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lOMoAR cPSD| 58562220 January
FUNDAMENTAL OF FINANCIAL MANAGEMENT 1, 2015 TUTORIAL: STOCKS
1. Textbook Chapter 7: 2, 3, 11, 13, 14, 15, 17, 19, 20, 21 p.217
2. The Jackson–Timberlake Wardrobe Co. just paid a dividend of $1.95 per share on its
stock. The dividends are expected to grow at a constant rate of 6 percent per year
indefinitely. If investors require an 11 percent return on The Jackson– Timberlake
Wardrobe Co. stock, what is the current price? What will the price be in three years? In 15 years? Solution:
The price of the stock today is:
P0 = D0 (1 + g) / (R – g) = $1.95 (1.06) / (.11 – .06) = $41.34 The
price of the stock in 3 years is:
P3 = D3 (1 + g) / (R – g) = D0 (1 + g)4 / (R – g) = $1.95 (1.06)4 / (.11 – .06) = $49.24
The price of the stock in 15 years is:
P15 = D15 (1 + g) / (R – g) = D0 (1 + g)16 / (R – g) = $1.95 (1.06)16 / (.11 – .06) = $99.07
3. The next dividend payment by Hot Wings, Inc., will be $2.10 per share. The dividends
are anticipated to maintain a 5 percent growth rate forever. If the stock currently sells
for $48 per share, what is the required return? Solution:
R = (D1 / P0) + g = ($2.10 / $48.00) + .05 = .0938 or 9.38%
4. Teder Corporation stock currently sells for $64 per share. The market requires a 10
percent return on the firm’s stock. If the company maintains a constant 4.5 percent
growth rate in dividends, what was the most recent dividend per share paid on the stock? Solution:
Using the constant dividend growth model, we get:
P0 = $64 = D0 (1 + g) / (R – g)
Solving this equation for the dividend gives us:
D0 = $64(.10 – .045) / (1.045) = $3.37
5. Antiques R Us is a mature manufacturing firm. The company just paid a $10.46
dividend, but management expects to reduce the payout by 4 percent per year
indefinitely. If you require an 11.5 percent return on this stock, what will you pay for a share today? Solution:
The price of the stock today will be:
P0 = D0 (1 + g) / (R – g)
P0 = $10.46(1 – .04) / [(.115 – (–.04)] = $64.78 lOMoAR cPSD| 58562220 January
FUNDAMENTAL OF FINANCIAL MANAGEMENT 1, 2015
6. Consider the following three stocks:
a) Stock A is expected to provide a dividend of $10 a share forever.
b) Stock B is expected to pay a dividend of $5 next year. Thereafter, dividend growth
is expected to be 4% a year forever.
c) Stock C is expected to pay a dividend of $5 next year. Thereafter, dividend growth
is expected to be 20% a year for five years (i.e., until year 6) and zero thereafter.
If the required rate of return for each stock is 10%, which stock is the most valuable?
What if the required rate of return is 7%? Solution: PA DIV1 $10 $100.00 r 0.10 PB DIV1 $5 $83.33 r g 0.10 0.04
PC DIV11 DIV22 DIV33 DIV44 DIV55 DIV66 DIV7 1 6 1.10 1.10 1.10 1.10 1.10 1.10 0.10 1.10
Or PC 5.001 6.002 7.203 8.644 10.375 12.446 12.44 1 6 $104.50 1.10 1.10 1.10 1.10 1.10 1.10 0.10 1.10
At a required rate of return of 10%, Stock C is the most valuable.
For a required rate of return of 7%, the calculations are similar. The results are: PA = $142.86 PB = $166.67 PC = $156.48
Therefore, Stock B is the most valuable.
7. Mexican Motors stock sells for 200 pesos per share and next year’s dividend is 8.5
pesos. Security analysts are forecasting earnings growth of 7.5% per year for the next five years.
a) Assume that earnings and dividends are expected to grow at 7.5% in perpetuity.
What rate of return are investors expecting? lOMoAR cPSD| 58562220 January
FUNDAMENTAL OF FINANCIAL MANAGEMENT 1, 2015
b) Mexican Motors has generally earned about 12% on book equity (ROE = 0.12) and
paid out 50% of earnings as dividends. Suppose it maintains the same ROE and
payout ratio in the long-run future. What is the implication for g? For r? Should you
revise your answer to part (a) of this question? Solution: a. r DIV1 g 8.5 0.075 0.1175 11.75% P0 200
b. g = Plowback ratio × ROE = (1 − 0.5) × 0.12 = 0.06 = 6.0%
The stated payout ratio and ROE are inconsistent with the security analysts’
forecasts. With g = 6.0% (and assuming r remains at 11.75%) then:
P0 DIV1 8.5 147.83 pesos r g 0.1175 -0.06
8. Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the
stock over the next nine years because the firm needs to plow back its earnings to
fuel growth. The company will pay a $10 per share dividend in 10 years and wil
increase the dividend by 5 percent per year thereafter. If the required return on this
stock is 14 percent, what is the current share price? Solution:
The price of the stock in Year 9 will be:
P9 = D10 / (R – g) = $10.00 / (.14 – .05) = $111.11 The
price of the stock today will be: P0 = $111.11 / 1.149 = $34.17
9. Far Side Corporation is expected to pay the following dividends over the next four
years: $11, $8, $5, and $2. Afterward, the company pledges to maintain a constant 5
percent growth rate in dividends forever. If the required return on the stock is 12
percent, what is the current share price? Solution:
The price of the stock in Year 4 is:
P4 = D4 (1 + g) / (R – g) = $2.00(1.05) / (.12 – .05) = $30.00 The
price of the stock today will be: lOMoAR cPSD| 58562220 January
FUNDAMENTAL OF FINANCIAL MANAGEMENT 1, 2015
P0 = $11.00 / 1.11 + $8.00 / 1.112 + $5.00 / 1.113 + $2.00 / 1.114 + $30.00 / 1.114 = $40.09
10. Chartreuse County Choppers Inc. is experiencing rapid growth. The company expects
dividends to grow at 25 percent per year for the next 11 years before leveling off at 6
percent into perpetuity. The required return on the company’s stock is 12 percent. If
the dividend per share just paid was $1.74, what is the stock price? Solution:
Using the two-stage dividend growth model for this problem, we have: ( ) ( ) ( ) * ( )+ ( ) Or [ ( ) ]
11. Storico Co. just paid a dividend of $2.45 per share. The company will increase its
dividend by 20 percent next year and will then reduce its dividend growth rate by 5
percentage points per year until it reaches the industry average of 5 percent dividend
growth, after which the company will keep a constant growth rate forever. If the
required return on Storico stock is 11 percent, what will a share of stock sell for today? Solution: The price in Year 3 will be:
P3 = $2.45(1.20)(1.15)(1.10)(1.05) / (.11 – .05) = $65.08 The
price of the stock today will be: ( ) ( )( ) ( )( )( ) ( ) ( )
12. JAH Ltd does not currently pay a dividend, but you expect that it will begin paying
$0.50 per share dividend at the end of year 2. The dividend is expected to grow at
20% per year for 3 years, and then slow to a sustained growth rate of 4% per year
thereafter. The market opportunity rate for investor in JAH shares is 13% p.a. What is
the price per share today that you expect JAH shares to sell at? Solution:
The price of JAH stock in year 5 will be: lOMoAR cPSD| 58562220 January
FUNDAMENTAL OF FINANCIAL MANAGEMENT 1, 2015 ( ) ( )
The price of JAH stock today is: ( ) ( ) ( ) ( ) ( ) ( ) ( )
13. Eva Corp. is experiencing rapid growth. Dividends are expected to grow at 25 percent
per year during the next three years, 15 percent over the following year, and then 8
percent per year indefinitely. The required return on this stock is 13 percent, and the
stock currently sells for $76 per share. What is the projected dividend for the coming year? Solution:
The dividend in Year 3 will be: D3
= D0 (1 + g1)3 = D0 (1.25)3 The dividend in Year 4 will be:
D4 = D0 (1 + g1)3 (1 + g2) = D0 (1.25)3 (1.15)
The stock begins constant growth in Year 4, so the price of the stock in Year 4 is:
P4 = D4 (1 + g3) / (R – g)
Now we substitute the previous dividend in Year 4 into the price of stock in Year 4 as follows:
P4 = D0 (1 + g1)3 (1 + g2) (1 + g3) / (R – g)
P4 = D0 (1.25)3 (1.15) (1.08) / (.13 – .08) = 48.52D0 The stock price today is: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
We can factor out D0 in the equation, and combine the last two terms. Doing so, we get: lOMoAR cPSD| 58562220 January
FUNDAMENTAL OF FINANCIAL MANAGEMENT 1, 2015 ( )
Reducing the equation even further by solving all of the terms in the braces, we get: $76 = $34.79D0 So D0 = $76 / $34.79 = $2.18
This is the dividend today, so the projected dividend for the next year will be: D1 = $2.18(1.25) = $2.73
14. Great Pumpkin Farms just paid a dividend of $3.50 on its stock. The growth rate in
dividends is expected to be a constant 5 percent per year indefinitely. Investors require
a 14 percent return on the stock for the first three years, a 12 percent return for the
next three years, and a 10 percent return thereafter. What is the current share price? Solution:
The price of the stock in Year 6 will be: ( ) ( )
Next, we need to find the price of the stock in Year 3 since the required return changes
at that time. The price of the stock in Year 3 is: ( ) ( )
Finally, the price of the stock today is: ( ) ( )
15. It is now 31 December, 2014. Wayne-Martin Electric Inc. (WME) has just developed
a solar panel capable of generating 200% more electricity than any solar panel
currently on the market. As a result, you expect that WME will experience a 20%
annual growth rate of earnings for the next 2 years and 15% for the subsequent 3
years. By the end of 5 years, you believe that other firms will have developed
comparable technology, and WME’s growth rate will slow to 5% per year indefinitely. lOMoAR cPSD| 58562220 January
FUNDAMENTAL OF FINANCIAL MANAGEMENT 1, 2015
You estimate that the required return on the WME’s shares is 12%. WME just reported
its annual earnings of $10.00 per share. WME follows a policy of maintaining constant
dividend payout ratio of 20% and pays dividends on the last day of each year based on reported earnings.
a) What is WME’s dividend per share for 2014?
b) Using a dividend growth model, estimate the value of one WME share today. Solution: Year Earnings Dividend 0 $10 $10 0.2 = $2 1 $10 1.2 = $12 $12 0.2 = $2.4 2 $10 1.22 = $14.4 $14.4 0.2 = $2.88 3 $14.4 1.15 = $16.56 $16.56 0.2 = $3.312 4 $14.4 1.152 = $19.044 $19.044 0.2 = $3.81 5
$14.4 1.153 = $21.9006 $21.9006 0.2 = $4.38 6 $21.9006 1.05 = $23 $23 0.2 = $4.6
The price of WME stock in year 6 is:
The price of WME stock today is: ( ) ( ) ( ) ( )