Question

Li’s firm is fast growing. Therefore, it will pay no dividend for the next 5 years. After that, Li’s firm will initiate dividend payment. The first dividend will be $2 (at the end of the 6^th year) and the dividend will grow at a rate of 5% for 10 years. Then the industry starts to stabilize, and Li’s firm will pay $3 forever. If the required rate of return is 10%, calculate the stock price. use the formulas, not excel

Answer 1

Given, Rate of return (r )= 10%

Stock price= PV of dividends expected

This comprise of 2 streams:

(a ): PV of constant dividend ($3 each) for year 17 onwards =

(D₁₇/r)* (PVIF 10%,16)

=(3/0.1)* 0.217629 = $30* 0.217629 = $6.53

(b ): PV of growing annuity for 11 years (dividend of $2 in year 6, to grow by 5% in years 7 through 16)

PV of this stream in at the end of year 5= (P/(r-g))*(1-((1+g)/(1+r))^n

Where

P= first dividend ($2 in year 6)

r = Required rate of return= 10% or 0.1

g= Growth rate= 5% or, 0.05   and

n= Number of dividend payments= 11

Plugging the inputs,

PV in year 5= (2/(0.1-0.05))*(1-((1+0.05)/(1+0.1))^11)

=40*(1- 0.599463511) = 40* 0.400536489 = $16.02

Present value of this stream now= 16.02/(1+10%)^5 = $9.95

Stock price= $6.53 + $9.95 = $16.48