Fundamentals of Corporate Finance

Fundamentals of Corporate Finance
Fourth Edition Chapter 7 Stock Valuation If this PowerPoint presentation contains mathematical equations, you may need to check that your computer has the following installed: 1) MathType Plugin 2) Math Player (free versions available) 3) NVDA Reader (free versions available) Copyright © 2018, 2015, 2012 Pearson Education, Inc. All Rights Reserved.

Chapter Outline 7.1 Stock Basics 7.2 The Mechanics of Stock Trades 7.3 The Dividend-Discount Model 7.4 Estimating Dividends in the Dividend-Discount Model 7.5 Limitations of the Dividend-Discount Model 7.6 Share Repurchases and the Total Payout Model 7.7 Putting It All Together

Learning Objectives Understand the tradeoff between dividends and growth in stock valuation Appreciate the limitations of valuing a stock based on expected dividends Value a stock as the present value of the company’s total payout Describe the basics of common stock, preferred stock, and stock quotes Compare how trades are executed on the NYSE and NASDAQ Value a stock as the present value of its expected future dividends

7.1 Stock Basics (1 of 3) Stock Market Reporting: Stock Quotes
Common Stock Ticker Symbol

Figure 7.1 Stock Price Quote for Nike (NKE)
This screenshot from Google Finance shows the basic stock price information and price history charting for the common stock of Nike. The historical price chart covers the period mid-February through late June The price of $60.39 is for June 25, 2013. Source :

7.1 Stock Basics (2 of 3) Common Stock Shareholder Voting
Straight Voting Cumulative Voting Classes of Stock Shareholder Rights Annual Meeting Proxy Proxy Contest

7.1 Stock Basics (3 of 3) Preferred Stock
Cumulative versus Non-Cumulative Preferred Stock Preferred Stock: Equity or Debt?

7.2 The Mechanics of Stock Trades
Market Order Limit Order Round Lot Super Display Book System Floor Broker Dealer

7.3 The Dividend-Discount Model (1 of 8)
A One Year Investor Two potential sources of cash flows from owning a stock: Dividends Selling Shares

A One Year Investor Since the cash flows are not risk-less, they must be discounted at the equity cost of capital

Dividend Yields, Capital Gains, and Total Returns Dividend Yield Capital Gain Capital Gains Rate Total Return

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

Example 7.1 Stock Prices and Returns (1 of 4)
Problem Suppose you expect Longs Drug Stores to pay an annual dividend of $0.56 per share in the coming year and to trade for $45.50 per share at the end of the year. If investments with equivalent risk to Longs’ stock have an expected return of 6.80%, what is the most you would pay today for Longs’ stock? What dividend yield and capital gain rate would you expect at this price?

Solution Plan We can use Eq. 7.1 to solve for the beginning price we would pay now (P0) given our expectations about dividends (Div1 = $0.56) and future price (P1 = $45.50) and the return we need to expect to earn to be willing to invest (rE = 0.068). We can then use Eq. 7.2 to calculate the dividend yield and capital gain rate.

Execute Using Eq. 7.1, we have Referring to Eq. 7.2, we see that at this price, Longs’ dividend yield is The expected capital gain is $45.50 − $43.13 = $2.37 per share, for a capital gain rate of

Evaluate At a price of $43.13, Longs’ expected total return is 1.30% % = 6.80%, which is equal to its equity cost of capital (the return being paid by investments with equivalent risk to Longs’). This amount is the most we would be willing to pay for Longs’ stock. If we paid more, our expected return would be less than 6.8% and we would rather invest elsewhere.

Example 7.1a Stock Prices and Returns (1 of 4)
Problem: Suppose you expect Koch Industries to pay an annual dividend of $2.31 per share in the coming year and to trade $82.75 per share at the end of the year. If investments with equivalent risk to Koch’s stock have an expected return of 8.9%, what is the most you would pay today for Koch’s stock? What dividend yield and capital gain rate would you expect at this price?

Solution: Plan: We can use Eq. 7.1 to solve for the beginning price we would pay now (P0) given our expectations about dividends (Div1=$2.31) and future price (P1=$82.75) and the return we need to expect to earn to be willing to invest (rE=0.089). We can then use Eq. 7.2 to calculate the dividend yield and capital gain.

Execute: Referring to Eq. 7.2 we see that at this price, Koch’s dividend yield is The expected capital gain is $82.75 − $78.11 = $4.64 per share, for a capital gain rate of

Evaluate: At a price of $78.11, Koch’s expected total return is 2.96% % = 8.90%, which is equal to its equity cost of capital (the return being paid by investments with equivalent risk to Koch’s). This amount is the most we would be willing to pay for Koch’s stock. If we paid more, our expected return would be less than 8.9% and we would rather invest elsewhere.

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:

A Multiyear Investor The formula for the stock price for a two-year investor is the same as that for a sequence of two one-year investments

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

Dividend-Discount Model Equation Alternatively, rather than having a stopping point where we sell the shares, we can rewrite the equation to show that the dividends go on into the future

7.4 Estimating Dividends in the Dividend-Discount Model (1 of 7)
Constant Dividend Growth Assumes that dividends will grow at a constant rate, g, forever The value of the firm depends on the dividend level of next year, divided by the equity cost of capital adjusted by the growth rate

Example 7.2 Valuing a Firm with Constant Dividend Growth (1 of 4)
Problem Consolidated Edison, Inc. (Con Ed) is a regulated utility company that services the New York City area. Suppose Con Ed plans to pay $2.30 per share in dividends in the coming year. If its equity cost of capital is 7% and dividends are expected to grow by 2% per year in the future, estimate the value of Con Ed’s stock.

Solution Plan Because the dividends are expected to grow perpetually at a constant rate, we can use Eq. 7.6 to value Con Ed. The next dividend (Div1) is expected to be $2.30, the growth rate (g) is 2%, and the equity cost of capital (rE) is 7%.

Execute

Evaluate You would be willing to pay 20 times this year’s dividend of $2.30 to own Con Ed stock because you are buying a claim to this year’s dividend and to an infinite growing series of future dividends.

Example 7.2a Valuing a Firm with Constant Dividend Growth (1 of 4)
Problem: Suppose Target Corporation plans to pay $0.68 per share in dividends in the coming year. If its equity cost of capital is 10% and dividends are expected to grow by 8.4% per year in the future, estimate the value of Target’s stock.

Solution: Plan: Because the dividends are expected to grow perpetually at a constant rate, we can use Eq. 7.6 to value Target. The next dividend (Div1) is expected to be $0.68, the growth rate (g) is 8.4% and the equity cost of capital (rE) is 10%.

Execute:

Evaluate: You would be willing to pay 62.5 times this year’s dividend of $0.68 to own Target stock because you are buying claim to this year’s dividend and to an infinite growing series of future dividends.

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

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

Dividends Versus Investment and Growth A Simple Model of Growth If all increases in future earnings result exclusively from new investment made with retained earnings, then:

Dividends Versus Investment and Growth A Simple Model of Growth New investment equals the firm’s earnings multiplied by its retention rate, or the fraction of current earnings that the firm retains:

Dividends Versus Investment and Growth A Simple Model of Growth Substituting Eq into Eq. 7.9 and dividing by earnings gives an expression for the growth rate of earnings:

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:

Example 7.3 Cutting Dividends for Profitable Growth (1 of 5)
Problem Crane Sporting Goods expects to have earnings per share of $6 in the coming year. Rather than reinvest these earnings and grow, the firm plans to pay out all of its earnings as a dividend. With these expectations of no growth, Crane’s current share price is $60. Suppose Crane could cut its dividend payout rate to 75% for the foreseeable future and use the retained earnings to open new stores. The return on its investment in these stores is expected to be 12%. If we assume that the risk of these new investments is the same as the risk of its existing investments, then the firm’s equity cost of capital is unchanged. What effect would this new policy have on Crane’s stock price?

Solution Plan To figure out the effect of this policy on Crane’s stock price, we need to know several things. First, we need to compute its equity cost of capital. Next, we must determine Crane’s dividend and growth rate under the new policy. Because we know that Crane currently has a growth rate of 0 (g = 0), a dividend of $6, and a price of $60, we can use Eq. 7.7 to estimate rE . Next, the new dividend will simply be 75% of the old dividend of $6. Finally, given a retention rate of 25% and a return on new investment of 12%, we can use Eq to compute the new growth rate (g). Finally, armed with the new dividend, Crane’s equity cost of capital, and its new growth rate, we can use Eq. 7.6 to compute the price of Crane’s shares if it institutes the new policy.

Execute Using Eq. 7.7 to estimate rE , we have In other words, to justify Crane’s stock price under its current policy, the expected return of other stocks in the market with equivalent risk must be 10%. Next, we consider the consequences of the new policy. If Crane reduces its dividend payout rate to 75%, then from Eq. 7.8 its dividend this coming year will fall to Div1 = EPS1 × 75% = $6 × 75% = $4.50.

At the same time, because the firm will now retain 25% of its earnings to invest in new stores, from Eq its growth rate will increase to Assuming Crane can continue to grow at this rate, we can compute its share price under the new policy using the constant dividend growth model of Eq. 7.6:

Evaluate Crane’s share price should rise from $60 to $64.29 if the company cuts its dividend in order to increase its investment and growth. By using its earnings to invest in projects that offer a rate of return (12%) greater than its equity cost of capital (10%), Crane has created value for its shareholders.

Example 7.3a Cutting Dividends for Profitable Growth (1 of 8)
Problem: Lengefeld Manufacturing expects to have earnings per share of $1.80 in the coming year. Rather than reinvest these earnings and grow, the firm plans to pay out all of its earnings as a dividend. With these expectations of no growth, Lengefeld’s current share price is $24.

Problem: Suppose Lengefeld could cut its dividend payout rate to 50% for the foreseeable future and use the retained earnings to open an additional factory. The return on investment in the new factory is expected to be 15%. If we assume that the risk of the new factory is the same as the risk of its existing factories, then the firm’s equity cost of capital is unchanged. What effect would this new policy have on Lengefeld’s stock price?

Solution: Plan: To figure out the effect of this policy on Lengefeld’s stock price, we need to know several things. First, we need to compute its equity cost of capital. Next we must determine Lengefeld’s dividend and growth rate under the new policy. Because we know that Lengefeld currently has a growth rate of 0 (g = 0), a dividend of $2.00 and a price of $24, we can use Eq. 7.7 to estimate rE.

Plan (cont'd): Next, the new dividend will simply be 50% of the old dividend of $ Finally, given a retention rate of 50% and a return on new investment of 15%, we can use Eq to compute the new growth rate (g). Finally, armed with the new dividend, Lengefeld’s equity cost of capital, and its new growth rate, we can use Eq. 7.6 to compute the price of Lengefeld’s shares if it institutes the new policy.

Execute: Using Eq. 7.7 to estimate rE we have In other words, to justify Lengefeld’s stock price under its current policy, the expected return of other stocks in the market with equivalent risk must be 8.33%.

Execute: Next, we consider the consequences of the new policy. If Lengefeld reduces its dividend payout rate to 50%, then from Eq. 7.8 its dividend this coming year will fall to Div1 = EPS1 × 50% = $2.00 × 50% = $1.0. At the same time, because the firm will now retain 50% of its earnings to invest in new stores, from Eq its growth rate will increase to:

Execute: Assuming Lengefeld can continue to grow at this rate, we can compute its share price under the new policy using the constant dividend growth model of Eq. 7.6

Evaluate: Lengefeld’s share price should rise from $24 to $ if the company cuts its dividend in order to increase its investment and growth, implying that the investment has positive NPV. By using its earnings to invest in projects that offer a rate of return (15%) greater than its equity cost of capital (8.33%), Lengefeld has created value for its shareholders.

Example 7.4 Unprofitable Growth (1 of 4)
Problem Suppose Crane Sporting Goods decides to cut its dividend payout rate to 75% to invest in new stores, as in Example 7.3. But now suppose that the return on these new investments is 8%, rather than 12%. Given its expected earnings per share this year of $6 and its equity cost of capital of 10% (we again assume that the risk of the new investments is the same as its existing investments), what will happen to Crane’s current share price in this case?

Solution Plan We will follow the steps in Example 7.3, except that in this case, we assume a return on new investments of 8% when computing the new growth rate (g) instead of 12% as in Example 7.3.

Execute Just as in Example 7.3, Crane’s dividend will fall to $6 × 0.75 = $4.50. Its growth rate under the new policy, given the lower return on new investment, will now be g = 0.25 × 0.08 = 0.02 = 2%. The new share price is therefore

Evaluate Even though Crane will grow under the new policy, the return on its new investments is too low. The company’s share price will fall if it cuts its dividend to make new investments with a return of only 8%. By reinvesting its earnings at a rate (8%) that is lower than its equity cost of capital (10%), Crane has reduced shareholder value.

Example 7.4a Unprofitable Growth (1 of 4)
Problem: Suppose Lengefeld Manufacturing decides to cut its dividend payout rate to 50% to invest in new stores, as in Example 7.3b. But now suppose that the return on these new investments is 8%, rather than 15%. Give its expected earnings per share this year of $2 and its equity cost of capital of 8.33% (we again assume that the risk of the new investments is the same as its existing investments), what will happen to Lengefeld’s current share price in this case?

Solution: Plan: We will follow the steps in Example 7.3b, except that in this case, we assume a return on new investments of 8% when computing the new growth rate (g) instead of 15% as in Example 7.3b.

Execute: Just as in Example 7.3b, Lengefeld’s dividend will fall to $2 × 50% = $2.00. Its growth rate under the new policy, given the lower return on new investment, will now be g = 50% × 8% = 4%. The new share price is therefore

Evaluate: Even though Lengefeld will grow under the new policy, the return on its new investments is too low. The company’s share price will fall if it cuts its dividend to make new investments with a return of only 8%. By reinvesting its earnings at a rate (8%) that is lower than its equity cost of capital (8.33%), Lengefeld has reduced shareholder value.

Changing Growth Rates If the firm is expected to grow at a long-term rate g after year N + 1, then from the constant dividend growth model:

Example 7.5 Valuing a Firm with Two Different Growth Rates (1 of 6)
Problem Small Fry, Inc., has just invented a potato chip that looks and tastes like a french fry. Given the phenomenal market response to this product, Small Fry is reinvesting all of its earnings to expand its operations. Earnings were $2 per share this past year and are expected to grow at a rate of 20% per year until the end of year 4. At that point, other companies are likely to bring out competing products. Analysts project that at the end of year 4, Small Fry will cut its investment and begin paying 60% of its earnings as dividends. Its growth will also slow to a long- run rate of 4%. If Small Fry’s equity cost of capital is 8%, what is the value of a share today?

Solution Plan We can use Small Fry’s projected earnings growth rate and payout rate to forecast its future earnings and dividends. After year 4, Small Fry’s dividends will grow at a constant 4%, so we can use the constant dividend growth model (Eq. 7.13) to value all dividends after that point. Finally, we can pull everything together with the dividend-discount model (Eq. 7.4).

Execute The following spreadsheet projects Small Fry’s earnings and dividends:

Starting from $2.00 in year 0, EPS grows by 20% per year until year 4, after which growth slows to 4%. Small Fry’s dividend payout rate is zero until year 4, when competition reduces its investment opportunities and its payout rate rises to 60%. Multiplying EPS by the dividend payout ratio, we project Small Fry’s future dividends in line 4. After year 4, Small Fry’s dividends will grow at the constant expected long-run rate of 4% per year. Thus, we can use the constant dividend growth model to project Small Fry’s share price at the end of year 3. Given its equity cost of capital of 8%,

We then apply the dividend-discount model (Eq. 7.4) with this terminal value:

Evaluate The dividend-discount model is flexible enough to handle any forecasted pattern of dividends. Here, the dividends were zero for several years and then settled into a constant growth rate, allowing us to use the constant dividend growth model as a shortcut.

Example 7.5a Valuing a Firm with Two Different Growth Rates (1 of 8)
Problem: Annie-Bell, Inc., has just invented hotdog/taco combo. Given the phenomenal market response to this product, Annie-Bell is reinvesting all of its earnings to expand its operations. Earnings were $5 per share this past year and are expected to grow at a rate of 30% per year until the end of year 3. At that point, other companies are likely to bring out competing products.

Problem: Analysts project that at the end of year 3, Annie-Bell will cut its investment and begin paying 75% of its earnings as dividends. Its growth will also slow to a long-run rate of 5%. If Annie-Bell’s equity cost of capital is 9%, what is the value of a share today?

Solution: Plan: We can use Annie-Bell’s projected earnings growth rate and payout rate to forecast its future earnings and dividends. After year 3, Annie-Bell’s dividends will grow at a constant 5%, so we can use the constant dividend growth model (Eq. 7.13) to value all dividends after that point. Finally, we can pull everything together with the dividend-discount model (Eq. 7.4).

Execute: The following spreadsheet projects Annie-Bell’s earnings and dividends:

Execute: Starting from $5.00 in year 0, EPS grows by 30% per year until year 3, after which growth slows to 5%. Annie-Bell’s dividend payout rate is zero until year 3, when competition reduces its investment opportunities and its payout rate rises to 75%. Multiplying EPS by the dividend payout ratio, we project Annie-Bell’s future dividends.

Execute: From year 3 onward, Annie-Bell’s dividends will grow at the expected long-run rate of 5% per year. Thus we can use the constant dividend growth model to project Annie-Bell’s share price at the end of year 3. Given its equity cost of capital of 9%,

Execute: We then apply the dividend discount model (Eq. 7.4) with this terminal value:

Evaluate: The dividend-discount model is flexible enough to handle any forecasted pattern of dividends. Here the dividends were zero for several years and then settled into a constant growth rate, allowing us to use the constant growth rate model as a shortcut.

Value Drivers and the Dividend-Discount Model The dividend-discount model includes an implicit forecast of the firm’s profitability which is discounted back at the firm’s equity cost of capital

The Dividend-Discount Model
Table 7.1: The Dividend-Discount Model General formula A formula: P naught = div sub 1 divided by 1 + r sub E, + div sub 2 divided by, 1 + r sub E, squared, and so on, plus div sub N divided by, 1 + r sub R, raised to the N power, + P sub n divided by, 1 + r sub E, raised to the N power. If dividend growth is constant A formula: P naught = div sub 1 divided by r sub E, minus g. If early growth is variable followed by constant growth A formula: P naught = div sub 1 divided by 1 + r sub E, + div sub 2 divided by, 1 + r sub E, squared, and so on, plus div sub N divided by, 1 + r sub E, raised to the N power, plus quantity, 1 divided by, 1 + r sub E, raised to the N power, end quantity, times quantity, div sub N + 1, divided by r sub E, minus g.

7.5 Limitations of the Dividend-Discount Model (1 of 2)
Uncertain Dividend Forecasts The dividend-discount model values a stock based on a forecast of the future dividends, but a firm’s future dividends carry a tremendous amount of uncertainty

Figure 7.2 NKE Stock Prices for Different Expected Growth Rates

7.5 Limitations of the Dividend-Discount Model (2 of 2)
Non-Dividend-Paying Stocks Many companies do not pay dividends, thus the dividend-discount model must be modified

7.6 Share Repurchases and the Total Payout Model (1 of 3)
The firm uses excess cash to buy back its own stock Two Consequences: The more cash the firm uses to repurchase shares, the less cash it has available to pay dividends By repurchasing shares, the firm decreases its share count, which increases its earnings and dividends on a per-share basis

In the dividend-discount model, a share is valued from the perspective of a single shareholder, discounting the dividends the shareholder will receive:

Values all of the firm’s equity, rather than a single share To use this model, discount the total payouts that the firm makes to shareholders, which is the total amount spent on both dividends and share repurchases

Example 7.6 Valuation with Share Repurchases (1 of 3)
Problem Titan Industries has 217 million shares outstanding and expects earnings at the end of this year of $860 million. Titan plans to pay out 50% of its earnings in total, paying 30% as a dividend and using 20% to repurchase shares. If Titan’s earnings are expected to grow by 7.5% per year and these payout rates remain constant, determine Titan’s share price assuming an equity cost of capital of 10%.

Solution Plan Based on the equity cost of capital of 10% and an expected earnings growth rate of 7.5%, we can compute the present value of Titan’s future payouts as a constant growth perpetuity. The only input missing here is Titan’s total payouts this year, which we can calculate as 50% of its earnings. The present value of all of Titan’s future payouts is the value of its total equity. To obtain the price of a share, we divide the total value by the number of shares outstanding (217 million).

Execute Titan will have total payouts this year of 50% × $860 million = $430 million. Using the constant growth perpetuity formula, we have

Example 7.6a Valuation with Share Repurchases (1 of 5)
Problem: 3M Co. has 698 million shares outstanding and expects earnings at the end of this year of $2.96 billion. 3M plans to pay out 50% of its earnings in total, paying 25% as a dividend and using 25% to repurchase shares. If 3M’s earnings are expected to grow by 9.2% per year and these payout rates remain constant, determine 3M’s share price assuming an equity cost of capital of 12%.

Solution: Plan: Based on the equity cost of capital of 12% and an expected earnings growth rate of 9.2% we can compute the present value of 3M’s future payouts as a constant growth perpetuity. The only input missing here is 3M’s total payouts this year, which we can calculate as 50% of its earnings. The present value of all of 3M’s future payouts is the value of its total equity. To obtain the price of a share, we divide the total value by the number of shares outstanding (698 million).

Execute: 3M will have total payouts this year of 50% × $2.96 billion = $1.48 billion. Using the constant growth perpetuity formula, we have This present value represents the total value of 3M’s equity (i.e. its market capitalization). To compute the share price, we divide by the current number of shares outstanding:

Evaluate: Using the total payout method, we did not need to know the firm’s split between dividends and share repurchases. To compare this method with the dividend-discount model, note that 3M will pay a dividend of 25% × $2.96 billion/(698 million shares) = $1.06 per share, for a dividend yield of

Evaluate: From Eq. 7.7, 3M’s expected EPS, dividend, and share price growth rate This growth rate exceeds the 9.2% growth rate of earnings because 3M’s share count will decline over time owing to its share repurchases.

7.7 Putting It All Together (1 of 3)
How would an investor decide whether to buy or sell a stock? She would value the stock using her own expectations If her expectations were substantially different, she might conclude that the stock was over- or under- priced Based on that conclusion, she would buy or sell the stock

How could a stock suddenly be worth more or less after an earnings announcement? As investors digest the news, they update their expectations and buying or selling pressure would then drive the stock price up or down until the buys and sells came into balance

What should managers do to raise the stock price further? The only way to raise the stocprice is to make value- increasing decisions

Chapter Quiz What are some key differences between preferred and common stock? What is the role of a floor broker at the NYSE? What discount rate do you use to discount the future cash flows of a stock? What are three ways that a firm can increase the amount of its future dividend per share? What are the main limitations of the dividend-discount model? How does the total payout model address part of the dividend- discount model’s limitations?

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