Chapter 10 Valuing Stocks.

Chapter 10 Valuing Stocks

Chapter Outline Stock Basics The Dividend-Discount Model
Estimating Dividends in the Dividend-Discount Model Total Payout and Free Cash Flow Valuation Models Valuation Based on Comparable Firms Information, Competition, and Stock Prices

Learning Objectives Read a stock quote
Value a stock as the present value of its expected future dividends Understand the tradeoff between dividends and growth in stock valuation Value a stock as the present value of either the company’s total payout or its free cash flows Value a stock by applying common multiples based on the values of comparable firms Compare and contrast different approaches to valuing a stock Understand how information is incorporated into stock prices through competition in efficient markets

Stock Basics Ticker symbols are used by a publicly traded company when its trades are reported on the real-time electronic display of trading activity (ticker). Common stock is a share of ownership in the corporation, which gives its owner rights to vote on the election of directors, mergers, or other major events. Common stock carries the right to share in the profits of the corporation through dividend payments. Dividends are periodic payments, usually in the form of cash that are made to shareholders as a partial return on their investment in the corporation. Shareholders are paid dividends in proportion to the amount of shares they own.

The Dividend-Discount Model
A One Year Investor Dividend Yields, Capital Gains, and Total Returns Multiyear Investor and Dividend-Discount Model Equation The Dividend-Discount Model Equation

The Dividend-Discount Model
Determine the expected cash flows that an investor will receive Considering cash flows for an investor with a one-year investment horizon Consider perspective of investors with long investment horizons Establish the first stock valuation method: the dividend-discount model

A One-Year Investor Two Potential Sources of Cash Flows from Stock
The firm might pay out cash to its shareholders in the form of a dividend The investor might generate cash by selling the shares at some future date

A One-Year Investor Equity Cost of Capital – RE – the expected return of other investments available in the market with equivalent risk to the firm’s share. If current stock prices are less than this amount, it would be a positive NPV investment. If the stock price exceeds this amount, selling it would produce a positive NPV and the stock price would quickly fall.

Dividend Yields, Capital Gains, and Total Returns
Dividend Yield: expected annual dividend of the stock divided by its current price. (First term on right side) Capital Gain: amount the investor will earn on the stock, difference between the expected sale price and the original purchase price for the stock . (Second term on right side) Total Return: sum of the dividend yield and the capital gain rate—the expected return that the investor will earn for a one-year investment in the stock. The expected total return of the stock should equal the expected return of other investments available in the market with equivalent risk.

Dividend Yields, Capital Gains, and Total Returns
The total return of a stock is equal to the dividend yield plus the capital gain rate. The expected total return of a stock should equal its equity cost of capital:

Example- Stock Prices and Returns
Problem: Suppose you expect Longs Drug Stores to pay an annual dividend of $.56 per share in the coming year and to trade $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?

Stock Prices and Returns
Solution: Plan: We can use Eq. 9.1 to solve for the beginning price we would pay now (P0) given our expectations about dividends (Div1=.56) and future price (P1=$45.50) and the return we need to expect to earn to be willing to invest (rE=6.8%). We can then use Eq. 9.2 to calculate the dividend yield and capital gain. (Eq. 9.1)

Execute: Referring to Eq. 9.2 we see that at this price, Longs’ dividend yield is Div1/P0 = 0.56/43.13 = 1.30%. The expected capital gain is $ $43.13 = $2.37 per share, for a capital gain rate of 2.37/43.13 = 5.50%.

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.

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 Longs’ 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. 9.1 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=8.9%). We can then use Eq. 9.2 to calculate the dividend yield and capital gain. (Eq. 9.1)

Execute: Referring to Eq. 9.2 we see that at this price, Koch’s dividend yield is Div1/P0 = 2.31/78.11 = 2.96%. The expected capital gain is $ $78.11 = $4.64 per share, for a capital gain rate of 4.64/78.11 = 5.94%.

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 We now extend the intuition we developed for the one-year investor’s return to a multiyear investor. Equation 9.1 depends upon the expected stock price in one year, P1. But 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 (Eq. 9.3)
As a two-year investor, we care about the dividend and stock price in year 2.

Dividend-Discount Model
(Eq. 9.4) This equation applies to a single N-year investor. 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
(Eq. 9.5) The price of a stock is equal to the present value of all of the expected future dividends it will pay (buy and hold, collecting dividends forever).

9.3 Estimating Dividends in the Dividend-Discount Model
Constant Dividend Growth Dividends Versus Investment and Growth Changing Growth Rate Limitations of Dividend-Discount Model

Constant Dividend Growth Model
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.

Valuing a Firm with Constant Dividend Growth
Problem: Consolidated Edison, Inc. (Con Edison), is a regulated utility company that services the New York City area. Suppose Con Edison 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 Edison’s stock.

Solution: Plan: Because the dividends are expected to grow perpetually at a constant rate, we can use constant growth model to value Con Edison. 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 Edison stock because you are buying claim to this year’s dividend and to an infinite growing series of future dividends.

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. 9.6 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.

Constant Dividend Growth Model
For another interpretation of Eq. 9.6, note that we can rearrange it as follows: The dividend each year is equal to the firm’s earnings per share (EPS) multiplied by its dividend payout rate. The firm can, therefore, increase its dividend in three ways: It can increase its earnings (net income). It can increase its dividend payout rate. It can decrease its number of shares outstanding. (Eq. 9.7)

Dividend Payout Rate If we define a firm’s dividend payout rate as the fraction of its earnings that the firm pays as dividends each year, then we can write the firm’s dividend per share at date t as follows:

A Simple Model of Growth
If all increases in future earnings result exclusively from new investment made with retained earnings, then: (Eq. 9.9)

Retention Rate New investment equals the firm’s earnings multiplied by its retention rate, or the fraction of current earnings that the firm retains: (Eq. 9.10)

Substituting Eq into Eq. 9.9 and dividing by earnings gives an expression for the growth rate of earnings: (Eq. 9.11)

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. 9.12)

Cutting Dividends for Profitable Growth
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.

Problem (cont'd): 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 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. 9.7 to estimate rE.

Plan (cont'd): 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. 9.6 to compute the price of Crane’s shares if it institutes the new policy.

Execute: Using Eq. 9.7 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%.

Execute (cont’d): Next, we consider the consequences of the new policy. If Crane reduces its dividend payout rate to 75%, then from Eq its dividend this coming year will fall to Div1 = EPS1 x 75% = $6 x 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

Execute (cont’d): 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. 9.6

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, implying that the investment has positive NPV. 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.

Problem: Pittsburgh & West Virginia Railroad (PW) expects to have earnings per share of $0.48 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, PW’s current share price is $10.

Problem (cont'd): Suppose PW could cut its dividend payout rate to 67% for the foreseeable future and use the retained earnings to expand. The return on investment in the expansion is expected to be 11%. 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 PW’s stock price?

Solution: Plan: To figure out the effect of this policy on PW’s stock price, we need to know several things. First, we need to compute its equity cost of capital. Next we must determine PW’s dividend and growth rate under the new policy. Because we know that PW currently has a growth rate of 0 (g = 0), a dividend of $0.48 and a price of $10, we can use Eq. 9.7 to estimate rE.

Plan (cont'd): Next, the new dividend will simply be 67% of the old dividend of $ Finally, given a retention rate of 33% and a return on new investment of 11%, we can use Eq to compute the new growth rate (g). Finally, armed with the new dividend, PW’s equity cost of capital, and its new growth rate, we can use Eq. 9.6 to compute the price of PW’s shares if it institutes the new policy.

Execute: Using Eq. 9.7 to estimate rE we have In other words, to justify PW’s stock price under its current policy, the expected return of other stocks in the market with equivalent risk must be 4.8%.

Execute (cont’d): Next, we consider the consequences of the new policy. If PW reduces its dividend payout rate to 67%, then from Eq its dividend this coming year will fall to Div1 = EPS1 x 67% = $0.48 x 67% = $0.32. At the same time, because the firm will now retain 33% of its earnings to invest in new stores, from Eq its growth rate will increase to

Execute (cont’d): Assuming PW 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. 9.6

Evaluate: PW’s share price should rise from $10 to $27.35 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 (11%) greater than its equity cost of capital (4.8%), PW has created value for its shareholders.

Unprofitable Growth Problem: Suppose Crane Supporting Goods decides to cut its dividend payout rate to 75% to invest in new stores, as in Example But now suppose that the return on these new investments is 8%, rather than 12%. Give 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?

Unprofitable Growth Solution: Plan:
We will follow the steps in Example 9.3, 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 9.3.

Unprofitable Growth Execute: Just as in Example 9.3, Crane’s dividend will fall to $6 x 75% = $ Its growth rate under the new policy, given the lower return on new investment, will now be g = 25% x 8% = 2%. The new share price is therefore

Unprofitable Growth Evaluate: Even though Crane will grow under the new policy, the new investments have a negative NPV. 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.

Unprofitable Growth Problem: Suppose Pittsburgh & West Virginia Railroad decides to cut its dividend payout rate to 67% to invest in new stores, as in Example 9.3a. But now suppose that the return on these new investments is 4%, rather than 11%. Give its expected earnings per share this year of $0.48 and its equity cost of capital of 4.8% (we again assume that the risk of the new investments is the same as its existing investments), what will happen to PW’s current share price in this case?

Copyright © 2009 Pearson Prentice Hall. All rights reserved.
Unprofitable Growth Solution: Plan: We will follow the steps in Example 9.3a, except that in this case, we assume a return on new investments of 4% when computing the new growth rate (g) instead of 11% as in Example 9.3a. Copyright © 2009 Pearson Prentice Hall. All rights reserved.

Unprofitable Growth Execute: Just as in Example 9.3a, PW’s dividend will fall to $0.48 x 67% = $ Its growth rate under the new policy, given the lower return on new investment, will now be g = 33% x 4% = 1.32%. The new share price is therefore

Unprofitable Growth Evaluate: Even though PW will grow under the new policy, the new investments have a negative NPV. The company’s share price will fall if it cuts its dividend to make new investments with a return of only 4%. By reinvesting its earnings at a rate (4%) that is lower than its equity cost of capital (4.8%), PW has reduced shareholder value.

Changing Growth Rates Specifically, if the firm is expected to grow at a long- term rate g after year N + 1, then from the constant dividend growth model: (Eq. 9.13)

Valuing a Firm with Two Different Growth Rates
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. 9.13) to value all dividends after that point. Finally, we can pull everything together with the dividend-discount model.

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

Execute (cont’d): 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. From year 4 onward, Small Fry’s dividends will grow at the 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%,

Execute (cont’d): We then apply the dividend discount model (Eq. 9.4) 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.

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 $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. Analysts project that at the end of year 3, Small Fry 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 Small Fry’s equity cost of capital is 9%, 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 3, Small Fry’s dividends will grow at a constant 5%, so we can use the constant dividend growth model (Eq. 9.13) to value all dividends after that point. Finally, we can pull everything together with the dividend-discount model.

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

Execute (cont’d): Starting from $5.00 in year 0, EPS grows by 30% per year until year 3, after which growth slows to 5%. Small Fry’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 Small Fry’s future dividends in line 7. From year 3 onward, Small Fry’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 Small Fry’s share price at the end of year 3. Given its equity cost of capital of 9%,

Execute (cont’d): We then apply the dividend discount model (Eq. 9.4) 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.

Changing Growth Rates and Limitations of Dividend-Discount Model
We cannot use the constant dividend growth model to value the stock of certain firms for two reasons: These firms often pay no dividends when they are young Their growth rate continues to change over time until they mature There is great uncertainty associated with any forecast of a firm’s future dividends in relationship to the Dividend-Discount Model

KCP Stock Prices for Different Expected Growth Rates

Total Payout and Free Cash Flow Valuation Models
Share Repurchases and the Total Payout Model The Discounted Free Cash Flow Model

Share Repurchases and the Total Payout Model
In the dividend-discount model, we valued a share from the perspective of a single shareholder, discounting the dividends the shareholder will receive:

Share Repurchases and the Total Payout Model

Discounted Free Cash Flow Model
The Discounted Free Cash Flow Model focuses on the cash flows to all of the firm’s investors, both debt and equity holders.

Valuation with Share Repurchases
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%. 82

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). 9-83 83

Execute: Titan will have total payouts this year of 50%  $860 million = $430 million. Using the constant growth perpetuity formula, we have 9-84 84

Execute (cont’d): This present value represents the total value of Titan’s equity (i.e., its market capitalization). To compute the share price, we divide by the current number of shares outstanding: 9-85 85

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 Titan will pay a dividend of 30%  $860 million/(217 million shares) = $1.19 per share, for a dividend yield of 1.19/79.26 = 1.50%. From Eq. 9.7, Titan’s expected EPS, dividend, and share price growth rate is g = rEDiv1/P0 = 8.50%. This growth rate exceeds the 7.50% growth rate of earnings because Titan’s share count will decline over time owing to its share repurchases. 9-86 86

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%. 9-87 87

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). 88

Execute: 3M will have total payouts this year of 50% x $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: 89

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% x $2.96 billion/(698 million shares) = $1.06 per share, for a dividend yield of $1.06/$75.73 = 1.40%. From Eq. 9.7, 3M’s expected EPS, dividend, and share price growth rate g = rE – Div1/P0 = 12% – 1.4% = 10.6%. 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. (Eq. 9.7) 90

Discounted Free Cash Flow Model
(Eq. 10.3) Given the enterprise value, V0, we can estimate the share price by using Eq to solve for the value of equity and then divide by the total number of shares outstanding. (Eq. 10.1) (Eq. 10.4)

Valuing Stock Using Free Cash Flows
Problem: Kenneth Cole Productions (KCP) had sales of $518 million in 2005. Suppose you expect its sales to grow at a rate of 9% in 2006, but then slow by 1% per year to the long-run growth rate that is characteristic of the apparel industry--4%--by 2011. Based on KCP’s past profitability and investment needs, you expect EBIT to be 9% of sales, increases in net working capital requirements to be 10% of any increase in sales, and capital expenditures to equal depreciation expenses. If KCP has $100 million in cash, $3 million in debt, 21 million shares outstanding, a tax rate of 37%, and a weighted average cost of capital of 11%, what is your estimate of the value of KCP’s stock in early 2006? 92

Solution: Plan: We can estimate KCP’s future cash flow by constructing a pro forma statement as we did for HomeNet in Chapter 9. The only difference is that the pro forma statement is for the whole company, rather than just one project. Further, we need to calculate a terminal (or continuation) value for KCP at the end of our explicit projections. Because we expect KCP’s free cash flow to grow at a constant rate after 2011, we can use Eq to compute a terminal enterprise value. The present value of the free cash flows during the years and the terminal value will be the total enterprise value for KCP. Using that value, we can subtract the debt, add the cash, and divide by the number of shares outstanding to compute the price per share (Eq. 10.4). 9-93 93

Execute: The spreadsheet below presents a simplified pro forma for KCP based on the information we have: 9-94 94

Execute: (continued) Because capital expenditures are expected to equal depreciation, lines 7 and 8 in the spreadsheet cancel out. We can set them both to zero rather than explicitly forecast them. Given our assumption of constant 4% growth in free cash flows after and a weighted average cost of capital of 11%, we can use Eq to compute a terminal enterprise value: 9-95 95

Execute: (continued) From Eq. 10.3, KCP’s current enterprise value is the present value of its free cash flows plus the firm’s terminal value: We can now estimate the value of a share of KCP’s stock using Eq : 9-96 96

Evaluate: The Value Principle tells us that the present value of all future cash flows generated by KCP plus the value of the cash held by the firm today must equal the total value today of all claims, both debt and equity, on those cash flows and cash. Using that principle, we calculate the total value of all of KCP’s claims and then subtract the debt portion to value the equity (stock). 9-97 97

Problem: Navarro had sales of $630 million in Suppose you expect its sales to grow at an 8% rate in 2010, but that this growth rate will slow by 2% per year to a long-run growth rate for the industry of 2% by 2013. Based on Navarro’s past profitability and investment needs, you expect EBIT to be 10% of sales, increases in net working capital requirements to be 8% of any increase in sales, and capital expenditures to equal depreciation expenses. If Navarro has $125 million in cash, $5 million in debt, 25 million shares outstanding, a tax rate of 35%, and a weighted average cost of capital of 12.5%, what is your estimate of the value of Navarro’s stock in early 2010? 9-98 98

Solution: Plan: We can estimate Navarro’s future free cash flow by constructing a pro forma statement as we did in Chapter 8. The only difference is that the pro forma statement is for the whole company, rather than just one project. Further, we need to calculate a terminal (or continuation) value for Navarro at the end of our explicit projections. Because we expect Navarro’s free cash flow to grow at a constant rate after 2013, we can use Eq to compute a terminal enterprise value. 99

Plan (cont’d): The present value of the free cash flows during the years – 2013 and the terminal value will be the total enterprise value for Navarro. Using that value, we can subtract the debt, add the cash, and divide by the number of shares outstanding to compute the price per share. 100

Execute: The spreadsheet below presents a simplified pro forma for Navarro based on the information we have: 101

Execute (cont’d): Because capital expenditures are expected to equal depreciation, lines 7 and 8 in the spreadsheet cancel out. We can set them both to zero rather than explicitly forecast them. Given our assumption of constant 2% growth in free cash flows after 2013 and a weighted average cost of capital of 12.5%, we can use Eq to compute a terminal enterprise value: 102

Execute (cont’d): From Eq. 10.5, Navarro’s current enterprise value is the present value of its free cash flows plus the firm’s terminal value: We can now estimate the value of a share of Navarro’s stock using Eq. 9.19: 103

Evaluate: The Value Principle tells us that the present value of all future cash flows generated by Navarro plus the value of the cash held by the firm today must equal the total value today of all the claims, both debt and equity, on those cash flows and cash. Using that principle, we can calculate the total value of all of Navarro’s claims and then subtract the debt portion to value the equity (stock). 104

Sensitivity Analysis for Stock Valuation
Problem: In the example, KCP’s EBIT was assumed to be 9% of sales. If KCP can reduce its operating expenses and raise its EBIT to 10% of sales, how would the estimate of the stock’s value change? 105

Solution: Plan: In this scenario, EBIT will increase by 1% of sales compared to previous example. From there, we can use the tax rate (37%) to compute the effect on the free cash flow for each year. Once we have the new free cash flows, we repeat the approach in the example to arrive at a new stock price. 9-106 106

Execute: In year 1, EBIT will be 1%  $564.6 million = $5.6 million higher. After taxes, this increase will raise the firm’s free cash flow in year 1 by (1 – 0.37)  $5.6 million = $3.5 million, to $30.9 million. Doing the same calculation for each year, we get the following revised FCF estimates: 9-107 107

Execute: We can now re-estimate the stock price as in the previous example. The terminal value is V2011 = [1.04/(0.11– 0.04)]  44.7 = $664.1 million, so The new estimate for the value of the stock is P0 = ( – 3)/21 = $29.02 per share, a difference of about 10% compared to the result found in previous example 9-108 108

Evaluate: KCP’s stock price is fairly sensitive to changes in the assumptions about its profitability. A 1% permanent change in its margins affects the firm’s stock price by 10%. 9-109 109

Problem: Navarro’s EBIT was assumed to be 10% of sales. If Navarro can reduce its operating expenses and raise its EBIT to 12% of sales, how would the estimate of the stock’s value change? 9-110 110

Solution: Plan: In this scenario, EBIT will increase by 2% of sales compared to its original numbers. From there, we can use the tax rate (35%) to compute the effect on the free cash flow for each year. Once we have the new free cash flows, we repeat the approach to arrive at a new stock price. 111

Execute: In year 1, EBIT will be 2% × $680.4 million = $13.6 million higher. After taxes, this increase will raise the firm’s free cash flow in year 1 by ( ) × $13.6 million = $8.8 million, to $49.0 million. Doing the same calculation for each year, we get the following revised FCF estimates: 112

Execute (cont’d): We can now re-estimate the stock price similar to the previous example. The terminal value is: so: 113

Execute (cont’d): The new estimate for the value of the stock is: This is a difference of about 16.3% compared to the result found in the previous example. 114

Evaluate: Navarro’s stock price is fairly sensitive to changes in the assumptions about its profitability. A 2% permanent change in its margins affects the firm’s stock price by 16.3%. 115

Valuation Based on Comparable Firms
Method of Comparables: estimate the value of the firm based on the value of other, comparable firms or investments that we expect will generate very similar cash flows in the future. Valuation Multiples: ratio of the value to some measure of the firm’s scale. Trailing Earnings: earnings over the prior 12 months Forward Earnings: expected earnings over the coming 12 months Trailing P/E: the resulting ratio from Trailing Earnings Forward P/E: the resulting ratio from Forward Earnings

Figure 9.3 A Comparison of Discounted Cash Flow Models of Stock Valuation

Relating the P/E Ratio to Expected Future Growth in the Dividend-Discount Model
$6.00 10.7 9.38 10.7 g 3% 2% 5% 4% P/E 10.71 9.38 14.42 12.5 9.38

Valuation Using the Price-Earnings Ratio
Problem: Suppose furniture manufacturer Herman Miller, Inc., has earnings per share of $1.38. If the average P/E of comparable furniture stocks is 21.3, estimate a value for Herman Miller’s stock using the P/E as a valuation multiple. What are the assumptions underlying this estimate? 119

Solution: Plan: We estimate a share price for Herman Miller by multiplying its EPS by the P/E of comparable firms: EPS  P/E = Earnings per Share  (Price per Share ÷ Earnings per Share) = Price per Share 9-120 120

Execute: P0 = $1.38  21.3 = $ This estimate assumes that Herman Miller will have similar future risk, payout rates, and growth rates to comparable firms in the industry. 9-121 121

Evaluate: Although valuation multiples are simple to use, they rely on some very strong assumptions about the similarity of the comparable firms to the firm you are valuing. It is important to consider whether these assumptions are likely to be reasonable--and thus to hold--in each case. 9-122 122

Problem: Suppose furniture manufacturer HNI Inc., has earnings per share of $ If the average P/E of comparable furniture stocks is 33, estimate a value for HNI’s stock using the P/E as a valuation multiple. What are the assumptions underlying this estimate? 9-123 123

Example 9.9a Valuation Using the Price-Earnings Ratio
Solution: Plan: We estimate a share price for HNI by multiplying its EPS by the P/E of comparable firms: EPS × P/E = Earnings per Share × (price per share ÷ earnings per share) = Price per Share 124

Execute: P0 = $0.83 × 33 = $27.39. This estimate assumes that HNI will have similar future risk, payout rates, and growth rates to comparable firms in the industry. 125

Evaluate: Although valuation multiples are simple to use, they rely on some very strong assumptions about the similarity of the comparable firms to the firm you are valuing. It is important to consider whether these assumptions are likely to be reasonable—and thus to hold—in each case. 126

Stock Valuation Techniques: The Final Word
No single technique provides a final answer regarding a stock’s true value Practitioners use a combination of these approaches Confidence comes from consistent results from a variety of these methods

Information, Competition, and Stock Prices
Information in Stock Prices Competition and Efficient Markets Lessons for Investors and Corporate Managers The Efficient Markets Hypothesis Versus No Arbitrage

Information in Stock Prices
For a publicly traded firm, its market price should already provide very accurate information, aggregated from a multitude of investors, regarding the true value of its shares. In most situations, a valuation model is best applied to tell us something about the firm’s future cash flows or cost of capital, based on its current stock price. Only in the relatively rare case in which we have some superior information that other investors lack regarding the firm’s cash flows and cost of capital would it make sense to second-guess the stock price.

The Valuation Triad

Using the Information in Market Prices
Problem: Suppose Tecnor Industries will pay a dividend this year of $5 per share. Its equity cost of capital is 10%, and you expect its dividends to grow at a rate of approximately 4%per year, though you are somewhat unsure of the precise growth rate. If Technor’s stock is currently trading for $76.92 per share, how would you update your beliefs about its dividend growth rate? 131

Solution: Plan: If we apply the constant dividend growth model based on a 4% growth rate, we can estimate a stock price using P=Div/(R-g). If the market price is higher than our estimate, it implies that the market expects higher growth in dividends than 4%. Conversely, if the Market price is lower than our estimate, the market expects dividend growth to be less than 4%. We can use the above equation to solve for the growth rate instead of price, allowing us to estimate the growth rate the market expects. 9-132 132

Execute: Using P=Div/(R-g), Div1 of $5, equity cost of capital (rE) of 10%, an dividend growth rate of 4%, we get P0 = 5/(0.10 – 0.04) = $ per share. The market price of $76.92, however, implies that most investors expect dividends to grow at a somewhat slower rate. In fact, if we continue to assume a constant growth rate, we can solve for the growth rate consistent with the current market price g = rE – Div1/P0 = 10% – 5/76.92 = 3.5% This 3.5% growth rate is lower than our expected growth rate of 4%. 9-133 133

Execute: Given the $76.92 market price for the stock, we should lower our expectations for the dividend growth rate from 4% unless we have very strong reasons to trust our own estimate. 9-134 134

Problem: Suppose SWGSB Industries will pay a dividend this year of $6.50 per share. Its equity cost of capital is 11.5%, and you expect its dividends to grow at a rate of about 5% per year, though you are somewhat unsure of the precise growth rate. If SWGSB’s stock is currently trading for $63.32 per share, how would you update your beliefs about its dividend growth rate? 9-135 135

Solution: Plan: If we apply the constant dividend growth model based on a 5% growth rate, we can estimate a stock price using Eq If the market price is higher than our estimate, it implies that the market expects higher growth in dividends than 5%. Conversely, if the market price is lower than our estimate, the market expects dividend growth to be less than 5%. We can use Eq. 9.7 to solve the growth rate instead of price, allowing us to estimate the growth rate the market expects. 136

Execute: Using Eq. 9.6 Div1 of $6.50, equity cost of capital (rE) of 11.5%, and a dividend growth rate of 5%, we get P0 = $6.50/(0.115 – 0.05) = $ per share. The market price of $63.32, however, implies that investors expect dividends to grow at a slower rate. 137

Execute (cont’d): In fact, if we continue to assume a constant growth rate, we can solve for the growth rate consistent with the current market price using Eq. 9.7: This 1.2% growth rate is lower than our expected growth rate of 5%. 138

Evaluate: Given the $63.32 market price for the stock, we should lower our expectations for the dividend growth rate from 5% unless we have very strong reasons to trust our estimate. 139

Competition and Efficient Markets
Efficient markets hypothesis: The idea that competition among investors works to eliminate all positive-NPV trading opportunities. It implies that securities will be fairly priced, based on their future cash flows, given all information that is available to investors. Public, Easily Available Information: Information available to all investors includes information in news reports, financial statements, corporate press releases, or other public data sources. Private or Difficult-to-Interpret Information

Stock Price Reactions to Public Information
Problem: Myox Labs announces that it is pulling one of its leading drugs from the market, owing to the potential side effects associated with the drug. As a result, its future expected free cash flow will decline by $85 million per year for the next 10 years. Myox has 50 million shares outstanding, no debt, and an equity cost of capital of 8%. If this news came as a complete surprise to investors, what should happen to Myox’s stock price upon the announcement?

Solution: Plan: In this case, we can use the discounted free cash flow method. With no debt, rwacc = rE = 8%. The effect on the Myox’s enterprise value will be the loss of a ten-year annuity of $85 million. We can compute the effect today as the present value of that annuity.

Execute: Using the annuity formula, the decline in expected free cash flow will reduce Myox’s enterprise value by: Thus the share price should fall by $570.36/50 = $11.41 per share.

Evaluate: Because this news is public and its effect on the firm’s expected free cash flow is clear, we would expect the stock price to drop by $11.41 per share nearly instantaneously.

Problem: Foundation Labs announces that it is pulling one of its leading drugs from the market, owing to the potential side effects associated with the drug. As a result, its future expected free cash flow will decline by $70 million per year for the next 8 years. Foundation has 30 million shares outstanding, no debt, and an equity cost of capital of 7%. If this news came as a complete surprise to investors, what should happen to Foundation’s stock price upon the announcement?

Solution: Plan: In this case, we can use the discounted free cash flow method. With no debt, rwacc = rE = 7%. The effect on the Foundation’s enterprise value will be the loss of an eight- year annuity of $70 million. We can compute the effect today as the present value of that annuity.

Execute: Using the annuity formula, the decline in expected free cash flow will reduce Foundation’s enterprise value by: Thus the share price should fall by $417.99/30 = $13.93 per share.

Evaluate: Because this news is public and its effect on the firm’s expected free cash flow is clear, we would expect the stock price to drop by $13.93 per share nearly instantaneously.

Possible Stock Price Paths for Phenyx Pharmaceuticals

Lessons for Investors and Corporate Managers
Consequences for Investors Implications for Corporate Managers Cash flows paid to investors determine value Focus on NPV and free cash flows Avoid accounting illusions Use financial transactions to support investment

The Efficient Markets Hypothesis Versus No Arbitrage
An arbitrage opportunity is a situation in which two securities (or portfolios) with identical cash flows have different prices. Because anyone can earn a sure profit in this situation by buying the low-priced security and selling the high-priced one, we expect investors to immediately exploit and eliminate these opportunities. Thus, in a normal market, arbitrage opportunities will not be found. The efficient markets hypothesis states that securities with equivalent risk should have the same expected return. The efficient markets hypothesis is, therefore, incomplete without a definition of “equivalent risk.” Furthermore, different investors may perceive risks and returns differently (based on their information and preferences). There is no reason to expect the efficient markets hypothesis to hold perfectly; rather, it is best viewed as an idealized approximation for highly competitive markets.

Chapter Quiz You notice that Dell computers has a stock price of $ and EPS of $1.49. Its competitor Hewlett Packard has EPS of $2.35. What is one estimate of the value of a share of Hewlett Packard stock? Summit Systems will pay a dividend of $2.10 this year. If you expect Summit’s dividend to grow by 4% per year, what is its price per share if the firm’s equity cost of capital is 9%? Anle Corporation has a current stock price of $18.00 and expected to pay a dividend of $.45 in one year. Its expected stock price right after paying that dividend is $ What’s Anle’s cost of capital?

Chapter 10 Valuing Stocks.

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