Question

A common stock is expected to pay no dividends during the next 7 quarters but at the end of 6th quarter, it is expected to pay DPS of $1.0 and thereafter dividends are expected to be paid quarterly and into indefinite future. The quarterly growth rate of dividends stream is 1.0% and it is expected to stay the same into indefinite future. The required expected rate of return on the common stock is 12% per annum.

Find:

(i)The current price per share of the stock.

(ii)The expected price per share at the beginning of the 8th quarter.

Answer 1

Given Information:

No Dividend in 7 quarters. Dividend from Quarter 8 = D₈ = $1 , Growth = 1%, Required return = 12% per annum

Quarterly required return = 12/ 4 = 3%

ii) Calculate the price of the stock at the start of the 8th Quarter or end of Quarter 7.

Price of any security is the present value of future ecoonomic benefits that security is going to generate discounted at required rate of return.

And if there is contant dividend and growth till perpetuity then Gordan growth model is widely used.

Formula =

And if you are calculating stock price at beginning of quarter 8 or end of Quarter 7 then replace P0 with P7 and D1 with D8.

So putting values in formula D8 =1, required return = 3%, Growth 1 %

= 1 / ( 0.03 - 0.01)

= 1 / 0.02

Price os stock at the Beiginning of 8th= 50

i) Calculate the share price today.

Calculate the Pv of the price today i.e. bring that price 7 quarters back. = 50 / (1.03)⁷

Stock price today = 40.6546