Question

Four years ago, Company A distributed a dividend to its shareholders of € 0.3858 per share. Today Company A paid a dividend of 0.80 € per share. In the past, the dividend policy of the company led to an increase in dividends each year at a steady rate. It is expected that the company will continue the same dividend policy for the next three years. Subsequently, the dividend growth rate will remain constant at 8% per annum for the foreseeable future. The current stock market price is 45 €. If investors require a 12% return on investing in equity-risk stocks, would you buy that share?

Answer 1

Growth rate of dividends during last 4 years (g)= [(D0/D-4)^(1/4)]-1

Where D0 = Last Dividend per share (given as €0.80) and D-4 = Dividend 4 years ago (0.3858)

Substituting the values, growth rate= (0.80/0/3858)^(1/4)-1 = 2.073613^(1/4)-1 = 20%

Given that this growth rate will apply for the next 3 years and then will be constant at 8% thereafter, for the foreseeable future.

Current value of the stock, as per Dividend Discount Model is 29.3265 €   as follows:

D 4 D1, D2 and D3 are arrived at from DO applying the growth rates g1, g2 and g3 for the respective years. 5 P3= Price after three years with constant growth rate (perpetual) which is ascertained as follows: 6 P3=D4/(r-g4) Where D4= Dividend for the fourth year which is D3*(1+34) 7 Where g4=constant growth rate after three years. 8 Present Dividend DO 0.80 € (Given value) 9 Growth rate of dividend for year 1 20% (As above) 10 Growth rate of dividend for year 2 20% (As above) 11 Growth rate of dividend for year 3 20% (As above) 12 Constant growth rate after 3 years 8% (Given value) 13 Required rate of return 12% (Given value) 14 Formula Cell reference Values 15 Dividend for year 1 (D1) DO*(1+g1) C8*(1+09) 0.96000000 16 D1/(1+r) D15/(1+C13) 0.85714286 17 Dividend for year 2 (D2) D1*(1+g2) D15*(1+C10) 1.15200000 18 D2/(1+r)^2 D17/(1+C13)^2 0.91836735 19 Dividend for year 3 (D3) D2*(1+g3) D17*(1+C11) 1.38240000 20 D3/(1+r)^3 D19/(1+C13)^3 0.98396501 21 Dividend for year 4 (D4) D3*(1+g4) D19*(1+C12) 1.49299200 22 Price after 3 years (P3) D4/(r-g4) D21/(C13-C12) 37.3248 23 P3/(1+r)^3 D22/(1+C13)^3 26.56705539 24 Current price (PO)=D1/(1+r) + D2/(1+r)^2 +D3/(1+r)^3 + P3/(1+r)^3 D16+D18+D20+D23 29.3265 € 25