Anderson corp just issued a stock dividend of$2.00 yesterday. the company plans on increasing the dividend by 6% per year for the next 5 years. after which, the dividend will grow at 3% forever. the required rate of return is 10%.

a) calculate the current price of the stock

b) calculate what the price of the stock should be in 1 year

c) calculate the dividend yield and capital gains yield during the first year.

A). The current price of stock=$38.24

B). The price of the stock at year 1=$30.29

C). The dividend yield=7%

D). Capital gains yield=6%

Explanation:

A). Determine the current price of the stock using the formula;

Required rate of return=(expected dividend payment/current stock price)+expected dividend growth rate

where;

Expected dividend payments for years 1-5 is given by the formula;

dividend payment(1+dividend growth rate). Substituting;

year 1=2(1+0.06)=2.12

year 2=2.12(1+0.06)=2.2472

year 3=2.2472(1+0.06)=2.3820

year 4=2.3820(1+0.06)=2.5250

year 5=2.5250(1+0.06)=2.6765

Expected dividend payments after 5 years=2.6765

Current stock price=unknown=C

Expected dividend growth rate=3%=3/100=0.03

Required rate of return=10%=10/100=0.1

replacing;

0.1=(2.6765/C)+0.03

(2.6765/C)=0.1-0.03=0.07

0.07 C=2.6765

C=2.6765/0.07=38.24

The current price of stock=$38.24

B). Price of the stock at 1 year

Using the expression above and substituting the following;

Expected dividend payments after 1 year=2.12

Current stock price=unknown=C

Expected dividend growth rate=3%=3/100=0.03

Required rate of return=10%=10/100=0.1

replacing;

0.1=2.12/C+0.03

2.12/C=0.1-0.03=0.07

0.07 C=2.12

C=2.12/0.07=30.29

The price of the stock at year 1=$30.29

C). The dividend yield is calculated as;

dividend yield=annual dividend/share price

where;

annual dividend=2.12

share price=30.29

replacing;

dividend yield=2.12/30.29=0.07=7%

The dividend yield=7%

D). The Capital gains yield is calculated as;

capital gains yield={(Current price-original price)/original price}×100

Current price at year 1=$30.29

Original price=O

0.1=2/O+0.03

2/O=0.07

O=2/0.07=28.57

Original price=$28.57

Capital gains yield={(30.29-28.57)/28.57}×100=6%

Capital gains yield=6%

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