Question

D0= $2, rs =13%, the growth rate of dividend, gL= 5%

Estimate the intrinsic stock value, (P_0 ) ̂, and then the Dividend Yield (Yd) and Capital Gain Yield (CGY) from above data

Estimate the expected or intrinsic stock price today, (P_0 ) ̂, if non-constant growth of dividend is 30% for year 0 to year 1, 20% for year 1 to year 2, 10% for year 2 to year 3; the growth rate of dividend is constant, gL= 5% after year 3; D0 = $2; Rs =13%.

*please show work and formulas used

Answer 1

intrinsic stock value = D₁/(rs - gL) or Dividend next year/(required rate of return - dividend growth rate)

D₁ = D₀*(1+gL) = $2*(1+0.05) = $2*1.05 = $2.1

intrinsic stock value = $2.1/(0.13 - 0.05) = $2.1/0.08 = $26.25

intrinsic stock price today = D₀*(1+year 1 growth rate)/(1+Rs) + D₁*(1+year 2 growth rate)/(1+Rs)² + D₂*(1+year 3 growth rate)/(1+Rs)³ + [D₃*(1+constant growth rate)/(rs - gL)]/(1+Rs)³

D₁ = $2*(1+0.30) = $2*1.30 = $2.6

D₂ = $2.6*1.20 = $3.12

D₃ = $3.12*1.10 = $3.432

D₄ = $3.432*1.05 = $3.6036

intrinsic stock price today = $2.6/1.13 + $3.12/1.13² + $3.432/1.13³ + [$3.6036/(0.13 - 0.05)]/1.13³

intrinsic stock price today = $2.30 + $3.12/1.2769 + $3.432/1.4429 + ($3.6036/0.05)/1.4429

intrinsic stock price today = $2.30 + $2.44 + $2.38 + $72.072/1.4429

intrinsic stock price today = $2.30 + $2.44 + $2.38 + $49.95 = $57.07

terminal value of $72.072 is discounted only for 3 years because this value we got at the beginning of year 4 or end of year 3. so only 3 year's discounting is needed.