Question

Nonconstant Growth Stock Valuation Assume that the average firm in your company's industry is expected to grow at a constant rate of 7% and that its dividend yield is 5%. Your company is about as risky as the average firm in the industry and just paid a dividend (D0) of $2.25. You expect that the growth rate of dividends will be 50% during the first year (g0,1 = 50%) and 20% during the second year (g1,2 = 20%). After Year 2, dividend growth will be constant at 7%. What is the estimated value per share of your firm’s stock? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Calculation of cost of equity(ke):

Let the price of one share in the industry be$100

Hence Dividend shall be $5(i.e.5%of 100)

P₀=D1/ke-g

where P₀=price of share now

D1= divident+growth (i.e.5+7% of 5)

=5.35

ke= cost of equity(required)

g= growth rate

Again

P₀=D1/ke-g

100=5.35/ke-.07

ke-.07=5.35/100

ke=.0535+.07

=.1235 or 12.35%

Calculation of value of share:

D0 is2.25 hence D1 shall be 3.375(2.25*1.5) and D2 shall be4.05(i.e.3.375*1.2) and D3 shall be 4.3335(i.e.4.05*1.07).

Value of share at 2nd year end=D3/ke-g

=4.3335/.1235-.07

=81

Value of share at Period 0 shall be comuted as follows:

A	B	C	D=B*C
Year	Dividend & Share Price	PV factor @12.35%	Present Value
1	3.375	0.890075656	3.00400534
2	4.05+81=85.05	0.792234674	67.37955904
			70.38356438

Hence value of share today shall be 70.3856

Please do not forget to upvote my solution if you like the same.

Feel free to ask any query via comments.

Good Luck!