Concept Questions and Exercises
CORPORATE FINANCE 11e by Ross, Westerfield, Jaffe
CHAPTER6
STOCK VALUATION
1. Stock Values Stock Values The next dividend payment by ECY, Inc., will be $2.85 per share. The
dividends are anticipated to maintain a 6 percent growth rate, forever. If ECY stock currently sells for
$58 per share, what is the required return?
Price of the stock = D1/(i-g)
Given, p = 58, D1=2.85, g=0.06
So, i = D1/P + g = 2.85/58+0.06=0.1091379
2. Stock Values For the company in the previous problem, what is the dividend yield? What is the
expected capital gains yield?
R = [D0(1 + g)/P0 ] + g
Dividend Yield = (D1/P0)
Capital Gains Yield = g (this was given)
3. Stock Values Shiller Corporation will pay a $2.75 per share dividend next year. The company
pledges to increase its dividend by 5 percent per year, indefinitely. If you require a return of 11 percent
on your investment, how much will you pay for the company’s stock today?
Price of the stock = D1/(i-g)
P=2.75/(11%-5%)=45.8333
4. Stock Valuation Suppose you know that a company’s stock currently sells for $67 per share and
the required return on the stock is 10.8 percent. You also know that the total return on the stock is
Concept Questions and Exercises
CORPORATE FINANCE 11e by Ross, Westerfield, Jaffe
evenly divided between a capital gains yield and a dividend yield. If it’s the company’s policy to
always maintain a constant growth rate in its dividends, what is the current dividend per share?
We know the stock has a required return of 11.5 percent, and the dividend and capital gains
yield are equal, so:
because R = Dividend yield + Capital gains yield
=> Dividend yield = 1/2(.108)
Dividend yield = .054
Therefor, capital gains yield = .054
Now we know both the dividend yield and capital gains yield. The dividend is simply the stock
price times the dividend yield, so:
D1 = .054($67)
D1 = $3.618
This is the dividend next year. The question asks for the dividend this year. Using the
relationship between the dividend this year and the dividend next year:
D1 = D0(1 + g)
We can solve for the dividend that was just paid:
D0 = $3.618 / 1.054
D0 = $3.43263
5. Growth Rate The newspaper reported last week that Bennington Enterprises earned $29 million
this year. The report also stated that the firm’s return on equity is 17 percent. Bennington retains 80
percent of its earnings. What is the firm’s earnings growth rate? What will next year’s earnings be?
Return on equity (ROE) = 17% or 0.17
Retention ratio ( b) = 0.80
Current earning = $29m
a)
Earnings growth rate = ROE *b
Earnings growth rate = 0.17*0.80= 0.136 or 13.60%
Concept Questions and Exercises
CORPORATE FINANCE 11e by Ross, Westerfield, Jaffe
b)
Next year earnings = Current earnings (1+ growth rate)
Next year earnings = $29m*(1+0.136)= $32.944m
6. Stock Valuation Universal Laser, Inc., just paid a dividend of $3.10 on its stock. The growth rate
in dividends is expected to be a constant 6 percent per year, indefinitely. Investors require a 15 percent
return on the stock for the first three years, a 13 percent return for the next three years, and then an 11
percent return thereafter. What is the current share price for the stock?
Hi, well, the problem here is that we have different discount rates, in other words the required
rate of return for the stock changes several times, therefore we are going to break this problem
Concept Questions and Exercises
CORPORATE FINANCE 11e by Ross, Westerfield, Jaffe
in 3 parts, or bring to present value all the cash flows in 3 steps. Let's start with the value of the
dividends.
We have to use the following formula.
Where, D(n-1) is last dividend and Dn is the dividend that we are looking for, for example, D1
= 3.10*(1+0.06)=3.29, D2=3.29*(1+0.06)=3.48, and so forth. The amount to pay on dividends per
share is,
D1=3.29; D2=3.48; D3=3.69; D4=3.91; D5=4.15; D6=4.40; D(7)=4.66
Since the first 3 years are to be discounted at a 15%, this is how the formula should look like.
Now, for the second part, we have to bring all cash flows to year 3 at r(2)=13% and then bring
it to present value at r(1)=15%. This is because we have 2 different discount rates, this is as
follows.
Finally, we need to bring all the future cash flows from year 7 and beyond, notice that we need
to use the return rate r(3) to bring everything to year 6, then we have to bring it to year 3 and
then to present value, everything as follows.
So, the price of the stock is PV(1) + PV(2) + PV(3), or:
Price= $56.82/share
Best of luck.
7. Nonconstant Growth Metallica bearings inc is a young start up company no dividends will be
paid on the stock over the next 8 years because the firm needs to plow back its earnings to fuel
Concept Questions and Exercises
CORPORATE FINANCE 11e by Ross, Westerfield, Jaffe
growth.The company will then pay a dividend of 16.50 per share 9 years from today and will increase
the dividend by 5.75 percent per year thereafter. the required return on the stock is 13.75 percent.
What is the price of the stock 8 years from today?
What is the current share price?
1)
Price at year 8 = D9 / required rate - growth rate
Price at year 8 = 16.50 / 0.1375 - 0.0575
Price at year 8 = 16.50 / 0.08
Price at year 8 = $206.25
2)
Current share price = Future value / (1 + r)n
Current share price = 206.25 / (1 + 0.1375)8
Current share price = 206.25 / 2.802923
Current share price = $73.58
8. Nonconstant Dividends Bucksnort, Inc., has an odd dividend policy. The company has just paid a
dividend of $10 per share and has announced that it will increase the dividend by $3 per share for
each of the next five years, and then never pay another dividend. If you require an 11 percent return
on the company’s stock, how much will you pay for a share today?
P0 = $13 /1.11 + $16/1.112 + $19/1.113 + $22/1.114 +$25/1.115 = $67.92
9. Differential Growth Dalda Foods is experiencing rapid growth. Dividends are expected to grow
at 30 percent per year during the next three years, 18 percent over the following year, and then 8
Concept Questions and Exercises
CORPORATE FINANCE 11e by Ross, Westerfield, Jaffe
percent per year indefinitely. The required return on this stock is 11 percent, and the stock currently
sells for PKR65 per share. What is the projected dividend for the coming year?
Concept Questions and Exercises
CORPORATE FINANCE 11e by Ross, Westerfield, Jaffe
10. Nonconstant Growth and Quarterly Dividends Pasqually Mineral Water, Inc., will pay a
quarterly dividend per share of $.90 at the end of each of the next 12 quarters. Thereafter, the dividend
will grow at a quarterly rate of 1 percent, forever. The appropriate rate of return on the stock is 10
percent, compounded quarterly. What is the current stock price?
value after 12 qtr= div per share/(rate of return - dividend growth rate) = 0.9/(.1-.01) = $10
current value=2.38/1.1^12=$3.186
11. Stock Valuation and Cash Flows Stock Valuation and Cash Flows Full Boat Manufacturing has
projected sales of $115 million next year. Costs are expected to be $67 million and net investment is
expected to be $12 million. Each of these values is expected to grow at 14 percent the following year, with
the growth rate declining by 2 percent per year until the growth rate reaches 6 per- cent, where it is
Concept Questions and Exercises
CORPORATE FINANCE 11e by Ross, Westerfield, Jaffe
expected to remain indefinitely. There are 5.5 million shares of stock outstanding and investors require a
return of 13 percent on the company's stock. The corporate tax rate is 21 percent. a. What is your estimate
of the current stock price? b. Suppose instead that you estimate the terminal value of the company using a
PE mul- tiple. The industry PE multiple is 11. What is your new estimate of the company's stock price?
12. Nonconstant Growth Storico Co. just paid a dividend of $3.02 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 13 percent, what will a share of stock sell for today?
a. Dividend at 0th time, D0 = 3.02/share
Dividend for next year, D1 = 3.02*(1+20%) = 3.624
Concept Questions and Exercises
CORPORATE FINANCE 11e by Ross, Westerfield, Jaffe
Dividend for year 2,D2 = +3.624*(1+15%) = 4.18
Dividend for year 3, D3 = +4.18*(1+10%) = 4.58
Dividend for year 4, D4 = +4.58*(1+5%) = 4.81
terminal value for all the next years at 4th year, T4 = D4*(1+g)/(r-g), where r is rate of return, 13%, g is
growth rate , 5%
T4 = +4.81*(1+5%)/(13%-5%) = 63.18
discounting all the cash flows to present value at 13%, the share price today is
=3.624/(1+13%)^1 + 4.18/(1+13%)^2+ 4.58/(1+13%)^3 + 4.81/(1+13%)^4 + 63.18/(1+13%)^4 = 68.51