Answer:
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%
Step-by-step 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%