No clue how to do these couple problems. any help would be appreciated. thanks.

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.

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