Question

Problems 9-11 are based on the following information: Consider a stock that will pay a $2 dividend per year for 10 years (from t=1 till t=10) after which the dividends are expect to increase at the constant growth rate of 3% per year (so, at=11 the dividend will be 2*1.03=$2.06, at t=12 it will be 2.06*1.03, etc. ) and the required return on the stock is 11%

Problem 9: Find the stock price today.

Problem 10: Find the capital gain yield during the first year:

Problem 11: Find the dividend yield during the 15th year

Answer 1

Solution:-

(9)

Stock price today= Present value of dividends for first 10 years + present value of terminal value

Present value of dividends for first 10 years= $2*cummulative present value factor @11% for 10 years

Cummulative present value factor @11% for 10 years= [1/(1+11%)] + [1/(1+11%)2] + [1/(1+11%)3] + [1/(1+11%)4]+........+ [1/(1+11%)10] = 5.889

Present value of dividends for first 10 years= $2*5.889 = $11.78

Present value of terminal value= Terminal value at the end of 10th year*[1/(1+11%)10] = [$2*(1+3%)/(11%-3%)]*[1/(1+11%)10] = $9.07

Therefore,

Stock price today= $11.78 + $9.07 = $20.85

(10)

Stock price one year from today= Present value (at year 1) of dividends for reamining 9 years + present value (at year 1) of terminal value

Present value (at year 1) of dividends for remaining 9 years= $2*cummulative present value factor @11% for 9 years = $2*5.537= $11.07

Present value (at year 1) of terminal value= Terminal value at the end of 10th year*[1/(1+11%)9] = [$2*(1+3%)/(11%-3%)]*[1/(1+11%)9] = $10.07

Stock price one year from today= $11.07 + $10.07 = $21.14

Capital gain yield for year 1= (Stock price one year from today - stock price today)/Stock price today= (21.14-20.85)/20.85 = 1.4%

(11)

Dividend yield during 15th year= (Expected dividend for year 15/Price at the beginning of year 15)*100

Expected dividend for year 15= $2*(1+3%)5 = $2.32

Price at the beginning of year 15= Expected dividend for the year/(Ke-growth rate) = 2.32/(11%-3%)= $29

Therefore,

Dividend yield during 15th year= (2.32/29)*100= 8%