Question

Carnes Cosmetics Co.'s stock price is $74.30, and it recently paid a $2.25 dividend. This dividend is expected to grow by 28% for the next 3 years, then grow forever at a constant rate, g; and rs = 13%. At what constant rate is the stock expected to grow after Year 3? Round your answer to two decimal places. Do not round your intermediate calculations.

Answer 1

D1= D0(1+g)

    = 2.25(1+.28)

    = 2.88

D2: 2.88 (1+.28)= 3.6864

D3 : 3.6864 (1+.28)= 4.718592

current stock price : [PVF 13%,1*D1]+[PVF13%,2*D2]+[PVF13%,3*D3]+[PVF13%,3*Terminal value]

74.30 = [.88496*2.88]+[.78315*3.6864]+[.69305*4.718592]+[.69305*terminal Value]

74.30 = 2.5487+ 2.8870+ 3.2702+ .69305TV

74.30 = 8.7059 +.69305TV

TV = [74.30-8.7059]/.69305

     = 94.64555

Terminal value =D3(1+g)/(Rs-g)

94.64555= 4.718592(1+g)/(.13-g)

94.64555/4.718592 = (1+g)/(.13-g)

20.0580 (.13-g) = (1+g)

   2.60754-20.0580g= 1+g

      2.60754-1 = g+20.0580 g

      1.60754 = 21.0580 g

       g = 1.60754 /21.0580

            = .0763 or 7.63%

constant growth afteryear3 = 7.63%