Q15) Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the
stock over the next9 years because the firm needs to plow back its earnings to fuel growth. The
company will pay $12 per share dividend in 10 years and will increase the dividend by 5% per
year thereafter. If the required rate of return on this stock is 13.5% what is the current stock
price?
Here we have a stock that pays no dividends for 10 years. Once the stock begins paying
dividends, it will have a constant growth rate of dividends. We can use the constant growth
model at that point. It is important to remember that general constant dividend growth
formula is:
Pt = [Dt × (1 + g)] / (R – g)
This means that since we will use the dividend in Year 10, we will be finding the stock price
in Year 9. The dividend growth model is similar to the PVA and the PV of a perpetuity: The
equation gives you the PV one period before the first payment. So, the price of the stock in
Year 9 will be:
P9 = D10 / (R – g) = $12.00 / (.135 – .05) = $141.18
The price of the stock today is simply the PV of the stock price in the future. We simply
discount the future stock price at the required return. The price of the stock today will be:
Q16) Maloney, Inc., has an odd dividend policy. The company has just paid a dividend of $3 per
share and has announced that it will the dividend by $5 per share for each of the next five years,
and never pay another dividend. If you require a return of 11% on the company’s stock, how
much will you pay for a share today?
The price of a stock is the PV of the future dividends. This stock is paying five dividends, so
the price of the stock is the PV of these dividends using the required return. The price of the
stock is:
P0 = $8 / 1.11 + $13 / 1.112 + $18 / 1.113 + $23 / 1.114 + $28 / 1.115 = $62.69
Q24) Thirsty Cactus Corp. just paid a dividend of $1.30 per share. The dividends are expected to
grow at 23% for the next eight years and then level off a growth rate of 6% indefinitely. If the
required return is 12%, what is the price of the stock today?
P0 = [D0(1 + g1)/(R – g1)]{1 – [(1 + g1)/(1 + R)]T}+ [(1 + g1)/(1 + R)]T[D0(1 + g2)/(R – g2)]
P0 = [$1.30(1.23)/(.12 – .23)][1 – (1.23/1.12)8] + [(1.23)/(1.12)]8[$1.30(1.06)/(.12 – .06)]
P0 = $64.82
Q25) Chartreuse County Choppers, Inc., is experiencing rapid growth. The company expects
dividends to grow at 18% per year for the next 11 years before leveling off at 5% into perpetuity.
The required rate of return on the this company is 12%. If dividends per share just paid was
$1.94, what is the stock price?
P0 = [D0(1 + g1)/(R – g1)]{1 – [(1 + g1)/(1 + R)]T}+ [(1 + g1)/(1 + R)]T[D0(1 + g2)/(R – g2)]
P0 = [$1.94(1.18)/(.12 – .18)][1 – (1.18/1.12)11] + [(1.18)/(1.12)]11[$1.94(1.05)/(.12 – .05)]
P0 = $81.25
Q32) Consider four different stocks, all of which have a required return of 17% and a most
recent dividend of $4.50 per share. Stocks W, X, and Y are expected to maintain constant growth
rates in dividends for the foreseeable future of 10%, 0%, and -5% per year, respectively. Stock Z
is a growth stock that will its dividend by 20% for the next two years and then maintain a
constant 12% growth rate thereafter. What is the dividend yield for each of these stocks? What is
the expected capital gains yield? Discuss the relationship among various returns that you find for
each of these stocks.
W: P0 = D0(1 + g) / (R – g) = $4.50(1.10)/(.17 – .10) = $70.71
Dividend yield = D1/P0 = $4.50(1.10)/$70.71 = .07, or 7%
Capital gains yield = .17 – .07 = .10, or 10%
X: P0 = D0(1 + g) / (R – g) = $4.50/(.17 – 0) = $26.47
Dividend yield = D1/P0 = $4.50/$26.47 = .17, or 17%
Capital gains yield = .17 – .17 = 0%
Y: P0 = D0(1 + g) / (R – g) = $4.50(1 – .05)/(.17 + .05) = $19.43
Dividend yield = D1/P0 = $4.50(0.95)/$19.43 = .22, or 22%
Capital gains yield = .17 – .22 = –.05, or –5%
Z:
P2 = D2(1 + g) / (R – g) = D0(1 + g1)2(1 + g2)/(R – g2) = $4.50(1.20)2(1.12)/(.17 – .12) =
$145.15
P0 = $4.50 (1.20) / (1.17) + $4.50 (1.20)2 / (1.17)2 + $145.15 / (1.17)2 = $115.38
Dividend yield = D1/P0 = $4.50(1.20)/$115.38 = .047, or 4.7%
Capital gains yield = .17 – .047 = .123, or 12.3%
In all cases, the required return is 17 percent, but the return is distributed differently between
current income and capital gains. High growth stocks have an appreciable capital gains
component but a relatively small current income yield; conversely, mature, negative-growth
stocks provide a high current income but also price depreciation over time.