FIN222 Week 4_T CH7: P1,4,6,7,12,13,14,15,16,19 (10 Questions, 15 parts)
CHAPTER 7 SHARE VALUATION
1. If you own 15 000 shares of BHP Billiton Ltd (BHP) and it pays a dividend of $0.27 per share,
what is the total dividend you will receive?
15,000 $0.27 = $4050.
4. Telford Corporation has a current share price of $20 and is expected to pay a dividend of $1 in
one year. Its expected share price right after paying that dividend is $22.
a. What is Telford’s equity cost of capital?
Div1 P1 P0
rE
P0 P0
𝟏 𝟐𝟐 𝟐𝟎
𝒓𝑬 𝟎. 𝟏𝟓 𝒐𝒓 𝟏𝟓%
𝟐𝟎 𝟐𝟎
b. How much of Telford’s equity cost of capital is expected to be satisfied by dividend yield and
how much by capital gain?
Div1 P1 P0
rE
P0 P0
Capital gain rate = 10% ((22-20)/20)
Dividend yield = 5% (1/20)
6. Bronco Limited has a preference share with a price of $20 and a dividend of $1.50 per year.
What is its dividend yield?
Div 1.50
Dividend yield 0.075 7.5%
P0 20.00
7. Suppose Maxwell Corporation will pay a dividend of $2.80 per share at the end of this year
and a dividend of $3 per share next year. You expect Maxwell’s share price to be $52 in two
years. Assume that Maxwell’s equity cost of capital is 10%.
a. What price would you be willing to pay for a Maxwell share today, if you planned to hold the
share for two years?
2.80 3.00 52.00
P 0 $48.00
1.10 1.102
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b. Suppose instead you plan to hold the share for one year. For what price would you expect to
be able to sell a Maxwell share in one year?
3.00 52.00
P 1 $50.00
1.10
c. Given your answer to part (b), what price would you be willing to pay for a Maxwell share
today, if you planned to hold the share for one year? How does this price compare to your
answer in part (a)?
2.80 50
𝑃 0 $48
1.1
12
Hardy Enterprises expects earnings next year of $4 per share and has a 40% retention rate,
which it plans to keep constant.
Div1= EPS1*(1- retention rate)= $4*(1-0.4)=$2.40
Its equity cost of capital is 10%, which is also its expected return on new investment. rE=10%,
return on new investment=10%.
Its earnings are expected to grow forever at a rate of 4% per year. g=0.04
(note: what if g was not given in the question? You can calculate g on your own.
g= retention rate * return on investment = 0.4*0.10 = 0.04)
If its next dividend is due in one year, what do you estimate the firm’s current share price to
be?
Div1 2.40
P0 $40
rE g 0.10 0.04
13.
RFK Limited expects earnings this year of $5 per share, and it plans to pay a $3 dividend
to shareholders. Div1=$3
RFK will retain $2 per share of its earnings to reinvest in new projects that have an
expected return of 15% per year.
Suppose RFK will maintain the same dividend payout rate, retention rate and return on
new investments in the future and will not change its number of outstanding shares.
a. What growth rate of earnings would you forecast for RFK?
g = Retention rate Return on new investment
= ($2/$5) 15% = 6%. Warning: I am NOT
in the formula sheet!
b. If RFK’s equity cost of capital is 12%, what price would you estimate for DFB shares?
Div1 3.00
P0 $50.00
rE g 0.12 0.06
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c.
Suppose instead that RFK paid a dividend of $4 per share this year (Div0=$4) and retained
only $1 per share in earnings.
That is, it chose to pay a higher dividend instead of reinvesting in as many new projects.
If RFK maintains this higher payout rate in the future, what share price would you
estimate for the firm now?
Should RFK follow this new policy?
g = Retention rate Return on new investment
=($1/$5) 15% = 3%
(Observation: Div less reinvestment g )
Div1= Div0(1+g)= $4*(1.03)
Div1 4.00(1 0.03)
P0 $45.78
rE g 0.12 0.03
When RFK’s growth rate is 6%, its shares will sell for $50.00. RFK should not raise the dividend because it
will result in a lower share price of $45.78.
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14.
Cooperaton Mining just announced it will cut its dividend from $4 to $2.50 per share and use
the extra funds to expand.
Prior to the announcement, Cooperaton’s dividends were expected to grow at a rate of 3% and
its share price was $50.
With the planned expansion, Cooperaton’s dividends are expected to grow at a rate of 5%.
What share price would you expect after announcement? (Assume that the new expansion does
not change Cooperton’s risk.)
Is the expansion a good investment?
We must estimate the share price of Cooperton Mining after the dividend cut and new investment
policy. If the share price were to fall we would not cut the dividend.
Before After
Div1 $4 $2.50
Growth rate 3% 5%
rE 𝑫𝒊𝒗𝟏 As Cooperation’s risk didn’t
𝒓𝑬 𝒈
𝑷𝟎 change, rE remains unchanged.
rE=11%
𝟒
𝒓𝑬 𝟎. 𝟎𝟑 𝟏𝟏%
𝟓𝟎
Share price $50 𝑫𝒊𝒗𝟏
𝑷𝟎 𝒓𝑬 𝒈
$𝟐. 𝟓𝟎
𝑷𝟎
𝟎. 𝟏𝟏 𝟎. 𝟎𝟓
$𝟒𝟏. 𝟔𝟕
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15.
Gillette Corporation will pay an annual dividend of $0.65 one year from now. Div1=$0.65
Analysts expect this dividend to grow at 12% per year thereafter until the fifth year.
After that, growth will level off at 2% per year. According to the dividend-discount model,
what is the value of a Gillette share if the firm’s equity cost of capital is 8%?
$0.65 0.728 0.8154 0.9132 1.0228 1.0228(1.02) 1.0228 (1.02)2
|_________|__g=12%_|_g=12%_|_g=12%__|__g=12%__|___g=2%__|___g=2%_______|_________......
1 2 3 4 5 6 7
P5=Div6/(rE‐g)
Div1=$0.65
Div2=Div1*(1+g) =0.65*(1.12)=$0.728
Div3=Div2*(1+g) =0.728*(1.12)=$0.8154
Div4=Div3*(1+g) =0.8154*(1.12)=$0.9132
Div5=Div4*(1+g) =0.9132*(1.12)=$1.0228
Div6 1.0228( 1.02 )
P5 $17.3876
rE g 0.08 0.02
Div1 Div2 Div3 Div4 Div5 P5
P0
( 1 rE )1 ( 1 rE )2 ( 1 rE )3 ( 1 rE )4 ( 1 rE )5
0.65 0.728 0.8154 0.9132 1.0228 17.3876
P0 1
2
3
4
( 1.08 ) ( 1.08 ) ( 1.08 ) ( 1.08 ) ( 1.08 )5
P0 $15.07
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16.
Highline Corporation has just paid an annual dividend of $0.96.
Analysts are predicting an 11% per year growth rate in earnings over the next five years.
After that, Highline’s earnings are expected to grow at the current industry average of 5.2%
per year.
If Highline’s equity cost of capital is 8.5% per year and its dividend payout ratio remains
constant, for what price does the dividend- discount model predict Highline shares should sell?
$0.96 1.0656 1.1828 1.3129 1.4573 1.6176 1.6176(1.052) 1.6176(1.052)2
|__g=11%_|__g=11%_|_g=11%_|_g=11%__|__g=11%__|___g=5.2%__|__g=5.2%__|_________......
1 2 3 4 5 6 7
P5=Div6/(rE‐g)
Div0=$0.96
Div1= Div0*(1+g)=$0.96*(1.11)=$1.0656
Div2=Div1*(1+g) =1.0656*(1.11)=$1.1828
Div3=Div2*(1+g) =1.1828*(1.11)=$1.3129
Div4=Div3*(1+g) =1.3129*(1.11)=$1.4573
Div5=Div4*(1+g) =1.4573*(1.11)=$1.6176
Div6 1.6176( 1.052 )
P5 $51.5671
rE g 0.085 0.052
Div1 Div2 Div3 Div4 Div5 P5
P0
( 1 rE )1 ( 1 rE )2 ( 1 rE )3 ( 1 rE )4 ( 1 rE )5
1.0656 1.1828 1.3129 1.4573 1.6176 51.5671
P0
( 1.085 )1 ( 1.085 )2 ( 1.085 )3 ( 1.085 )4 ( 1.085 )5
P0 $39.44
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19. AFW Industries has 200 million shares outstanding and expects earnings at the end of this year of
700 million. AFW plans to pay out 60% of its earnings in total, paying 40% as a dividend and using
20% to repurchase shares. If AFW’s earnings are expected to grow by 8% per year and these payout
rates remain constant, determine AFW’s share price assuming an equity cost of capital of 12%.
With constant payout rates, earnings growth equals payout growth. Using the total payout
model, we can value AFW’s equity using the growing perpetuity formula.
Total payouts1 = $700 million (0.60) = $420 million.
420 million
PV $10,500 million $10.5 billion
0.12 0.08
AFW has 200 million shares outstanding, so the price per share is $10,500,000,000/200,000,000 =
$52.50.
Holding the payout ratio constant, the earnings growth rate implies the same payout growth rate. Given
the total expected payout over time, the current price per share should be $52.50.
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