Chapter 10
Stocks and Their Valuation
ANSWERS TO END-OF-CHAPTER QUESTIONS
10-1 a. A proxy is a document giving one person the authority to act for another, typically the power to vote shares of common stock. If earnings are poor and stockholders are dissatisfied, an outside group may solicit the proxies in an effort to overthrow management and take control of the business, known as a proxy fight. A takeover is an action whereby a person or group succeeds in ousting a firm’s management and taking control of the company.
b. The preemptive right gives the current shareholders the right to purchase any new shares issued in proportion to their current holdings. The preemptive right may or may not be required by state law. When granted, the preemptive right enables current owners to maintain their proportionate share of ownership and control of the business. It also prevents the sale of shares at low prices to new stockholders which would dilute the value of the previously issued shares.
c. Classified stock is sometimes created by a firm to meet special needs and circumstances. Generally, when special classifications of stock are used, one type is designated “Class A”, another as “Class B”, and so on. Class A might be entitled to receive dividends before dividends can be paid on Class B stock. Class B might have the exclusive right to vote. Founders’ shares are stock owned by the firm’s founders that have sole voting rights but restricted dividends for a specified number of years.
d. Some companies are so small that their common stocks are not actively traded; they are owned by only a few people, usually the companies’ managers. Such firms are said to be closely held corporations. In contrast, the stocks of most larger companies are owned by a large number of investors, most of whom are not active in management. Such companies are said to be publicly owned corporations.
e. The over-the-counter (OTC) market is the network of dealers that provides for trading in unlisted securities. An organized security exchange is a formal organization, having a tangible physical location, that facilitates trading in designated (“listed”) securities. The two major U.S. security exchanges are the New York Stock Exchange (NYSE) and the American Stock Exchange (AMEX).
outstanding, shares of established, publicly owned companies. The company receives no new money when sales are made in the secondary market. The primary market handles additional shares sold by established, publicly owned companies. Companies can raise additional capital by selling in this market.
g. Going public is the act of selling stock to the public at large by a closely held corporation or its principal stockholders, and this market is often termed the initial public offering (IPO) market.
h. Intrinsic value (Pˆ ) is the present value of the expected future cash 0 flows. The market price (P0) is the price at which an asset can be sold.
i. The required rate of return on common stock, denoted by ks, is the minimum acceptable rate of return considering both its riskiness and the returns available on other investments. The expected rate of return, denoted by kˆ , is the rate of return expected on a stock s given its current price and expected future cash flows. If the stock is in equilibrium, the required rate of return will equal the expected rate of return. The realized (actual) rate of return, denoted by
s
k , is the rate of return that was actually realized at the end of some holding period. Although expected and required rates of return must always be positive, realized rates of return over some periods may be negative.
j. The capital gains yield results from changing prices and is calculated as (P1 - P0)/P0, where P0 is the beginning-of-period price and P1 is the end-of-period price. For a constant growth stock, the capital gains yield is g, the constant growth rate. The dividend yield on a stock can be defined as either the end-of-period dividend divided by the beginning-of-period price, or the ratio of the current dividend to the current price. Valuation formulas use the former definition. The expected total return, or expected rate of return, is the expected capital gains yield plus the expected dividend yield on a stock. The expected total return on a bond is the yield to maturity.
k. A zero growth stock has constant earnings and dividends; thus, the expected dividend payment is fixed, just as a bond’s coupon payment. Since the company is presumed to continue operations indefinitely, the dividend stream is a perpetuity. A perpetuity is a security on which the principal never has to be repaid.
l. Normal, or constant, growth occurs when a firm’s earnings and dividends grow at some constant rate forever. One category of nonconstant growth stock is a “supernormal” growth stock which has one or more years of growth above that of the economy as a whole, but at some point the growth rate will fall to the “normal” rate. This occurs, generally, as part of a firm’s normal life cycle.
l. Equilibrium is the condition under which the expected return on a security is just equal to its required return, kˆ = k, and the price is stable.
n. The Efficient Markets Hypothesis (EMH) states (1) that stocks are always in equilibrium and (2) that it is impossible for an investor to consistently “beat the market.” In essence, the theory holds that the price of a stock will adjust almost immediately in response to any new developments. In other words, the EMH assumes that all important information regarding a stock is reflected in the price of that stock. Financial theorists generally define three forms of market efficiency: weak-form, semistrong-form, and strong-form.
Weak-form efficiency assumes that all information contained in past price movements is fully reflected in current market prices. Thus, information about recent trends in a stock’s price is of no use in selecting a stock. Semistrong-form efficiency states that current market prices reflect all publicly available information. Therefore, the only way to gain abnormal returns on a stock is to possess inside information about the company’s stock. Strong-form efficiency assumes that all information pertaining to a stock, whether public or inside information, is reflected in current market prices. Thus, no investors would be able to earn abnormal returns in the stock market.
o. Preferred stock is a hybrid--it is similar to bonds in some respects and to common stock in other respects. Preferred dividends are similar to interest payments on bonds in that they are fixed in amount and generally must be paid before common stock dividends can be paid. If the preferred dividend is not earned, the directors can omit it without throwing the company into bankruptcy. So, although preferred stock has a fixed payment like bonds, a failure to make this payment will not lead to bankruptcy. Most preferred stocks entitle their owners to regular fixed dividend payments.
10-2 True. 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.
10-3 A perpetual bond is similar to a no-growth stock and to a share of preferred stock in the following ways:
1. All three derive their values from a series of cash inflows--coupon 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.
10-4 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.
10-5 No. The correct equation has D1 in the numerator and a minus sign in the denominator.
10-6 a. The average investor in a listed firm is not really interested in maintaining his proportionate share of ownership and control. If he wanted to increase his ownership, he 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 firms whose owners are interested in maintaining their relative control positions.
10-1 D0 = $1.50; g1-3 = 5%; gn = 10%; D1 through D5 = ? D1 = D0(1 + g1) = $1.50(1.05) = $1.5750. D2 = D0(1 + g1)(1 + g2) = $1.50(1.05)2 = $1.6538. D3 = D0(1 + g1)(1 + g2)(1 + g3) = $1.50(1.05)3 = $1.7364. D4 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn) = $1.50(1.05)3(1.10) = $1.9101. D5 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn)2 = $1.50(1.05)3(1.10)2 = $2.1011. 10-2 D1 = $0.50; g = 7%; ks = 15%; Pˆ = ? 0 0 Pˆ = g k D s 1 − = 0.15 0.07 50 . 0 $ − = $6.25. 10-3 P0 = $20; D0 = $1.00; g = 10%; Pˆ = ?; 1 kˆ = ? s 1 Pˆ = P0(1 + g) = $20(1.10) = $22. s kˆ = 0 1 P D + g = 20 $ ) 10 . 1 ( 00 . 1 $ + 0.10 = 20 $ 10 . 1 $ + 0.10 = 15.50%. s kˆ = 15.50%. 10-4 Dps = $5.00; Vps = $60; kps = ? kps = ps ps v D = 00 . 60 $ 00 . 5 $ = 8.33%. 10-5 0 1 2 3 | | | | D0 = 2.00 D1 D2 D3 2 Pˆ
Step 1: Calculate the required rate of return on the stock: ks = kRF + (kM - kRF)b = 7.5% + (4%)1.2 = 12.3%.
Step 2: Calculate the expected dividends: D0 = $2.00
D1 = $2.00(1.20) = $2.40 D2 = $2.00(1.20)2 = $2.88 D3 = $2.88(1.07) = $3.08
Step 3: Calculate the PV of the expected dividends:
PVDiv = $2.40/(1.123) + $2.88/(1.123)2 = $2.14 + $2.28 = $4.42.
Step 4: Calculate Pˆ : 2
2
Pˆ = D3/(ks - g) = $3.08/(0.123 - 0.07) = $58.11. Step 5: Calculate the PV of
2 Pˆ :
PV = $58.11/(1.123)2 = $46.08.
Step 6: Sum the PVs to obtain the stock’s price:
0
Pˆ = $4.42 + $46.08 = $50.50.
Alternatively, using a financial calculator, input the following:
CF0 = 0, CF1 = 2.40, and CF2 = 60.99 (2.88 + 58.11) and then enter I = 12.3 to solve for NPV = $50.50.
10-6 The problem asks you to determine the constant growth rate, given the following facts: P0 = $80, D1 = $4, and ks = 14%. Use the constant growth rate formula to calculate g:
s kˆ = 0 1 P D + g 0.14 = 80 $ 4 $ + g g = 0.09 = 9%.
10-7 The problem asks you to determine the value of Pˆ , given the following 3 facts: D1 = $2, b = 0.9, kRF = 5.6%, RPM = 6%, and P0 = $25. Proceed as follows:
Step 1: Calculate the required rate of return:
ks = kRF + (kM - kRF)b = 5.6% + (6%)0.9 = 11%.
Step 2: Use the constant growth rate formula to calculate g:
kˆ = s 0 1 P D + g 0.11 = 25 $ 2 $ + g g = 0.03 = 3%. Step 3: Calculate 3 Pˆ : 3 Pˆ = P0(1 + g)3 = $25(1.03)3 = $27.3182 $27.32.
Alternatively, you could calculate D4 and then use the constant growth rate formula to solve for
3 Pˆ : D4 = D1(1 + g)3 = $2.00(1.03)3 = $2.1855. 3 Pˆ = $2.1855/(0.11 - 0.03) = $27.3188 ≈ $27.32. 10-8 Vps = Dps/kps; therefore, kps = Dps/Vps. a. kps = $8/$60 = 13.3%. b. kps = $8/$80 = 10%. c. kps = $8/$100 = 8%. d. kps = $8/$140 = 5.7%. 10-9 Pˆ = 0 g k D s 1 − = k g ) g 1 ( D s 0 − + = )] 05 . 0 ( 15 . 0 )] 05 . 0 ( 1 [ 5 $ − − − + = 05 . 0 15 . 0 ) 95 . 0 ( 5 $ + = 0.20 75 . 4 $ = $23.75. 10-10 a. ki = kRF + (kM - kRF)bi. kC = 9% + (13% - 9%)0.4 = 10.6%. kD = 9% + (13% - 9%)-0.5 = 7%.
Note that kD is below the risk-free rate. But since this stock is like an insurance policy because 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:
C
However, the required rate of return is 10.6 percent. Investors will seek to sell the stock, dropping its price to the following:
C Pˆ = 04 . 0 106 . 0 50 . 1 $ − = $22.73. At this point, C kˆ = 73 . 22 $ 50 . 1 $
+ 4% = 10.6%, and the stock will be in equilibrium. 10-11 D0 = $1, kS = 7% + 6% = 13%, g1 = 50%, g2 = 25%, gn = 6%. 0 1 2 3 4 | | | | | 1.50 1.875 1.9875 1.327 + 28.393 = 1.9875/(0.13 - 0.06) = 30.268 23.704 $25.03
10-12 Calculate the dividend stream and place them on a time line. Also, calculate the price of the stock at the end of the supernormal growth period, and include it, along with the dividend to be paid at t = 5, as CF5. Then, enter the cash flows as shown on the time line into the cash flow register, enter the required rate of return as I = 15, and then find the value of the stock using the NPV calculation. Be sure to enter CF0 = 0, or else your answer will be incorrect.
D0 = 0; D1 = 0, D2 = 0, D3 = 1.00 D4 = 1.00(1.5) = 1.5; D5 = 1.00(1.5)2 = 2.25; D6 = 1.00(1.5)2(1.08) = $2.43. 0 Pˆ = ? 0 1 2 3 4 5 6 | | | | | | | 1.00 1.50 2.25 0.66 34.71 0.86 36.96 18.38 $19.89 = 0 Pˆ 5
Pˆ = D6/(ks - g) = 2.43/(0.15 - 0.08) = 34.71. This is the price of the stock at the end of Year 5.
CF0 = 0; CF1-2 = 0; CF3 = 1.0; CF4 = 1.5; CF5 = 36.96; I = 15%.
With these cash flows in the CFLO register, press NPV to get the value of the stock today: NPV = $19.89.
ks = 13% g1 = 50% g2 = 25% g1 = 6% 08 . 0 15 . 0 43 . 2 − ks = 15% g = 50% g = 8%
10-13 a. Vps = ps ps k D = 08 . 0 10 $ = $125. b. Vps = 12 . 0 10 $ = $83.33. 10-14 0 1 2 3 4 | | | | | D0 = 2.00 D1 D2 D3 D4 3 Pˆ a. D1 = $2(1.05) = $2.10. D2 = $2(1.05)2 = $2.21. D3 = $2(1.05)3 = $2.32. b. PV = $2.10(0.8929) + $2.21(0.7972) + $2.32(0.7118) = $5.29.
Calculator solution: Input 0, 2.10, 2.21, and 2.32 into the cash flow register, input I = 12, PV = ? PV = $5.29.
c. $34.73(0.7118) = $24.72.
Calculator solution: Input 0, 0, 0, and 34.73 into the cash flow register, I = 12, PV = ? PV = $24.72.
d. $24.72 + $5.29 = $30.01 = Maximum price you should pay for the stock. e. 0 Pˆ = g k ) g 1 ( D s 0 − + = g k D s 1 − = 0.12 0.05 10 . 2 $ − = $30.00.
f. 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 Part e except for a small rounding error. Any other holding period would produce the same value of
0
Pˆ ; that is, Pˆ = $30.00. 0
10-15 a. g = $1.1449/$1.07 - 1.0 = 7%.
Calculator solution: Input N = 1, PV = -1.07, PMT = 0, FV = 1.1449, I = ? I = 7.00%. b. $1.07/$21.40 = 5%. c. s kˆ = D1/P0 + g = $1.07/$21.40 + 7% = 5% + 7% = 12%. g = 5%
10-16 a. 1. 0 Pˆ = 05 . 0 15 . 0 ) 05 . 0 1 ( 2 $ + − = 20 . 0 90 . 1 $ $9.50. 2. 0 Pˆ = $2/0.15 = $13.33. 3. Pˆ = 0 05 . 0 15 . 0 ) 05 . 1 ( 2 $ − = 0.10 10 . 2 $ = $21.00. 4. 0 Pˆ = 10 . 0 15 . 0 ) 10 . 1 ( 2 $ − = 0.05 20 . 2 $ = $44.00. b. 1. Pˆ = $2.30/0 = Undefined. 0 2. 0 Pˆ = $2.40/(-0.05) = -$48, which is nonsense.
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.
10-17 The answer depends on when one works the problem. We used the June 16, 2000, Wall Street Journal:
a. $33½ to $61.
b. Current dividend = $0.88. Dividend yield = $0.88/$33.9375 2.6%. You might want to use an expected dividend yield of ($0.88)(1 + g)/$33.9375, with g estimated somehow.
c. The $33.9375 close was up 5/8 from the previous day’s close.
d. The return on the stock consists of a dividend yield of about 2.6 percent plus some capital gains yield. We would expect the total rate of return on stock to be in the 10 to 12 percent range.
10-18 a. End of Year: 01 02 03 04 05 06 07 | | | | | | | D0 = 1.75 D1 D2 D3 D4 D5 D6 Dt = D0(1 + g)t D2002 = $1.75(1.15)1 = $2.01. D2003 = $1.75(1.15)2 = $1.75(1.3225) = $2.31. D2004 = $1.75(1.15)3 = $1.75(1.5209) = $2.66. D2005 = $1.75(1.15)4 = $1.75(1.7490) = $3.06. D2006 = $1.75(1.15)5 = $1.75(2.0114) = $3.52. b. Step 1 PV of dividends =
∑
= + 5 1 t t s t ) k 1 ( D . PV D2002 = $2.01(PVIF12%,1) = $2.01(0.8929) = $1.79 PV D2003 = $2.31(PVIF12%,2) = $2.31(0.7972) = $1.84 PV D2004 = $2.66(PVIF12%,3) = $2.66(0.7118) = $1.89 PV D2005 = $3.06(PVIF12%,4) = $3.06(0.6355) = $1.94 PV D2006 = $3.52(PVIF12%,5) = $3.52(0.5674) = $2.00 PV of dividends = $9.46 Step 2 2006P
ˆ
= n s 2007g
k
D
−
= s n n 2006g
k
)
g
(1
D
−
+
= 05 . 0 12 . 0 ) 05 . 1 ( 52 . 3 $ − = 0.07 70 . 3 $ = $52.80.This is the price of the stock 5 years from now. The PV of this price, discounted back 5 years, is as follows:
PV of
P
ˆ
2006 = $52.80(PVIF12%,5) = $52.80(0.5674) = $29.96. Step 3The price of the stock today is as follows:
0
Pˆ = PV dividends Years 2002-2006 + PV of
P
ˆ
2006 = $9.46 + $29.96 = $39.42.This problem could also be solved by substituting the proper values into the following equation:
0 Pˆ = . k 1 1 g k D ) k 1 ( ) g 1 ( D 5 1 t 5 s n s 6 t s t s 0
∑
= ++ + − + Calculator solution: Input 0, 2.01, 2.31, 2.66, 3.06, 56.32 (3.52 + 52.80) into the cash flow register, input I = 12, PV = ? PV = $39.43.
k = 12%
g = 5% g = 15%
c. 2002
D1/P0 = $2.01/$39.42 = 5.10% Capital gains yield = 6.90* Expected total return = 12.00% 2007
D6/P5 = $3.70/$52.80 = 7.00% Capital gains yield = 5.00 Expected total return = 12.00%
*We know that k is 12 percent, and the dividend yield is 5.10 percent; therefore, the capital gains yield must be 6.90 percent. The main points to note here are as follows:
1. The total yield is always 12 percent (except for rounding errors).
2. The capital gains yield starts relatively high, then declines as the supernormal growth period approaches its end. The dividend yield rises.
3. After 12/31/06, the stock will grow at a 5 percent rate. The dividend yield will equal 7 percent, the capital gains yield will equal 5 percent, and the total return will be 12 percent.
d. People in high income tax brackets will be more inclined to purchase “growth” stocks to take the capital gains and thus delay the payment of taxes until a later date. The firm’s stock is “mature” at the end of 2003.
e. Since the firm’s supernormal and normal growth rates are lower, the dividends and, hence, the present value of the stock price will be lower. The total return from the stock will still be 12 percent, but the dividend yield will be larger and the capital gains yield will be smaller than they were with the original growth rates. This result occurs because we assume the same last dividend but a much lower current stock price.
f. As the required return increases, the price of the stock goes down, but both the capital gains and dividend yields increase initially. Of course, the long-term capital gains yield is still 4 percent, so the long-term dividend yield is 10 percent.
10-19 a. Part 1. Graphical representation of the problem: Supernormal Normal growth growth 0 1 2 3 | | | | | D0 D1 (D2 + Pˆ ) D32 D PVD1 PVD2 PV 2 Pˆ P0 D1 = D0(1 + gs) = $1.6(1.20) = $1.92. D2 = D0(1 + gs)2 = $1.60(1.20)2 = $2.304. 2 Pˆ = n s 3 g k D − = s n n 2 g k ) g 1 ( D − + = 06 . 0 10 . 0 ) 06 . 1 ( 304 . 2 $ − = $61.06. 0 Pˆ = PV(D1) + PV(D2) + PV(Pˆ ) 2 = 2 s 2 2 s 2 s 1 ) k 1 ( P ˆ ) k 1 ( D ) k 1 ( D + + + + + = $1.92(0.9091) + $2.304(0.8264) + $61.06(0.8264) = $54.11.
Calculator solution: Input 0, 1.92, 63.364(2.304 + 61.06) into the cash flow register, input I = 10, PV = ? PV = $54.11.
Part 2.
Expected dividend yield: D1/P0 = $1.92/$54.11 = 3.55%.
Capital gains yield: First, find 1
Pˆ which equals the sum of the present values of D2 and Pˆ , discounted for one year. 2
1 Pˆ = D2(PVIF10%, 1) + Pˆ (PVIF10%, 12 ) = 1 ) 10 . 1 ( 06 . 61 $ 304 . 2 $ + = $57.60.
Calculator solution: Input 0, 63.364(2.304 + 61.06) into the cash flow register, input I = 10, PV = ? PV = $57.60.
Second, find the capital gains yield:
0 0 1 P P P ˆ − = 11 . 54 $ 11 . 54 $ 60 . 57 $ − = 6.45%. Dividend yield = 3.55% Capital gains yield = 6.45
b. Due to the longer period of supernormal growth, the value of the stock will be higher for each year. Although the total return will remain the same, ks = 10%, the distribution between dividend yield and capital gains yield will differ: The dividend yield will start off lower and the capital gains yield will start off higher for the 5-year supernormal growth condition, relative to the 2-year supernormal growth state. The dividend yield will increase and the capital gains yield will decline over the 5-year period until divi-dend yield = 4% and capital gains yield = 6%.
c. Throughout the supernormal growth period, the total yield will be 10 percent, but the dividend yield is relatively low during the early years of the supernormal growth period and the capital gains yield is relatively high. As we near the end of the supernormal growth period, the capital gains yield declines and the dividend yield rises. After the supernormal growth period has ended, the capital gains yield will equal gn = 6%. The total yield must equal ks = 10%, so the dividend yield must equal 10% - 6% = 4%.
d. Some investors need cash dividends (retired people) while others would prefer growth. Also, investors must pay taxes each year on the dividends received during the year, while taxes on capital gains can be delayed until the gain is actually realized.
10-20 a. ks = kRF + (kM - kRF)b = 11% + (14% - 11%)1.5 = 15.5%.
0
Pˆ = D1/(ks - g) = $2.25/(0.155 - 0.05) = $21.43.
b. ks = 9% + (12% - 9%)1.5 = 13.5%. Pˆ = $2.25/(0.135 - 0.05) = $26.47. 0 c. ks = 9% + (11% - 9%)1.5 = 12.0%. Pˆ = $2.25/(0.12 - 0.05) = $32.14. 0 d. New data given: kRF = 9%; kM = 11%; g = 6%, b = 1.3.
ks = kRF + (kM - kRF)b = 9% + (11% - 9%)1.3 = 11.6%. 0 Pˆ = D1/(ks - g) = $2.27/(0.116 - 0.06) = $40.54. 10-21 a. Old ks = kRF + (kM - kRF)b = 9% + (3%)1.2 = 12.6%. New ks = 9% + (3%)0.9 = 11.7%. Old price: 0 Pˆ = g k D s 1 − = k g ) g 1 ( D s 0 − + = 0.07 -0.126 ) 07 . 1 ( 2 $ = $38.21. New price: 0 Pˆ = 05 . 0 117 . 0 ) 05 . 1 ( 2 $ − = $31.34.
Since the new price is lower than the old price, the expansion in consumer products should be rejected. The decrease in risk is not sufficient to offset the decline in profitability and the reduced
growth rate. b. POld = $38.21. PNew = 05 . 0 k ) 05 . 1 ( 2 $ s − .
Solving for ks we have the following:
$38.21 = 05 . 0 k 10 . 2 $ s − $2.10 = $38.21(ks) - $1.9105 $4.0105 = $38.21(ks) ks = 0.10496. Solving for b: 10.496% = 9% + 3%(b) 1.496% = 3%(b) b = 0.49865. Check: ks = 9% + (3%)0.49865 = 10.4960%. 0 Pˆ = 05 . 0 104960 . 0 10 . 2 $ − = $38.21.
Therefore, only if management’s analysis concludes that risk can be lowered to b = 0.49865, or approximately 0.5, should the new policy be put into effect.
SOLUTION TO SPREADSHEET PROBLEMS
10-22 The detailed solution for the problem is available both on the instructor’s resource CD-ROM (in the file Solution for Ch 10-22 Build a
Model.xls) and on the instructor’s side of the Harcourt College
Publishers’ web site, http://www.harcourtcollege.com/finance/theory10e. 10-23 a. Supernormal growth rate = 12%; normal growth rate = 4%
INPUT DATA: KEY OUTPUT:
Supernormal growth 12.00% Current price (P0) $31.50 Normal growth rate 4.00% Price at 12/31/2006 $40.09 Req. rate of return 12.00% Dividend yield 2002 6.22% Last dividend (D0) $1.75 “ “ 2007 8.00% Supernormal period 5 years Cap. gains yield 2002 5.78% “ “ “ 2007 4.00% Total return both yrs. 12.00% MODEL-GENERATED DATA:
Expected dividends: PV of dividends: 2002 $1.96 1999 $1.75 2003 2.20 2000 1.75 2004 2.46 2001 1.75 2005 2.75 2002 1.75 2006 3.08 2003 1.75 Stock price Stock price
at 12/31/2006: $40.09 at 1/1/2002: $31.50 Yields in 2007: Yields in 2002:
Dividend 8.00% Dividend 6.22% Capital Gain 4.00% Capital Gain 5.78% Total 12.00% Total 12.00% b. 1. k = 13 percent
INPUT DATA: KEY OUTPUT:
Supernormal growth 12.00% Current price (P0) $27.86 Normal growth rate 4.00% Price at 12/31/2006 $35.64 Req. rate of return 13.00% Dividend yield 2002 7.03% Last dividend (D0) $1.75 “ “ 2007 9.00% Supernormal period 5 years Cap. gains yield 2002 5.97% “ “ “ 2007 4.00% Total return both yrs. 13.00%
2. k = 15 percent
INPUT DATA: KEY OUTPUT:
Supernormal growth 12.00% Current price (P0) $22.59 Normal growth rate 4.00% Price at 12/31/2006 $29.16 Req. rate of return 15.00% Dividend yield 2002 8.68% Last dividend (D0) $1.75 “ “ 2007 11.00% Supernormal period 5 years Cap. gains yield 2002 6.32% “ “ “ 2007 4.00% Total return both yrs 15.00% 3. k = 20 percent
INPUT DATA: KEY OUTPUT:
Supernormal growth 12.00% Current price (P0) $15.20 Normal growth rate 4.00% Price at 12/31/2006 $20.05 Req. rate of return 20.00% Dividend yield 2002 12.89% Last dividend (D0) $1.75 “ “ 2007 16.00% Supernormal period 5 years Cap. gains yield 2002 7.11% “ “ “ 2007 4.00% Total return both yrs 20.00%
CYBERPROBLEM
10-24 The detailed solution for the cyberproblem is available on the instructor’s side of the Harcourt College Publishers’ web site: http://www.harcourtcollege.com/finance/theory10e.
