Accounting - Stock dividend question?

Question

A stock just paid a dividend of $2.00. Due to the introduction of a proprietary product, the dividend growth rate is expected to be 30 percent for the next two years, 15 percent for years 3 and 4, and then return to a constant growth rate assumption of 4 percent, thereafter. The required return on the stock is 18 percent.

Does anyone know any of the following:

(a) What is the current expected price of stock

(b) What is the expected price of the stock at Year 6

Answer 1

a) This question assumes a "Dividend Discount Model" (DDM). DDM discounts the dividend cash flows back at its present value.

NPV = CF1/(1+r)^1 + CF2/(1+r)^2 ... + perpetuity/(1+r)^n

CF0 = $2.00
PV(CF1) = ($2.00 x 1.30)/(1+r) = $2.60/(100%+18%) = $2.2034
PV(CF2) = ($2.60 x 1.30)/(1+r)^2 = $3.38/1.3924
PV(CF3) = ($3.38 x 1.15 )/ (1+r)^3= $3.887/1.643032
PV(CF4) = ($3.387 x 1.15) / (1+r)^4= $4.47005/1.938778
Perpetuity = coupon/(r-g)
coupon = $4.47005 x 1.04 = $4.648852
r = 18%
g = 4%
Perpetuity = $33.20608571
PV(Perpetuity) = $33.20608571 / (1+r)^5 = $14.51469


PV of all that is: $23.81689

b) Assuming you have NOT collected dividends for Year 6, the value is $34.54433 [Year 6 dividends/(r-g)]
Assuming you have collected dividends for Year 6 (which means you want the present value of the perpetuity one year forward is: [CF7/(r-g)]/(100%+r) = $30.43704