Hi!!
Preferred Stock. Preferred Products has issued preferred stock with an
$8 annual dividend that will be paid in perpetuity.
a. If the discount rate is 12 percent, at what price should the preferred sell?
Preferred stock is basically a perpetuity, it pays the same equal
dividends forever. According to the fundamental theory of value, the
value of a financial asset at any point in time equals the present
value of all future dividends. If all future dividends are the same,
the present value of the dividend stream constitutes a perpetuity.
The present value of a perpetuity is equal to:
PV = C/r
Then the price of a preferred stock is:
Preferred stock Price = Dividend / Discount rate =
= $8 / 0.12 =
= $66.67
b. At what price should the stock sell 1 year from now?
Without changes on the discount rate, the stock price will not change.
c. What is the dividend yield, the capital gains yield, and the
expected rate of return of the stock?
Dividend Yield = Dividend / Price =
= $8 / $66.67 =
= 0.12 or 12%
Capital gains yield is the percentage of the original price that is
accounted for by the price changing. The capital gains yield here is
zero because there will be no capital gains income from the preferred
stock.
Rate of return of the stock = Dividend Yield + Capital gains yield = $0.00
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Stock Values. Integrated Potato Chips paid a $1 per share dividend
yesterday. You expect the dividend to grow steadily at a rate of 4
percent per year.
a. What is the expected dividened in each of the (next?) 3 years?
Define the variables:
Pi = price at year i
P0 = today's price
Di = dividends in period i
r = market required rate of return
g = constant growth rate
Given a growth rate g, the expected dividend in years i is:
Di = D0*(1+g)^i (D0 = $1)
D1 = $1*1.04 = $1.040
D2 = $1*1.04^2 = $1.082
D3 = $1*1.04^3 = $1.125
b. If the discount rate for the stock is 12 percent, at what price will
the stock sell?
P0 = D1 / (r-g) =
= $1.04 / (0.12-0.04) =
= $1.04 / 0.08 =
= $13
c. What is the expected stock price 3 years from now?
Pi = D_(i+1) / (r-g)
and
D_(i+1) = Di*(1+g)
According to this we have that:
D4 = D3*(1+g) =
= $1.125*1.04 =
= $1.17
Then:
P3 = D4 / (r-g) =
= $1.17 / (0.12-0.04) =
= $1.17 / 0.08 =
= $14.62
d. If you buy the stock and plan to hold it for 3 years, what payments
will you receive? What is the present value of those payments? Compare
your answer to (b).
Payments = D1 + D2 + D3 =
= $1.040 + $1.082 + $1.125 =
= $3.247
D1 D2 D3
PV = --------- + ---------- + ---------- =
(1 + r)^1 (1 + r)^2 (1 + r)^3
= $1.04/(1.12) + $1.082/(1.12)^2 + $1.125/(1.12)^3 =
= $2.592
The present value of the first 3 years cover almost the 20% of the
stock value. As farter off in the time is a payment less worth it has
in the present, this is why the 3 first payments cover 1/5 of the
total stock value. It will take more time to comprise another 20% (at
least the next 4 years).
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Constant-Growth Model. Here are data on two stocks, both of which have
discount rates of 15 percent:
Stock A Stock B
Return of Equity (ROE) 15% 10%
Earnings Per Share (EPS) $2.00 $1.50
Dividends Per Share (DPS) $1.00 $1.00
a. What are the dividend payout ratios for each firm?
DPR = DPS / EPS
Stock A:
DPR = $1.00/$2.00 = 0.5 = 50%
Stock B:
DPR = $1.00/$1.50 = 0.6667 = 66.67%
b. What are the expected dividend growth rates for each firm?
g = ROE * Retention rate
The retention rate is one minus the firm?s dividend payout ratio, then:
g = ROE * (1-DPR) =
Stock A:
g = ROE * (1-DPR) =
= 0.15 * 0.5 =
= 0.075
g = 7.5%
Stock B:
g = ROE * (1-DPR) =
= 0.1 * 0.333 =
= 0.0333
g = 3.33%
c. What is the proper stock price for each firm?
P = D1 / (r-g) = DPS*(1+g) / (r-g)
Stock A:
P = DPS*(1+g) / (r-g) =
= $1.00*1.075 / (0.15-0.075) =
= $1.075 / 0.075 =
= $14.33
Stock B:
P = DPS*(1+g) / (r-g) =
= $1.00*1.0333 / (0.15-0.0333) =
= $1.0333 / 0.1167 =
= $8.85
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Calculating WACC. Reactive Industries has the following capital
structure. Its corporate tax rate is 35 percent. What is its WACC?
Security Market Value Required Rate of Return
Debt $20 million 6%
Preferred stock $10 million 8%
Common stock $50 million 12%
Total $80 million 100%
To calculate WACC you must multiply the cost of each capital component
by its proportional weight and then sum, the resulted formula is:
WACC = Wd*Kd*(1-Tax) + Ws*Ks + Wp*Kp ;
where:
Wd = weight of debt = $20m/$80m = 0.250 or 25%
Ws = weight of common stocks = $50m/$80m = 0.625 or 62.5%
Wp = weight of preferred stocks = $10m/$80m = 0.125 or 12.5%
Kd = cost of debt
Ks = cost of common stocks
Kp = cost of preferred stocks
WACC is:
WACC = 0.250*0.06*(1-0.35) + 0.625*0.12 + 0.125*0.08 =
= 0,00975 + 0,075 + 0.01 =
= 0,09475 or 9.475%
The WACC is 9.475% .
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I hope that this helps you. feel free to request for a clarification
if you need it.
Regards.
livioflores-ga |
