Question

A company is currently paying a dividend of INR 5 per share. The dividend is expected to grow

at a 15 percent rate for three years, then at 10 percent rate for the next three years, after which it is

expected to grow at a 5 percent rate forever. What is the Present Value of the share if the capitalization

rate is 9 percent?

Answer 1

Consider this solution:

Current dividend =INR 5 per share

Growth rate for three year = 15 percent

Growth rate for next three year = 10 percent

Constant growth rate = 5 percent

Required rate of return (r) = 9 percent

$D_1=5\times(1+0.15)=5.75$

$D_2=5.75\times(1+0.15)=6.61$

$D_3=6.61\times(1+0.15)=7.60$

$D_4=7.60\times(1+0.10)=8.36$

$D_5=8.36\times(1+0.10)=9.20$

$D_6=9.20\times(1+0.10)=10.12$

D₆ will grow at a constant growth rate of 5 percent, Hence

$V_5=\frac{10.12}{0.09-0.05}=253$

$V_0=\frac{5.75}{(1.09)}+\frac{6.61}{(1.09)^2}+\frac{7.60}{(1.09)^3}+\frac{8.36}{(1.09)^4}+\frac{9.20}{(1.09)^5}+\frac{253}{(1.09)^5}$

$V_0=5.28+5.56+5.87+5.92+5.98+164.43$

$V_0=193.04$

The Present Value of the share is INR 193.04 per share.