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**FINC4101 Investment Analysis**

Instructor: Dr. Leng Ling Topic: Equity Valuation

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Learning objectives Distinguish between the intrinsic value and price of a share of common stock. Calculate the intrinsic value of a firm using dividend discount models Constant dividend growth model Multistage dividend growth model Use the constant growth model to relate growth opportunities to stock value. Calculate the P/E ratio for a constant growth firm. Discuss the free cash flow valuation methods.

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**Concept Map FI400 Theory Portfolio Pricing Asset Equity Fixed Income**

Efficiency Market Derivatives Exchange Foreign

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**Identify mispriced equity securities.**

Why equity valuation? Identify mispriced equity securities. How? By calculating “intrinsic” or “true” value of a stock using valuation models. These valuation models make use of information concerning current & future profitability. This approach of identifying mispriced stocks is called fundamental analysis. In this chapter, the information concerning current and future profitability will be information like dividends, earnings, dividend growth rate (g), required rate of return, ROE, retention rate/dividend payout ratio, etc. Next slide explains “intrinsic” value.

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**Intrinsic value vs. market price (1)**

Present value of all expected future cash flows to the stock investor. The cash flows are discounted at the appropriate required rate of return, k. Expected future cash flows consist of: cash dividends sale price: proceeds from the ultimate sale of the stock

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**Intrinsic value vs. market price (2)**

Intrinsic value is your (the analyst’s) estimate of what a stock is really worth. Intrinsic value (V0) can differ from the current market price (P0). If V0 > P0: stock is underpriced => buy If V0 < P0: stock is overpriced => sell or don’t buy. When V0 differs from P0, then investor must disagree with some or all of the market consensus estimates of future cash flows (dividends or sale price) or k.

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**Market equilibrium In market equilibrium,**

Everyone has the same intrinsic value. So, intrinsic value equals market price, i.e., V0 = P0. Everyone also demands the same required rate of return from the stock. So everyone has the same k. In addition, expected HPR = k. This common required rate of return is called the market capitalization rate. Market capitalization rate: required rate of return which the market (i.e., everyone) uses to discount future cash flows. Bring in the powerful concept of market equilibrium. From asset pricing topic, we know that in market equilibrium (and assuming everyone agrees on the expected future cash flows and riskiness), required rate of return must equal expected HPR. Otherwise, people will continue to trade and prices will continue to change. This slide is saying that there is a special name for the required rate of return in equilibrium. That name is “market capitalization rate”. Tell class that the market capitalization rate is the discount rate that gives rise to the observed market price. So later we see how we can use valuation models to infer or ‘back out’ the market capitalization rate.

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**Equity valuation models**

Dividend discount models Constant dividend growth model Multistage (non-constant) dividend growth model Price-earnings ratio (P/E) Free cash flow models

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**Dividend discount models (DDMs)**

Dividend discount models say that the intrinsic value of a stock is equal to the present value of all expected future dividends. What about cash flow from the ultimate sale of the stock? Is that included? Yes, because stock price at time of sale is again determined by expected dividends at the time of sale. Show that price is ultimately determined by dividends, so intrinsic value is ultimately determined by dividends. V0 = D1/(1+k) What is P1? Assuming that P1=V1, we know that V1 = (D2 + P2)/(1 + k). Substitute this for P1, and we get V0 = D1/(1+k) + (D2 + P2)/(1 + k)2 This says that the intrinsic value of the stock is the PV of dividends plus sales price for a two-year holding period. So both dividends and sales price appear in the valuation of the stock. If we plan to hold the stock for H years, we can continue with this type of substitution and write the stock price as the PV of dividends over the H years, plus the ultimate sales price, PH , V0 = D1/(1+k) + (D2 + P2)/(1 + k)2 + ….. + (DH + PH)/(1 + k)H We can continue to substitute for price indefinitely to conclude: V0 = D1/(1+k) + (D2 + P2)/(1 + k)2 + (D3 + P3)/(1 + k)3 ….. This states that the stock price should equal the PV of all expected future dividends into perpetuity. This is the dividend discount model (DDM) of stock prices.

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**Dividend discount model: General formula**

This formula cannot be implemented because it requires dividend forecasts every year into the indefinite future. To implement the DDM, we make assumptions about how dividends evolve over time.

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**Two versions of DDM We look at 2 assumptions:**

Dividends grow at constant rate Constant dividend growth model Dividends grow at different rates over different periods. At some future date, dividend growth settles down to a constant rate. Multistage (non-constant) dividend growth model Note that the constant dividend stream assumption is just a special case of the constant growth rate assumption where we assume dividends don’t grow at all, i.e., g=0.

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**Constant dividend growth model (1)**

Assume that dividends grow at a constant rate, g, per period forever. Given this assumption, the intrinsic value equals Don’t panic. D1 = D0(1 + g) D0 = Dividend that the firm just paid This model is also called the Gordon model, after Myron J. Gordon, who popularized the model. Students need to know both versions of the constant growth formula. If dividends were expected not to grow (g=0), then the dividend stream would be a simple perpetuity, and the valuation formula for such a no growth stock would be P0 = D1/k, which is the formula for the PV of a perpetuity (covered this in FI3300 as the case of a constant dividend stream). Required rate of return or discount rate Dividend growth rate

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**Constant dividend growth model (2)**

Warning: The model works only if k > g. Useful properties. All other things unchanged, If D1 increases (decreases), V0 increases (decreases). If g increases (decreases), V0 increases (decreases). If k increases (decreases), V0 decreases (increases). If k < g, then mathematically, V0 would be negative, which does not make sense. Economically, if k < g, that means dividends are expected to grow at a rate faster than k. Such a (high) growth rate must be unsustainable over the long run. The appropriate valuation model to use in this case is a non-constant dividend growth model.

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**Constant dividend growth model (3)**

Suppose the market is in equilibrium. This means that stock price is equal to intrinsic value, i.e., P0 = V0. Then, stock price is expected to grow at the same rate as dividends. That is, the expected rate of price appreciation in any year will equal the constant growth rate, g. P1 = P0 ( 1 + g ) = V1 = V0 ( 1 + g ) Need the first point, so that I can write P0 = D1/(k-g) How to show the result: P0 = D1/(k-g) Suppose, we are at t=1, then stock price, P1 = D2/(k-g). But D2 = D1(1+g), so P1 = D1(1+g)/(k-g) = [D1/(k-g)] x (1+g) = P0 x (1 + g) Thus, we say that price is expected to grow at the same rate of dividends, g.

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**Expected HPR and k (1) Continue to assume that P0 = V0 .**

Then, expected HPR, E(r) is, The discussion implicitly assumes market equilibrium. Assuming that P0 = V0 allows us to go from the first line to the second line. Details: E(r) = D1/P0 + (P1 – P0)/P0 = D1/P0 + (P0(1 + g) – P0)/P0 = D1/P0 + (P0 + (P0 x g) – P0)/P0 = D1/P0 + (P0 x g)/P0 = D1/P0 + g Dividend yield Capital gains yield

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**Expected HPR and k (2) If stock is selling at intrinsic value, P0 = V0**

Then required rate of return, k, must equal the expected HPR. Therefore, When everyone agrees on the same k (in equilibrium), we can use the above formula to compute market capitalization rate. The discussion implicitly assumes market equilibrium. Earlier in the slides, already said that in equilibrium, we have P0 = V0 . So, by assuming that P0 = V0, we are assuming market equilibrium. From this, we also concluded that expected HPR = k and that k is also called the market capitalization rate since it is the required rate of return shared by everyone in the market.

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**Constant dividend stream**

If g = 0, then dividends do not grow and stay the same forever. We have a constant dividend stream – a perpetuity. The constant dividend stream assumption is a special case of the constant growth model with g = 0. Implication: with constant dividend stream, we continue to use the preceding equations but set g to 0.

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**Applying the constant growth DDM (1)**

A common stock pays an annual dividend per share of $2.10. The risk-free rate is 7% and the risk premium for this stock is 4%. If the annual dividend is expected to remain at $2.10 forever, what is the value of the stock? (to two decimal places) Verify that V0 = $19.09 In the following problems, we assume that the market is in equilibrium. Thus, Value and Price mean the same thing, i.e., V0 = P0. BKM Q1 This is the no growth case, g = 0. therefore, in the constant growth model, V0 = D1/k. The intermediate step is to solve for the required rate of return, k. the question wants us to use the CAPM to get k. This question illustrates that we can combine what we know from asset pricing with stock valuation. K = (risk premium = beta x market risk premium). = 11%. Therefore, V0 = 2.1/0.11 = (to two decimal places).

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**Applying the constant growth DDM (2)**

The risk-free rate of return is 10%, the required rate of return on the market is 15%, and High-Flyer stock has a beta coefficient of 1.5. If the dividend per share expected during the coming year, D1, is $2.50 and g = 5%, at what price should a share sell? Hint: use the CAPM to get the market capitalization rate. “the required rate of return on the market” = E(rm). Market capitalization rate, k = (15 – 10) = (5) = 17.5% P0 = 2.5/(0.175 – 0.05) = 2.5/0.125 = $20.

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**Applying the constant growth DDM (3)**

Big Oil Inc. just paid a dividend of $10 (i.e., D0 = 10.00). Its dividends are expected to grow at a 4% annual rate forever. The market capitalization rate is 15%. What is the price of Big Oil’s common stock? (to 2 decimal places) Verify that price = $94.55 The differences from the previous slide: (1) need to work out D1, given D0 and (2) k is given. D1 = 10 x 1.04 = 10.4 P0 = 10.4/(0.15 – 0.04) = 10.4/0.11 = = $94.55

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**Applying the constant growth DDM (4)**

The price of a stock in the market is $62. You know that the firm has just paid a dividend of $5 per share (i.e., D0 = 5). The dividend growth rate is expected to be 6 percent forever. What is the market capitalization rate for this stock (to 2 decimal places)? Assume that the market is in equilibrium, so you can use the formula k = D1/P0 + g. D1 = 5 x 1.06 = 5.30 k = 5.3/ = or 14.55%

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**Applying the constant growth DDM (5)**

A firm is expected to pay a dividend of $5.00 on its stock next year. The current price of this stock is $40 and investors require a return of 20%. The firm’s dividends grow at a constant rate. What is the constant dividend growth rate (g)? use k = (D1/P0) + g Verify that g = 7.5% Note: the investors’ required rate of return is just the market capitalization rate. D1/P0 = 5/40 = 0.125 k = 0.2 0.20 = g So, g = 0.20 – = or 7.5%

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**Applying the constant growth DDM (6)**

In order to use the constant dividend growth model to value a stock it must be true that: a. The required rate of return is less than the expected dividend growth rate. b. The expected dividend growth rate is greater than zero. c. The next dividend (D1) is expected to be greater than $1.00. d. The expected dividend growth rate is less than the required rate of return. Which statement is correct? (d) Is correct. Basically, tests understanding of underlying relationship between required ror and dividend growth rate. c) Not correct because there is no restriction on the expected growth rate being = 0.

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**Stock prices & investment/growth opportunities**

How do we figure out dividend growth rate, g ? Growth rate depends on: Investment opportunities embodied in return on equity, ROE Reinvestment of earnings, represented by earnings retention ratio, b. Earnings retention ratio is also called the plowback ratio. Growth rate, g = ROE x b We can back out the (implied) growth rate, g, using observed price and required rate of return, k. in addition, we can also work out g based on ROE and company’s dividend policy (as represented by the retention ratio). Now, we want to relate g to a company’s investment/growth opportunities. This allows us to see how a company’s investment opportunities can affect the value of its common stock. Earnings retention ratio is the proportion of the firm’s earnings that is reinvested in the biz (and not paid out as dividends). Ok, so we know how growth rate can be calculated. Next, we look at how b ca be calculated. See next slide.

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**Earnings retention ratio and dividend payout ratio**

Earnings retention rate = reinvested earnings/ total earnings. A related measure is the dividend payout ratio. Dividend payout ratio = dividends paid/ total earnings = 1 – retention rate A related measure is the dividend payout ratio, which is the proportion of earnings paid out as dividends. On the next slide, we see how these ratios are calculated. Remember that companies can only do two things with earnings/profits: payout as dividends or reinvest the earnings. So, we can also compute the company’s dividend payout ratio. Dividend payout ratio = dividends paid/total earnings = (total earnings – reinvested earnings)/total earnings = 1 – (reinvested earnings/total earnings) = 1 – retention ratio. Therefore, dividend payout ratio = 1 – retention ratio. Of course, this implies that the retention ratio = 1 – dividend payout ratio.

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Problem Geoscience Corp. has a beta of 1.2 and its most recent EPS is $10 per share. The company just paid 40% of its earnings in dividends. Geoscience Corp will earn an ROE of 20% per year on all reinvested earnings forever. The risk-free rate is 8% and the expected return on the market portfolio is 15%. What is the intrinsic value (V0) of a share of Geoscience’s stock (to two decimal places)? If the market price of a share is currently $100, and you expect the market price to be equal to the intrinsic value one year from now, what is your expected one-year HPR on Geoscience Corp.’s stock? BKM Q22 Retention ratio = 1 – 0.4 = 0.6. G = 20 x 0.6 = 12% K = (15 – 8) = 16.4% D0 = 10 x 0.4 = 4 V0 = (4 x (1.12))/(0.164 – 0.12) = 4.48/0.044 = , or $ (to 2 decimal places) b) Find the stock price one year from now, P1=V1 = V0 x (1.12) = x (1.12) = , or (to 2 decimal places) D1 = 4 x (1.12) = 4.48 Purchase price = P0 = 100 Expected HPR = ( )/100 = /100 = or 18.52%

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**Earnings retention ratio affects growth**

Suppose ROE > 0 Growth policy No-growth policy Earnings retention ratio, b b > 0 b = 0 Growth rate, g g > 0 g = 0 This slides shows how retention ratio (equivalently, dividend policy or dividend payout ratio) affects dividend growth rate. Suppose ROE > 0. If a company pursues a growth policy, it re-invests/retains some of its earnings. b > 0. Therefore, g = ROE x b > 0. There is growth in earnings and dividends. If a company pursues a no-growth policy, it does not retain any earnings and pays out all earnings as dividends. b = 0. Therefore, g = 0. There is no growth in earnings and dividends. Bottomline: If a company reinvests some portion of earnings back into the business (b > 0), future earnings and dividends will grow (i.e., g > 0). Otherwise, earnings and dividends will not grow.

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**Is growth always beneficial?**

Does having positive growth always increase stock price? No. It depends on the attractiveness of the firm’s investment opportunities, ROE. Compared to a no-growth policy, If ROE > k, then retaining earnings (i.e., b > 0) will increase stock price. If ROE < k, then retaining earnings will decrease stock price. Remember that k is the investor’s required rate of return on investment in the firm, and more generally, the required rate of return on investments of similar risk. Growth enhances company value only if it is achieved by investment in projects with attractive profit opportunities (ROE > k). When this happens, the NPV of investments is positive and the share price is raised by this amount. However, if investment projects have a return less than k, then retaining earnings to invest in these opportunities will result in a negative NPV. This will lower the share price.

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**Consider two companies**

Growth Prospects, Inc (GP) Dead Beat, Inc (DB) No-growth earnings per share $5 Market capitalization rate, k 12.5% No-growth price per share 5/0.125 = 40 ROE 15% 10% Again, assume market in equilibrium so value=price. Assume that both companies are 100% equity financed. The assets in place in each company allows each company to generate a perpetual earnings stream of $5 per share forever. The first row says that if both companies pursue a NO-GROWTH policy and pay out all earnings as dividends (E=D), then each company can expect to generate a constant earnings stream of $5 per share forever. Since all earnings are paid out as dividends, the constant earnings stream is exactly equal to the dividend stream. Naturally, next year’s expected EPS is $5/share. Both companies have the same market capitalization rate of 15%. Under the no-growth policy, dividend per share is $5 forever for both companies. So each companies share value is given by PV of a perpetuity, P0 = 5/0.125 =$40. you can think of $40 as the price (value) per share of the assets the company already has in place. Now, suppose GP can invest in projects providing an ROE of 15% while DB can invest in projects providing an ROE of 10%.

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**Suppose both companies reinvest 60% of next year’s earnings…**

Growth Prospects, Inc (GP) Dead Beat, Inc (DB) Earnings retention ratio, b 0.6 Next year’s dividend per share, D1 = (1 – b) x 5 $2 Dividend growth rate, g = ROE x b 9% 6% Constant dividend growth model share price 2/(0.125 – 0.09) = 57.14 2/(0.125 – 0.06) = 30.77 Suppose both GP and DB decide to reinvest 60% of its current earnings and only pay out 40% as dividends. Remember that the current EPS is $5. Then D0= 0.4 x 5 = 2. Note that the retention ratio and dividend payout ratio apply to total earnings and also EPS. GP: === Dividend growth rate is now g = 15 x 0.6 = 9%. Assume that GP can sustain the 15% ROE and the 0.6 retention ratio forever. So g of 9% is the growth rate forever. Next year’s dividend per share = 5 x (1 – 0.6) = 2 Therefore, we use the constant growth model to calculate stock price. P0 = 2/( ) = So, with the growth policy, GP’s share price is $57.14 DB: Dividend growth rate is now g = 10 x 0.6 = 6%. Assume that GP can sustain the 10% ROE and the 0.6 retention ratio forever. So g of 6% is the growth rate forever. Therefore, we use the constant growth model to calculate stock price. P0 = 2/( ) = 30.77 So, with the growth policy, DB’s share price is $30.77

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**Compare GP and DB PVGO = Price per share – no-growth price per share**

Growth Prospects, Inc (GP) Dead Beat, Inc (DB) ROE 15% 10% Market capitalization rate, k 12.5% No-growth price per share (1) 40 Constant div. growth Price (2) 57.14 30.77 Present value of growth opportunities, PVGO = (2) – (1) 17.14 -9.23 For GP, the increase in share price above the no-growth share price = – 40 = This increase represents the present value of growth opportunities. It is the increase in share price due to the fact that the company can invest in projects with a return bigger than investors’ required ror, i.e., 15% > 12.5%. For DB, there is a decrease in share price from the no-growth share price = – 40 = This fall in price arises because the company is investing in opportunities which generate a return which is less than the investor’s required rate of return, i.e., 10% < 12.5%. This example demonstrates that when ROE > k, re-investing earnings to pursue a growth policy raises share price above the no-growth share price. In contrast, when ROE < k, re-investing earnings actually reduces share price below the no-growth share price. GP: The increase in stock price reflects the fact that planned investments provide an expected rate of return greater than the required rate. In other words, the investment opportunities have positive NPV. The value of the firm rises by the NPV of these investment opportunities. This NPV is called the present value of growth opportunities (PVGO). Therefore, we can think of the value of the firm as the sum of the value of assets already in place, or the no-growth value of he firm, plus the NPV of the future investments the firm will make, which is the PVGO. Price = No-growth value per share + PVGO P0 = E1/k + PVGO Note that if ROE = K, then retaining earnings will not change share price. In other words, the no-growth and growth policies will not affect share price. The dividend reduction that frees funds for reinvestment in the firm generates only enough growth to maintain the stock price at the current level. This is as it should be: if the firm’s projects yield only what investors can earn on their own, then NPV is 0, and shareholders cannot be made better off by a high reinvestment rate policy. This demonstrates that “growth” is not the same as growth opportunities. To justify reinvestment, the firm must engage in projects with better prospective returns than those shareholders can find elsewhere (ROE > K). PVGO = Price per share – no-growth price per share

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**Problems involving growth (1)**

MF Corp. has an ROE of 16% and a plowback ratio of 50%. If the coming year’s earnings are expected to be $2 per share. The market capitalization rate is 12%. At what price will the stock sell today? At what price do you expect MF shares to sell for in 3 years? BKM Q6. a) G = 16 x 0.5 = 8% D1 = 2 x (1 – 0.5) = 1 P0 = 1/(0.12 – 0.08) = 1/0.04 = $25. b) Use the fact that price appreciates at the rate of g. So, share price in 3 years, P3 = P0 x ( )3 = 25 x ( )3 = $ , or $31.49.

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**Problems involving growth (2)**

Even Better Products has come out with a new and improved product. As a result, the firm projects an ROE of 20%, and it will maintain a retention ratio of Its earnings in one year will be $2 per share. Investors expect a 12% rate of return on the stock. Calculate the stock price. What is the present value of growth opportunities (PVGO)? What would be the stock price and PVGO if the firm reinvests only 20% of its earnings? BKM Q5 G = 20 x 0.3 = 6%, k = 0.12. Important: the $2 EPS is E1. Important to mention that $2 is also the no-growth perpetual dividend, although the question is not explicit about this. D1 = 2 x (1 – 0.3) = 1.4 P0 = 1.4/(0.12 – 0.06) = 1.4/0.06 = $23.33 b) No-growth price per share = 2/0.12 = (to 2 d.p.) PVGO = – = $6.66 c) G = 20 x 0.2 = 4% D1 = 2 x (1 – 0.2) = 1.6 P0 = 1.6/(0.12 – 0.04) = $20 PVGO = 20 – = $ 3.33

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**Multi-stage dividend growth 1**

With this assumption, dividends grow at different rates for different periods of time. Eventually, dividends will grow at a constant rate forever. Time line is very useful for valuing this type of stocks. To value such stocks, also need the constant growth formula. Best way to learn is through an example. The constant growth model is convenient but may not be realistic. The multi-stage dividend growth model assumes that dividends grow at different rates initially, and eventually settle down to a constant growth rate forever. Rationale for multi-stage model: firms typically pass through life cycles with very different dividend profiles in different phases. In early years, there are ample opportunities for profitable reinvestment in the company. Payout ratios are low, and growth (dividend and earnings) is high. In later years, the firm matures, production capacity is sufficient to meet market demand, competitors enter the market, and attractive opportunities for reinvestment may become harder to find. In this mature phase, the firm may choose to increase the dividend payout ratio, rather than retain earnings. The dividend level increases, but thereafter it grows at a slower rate because the company has fewer growth opportunities. General idea: Dividends in the early high-growth period are forecast and their combined PV is calculated. Then, once the firm is projected to settle down to a steady growth phase, the constant growth DDM is applied to value the remaining stream of dividends.

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**Multi-stage dividend growth 2**

ABC Co. is expected to pay dividends at the end of the next three years of $2, $3, $3.50, respectively. After three years, the dividend is expected to grow at 5% constant annual rate forever. If the market capitalization rate for this stock is 15%, what is the current stock price? Dividends grow at 5% forever $2.00 $3.00 $3.50 in valuing the stock of ABC Corp. suppose that you forecast that dividends will be $2, $3, and $3.50 in the next three years, respectively. After that you expect dividends to grow at a rate of five percent per year forever. Let us suppose that the appropriate discount rate for ABC's stock is 15 percent. The projected future dividends are: D1 = $2.00, D2 = $3.00, D3 = $3.50, D4 = $3.50 x (1.05) = $3.675, and so on. T = 0 T =1 T = 2 T = 3 T = 4

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What to do? Place yourself at t = 3 and use the constant growth formula to find PV of dividend stream after year 3. Call this P3. Find the PV of P3. Find PV of dividends at t=1, t=2 and t=3. Current stock price = sum of 2, 3 and 4. For point 2, think of it as you selling the stock at t=3 and receiving the proceeds. That’s why you add P3 to dividend. You can also interpret P3 as the forecast price at which you can sell ABC shares at the end of year 3, when dividends enter their constant growth phase. Whichever interpretation you prefer is fine. Tell the class that the method can be adapted to longer periods.

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**Apply the method to find ABC’s stock price**

P3 = (3.5 x (1.05))/(0.15 – 0.05) = 36.75 Current stock price, P0 Since 3.50 and have the same denominator, we can combine the numerator and have = This is mathematically valid. In addition, because the two values are at the same point in time, by the value additivity principle, we can combine their values. The last equation combines the remaining steps.

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**Another type of multi-stage growth problem**

Malcolm Manufacturing, Inc. just paid a $2.00 annual dividend (that is, D0 = 2.00). Investors believe that the firm will grow at 10% annually for the next 2 years and 6% annually forever thereafter. Assuming a required return of 15%, what is the current price of the stock (to 2 decimal places)? Use timeline to ‘see’ the problem better. Verify that stock price = $25.29 Equivalent to BKM Q23. Here, you are given the growth rate and you need to work out the dividends. Find t=1 dividend, D(t=1) = 2 x 1.1 = 2.2 Find t=2 dividend, D(t=2) = 2 x (1.1)2 = 2.42 Find stock price at the end of t=2. use constant growth formula. P2 = (2.42 x 1.06)/( ) = /(0.09) = (keep up to 4 decimal places) 4) Cash flow at t= 2 = = 5) Stock price = 2.2/ /(1.15)2 = $25.29

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**Price-earnings (P/E) ratios**

P/E ratio is the ratio of current price per share (P0) to next year’s expected earnings per share (EPS). How do we use P/E ratio to value a stock? Forecast next year’s EPS, E1. Forecast P/E ratio, P0/E1. Multiple P/E by EPS to get current estimate of price. (P0/E1) x E1 = P0 Much of the real-world discussion of stock market valuation concentrates on the firm’s price-earnings multiples, the ratio of price per share to earnings per share, commonly called the p/e ratio. In fact, one common approach to valuing a firm is to use an earnings multiplier. The value of the stock is obtained by multiplying projected EPS by a forecast of the P/E ratio. This procedure seems simple, but its apparent simplicity is deceptive. Forecasting eps and p/e are difficult. The valuation method again assumes market equilibrium, so that value = price. (P0/E1) x E1 = P0

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**P/E ratio and constant growth model**

If a company has a constant dividend growth rate and the market is in equilibrium (i.e., V0=P0), then we have an explicit formula for the P/E ratio! Derived from constant growth DDM. Assume that we can get an estimate of next year’s EPS. So the crucial question is how to estimate/compute P/E? If a company has a constant dividend growth rate and the market is in equilibrium (i.e., V0=P0), then we have an explicit formula for the P/E ratio! (Eq.12.8 from p.404). Recall that b = retention ratio, k = market capitalization rate.

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P/E questions (1) ABC Co. has an ROE of 25%, a CAPM beta of 1.2 and a retention ratio of 40%. The risk-free rate is 6% and the market risk premium is 5%. What is ABC’s P/E ratio? Find discount rate, k. K = (5) = 12% G = ROE x b = 25 x 0.4 = 10%. Use eq (12.8) to compute P/E. P/E = (1 – 0.4)/(0.12 – 0.1) = 0.6/0.02 = 30 x

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P/E questions (2) Analog Electronic Corporation has an ROE = 9% and a beta of It plans to maintain indefinitely its traditional plowback ratio of 2/3. The most recent earnings per share is $3 per share. The expected market return is 14% and the risk-free rate is 6%. What is Analog’s stock price? Calculate the P/E (P0/E1) ratio. Calculate the PVGO. This question illustrates another way of calculating P/E. Use capm to compute discount rate. K = (14 – 6) = 16% Growth rate, g = 9 x 2/3 = 6% E0 = 3. E1 = 3 x (1.06) = [earnings grow at the same rate as dividends] D1 = 3.18 x (1 – 2/3) = 1.06 P0 = 1.06/(0.16 – 0.06) = 1.06/0.10 = $10.60 b) P/E = P0/E1 = 10.60/3.18 = 3.33 c) PVGO = P0 – No-growth price per share = P0 – (E0/k) = – (3/0.16) = – = The low P/E ratios and negative PVGO are due to a poor ROE (9%) that is less than the market capitalization rate (16%).

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**Free Cash Flow Valuation Approach**

Dividend discount models don’t work for companies which do not pay dividends. For non-dividend paying companies, we can use free cash flow valuation approach. There are two versions: Free cash flow to the firm (FCFF) Free cash flow to equity holders (FCFE) We discuss two versions of the Free Cash Flow valuation approach, one uses FCFF and the other uses FCFE.

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**Free Cash Flow to the Firm (FCFF) (1)**

FCFF: cash flow that accrues from the firm’s operations, net of investments in capital and net working capital. FCFF represent cash flows available to both debt and equity holders. FCFF = EBIT(1 – tc) + Depreciation – capital expenditures – increase in NWC EBIT = earnings before interest and taxes tc = corporate tax rate NWC (net working capital) = current asset – current liability

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**Free Cash Flow to the Firm (FCFF) (2)**

Capital expenditure includes: acquiring fixed, and in some cases, intangible assets repairing an existing asset so as to improve its useful life upgrading an existing asset if its results in a superior fixture preparing an asset to be used in business restoring property or adapting it to a new or different use starting or acquiring a new business

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**Free Cash Flow to the Firm (FCFF) (3)**

Find the PV of the firm by discounting the year-by-year FCFF plus some estimate of terminal value, PT. Firm Value= where Use constant growth model to estimate the terminal value, PT. The appropriate discount rate is the weighted average cost of capital. To find the equity value, we subtract the existing market value of debt from the derived value of the firm. As in the dividend discount model, free cash flow models use a terminal value to avoid adding the present values of an infinite sum of cash flows. That terminal value may be the PV of a constant-growth perpetuity or it may be based on a multiple of EBIT, book value, earnings or free cash flow. Market value of equity = Firm value – market value of debt.

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**Free Cash Flow to Equity Holders (FCFE)**

FCFE: Free cash flow available to equity holders. FCFE = FCFF – interest expense(1 – tc) + increases in net debt Find the market value of equity by discounting the year-by-year FCFE plus some estimate of terminal value, PT. is the cost of equity.

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**Summary Distinguish between the intrinsic value and price.**

Calculate intrinsic value using dividend discount models Constant dividend growth model Multistage dividend growth model Discuss the use of the P/E ratio to value common stock. Calculate the P/E ratio for a constant growth firm. Discuss the free cash flow valuation methods.

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Practice 5 Chapter 13: 5,6,7,10,11,13,15, 17,19,

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