Question

Consider a stock that plans to pay a dividend in year of 4$. The dividends will increase from that point forward permanently at a rate of 2% per year. The required return is 14%.

a. What is the stock price today, in two years, and in 16 years?

b. What are the dividend yield and capital gains yield for this stock this year, in two years, and in 16 years?

Thank you.

Answer 1

Solution:

(a) Data given Dividend at the year 1 =$4; Dividend Growth Rate= 2% ; Required Return =14%

Price=

Price (Year 0) = Dividend at Year 1/ (Required Rate - Growth Rate)

=$4 / (14%-2%) = $ 33.33

Price (Year 2) = Dividend at Year 3/ (Required Rate - Growth Rate)

=$4.16 / (14%-2%) = $ 34.68

Price (Year 16) = Dividend at Year 17/ (Required Rate - Growth Rate)

=$5.49 / (14%-2%) = $ 45.76

(b) 1) Dividend Yield= Dividend at year end / Present Price

Dividend Yield (Year 0) = Dividend at Year 1 / Price Year 0

=$4 / $ 33.33 = 12%

Dividend Yield (Year 2) = Dividend at Year 3 / Price Year 2

=$4.16 / $ 34.68 = 12%

Dividend Yield (Year 16) = Dividend at Year 17 / Price Year 16

=$5.49 / $ 45.76 = 12%

(b) 2) Capital Gain Yield= (Price at Particular Year -Price at Year 0) / Price at Year 0

Capital Gain Yield (Year 0)= (Price at Year End -Price at Year 0) / Price at Year 0

=$(34-33.33) / $ 33.33 = 2%

Capital Gain Yield (Year 2)= (Price at Year 2 -Price at Year 0) / Price at Year 0

=$(34.68-33.33) / $ 33.33 = 4.05 %

Capital Gain Yield (Year 16)= (Price at Year 16 -Price at Year 0) / Price at Year 0

=$(45.76-33.33) / $ 33.33 = 37.30%

Working Notes:

Calculation of Price and Dividend
Year	Price	Dividend
0	$               33.33
1	$               34.00	$                      4.00
2	$               34.68	$                      4.08
3	$               35.37	$                      4.16
4	$               36.08	$                      4.24
5	$               36.80	$                      4.33
6	$               37.54	$                      4.42
7	$               38.29	$                      4.50
8	$               39.06	$                      4.59
9	$               39.84	$                      4.69
10	$               40.63	$                      4.78
11	$               41.45	$                      4.88
12	$               42.27	$                      4.97
13	$               43.12	$                      5.07
14	$               43.98	$                      5.17
15	$               44.86	$                      5.28
16	$               45.76	$                      5.38
17		$                      5.49