Question

Assume you are considering a stock which oddly pays a dividend at the end of each year. Your required rate of return is 8.5%. The expected dividend at the end of year 1 is $5.50. In year 2, the dividend is expected to grow by 11%. The year after that, the dividend is expected to be up 12%. In year 4 and 5 it is expected to grow at 15%. (1) If your holding period for this stock is 5 years, what is the present value of dividends? (2) If stock price is currently $40 and is expected to go to $80 by year 5, what is the present value of the stock from the end of your holding period? (3) If as investor, you only want to purchase stocks when Mr. Market sells them at 60% of intrinsic value, then what is the most you will pay for this stock? Please show your work.

Answer 1

1. Formula to find out present value of dividend= Po= Div1/r-g

Where,

Po=Present value of dividend

Div1=estimated dividend for next year

r=rate of return

g= growth rate

So,

5.50/0.085-0.15=5.50/0.07225=7.61

      2.    D+E/(1+R)^Y

Where,

D is any dividends expected to be paid during the period,

E is the expected stock price,

Y is the number of years down the line, and

R is the real rate of return you estimated.

5.50+80/(1+12)5=1.31 or 13%.

3. Intrinsic Price of Stock = DPS1 / (r - g)

where:

DPS1 = Expected dividends one year from the present

r = The discount rate or required rate of return on the investment

g = The annual growth rate of dividends in perpetuity

7.61860/100=4.566 is the intrinsic value of return