CHAPTER 13 Common Stock Valuation

Cleary/Jones Investments: Analysis and Management, Second Canadian Edition CHAPTER 13 Common Stock Valuation REVIEW QUESTIONS 13-1. The intrinsic v...
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Cleary/Jones

Investments: Analysis and Management, Second Canadian Edition

CHAPTER 13 Common Stock Valuation REVIEW QUESTIONS 13-1.

The intrinsic value of an asset is its fair economic value as estimated by investors. This value is a function of certain underlying economic variables, specifically, expected returns and risk. Traditionally, intrinsic value is determined through a present value process. The future expected cash flows on an asset are discounted at a required rate of return.

13-2.

Earnings cannot be used directly in the present value approach because reinvested earnings would be double-counted, first as earnings reinvested currently and later as dividends paid. If properly defined and separated, these two variables will produce the same results. Dividends, however, can be used directly.

13-3.

The problems encountered in using the dividend discount model include: • We are dealing with infinity • The dividend stream is uncertain • The required rate of return has to be determined

13-4.

The three possibilities for dividend growth are: (1) (2) (3)

13-5.

no growth – the dollar dividend will remain fixed. constant growth – the dividend will grow at a steady (constant) rate over time. multiple (super growth) – at least two different growth rates are involved. Many multiple-growth-rate companies grow rapidly for some years and then slow down to a more normal growth rate.

Ignoring the no-growth case, and although dividends are paid to infinity, they can be modeled as either a constant growth rate or a super-growth situation involving rapid growth for some years plus a constant growth situation for the remainder. In either case, the infinity sign is eliminated. On a practical basis, after 30 or 40 years dividends discounted at rates of 10%, 20%, or higher, will have insignificant value and can be ignored.

13-6.

Investors compare intrinsic value (IV) to the current market price (CMP) of the stock.

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If IV > CMP, the stock is undervalued – buy. If IV < CMP, the stock is overvalued – sell. If IV = CMP, the stock is correctly valued and in equilibrium. 13-7.

The required rate of return for a stock is the minimum expected rate of return necessary to induce an investor to purchase a stock. It accounts for opportunity cost and the risk involved for a particular stock. If an investor can expect to earn the same return elsewhere at a lesser risk, why buy the stock under consideration? In other words, if your opportunity cost for a given risk level is 15%, you should not purchase a stock with that risk level unless you can expect to earn 15% or more from that stock.

13-8.

The Dividend Discount Model (DDM) is a widely used method of valuing common stocks. A present value process is used to discount expected future dividends at an appropriate required rate of return. The equation is: PV = D1/(1+k) + D2/(1+k)2 + D3/(1+k)3 + ….. + Dn/(1+k)n

13-9.

The combination of a specified number of dividends and a terminal price is exactly equivalent to an infinite number of dividends, since the terminal price at a particular point in time is equal to the discounted value of all future dividends from that point onward.

13-10.

P/E ratios reflect the current market price of the stock divided by the latest 12 month earnings. Therefore, they show only the current multiple for a stock. While this can be a useful reference point, investors seeking to value a stock will need an estimate of the future multiplier.

13-11.

The P/E ratio is affected by: • • •

The expected dividend payout ratio The required rate of return The expected growth rate of dividends

The P/E ratio is quite sensitive to a change in these factors. A one percentage point change in the required rate of return, for example, can easily change the price of a stock by 30 or 40%. A one percentage point change in the expected growth rate of dividends also has a significant impact, but not as large as a change in the required rate of return. Both of these factors usually have more impact than the payout ratio. 13-12.

The two investors are likely to derive different prices because they will probably use different estimates of “g”, the expected growth rate in dividends and, they are likely to use different required rates of return.

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13-13.

Investments: Analysis and Management, Second Canadian Edition

Some analysts argue that the dividend discount model is unrealistic because it requires a forecast of dividends into the distant future (technically, infinity). Also, many investors are seeking capital gains, while this model seemingly focuses on dividends. In response, it should be noted that the dividend growth rate can be modeled in a workable manner, avoiding the infinite horizon problem. Furthermore, investors can structure a stream of dividends and a terminal price (which allows for capital gains), and have an alternative that is equivalent to the basic model. Perhaps the most important point here is that either model, the dividend discount model or the multiplier model, requires estimates of the future. These estimates cannot be avoided. Whether the inputs for one model as opposed to the other model are more realistic is probably an unresolvable argument.

13-14.

P/E = (D/E)/(k - g). (a) (b) (c) (d)

Decrease - since D decreases. Decrease - since k increases. Increase - since g increases. Increase* - since k decreases. *The riskless rate of return is a component of the required rate of return, which has an inverse relationship with the P/E ratio.

13-15.

M/B = [ROE x Payout Ratio x (1 + g)]/(k - g) (a) (b) (c) (d) (e)

13-16.

Decrease - since Payout Ratio decreases. Decrease - since k increases. Increase - since g increases. Increase - since k decreases. Increase - since ROE increases.

P/S = [NI% x Payout Ratio x (1 + g)]/(k - g) (a) (b) (c) (d) (e)

Decrease - since Payout Ratio decreases. Decrease - since k increases. Increase - since g increases. Increase - since k decreases. Decrease - since NI% decreases.

13-17.

C

13-18.

A

P/E = Payout / (K – g)

13-19.

C

P/E = Payout / (K –g); K = RF + RP

13-20.

Negatively. P/E = P0 / EPS, so higher P0, higher P/E DY = Div / P0, so higher P0, lower DY

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PROBLEMS 13-1.

Using the constant growth version of the Dividend Discount Model: k = D1/P0 + g = $2.00/$45 + .05 = .0944 or 9.44%

13-2.

P0 = D1/(k-g) = D0(1+g)/(k-g) = $2.25(1+.06) / (.13-.06) = $2.12/.07 = $30.29

13-3. Using the constant growth version of the Dividend Discount Model, solve for g: k = D1/P0 + g k-g = D1/P0 -g = D1/P0 - k g = k - D1/P0 or:

g = k - [(D0(1+g))/P0]

Therefore: g = .15 - [($3.00(1+g))/50] 50g = 7.50 - 3 - 3g 53g = 7.50 - 3 53g = 4.50 g = .0849 or 8.49% 13-4.

P = D0/k = 1.50/.15 = $10.00

13-5.

(a)

k = D0/P0 = $3.00/$40 = .075 = 7.5%

(b)

The price will decline because required rates of return rise while dividends remain fixed. Specifically, P = $3.00/.09 = $33.33

13-6.

P0 = 1.30(1.055)/ (.1575-.055) = 1.3715/0.1025 = $13.38

13-7.

P0 = 1.30(1.07)/ (.1575-.07) = 1.391/0.0875 = $15.90

13-8.

P0 = 1.60(1.04)/(.16-.04) = 1.664/.12 = $13.87

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13-9.

k = D0 / P0 = 1/12 = .0833 = 8.33%

13-10.

k = D1 / P0 + g = 2.00 (1.07) / $40 + .07 = .1235 = 12.35%

13-11.

k = D1/P0 + g g = k - D1/P0 g = .10 - 2.00/50 = .06 = 6%

13-12.

Given a one year horizon, this problem can be formulated as: P0 = D1/(1+k) + P1/(1+k) 25 = 3/(1+k) + 30/(1+k) (1+k)25 = 3 + 30 1+k = 33/25 =1.32 k = .32 = 32%

13-13.

(a)

(b)

(i) Stock A

kA = RF + ßA (RM-RF) = .10 + 1.0(.15 -.10) = .15 = 15%

(ii) Stock B

kB = .10 + 1.7(.15-.10) = .185 = 18.5%

(iii) Stock C

kC = .10 + .8(.15-.10) = .14 = 14%

If RF increases to .12, required rates of return are: kA = .12 + 1.0(.03) = .15 = 15% kB = .12 + 1.7(.03) = .171 = 17.1% kC = .12 + 0.8(.03) = .144 = 14.4%

(c)

If RM increases to 17%, the required rates of return also rise. The new results are: kA = .10 + 1.0(.17-.10) = .17 = 17% kB = .10 + 1.7(.17-.10) = .219 = 21.9% kC = .10 + 0.8(.17-.10) = .156 = 15.6%

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13-14.

(a)

Investments: Analysis and Management, Second Canadian Edition

Solving for k as the expected rate of return, k = [1.80(1.05)]/36 + .05 = .0525+ .05 = .1025= 10.25% Since the expected return of 10.25% is less than the required rate of return of 14%, this stock is not a good buy.

(b)

P0 = D1/(k-g) = [1.80(1.05)]/[.14-.05] = $21 An investor should not pay more than $21 if his or her required rate of return is 14%. If the required rate of return is 15%, the maximum an investor should pay is obviously less than in the previous problem. Specifically, P0 = [1.80(1.05)]/[.15-.05] = $18.9

13-15.

(a)

The current P/E ratio is $32/$4 = 8

(b)

E0 = $4 E1 = E0(1+g) = $4(1+.06) = $4.24 With an unchanged P/E of 8, the new price will be 8 x $4.24 = $33.92

(c)

D/E = 50% - payout ratio g = 6% - expected growth rate of dividends k = 16% - required rate of return expected rate of return = D1/P0 + g = $2.20/$32 + .06 = .129or 12.9% Alternatively, P0 = D1/(k-g) = 2.20/(.16-.06) = $22

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This stock is not a good buy because the expected return does not exceed the required return or, alternatively, the estimated value (price) of the stock does not exceed the current market price. (d)

If interest rates are expected to decline, the likely effect is an increase in the P/E ratio for Joy Juice as well as other stocks.

13-16.

P0 = $32.29

13-17.

$2.00(.40) = $0.80 = D1 The correct growth rate to use is the expected growth rate of 7%. P0 = $0.80/.08 = $10

13-18.

P0 = $0.60(.847) + $1.10(.718) + $1.25(5.556)(.718) = $0.51 + $0.79 + $4.99 = $6.29 NOTE: 5.556 is 1/.18 (to account for the perpetuity). This value must then be discounted back to today using the 2-year factor, since the perpetuity is valued as of the beginning of year three, which is the same as the end of year two.

13-19.

P0 = ($3.00/.25)/(1.25)5 = 12/3.0518 = $3.93

13-20.

P0 = $10(4.192) + $15(5)(.162) = $41.92 + $12.15 = $54.07 NOTE: The present value of an annuity factor for 10 periods at 20% is 4.192. The perpetuity factor for 20% is 5, and the present value factor is .162 for 10 periods, 20%.

13-21.

This is a 2-stage growth model, or supergrowth. We must find the present value of all dividends from now to infinity.

D0 = $1.00 D1 = 1.00(1.25) = 1.25 D2 = 1.00(1.25)2 = 1.56 D3 = 1.00(1.25)3 = 1.95 D4 = 1.00(1.25)4 = 2.44 D5 = 1.00(1.25)5 = 3.05

PVIF(.18) .847 .718 .609 .516 .437

Present Value 1.06 1.12 1.19 1.26 1.33 5.96

PV of dividends for first 5 years = $5.96

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P5 = [D5(1+gc)]/(k-gc) = [3.05(1.07)]/(.18-.07) = 3.26/.11 = $29.67 We must discount P5 back to time period zero and add this value to the present value of the first five years of dividends. NOTE: P5 is the price at the end of year five; therefore, we use the discount factor for 5 years, not 6 years. P5 discounted to time period zero: P5 (PVIF.18,5) = $29.67(.437) = $12.97 P0 = $5.96 + $12.97 = $18.93 13-22.

This is a case of three years of zero dividends, followed by a no-growth period of infinite length. Note that one year prior to the start of the no-growth period is year 3. Therefore, P3 = D4/k = $1/.14 = $7.14 P0 = P3(PVIF.10,3) = $7.14 (0.675) = $4.82

13-23.

(a)

It is necessary to calculate the growth rate since it is not given. Referring to the future (compound) value table at the end of the text and reading across the 12 year row, we find a factor of about 2.0 (exactly, 2.0122) at the intersection of the 6% column (or, using the rule of 72, 72/12 = 6%). Therefore g = 6% and k = [$3.00(1.06)]/$60 + .06 = .053 + .06 = .113 or 11.3%

(b)

Using the same table to find a factor of 3.0 on the 6 year row, we find g to be approximately 20% (the exact factor at 20% is 2.986). Therefore, using g = 20%, k = [$3.00(1.20)]/$60 + .20 = .06 + .20 = .26 or 26%

13-24.

P0 = $27.50

13-25.

P0 = $23.08 Lowering the growth rate in the first supernormal growth period from 30% to 25% will clearly result in a lower price because of the lesser growth rate in dividends and the lesser dollar value of the resulting dividend stream.

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13-26.

Investments: Analysis and Management, Second Canadian Edition

D1 = $1.80(1.06) = $1.91 B = .90 (since the stock is 10% less risky than the market) k = 5% + .9(7%) = 11.3% P0 = 1.91/(.113-.06) = $36.04

13-27.

This is a three stage growth model. It is unusual in that in the second stage of growth, the growth rate is equal to the discount rate. The process remains the same. Present D0 = $2.00 PVIF(.20) Value D1 = 2.00(1.30) = 2.60 .833 2.17 D2 = 2.00(1.30)2 = 3.38 .694 2.35 3 D3 = 2.00(1.30) = 4.39 .579 2.54 D4 = 4.39(1.20) = 5.27 .482 2.54 D5 = 5.27(1.20) = 6.32 .402 2.54 D6 = 6.32(1.20) = 7.58 .335 2.54 D7 = 7.58(1.20) = 9.10 .279 2.54 D8 = 9.10(1.20) = 10.92 .233 2.54 $19.76 P8 = [D8(1.06)]/(.20-.06) = [10.92(1.06)]/.14 = 11.58/.14 = $82.71 Discounting P8 back eight periods: $82.71/(1.20)8 = $19.24 P0 = $19.76 + $19.24 = $39.00

13-28.

(1)

Using the DDM, P0 = D1/(k-g) = [3.45(.456)]/(.0968-.08) = 1.5732/.0168 = $93.64

(2)

Using the P/E ratio approach (assuming the five year average P/E ratio is appropriate), P0 = E1 x Justified P/E Ratio = 3.45 x 26.68 = $92.05

(3)

13-29.

The Market-to-Book (M/B) ratio and/or the Price/Sales (P/S) ratio can also be used to estimate SLC’s value. These methods are utilized in Problems 13-29 and 13-30, respectively.

P0 = [ROE0 x BV0 x Payout Ratio x (1+g)]/(k-g) = [.1792 x 17.86 x .456 x 1.08]/(.0968-.08) = 1.576188/.0168 = $93.82

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13-30.

P0 = [NI% x Sales0 x Payout Ratio x (1+g)]/(k-g) = [.0331 x 85.71 x .456 x 1.08]/.0168 = 1.397166/.0168 = $83.16

13-31.

(a)

P0/E1 = (D1/E1)/(k-g) = 0.60/(.13-.08) = 0.60/.05 = 12

(b)

P0/E1 = 0.80/.05 = 16

(a)

M/B = [ROE0 x Payout Ratio x (1+g)]/(k-g) = [.20 x .40 x 1.06]/(.14-.06) = .0848/.08 = 1.06

(b)

BV = $1,000,000/100,000 = $10/share

13-32.

If M/B = 1.06, then the price per share would be $10.60. 13-33.

P0 = [NI% x Sales0 x Payout Ratio x (1+g)]/(k-g) = [(5,000,000/50,000,000) x (50,000,000/20,000,000) x .50 x 1.06]/ (.16-.06) = [.10 x 2.50 x .50 x 1.06]/.10 = .1325/.10 = $1.325

13-34.

EPS (payout) = DPS EPS = 2.20 / 0.45 = $4.89 P/E = 75 / 4.89 = 15.34

13-35.

r = D1 / P0 + g g = ROE * (1 – payout) ROE = ROA * leverage = 5 * 2 = 10% Payout = 0.50 / 2.00 = 0.25 g = 10% * (1 – 0.25) = 7.5% D1 = $0.50 * 1.075 = $0.5375 r = 0.5375 / 30 + 0.075 = 0.0179 + 0.075 = 0.0929

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CFA PRACTICE QUESTIONS 1.

B

1st: ke = Rf + ß (RM – Rf) = 8 + 1.2(13 – 8) = 8 + 6 = 14% 2nd: D1 = D0 (1 + g) = 1.00(1.10) = $1.10 D + V1 $1.10 + 25 3rd: V0 = 1 = = $22.89 1 (1.14) (1 + k e )

2.

B

1st: ke = Rf + ß (RM – Rf) = 6 + 1.2(13 – 6) = 6 + 8.4 = 14.4% 2nd: D1 P 0.60 E1 = = = 8.11 E k e − g (0.144 − .07)

3.

C An increase in beta, would increase ke, therefore the P/E would decline all else being equal).

4.

C

1st: D0 = 0.40 × $5.00 = $2.00 2nd: D1 = D0 (1 + g) = 2.00(1.08) = $2.16 3rd: D 2.16 ke = 1 + g = + 0.08 = 0.048 + 0.08 = 0.128 = 12.8% P0 45.00

5.

C

1st: D0 = D1 = D2 = D3 = D4 = 0 2nd: D5 0.50 V4 = = = $7.14 k e − g 0.12 − 0.05 3rd:

6.

A

7.

B

8.

C

V0 =

7.14 = $4.54 (1.12) 4

PAST CFA EXAM PROBLEMS 1.

(a)

VALUE0 = D1/(k – g) D1 = next year's dividend k = required rate of return g = constant growth rate

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D1 = (EPS0)(1 + g)(P/0) = (4.50)(1.045)(.55) = $2.59 k = given at 11% or .11 g = (ROE)(1 - P/0) = (.10)(1 - .55) = .045 VALUE0 = 2.59/(.11-.045) = 2.59/.065 = $39.85 (b)

Multi-stage Dividend Discount Model (where g1 = .15 and g2 is .045): VALUE1 = D1/(1+k) + D2/(1+k)2 + [D3/(k-g2)]/(1+k)2 D1 = (EPS0)(1 + g1)(P/0) = (4.50)(1.15)(.55) = $2.85 D2 = (D1)(1 + g1) = ($2.85)(1.15) = $3.27 k = given at 11% or .11 g2 = .045 D3 = (D2)(1 + g2) = ($3.27)(1.045) = $3.42 VALUE0 = 2.85/1.11 + 3.27/(1.11)2 + [3.42/(.11-.045)]/ (1.11)2 = $2.57 + $2.65 + $42.71 = $47.92

2.

(a)

The dividend discount model is:

P0 = D1/( k – g) k = D1/Po + g

So k becomes the estimate for the long-term return of the stock. k = .60/20.00 + .08 = .03 + .08 = .11 = 11% (b)

Many professional investors shy away from the dividend discount framework analysis due to its many inherent complexities. (1)

The model cannot be used where companies pay very small or no dividends and speculation on the level of future dividends could be futile (dividend policy may be arbitrary).

(2)

The model presumes one can accurately forecast long term growth of earnings (dividends) of a company. Such forecasts become quite tenuous beyond two years out (a short-term valuation may be more pertinent).

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(c)

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(3)

For the variable growth models, small differences in g for the first several years produce large differences in the valuations.

(4)

The correct discount rate is difficult to estimate for a specific company as an infinite number of factors affect it, which are themselves difficult to forecast (e.g., inflation, riskless rate of return, risk premium on stocks, and other uncertainties).

(5)

The model is not definable when g > k as with growth companies, so it is not applicable to a large number of companies.

(6)

Where a company has low or negative earnings per share or has a poor balance sheet, the ability to continue the dividend is questionable.

(7)

The components of income can differ substantially, reducing comparability.

Alternative methods of valuation would include:

• Price/Earnings ratios • Price/Asset value ratios (including market and book asset values) • Price/Sales ratios • Liquidation or breakup value • Price/cash flow ratios

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