Question

New Gadgets, Inc., currently pays no dividend but is expected to pay its first annual dividend of $5.50 per share exactly 7 years from today. After that, the dividends are expected to grow at 3.5 percent forever. If the required return is 12.5 percent, what is the price of the stock today? $35.17 $61.11 $26.79 $30.14 $49.71

Answer 1

Price of a stock is the present value of all future cash flows receivable from the stock discounted at required rate of return

Future cash flows are dividends and present value of future dividends growing at constant rate

Dividend at the end of 7th year = $5.50

Dividend expected at the end of 8th year

= Dividend of 7th year x (1 + Growth rate)

= $5.5 x 1.035

= $ 5.6925

So, present value of all future dividends receivable at the end of 7th year

= Dividend of 8th year / ( Required rate of return - Growth rate)

= $5.6925 / ( 0.125 - 0.035)

= $63.25

So, value to be received at the end of 7th year

= $5.50 + $63.25

= $68.75

So, present value factor for 7 years

= 1 / ( 1 + Re ) ^ n

Where,

Re = required rate of return = 12.5 %

And n = years = 7

So, present value factor

= 1 / (1.125 ^ 7)

= 1 / 2.28070

= 0.438461

So, value of stock today

= Amount receivable x present value factor

= $68.75 x 0.438461

= $30.14

So, as per above calculations, option D is the correct option