NU YU announced today that it will begin paying annual dividends. The first dividend will be paid next year in the amount of $.31 a share. The following dividends will be $.36, $.51, and $.81 a share annually for the following three years, respectively. After that, dividends are projected to increase by 2.5 percent per year. How much are you willing to pay today to buy one share of this stock if your desired rate of return is 10 percent

The dividend discount model (DDM) can be used to calculate the price of the stock today. DDM calculates the price of a stock based on the present value of the expected future dividends from the stock. The formula for price today under DDM is,

P0 = D1 / (1+r) + D2 / (1+r)^2 + ... + Dn / (1+r)^n + [(Dn * (1+g) / (r - g)) / (1+r)^n]

Where,

D1, D2, ... , Dn is the dividend expected in Year 1,2 and so on

g is the constant growth rate in dividends

r is the discount rate or required rate of return

P0 = 0.31 / (1+0.1) + 0.36 * / (1+0.1)^2 + 0.51 / (1+0.1)^3 + 0.81 / (1+0.1)^4 +

[(0.81 * (1+0.025) / (0.1 - 0.025)) / (1+0.1)^4]

P0 = $9.0767092 rounded off to $9.08