Did I answer this question correctly:
The average firm in your company's industry grows at a constant
rate of 6% and the dividend yield is 7%. Your company is about as risky as the average firm in the industry, however, due to recent innovations, earnings and dividends for the next two years, are expected to grow at 50% and 25%, respectfully. After two years, growth is expected to settle down to the industry average of 6%. The current dividend is $1. What is the current share price of the firm's stock?
Do (dividend per year) = $1.00
G (growth rate year 1) = 50 %
G2 (growth rate year 2) = 25 %
Gn (growth rate after year 2) = 6 %
B (beta) =
Krf (risk-free return) =
RPm (market risk premium) =
Po (value of stock) =
Steps:
a. Calculate the dividends expected at the end of each year during the supernormal growth period. Calculate the dividends:
Do = $1.00
D1 = Do (1 + g) = $1.00 (1 + 0.50) = $1.00 (1.50) = $1.50
D2 = D1 (1 + g) = $1.50 (1 + 0.25) = $1.50 (1.25) = $1.875
D3 = D2 (1 + g) = $1.875 (1 + .06) = $1.875 (1.06) = $1.9875
G = 50% G = 25% G=6% G=6%
0 1 2 3
Do = 1.00 D1 = 1.50 D2 = 1.875 D3 = 1.9875
b. The price of stock is the PV of dividends from time 1 to infinity, so in
theory we could project each future dividend, with the normal growth rate, gn = 6% used to calculate D3 = $1.875(1.06) = $1.9875 for use in the formula, then we calculate P3 as follows:
Ks = Krf + (RPm)(bi)
7 % = 1.9875
x
0.07x = 1.9875
x = 28.392857
P = D
Ks – g
= 1.9875 = 28.392857
x – 0.06
= 1.9875 = 28.392857x – 1.7035714
= 1.9875 + 1.7035714 = 28.392857x
= 3.6910714 = 28.392857x
= 0.12999 or 12.99 %
P2 = 1.9875
.1299 - .06
= 1.9875
0.0699
= 28.433476 + 1.9875
= 30.420976
1.50 / (1.1299)^1 = 1.3275511
1.875 / (1.1299)^2 = 1.875 / 1.276674 = 1.4686599
30.420976 / (1.1299)^2 = 30.420976 / 1.276674 = 23.828303
= 1.3275511 + 1.468599 + 23.82303
= 26.624453
The current share price of the firm's stock is $26.62.