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A fast growth share has the first dividend (t=1) of $1.48. Dividends are then expected to...

A fast growth share has the first dividend (t=1) of $1.48. Dividends are then expected to grow at a rate of 6 percent p.a. for a further 2 years. It then will settle to a constant-growth rate of 2.3 percent. . If the required rate of return is 12 percent, what is the current price of the share? (

Expert Solution

D₁ = $ 1.48

D₂ = D₁ x (1+g) = $ 1.48 x 1.06 = $ 1.5688

D₃ = D₂ x (1+g) = $ 1.5688 x 1.06 = $ 1.662928

D₄ = D₃ x (1+g) = $ 1.662928 x 1.023 = $ 1.701175344

Price of share in year 3, P₃ can be computed using dividend discount model as,

P₃ = D₄/(r-g)

r = cost of capital = 12 % or 0.12

g = Constant growth rate of dividends = 2.3 % or 0.023

P₃ = $ 1.701175344/ (0.12 – 0.023)

= $ 1.701175344/ 0.097

= $ 17.5378901443299

Current stock price, P = D₁/ (1+r) + D₂/ (1+r) ² + D₃/ (1+r) ³ + P₃/ (1+r) ³

= $ 1.48/ (1+0.12) + $ 1.5688/ (1+0.12) ² + $ 1.662928/ (1+0.12) ³+ $17.5378901443299/ (1+0.12) ³

= $ 1.48/ (1.12) + $ 1.5688/ (1.12) ² + $ 1.662928/ (1.12) ³ + $ 17.5378901443299/ (1.12) ³

= $ 1.48/ 1.12 + $ 1.5688/ 1.2544 + $ 1.662928/ 1.404928 + $ 17.5378901443299/ 1.404928

= $ 1.32142857142857 + $ 1.25063775510204 + $ 1.18363930393586 + $ 12.4831237930555

= $ 16.23882942352197 or $ 16.24

Current price of each share is $ 16.24

jeff jeffy answered 11 months ago

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