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ch10^Stocks and Their Valuation

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ch10^Stocks and Their Valuation

Chapter 10

Stocks and Their Valuation

Learning Objectives

After reading this chapter, students should be able to:

; Identify some of the more important rights that come with stock ownership and define the following

terms: proxy, proxy fight, takeover, and preemptive right.

; Briefly explain why classified stock might be used by a corporation and what founders’ shares are.

; Determine the value of a share of common stock when: (1) dividends are expected to grow at some

constant rate, (2) dividends are expected to remain constant (zero growth), and (3) dividends are

expected to grow at some supernormal, or nonconstant, growth rate.

; Calculate the expected rate of return on a constant growth stock.

; Apply the total company (corporate valuation) model to value a firm in situations where future

dividends are not easily predictable.

; Explain why a stock’s intrinsic value might differ between the total company model and the dividend

growth model.

; Explain the following terms: equilibrium and marginal investor. Identify the two related conditions that

must hold in equilibrium.

; Explain how changes in the risk-free rate, the market risk premium, the stock’s beta, and the expected

growth rate impact equilibrium stock price.

; Explain the reasons for investing in international stocks and identify the ―bets‖ an investor is making

when he does invest overseas.

; Define preferred stock, determine the value of a share of preferred stock, or given its value, calculate

its expected return.

Chapter 9: Stocks and Their Valuation Learning Objectives 213

Lecture Suggestions

This chapter provides important and useful information on common and preferred stocks. Moreover, the valuation of stocks reinforces the concepts covered in Chapters 2, 7, and 8, so Chapter 9 extends and reinforces concepts discussed in those chapters.

We begin our lecture with a discussion of the characteristics of common stocks and how stocks are valued in the market. Models are presented for valuing constant growth stocks, zero growth stocks, and nonconstant growth stocks. We conclude the lecture with a discussion of preferred stocks.

What we cover, and the way we cover it, can be seen by scanning the slides and Integrated Case solution for Chapter 9, which appears at the end of this chapter solution. For other suggestions about the lecture, please see the ―Lecture Suggestions‖ in Chapter 2, where we describe how we conduct our classes.

DAYS ON CHAPTER: 3 OF 58 DAYS (50-minute periods)

214 Lecture Suggestions Chapter 9: Stocks and Their Valuation

9-1 a. The average investor of a firm traded on the NYSE is not really interested in maintaining his or

her proportionate share of ownership and control. If the investor wanted to increase his or her

ownership, the investor could simply buy more stock on the open market. Consequently, most

investors are not concerned with whether new shares are sold directly (at about market prices)

or through rights offerings. However, if a rights offering is being used to effect a stock split, or

if it is being used to reduce the underwriting cost of an issue (by substantial underpricing), the

preemptive right may well be beneficial to the firm and to its stockholders.

b. The preemptive right is clearly important to the stockholders of closely held (private) firms

whose owners are interested in maintaining their relative control positions.

9-2 No. The correct equation has D in the numerator and a minus sign in the denominator. 1

9-3 Yes. If a company decides to increase its payout ratio, then the dividend yield component will rise,

but the expected long-term capital gains yield will decline.

9-4 Yes. The value of a share of stock is the PV of its expected future dividends. If the two investors

expect the same future dividend stream, and they agree on the stock’s riskiness, then they should

reach similar conclusions as to the stock’s value.

9-5 A perpetual bond is similar to a no-growth stock and to a share of perpetual preferred stock in the

following ways:

1. All three derive their values from a series of cash inflowscoupon payments from the perpetual

bond, and dividends from both types of stock.

2. All three are assumed to have indefinite lives with no maturity value (M) for the perpetual bond

and no capital gains yield for the stocks.

However, there are preferreds that have a stated maturity. In this situation, the preferred

would be valued much like a bond with a stated maturity. Both derive their values from a series

of cash inflowscoupon payments and a maturity value for the bond and dividends and a stock

price for the preferred.

Chapter 9: Stocks and Their Valuation Integrated Case 215

Solutions to End-of-Chapter Problems

9-1 D = \$1.50; g = 7%; g = 5%; D through D = ? 01-3n15

D = D(1 + g) = \$1.50(1.07) = \$1.6050. 101

2D = D(1 + g)(1 + g) = \$1.50(1.07) = \$1.7174. 2012

3D = D(1 + g)(1 + g)(1 + g) = \$1.50(1.07) = \$1.8376. 30123

3D = D(1 + g)(1 + g)(1 + g)(1 + g) = \$1.50(1.07)(1.05) = \$1.9294. 40123n

232D = D(1 + g)(1 + g)(1 + g)(1 + g) = \$1.50(1.07)(1.05) = \$2.0259. 50123n

ˆ P9-2 D = \$0.50; g = 7%; r = 15%;= ?1s0

D\$0.501ˆ P\$6.25.0rg0.150.07s

ˆ9-3 P = \$20; D = \$1.00; g = 6%; = ?; r = ? P00s1

ˆ P= P(1 + g) = \$20(1.06) = \$21.20. 01

D\$1.00(1.06)1ˆ = + g = + 0.06 rsP\$200

\$1.06 = + 0.06 = 11.30%. r = 11.30%. s\$20

9-4 a. The terminal, or horizon, date is the date when the growth rate becomes constant. This occurs

at the end of Year 2.

b. 0 1 2 3 r = 10% s | | | | g = 20% g = 20% g = 5% ssn 1.25 1.50 1.80 1.89

1.89 37.80 = 0.100.05

The horizon, or terminal, value is the value at the horizon date of all dividends expected

thereafter. In this problem it is calculated as follows:

\$1.80(1.05) \$37.80.0.100.05

216 Integrated Case Chapter 9: Stocks and Their Valuation

c. The firm’s intrinsic value is calculated as the sum of the present value of all dividends during

the supernormal growth period plus the present value of the terminal value. Using your

= 0, CF = 1.50, CF = 1.80 + 37.80 = financial calculator, enter the following inputs: CF012

39.60, I/YR = 10, and then solve for NPV = \$34.09.

9-5 The firm’s free cash flow is expected to grow at a constant rate, hence we can apply a constant growth formula to determine the total value of the firm.

Firm value = FCF/(WACC g) 1

= \$150,000,000/(0.10 0.05)

= \$3,000,000,000.

To find the value of an equity claim upon the company (share of stock), we must subtract out the market value of debt and preferred stock. This firm happens to be entirely equity funded, and this step is unnecessary. Hence, to find the value of a share of stock, we divide equity value (or in this case, firm value) by the number of shares outstanding.

Equity value per share = Equity value/Shares outstanding

= \$3,000,000,000/50,000,000

= \$60.

Each share of common stock is worth \$60, according to the corporate valuation model.

9-6 D = \$5.00; V = \$60; r = ? ppp

D\$5.00pr = = = 8.33%. p\$60.00Vp

9-7 V = D/r; therefore, r = D/V. pppppp

a. r = \$8/\$60 = 13.33%. p

b. r = \$8/\$80 = 10.0%. p

c. r = \$8/\$100 = 8.0%. p

d. r = \$8/\$140 = 5.71%. p

D\$10p10-9 a. V\$125.pr0.08p

\$10b. V\$83.33.p0.12

Chapter 9: Stocks and Their Valuation Integrated Case 217

10-10 a. The preferred stock pays \$8 annually in dividends. Therefore, its nominal rate of return would

be:

Nominal rate of return = \$8/\$80 = 10%.

Or alternatively, you could determine the security’s periodic return and multiply by 4.

Periodic rate of return = \$2/\$80 = 2.5%.

Nominal rate of return = 2.5% 4 = 10%.

4/4)b. EAR = (1 + r 1 NOM4 = (1 + 0.10/4) 1

= 0.103813 = 10.3813%.

D(1;g)D \$5[1;(0.05)]\$5(0.95)\$4.75 01ˆ9-10 P\$23.75.0rgrg0.15(0.05)0.15;0.050.20ss

10-12 First, solve for the current price.

ˆ = D/(r g) P1s0

= \$0.50/(0.12 0.07)

= \$10.00.

If the stock is in a constant growth state, the constant dividend growth rate is also the capital gains

yield for the stock and the stock price growth rate. Hence, to find the price of the stock four years

from today:

4ˆ = P(1 + g) P044 = \$10.00(1.07)

= \$13.10796 ? \$13.11.

\$2(10.05)\$1.90 ˆ10-13 a. 1. P\$9.50.00.15;0.050.20

ˆ2. = \$2/0.15 = \$13.33. P0

\$2(1.05)\$2.10 ˆ3. P\$21.00.00.150.050.10

\$2(1.10)\$2.20 ˆ4. P\$44.00.00.150.100.05

ˆb. 1. = \$2.30/0 = Undefined. P0

ˆ2. = \$2.40/(-0.05) = -\$48, which is nonsense. P0

218 Integrated Case Chapter 9: Stocks and Their Valuation

These results show that the formula does not make sense if the required rate of return is equal

to or less than the expected growth rate.

c. No, the results of part b show this. It is not reasonable for a firm to grow indefinitely at a rate

higher than its required return. Such a stock, in theory, would become so large that it would

eventually overtake the whole economy.

= r + (r r)b. 9-13 a. riRFMRFi

r = 7% + (11% 7%)0.4 = 8.6%. C

r = 7% + (11% 7%)(-0.5) = 5%. D

Note that r is below the risk-free rate. But since this stock is like an insurance policy because D

it ―pays off‖ when something bad happens (the market falls), the low return is not

unreasonable.

b. In this situation, the expected rate of return is as follows:

ˆ = D/P + g = \$1.50/\$25 + 4% = 10%. r10C

However, the required rate of return is 8.6%. Investors will seek to buy the stock, raising its

price to the following:

\$1.50ˆ P\$32.61.C0.0860.04

\$1.50ˆAt this point, , and the stock will be in equilibrium. r;4%8.6%C\$32.61

ˆ10-14 The problem asks you to determine the value of , given the following rPfacts:D = \$2, b = 0.88,RF13

RP P = 5.6%,= 6%, and= \$25. Proceed as follows: M0

Step 1: Calculate the required rate of return:

r = r + (r r)b = 5.6% + (6%)0.88 =10.88%= 11%. sRFMRF

Step 2: Use the constant growth rate formula to calculate g:

D1ˆr;gsP0

\$20.11;g \$25

g0.033%.

ˆStep 3: Calculate : P3

33ˆ = P(1 + g) = \$25(1.03) = \$27.3182 ( \$27.32. P03

Chapter 9: Stocks and Their Valuation Integrated Case 219

ˆAlternatively, you could calculate D and then use the constant growth rate formula to solve for : P43

33D = D(1 + g) = \$2.00(1.03) = \$2.1855. 41

ˆ = \$2.1855/(0.11 0.03) = \$27.3182 ( \$27.32. P3

9-15 a. r = r + (r r)b = 6% + (10% 6%)1.5 = 12.0%. sRFMRF

ˆ = D/(r g) = \$2.25/(0.12 0.05) = \$32.14. P1s0

ˆb. r = 5% + (9% 5%)1.5 = 11.0%. = \$2.25/(0.110 0.05) = \$37.50. Ps0

ˆc. r = 5% + (8% 5%)1.5 = 9.5%. = \$2.25/(0.095 0.05) = \$50.00. Ps0

d. New data given: r = 5%; r = 8%; g = 6%, b = 1.3. RFM

r = r + (r r)b = 5% + (8% 5%)1.3 = 8.9%. sRFMRF

ˆ = D/(r g) = \$2.27/(0.089 0.06) = \$78.28. P1s0

10-15 Calculate the dividend cash flows and place them on a time line. Also, calculate the stock price at the

end of the supernormal growth period, and include it, along with the dividend to be paid at t = 5, as

CF. Then, enter the cash flows as shown on the time line into the cash flow register, enter the 5

required rate of return as I/YR = 14, and then find the value of the stock using the NPV calculation.

Be sure to enter CF = 0, or else your answer will be incorrect. 0

2D = 0; D = 0; D = 0; D = 1.00; D = 1.00(1.5) = 1.5; D = 1.00(1.5) = 2.25; D = 01234562ˆ1.00(1.5)(1.08) = \$2.43. = ? P0

0 1 2 3 4 5 6 r = 15% s | | | | | | | g = 50% g = 8% sn 1.00 1.50 2.25 2.43

32.43 1/(1.14) 0.675 +40.5 = 4 1/(1.14) 0.888 0.140.085 1/(1.14) 22.203 42.75

ˆ\$23.77 = P0

ˆ = D/(r g) = \$2.43/(0.14 0.08) = \$40.5. This is the stock price at the end of Year 5. P6s5

CF = 0; CF = 0; CF = 1.0; CF = 1.5; CF = 40.5; I/YR = 14%. 01-2345

With these cash flows in the CFLO register, press NPV to get the value of the stock today: NPV =

\$23.77.

220 Integrated Case Chapter 9: Stocks and Their Valuation

\$42.80\$40(1.07) = = \$713.33 million. 10-16 a. Terminal value = 0.130.070.06

b. 0 1 2 3 4 WACC = 13% | | | | | g = 7% n -20 30 40 42.80 1/1.13 (\$ 17.70) 2 1/(1.13) 23.49 = 713.33 Vop33 1/(1.13) 522.10 753.33

\$527.89

Using a financial calculator, enter the following inputs: CF = 0; CF = -20; CF = 30; CF = 0123

753.33; I/YR = 13; and then solve for NPV = \$527.89 million.

c. Total value = \$527.89 million. t=0

Value of common equity = \$527.89 \$100 = \$427.89 million.

\$427.89Price per share = = \$42.79. 10.00

10-17 The value of any asset is the present value of all future cash flows expected to be generated from the asset. Hence, if we can find the present value of the dividends during the period preceding long-run constant growth and subtract that total from the current stock price, the remaining value would be the present value of the cash flows to be received during the period of long-run constant growth.

11D = \$2.00 (1.25) = \$2.50 PV(D) = \$2.50/(1.12) = \$2.2321 1122D = \$2.00 (1.25) = \$3.125 PV(D) = \$3.125/(1.12) = \$2.4913 2233D = \$2.00 (1.25) = \$3.90625 PV(D) = \$3.90625/(1.12) = \$2.7804 33

PV(D to D) = \$7.5038 13

Therefore, the PV of the remaining dividends is: \$58.8800 \$7.5038 = \$51.3762. Compounding

this value forward to Year 3, we find that the value of all dividends received during constant growth 3is \$72.18. [\$51.3762(1.12) = \$72.1799 ( \$72.18.] Applying the constant growth formula, we can solve for the constant growth rate:

ˆ = D(1 + g)/(r g) P3s3

\$72.18 = \$3.90625(1 + g)/(0.12 g)

\$8.6616 \$72.18g = \$3.90625 + \$3.90625g

\$4.7554 = \$76.08625g

0.0625 = g

6.25% = g.

Chapter 9: Stocks and Their Valuation Integrated Case 221

10-18 0 1 2 3 4 r = 12% s | | | | | g = 5% = 2.00 D D D D D01234

ˆ P3

23a. D = \$2(1.05) = \$2.10; D = \$2(1.05) = \$2.2050; D = \$2(1.05) = \$2.31525. 123

b. Financial calculator solution: Input 0, 2.10, 2.2050, and 2.31525 into the cash flow register,

input I/YR = 12, PV = ? PV = \$5.28.

c. Financial calculator solution: Input 0, 0, 0, and 34.73 into the cash flow register, I/YR = 12, PV

= ? PV = \$24.72.

d. \$24.72 + \$5.28 = \$30.00 = Maximum price you should pay for the stock.

D(1;g)D\$2.1001ˆe. P\$30.00.0rgrg0.120.05ss

f. No. The value of the stock is not dependent upon the holding period. The value calculated in

Parts a through d is the value for a 3-year holding period. It is equal to the value calculated in

ˆˆPart e. Any other holding period would produce the same value of ; that is, = \$30.00. PP00

9-20 a. Part 1: Graphical representation of the problem:

Supernormal Normal

growth growth

0 1 2 3

| | | | |

ˆ D D (D + ) D D P01232

PVD 1

PVD 2

ˆ PVP2

P 0

D = D(1 + g) = \$1.6(1.20) = \$1.92. 10s

22D = D(1 + g) = \$1.60(1.20) = \$2.304. 20s

DD(1;g) \$2.304(1.06) 32nˆ P\$61.06.2rgrg0.10-0.06snsn

ˆˆ = PV(D) + PV(D) + PV() PP1202

ˆDDP122;; = 22(1;r)(1;r)(1;r)sss22 = \$1.92/1.10 + \$2.304/(1.10) + \$61.06/(1.10) = \$54.11.

222 Integrated Case Chapter 9: Stocks and Their Valuation

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