Question

NU YU announced today that it will begin paying annual dividends. The first dividend will be paid next year in the amount of .57 a share. The following dividends will be .62, .77, and 1.07 a share annually for the following three years. After that, dividends are projected to increase by 3.8 percent per year. How much are you willing to pay today to buy one share of this stock if your desired rated of return is 12 percent

Answer 1

Dividend per share for 1st year, D1 = 0.57

Dividend per share for 2nd year, D2 = 0.62

Dividend per share for 3rd year, D3 = 0.77

Dividend per share for 4th year, D4 = 1.07

After 4th year, dividend will increase at a rate of 3.8% per year

growth rate of dividend after 4 years,g = 3.8% = 0.038

required rate of return, R = 12% = 0.12

current price,P = [D1/(1+R)] + [D2/(1+R)²] + [D3/(1+R)³] + [D4/(1+R)⁴] + PV of dividends after 4th year

P = [0.57/1.12] + [0.62/(1.12)²] + [0.77/(1.12)³] + [1.07/(1.12)⁴] + PV of dividends after 4th year

= 0.508928571 + 0.494260204 + 0.54807079 + 0.680004343 +  PV of dividends after 4th year

= 2.231263908 +  PV (present value) of dividends after 4th year

Total value of dividends after 4th year = [D4*(1+g)]/(R-g) = [1.07*(1.038)]/(R-g) = 1.11066/(0.12 - 0.038) = 1.11066/0.082

= 13.54463415

PV of dividends after 4th year = Total value of dividends after 4th year/(1+R)⁴ = 13.54463415/(1.12)⁴

= 13.54463415/1.57351936 = 8.607859868

Current price ,P = 2.231263908 + PV of dividends after 4th year = 2.231263908 + 8.607859868 = 10.83912378

this is the price per share that you will be willing to pay given required rate of return of 12%