at 12.5% per year over the next five years, slower than the 14.7% forecast for the sector as a whole.
We can accommodate a phase of fast growth in the Dividend Discount Model. Suppose you have specific predictions for the dividend in each of the following three years that take into account the fast growth in the initial phase. Starting in year 4, the company’s earnings and dividends will grow at a slower and constant rate. Then, the price in year 3 will be given by the Gordon growth model: P3=D3(1+g)/(R-g).
The price of the company in year zero is the present discounted value of the CF in years 1 through 3 plus the expected present discounted value of the price at the end of year 3. The latter is E[P3]/(1+R)^3.
7mins/54mins
Limitations
Uncertainty in dividend forecasts
Difficult to estimate the growth rate
Issue of non-dividend paying stock
Eg., Amazon, Google
How do we value them?
Valuation Based on Comparable Firms
Estimate Stock price based on the price of comparable firms
Match on characteristics including industry, cost structure, capital structure, growth potential, life-cycle and presence or absence of strategic/growth options.
But no two investments are identical - you must assess the extent to which the differences across assets are likely to have a material effect on the valuation multiples and adjust.
PE Ratio
PE = Price / EPS
Example – Apple
Apple’s forward EPS = $8.95
Stock price = 11.85*8.95 = $106.06
But Apple’s closing stock price was $112.88 and forward PE was 12.61.
| Fwd PE Dec 31, 2013 | |
| HP | 7.65 |
| Intel | 13.89 |
| Microsoft | 14.00 |
| Mean | 11.85 |
Source: Capital IQ
10/19/2017
32
You want to know whether Amazon is over- or under-valued using a PE ratio approach.
Information on forward PE ratios:
Source: Capital IQ
| Fwd Dec 31, 2013 | |
| Amazon (AMZN) | 175.20 |
| Target (TGT) | 14.50 |
| Expedia (EXPE) | 19.17 |
| Ebay (EBAY) | 15.02 |
Markets: US Cyclically adjusted P/E Ratio
Price divided by earnings, averaged over last 10 years (to smoothen out some earnings volatility) for the entire stock market. These data go from January 1881 until July 2009.
http://www.econ.yale.edu/~shiller/data.htm
Historical evidence shows 2 periods with very high P/E ratios: 1929 (33) and 2000 (45). The average P/E ratio since 1900 is 16.25.
In June 2009, stocks were right around that historical average: 16.38, up from 13.32 in March 2009, but down from 27.40 in June 2007.
The last data point is October 16, 2009. We are back to 19.48. So the stock market’s valuation is back above average levels.
Q: Why would this series move so much over time?
Price-Earnings Ratio (CAPE, P/E10)
Long-Term Interest Rates
10/19/2017
36
Year
Real S&P Composite Stock Price Index
Real S&P Composite Earnings
(
)
(
)
1
1
)
(
)
(
0
1
1
1
1
0
-
+
=
Û
+
+
=
V
P
E
D
E
r
r
P
E
D
E
V
E
E
(
)
(
)
E
r
P
P
E
D
E
¹
-
+
1
0
1
1
(
)
122
0
2
1
1
E
E
DivDivP
P
r
r
+
=+
+
+
(
)
(
)
(
)
12
0
2
1
111
NN
NN
E
EEE
DivP
DivDiv
P
r
rrr
=++++
+
+++
L
å
¥
=
+
=
+
+
+
+
+
+
+
+
=
+
+
+
+
=
+
+
+
=
+
+
=
1
4
4
3
3
2
2
1
2
2
2
1
1
1
1
1
0
)
1
(
)
(
...
)
1
(
)
(
)
1
(
)
(
)
1
(
)
(
1
)
(
)
1
(
)
(
)
(
1
)
(
1
)
(
1
)
(
1
)
(
)
(
i
i
E
i
E
E
E
E
E
E
E
E
E
r
D
E
r
D
E
r
D
E
r
D
E
r
D
E
r
P
E
D
E
r
D
E
r
P
E
r
D
E
r
P
E
D
E
V
E
E
E
E
E
E
E
E
r
D
E
r
D
r
D
r
D
r
D
r
D
E
r
D
E
r
D
E
V
)
(
...
)
1
(
)
1
(
1
...
)
1
(
)
(
)
1
(
)
(
1
)
(
1
0
3
0
2
0
0
3
3
2
2
1
0
=
=
+
+
+
+
+
+
=
+
+
+
+
+
+
=
Earnings next year
= Earnings
this year
+
Retained earnings
this year
× Return on retained earnings
Increase in earnings ! "##################
Change in Earnings = New Investment Ret
urn on New Investment
´
New InvestmentEarningsRetention Rate
=´
Change in Earnings
Earnings Growth Rate =
Earnings
Retention RateReturn on New Investment
=´
Retention RateReturn on New Investment
g
=´
g
r
D
E
g
r
g
D
r
g
D
r
g
D
r
g
D
r
D
E
r
D
E
r
D
E
V
E
E
E
E
E
E
E
E
-
=
-
+
=
+
+
+
+
+
+
+
+
+
=
+
+
+
+
+
+
=
)
(
)
1
(
...
)
1
(
)
1
(
)
1
(
)
1
(
1
)
1
(
...
)
1
(
)
(
)
1
(
)
(
1
)
(
1
0
3
3
0
2
2
0
0
3
3
2
2
1
0
g
r
D
g
P
-
+
=
3
3
)
1
(
)
(
)
1
(
)
E(
)
1
(
)
1
(
)
E(
)
1
(
)
E(
1
)
E(
3
3
3
3
2
2
1
0
g
r
r
D
g
r
D
r
D
r
D
P
-
+
+
+
+
+
+
+
+
=
