Question

Carnes Cosmetics Co.’s stock price is $55, and it recently paid a $2.00 dividend. This

dividend is expected to grow by 25% for the next 3 years, then grow forever at a constant

rate, g; and rs = 7%. At what constant rate is the stock expected to grow after Year 3?

Answer 1

Here as the growth rate for the stock happens in 2 stages, the appropriate model to be used is the H models per which the value of stock is calculated as:

Stock price V =[ D0 × (1+Gl)/(r-Gl)] +[ D0 ×H0×(Gs-Gl)/(r-Gl)]

Where D0 is the recently declared dividend

GI is the long term growth rate of stock

Gs is the short term growth rate of stock

R is the rate of return expected by investor

H0 is the half life which is the half is the time period for which the short term growth of stock is considered.

Thus to apply the above formula to the question we have,

D0=$2 H=3/2=1.5 R=7% Gs=25% V=$55 Gl=?

55= [ 2×(1+Gl)/(0.07-Gl)]+[2×1.5×(0.25-GI)/(0.07-Gl)]

Rearranging the above equation we get

55(0.07-Gl) = 2+ 2Gl+0.75-3Gl

Thus 56Gl=1.1

Thus Gl= 1.96%

Thus long term growth rate is 2% after rounding off