No clue how to do these couple problems. any help would be appreciated. thanks.
ID: 1171558 • Letter: N
Question
No clue how to do these couple problems. any help would be appreciated. thanks.
Stana, Inc., has preferred stock outstanding that sells for $102.63 per share. If the required return is 4.11 percent, what is the annual dividend?
There is a zero coupon bond that sells for $331.08 and has a par value of $1,000. If the bond has 22 years to maturity, what is the yield to maturity? Assume semiannual compounding.
Santa Klaus Toys just paid a dividend of $2.80 per share. The required return is 11.1 percent and the perpetual dividend growth rate is 3.7 percent. What price should this stock sell for five years from today?
Explanation / Answer
Solution:-
a) Calculation of current dividend of preferred stock .
The current price of preferred stock is calculated by formula:-
Price of preferred stock = Annual dividend/ Required return
$102.63= Annual dividend/4.11%
Annual dividend =$102.63*4.11%= $4.22
Hence the annual dividend of preferred stock = $4.22.
b) Calculation of YTM of zero coupon bond
Current price of bond = $331.08
Par value of bond = $1000
Years to maturity = 22 years
No of semiannual periods = 22*2= 44
We can simply find the semiannual YTM of zero coupon bond by following equation.
$331.08*(1+R)44=1000
(1+R)44=1000/331.08
R=( 3.020418)(1/44)
R= 2.5441%
This is semiannual YTM , hence the annual YTM = 2*2.5441%
=5.0882%
Hence the YTM of the bond= 5.08%
c) Calculation of share price 5 years from now
Dividend at year 1(DPS1)= Current dividend*(1+growth rate) =2.80*(1+0.037)=$2.9036
Dividend at year 2(DPS2)=DPS2*(1+g)= 2.9036*1.037=$3.0110332
Dividend at year 3(DPS2)=DPS2*1.037=3.011*1.037= $3.12244
DPS4= DPS3*1.037= 3.12244*1.037=$3.23797
DPS5=DPS4*1.037=3.23797*1.037=$3.3577767
DPS6= DPS5*1.037=3.3577767*1.037=$3.4820145
Using DDM,
Price of stock at in five years = DPS6/(RR-g)
= 3.4820144/(11.1%-3.7%)
=$47.05
Hence the price of stock in five years = $47.05
Note:- The price of stock depends upon future inflows not on the past inflows.
Please feel free to ask if you have any query in the comment section.