Finance reserch report based on provided data
Stock Valuation
Chapter 9
Copyright © 2013 by the McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin
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Key Concepts and Skills
- Understand how stock prices depend on future dividends and dividend growth
- Be able to compute stock prices using the dividend growth model
- Understand how growth opportunities affect stock values
- Understand valuation comparables
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Chapter Outline
9.1 The Present Value of Common Stocks
9.2 Estimates of Parameters in the Dividend Discount Model
9.3 Growth Opportunities
9.4 Comparables
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9.1 The PV of Common Stocks
- The value of any asset is the present value of its expected future cash flows.
- Stock ownership produces cash flows from:
- Dividends
- Capital Gains (the same as dividens, why?)
- Valuation of Different Types of Stocks
- Zero Growth
- Constant Growth
- Differential Growth
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derivation
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Case 1: Zero Growth
- Assume that dividends will remain at the same level forever
- Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity:
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Case 2: Constant Growth
Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity:
Assume that dividends will grow at a constant rate, g, forever, i.e.,
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Constant Growth Example
- Suppose Big D, Inc., just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk level, how much should the stock be selling for?
- P0 = .50 / (.15 - .02) = $3.92
- P0 = .50(1+.02) / (.15 - .02) = $3.92
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The biggest mistake that students make with the DGM is using the incorrect dividend. Be sure to emphasize that we are finding a present value, so the dividend needed is the one that will be paid NEXT period, not the one that has already been paid.
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Case 3: Differential Growth
- Assume that dividends will grow at different rates in the foreseeable future and then will grow at a constant rate thereafter.
- To value a Differential Growth Stock, we need to:
- Estimate future dividends in the foreseeable future.
- Estimate the future stock price when the stock becomes a Constant Growth Stock (case 2).
- Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate.
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Case 3: Differential Growth
- Assume that dividends will grow at rate g1 for N years and grow at rate g2 thereafter.
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Case 3: Differential Growth
Dividends will grow at rate g1 for N years and grow at rate g2 thereafter
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0 1 2
…
N N+1
…
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Case 3: Differential Growth
We can value this as the sum of:
- a T-year annuity growing at rate g1
- plus the discounted value of a perpetuity growing at rate g2 that starts in year T+1
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It may be good to point out that we have assumed the discount rate is constant; however, it could change across periods, or even across years.
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Case 3: Differential Growth
Consolidating gives:
Or, we can “cash flow” it out.
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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.
What is the stock worth? The discount rate is 12%.
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With the Formula
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With Cash Flows
…
0 1 2 3 4
0 1 2 3
The constant growth phase beginning in year 4 can be valued as a growing perpetuity at time 3.
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This type of problem generally separates the “A” students from the rest of the class.
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9.2 Estimates of Parameters
- The value of a firm depends upon its growth rate, g, and its discount rate, R.
- Where does g come from?
g = Retention ratio × Return on retained earnings (e.g. ROE, how to calculate?)
Retention rato = 1 – payout ratio
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ROE = net income from income statement/shareholder’s equity (assets-liabilities)
Earnings next year = Earnings this year + Retained earnings this year × Return on retained earnings
1 + g = 1 + Retention ratio * Return on retained earnings
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Where Does R Come From?
- The discount rate can be broken into two parts.
- The dividend yield
- The growth rate g (capital gains yield)
- Example: price is $20, dividend is $1, g = 10%
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Using the DGM to Find R
- Start with the DGM:
Rearrange and solve for R:
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Point out that D1 / P0 is the dividend yield and g is the capital gains yield.
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Practical issues
- In practice, there is a great deal of estimation error involved in estimating R and g.
- R is sensitive to g, but g is not predictable
- When firms start paying dividend, g goes to infinite
- When g >= R
- Firms cannot maintain a high g forever
- Why are the stock prices of no-dividend firms positive?
Differential dividend growth?
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9.3 Growth Opportunities
- Growth opportunities are opportunities to invest in positive NPV projects.
- The value of a firm can be conceptualized as the sum of the value of a firm that pays out 100% of its earnings as dividends plus the net present value of the growth opportunities.
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A firm that pays out 100% of its earnings is essentially a zero growth firm since the retention rate is zero. This, however, does not imply the firm is not profitable.
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NPVGO Model: Example
Consider a firm that has forecasted EPS of $5, a discount rate of 16%, and is currently priced at $75 per share.
- We can calculate the value of the firm as a cash cow.
- So, NPVGO must be: $75 - $31.25 = $43.75
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You may wish to ask the students if this stock is a “value” stock or “growth” stock. The large relative NPVGO would suggest it is a growth stock.
Example: 1 million earnings, 100,000shares, R = 10%, opportunity to invest in date 1 to increase earnings by 210,000 every year, what are the prices if pay out all or retain for one year
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- The stock price should reflect the market’s estimate of the firm’s NPVGO.
- Corporate governance and stock prices
- Negative NPV project
- Project return less than required return
- Increasing earnings doesn’t necessarily mean higher firm value (stock price)
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9.4 Comparables
- Comparables are used to value companies based primarily on multiples.
- Common multiples include:
- Price-to-Earnings
- Enterprise Value Ratios
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Price-Earnings Ratio
- The price-earnings ratio is calculated as the current stock price divided by annual EPS. (equity ratio)
- The Wall Street Journal uses last 4 quarter’s earnings
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PE and NPVGO
- Recall,
- Dividing every term by EPS provides the following description of the PE ratio:
- So, a firm’s PE ratio is positively related to growth opportunities and negatively related to risk (R)
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Accounting policies will also impact the PE ratio, as conservative policies are generally associated with higher PE ratios.
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Enterprise Value Ratios
- The PE ratio focuses on equity, but what if we want the value of the firm?(both equity and debt)
- Use Enterprise Value:
- EV = market value of equity + market value of debt - cash
- Like PE, we compare the value to a measure of earnings. From a firm level, this is EBITDA, or earnings before interest, taxes, depreciation, and amortization.
- EBITDA represents a measure of total firm cash flow
- The Enterprise Value Ratio = EV / EBITDA
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Accounting policies will also impact the PE ratio, as conservative policies are generally associated with higher PE ratios.
Enterprise value can be thought of as the theoretical takeover price if the company were to bought. In the event of such a buyout, an acquirer would generally have to take on the company's debt, but would pocket its cash for itself.
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Quick Quiz
- What determines the price of a share of stock?
- What determines g and R in the DGM?
- Decompose a stock’s price into constant growth and NPVGO values.
- Discuss the importance of valuation ratios.
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derivation
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The biggest mistake that students make with the DGM is using the incorrect dividend. Be sure to emphasize that we are finding a present value, so the dividend needed is the one that will be paid NEXT period, not the one that has already been paid.
*
*
*
*
It may be good to point out that we have assumed the discount rate is constant; however, it could change across periods, or even across years.
*
*
*
*
This type of problem generally separates the “A” students from the rest of the class.
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ROE = net income from income statement/shareholder’s equity (assets-liabilities)
Earnings next year = Earnings this year + Retained earnings this year × Return on retained earnings
1 + g = 1 + Retention ratio * Return on retained earnings
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Point out that D1 / P0 is the dividend yield and g is the capital gains yield.
Differential dividend growth?
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A firm that pays out 100% of its earnings is essentially a zero growth firm since the retention rate is zero. This, however, does not imply the firm is not profitable.
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You may wish to ask the students if this stock is a “value” stock or “growth” stock. The large relative NPVGO would suggest it is a growth stock.
Example: 1 million earnings, 100,000shares, R = 10%, opportunity to invest in date 1 to increase earnings by 210,000 every year, what are the prices if pay out all or retain for one year
*
*
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Accounting policies will also impact the PE ratio, as conservative policies are generally associated with higher PE ratios.
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Accounting policies will also impact the PE ratio, as conservative policies are generally associated with higher PE ratios.
Enterprise value can be thought of as the theoretical takeover price if the company were to bought. In the event of such a buyout, an acquirer would generally have to take on the company's debt, but would pocket its cash for itself.
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