Question

Help! I cannot get to the answer to this question. can someone please assist? Carnes Cosmetics Co.'s stock price is $46, and it recently paid a $1.00 dividend. This dividend is expected to grow by 29% for the next 3 years, then grow forever at a constant rate, g; and rs = 16%. At what constant rate is the stock expected to grow after Year 3? Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

Answer:-

Given

stock price = $ 46
Dividend (Do) = $ 1.00
Dividend Year 1 (D1) =Do (1+0.29) = $ 1.0 x ( 1.29) = $ 1.29

Dividend year 2 (D2) = $ 1.29 x 1.29 = $ 1.664
Dividend year 3 (D3) = $ 1.664 x 1.29 = $ 2.146

Given

V0 = D1 / 1+rs + D2 / (1+rs)² + D3 / (1+rs)³ + D3 ( 1+g) / (1+rs)³ x (rs - g)
$ 46 = $ 1.29 / 1.16 + $ 1.664 / 1.16² + $ 2.146 / 1.16³ + $ 2.146 ( 1+g) / 1.16³ x (0.16 - g)
$ 46 =  $ 1.11 + $ 1.236 + $ 1.375 + $ 1.375 x ( 1+g) / (0.16 - g)
$ 1.375 x ( 1+g) / (0.16 - g) = $ 46 - $ 3.72
$ 1.375 x ( 1+g) / (0.16 - g) = $ 42.28
( 1+g) / (0.16 - g) = $ 42.28 / $ 1.375
( 1+g) / (0.16 - g) = 30.75
1+g = 30.75 ( 0.16 - g)
1 +g = 4.92 - 30.75 g
g + 30.75 g = 4.92 - 1
31.75 g = 3.92
g = 3.92 / 31.75
g = 0.1235
g = 12.35%