Question

(a): The dividends that a firm pays to its stockholders are expected to grow at 3% per quarter for the next four quarters. From t=4 onwards, i.e. from the beginning of the fifth quarter the growth rate in dividends will drop to 1.5% per quarter, and the firm expects to be able to sustain it at this level. Assuming that the market capitalization rate is 2.5% per quarter, work out the price of the firm’s stock assuming that the dividend expected to be paid at t=1, i.e., at the end of the first quarter is $2.25

.(b): Rework your answer assuming that gH, the rate at which the dividends are expected to grow for the first four quarters is 2.5% per quarter.

Answer 1

a]	Price of the stock today is the PV of the expected dividends
	when discounted at the required rate of return of 10%.
	Quarter	Dividend	PVIF at 2.5%	PV at 2.5%
	1	$              2.25	0.97561	$               2.20
	2	$              2.32	0.95181	$               2.21
	3	$              2.39	0.92860	$               2.22
	4	$              2.46	0.90595	$               2.23
	Sum of PV of dividends of years 1 to 4			$               8.84
	Continuing value of dividends at t4 = 2.46*1.015/(0.025-0.015) =			$            249.69
	PV of continuing value = 246.69*0.90595 =			$ 226.21
	Market value of the stock today = 8.84+226.21 =			$ 235.05
b]	Quarter	Dividend	PVIF at 2.5%	PV at 2.5%
	1	$              2.25	0.97561	$               2.20
	2	$              2.31	0.95181	$               2.20
	3	$              2.36	0.92860	$               2.20
	4	$              2.42	0.90595	$               2.20
	Sum of PV of dividends of years 1 to 4			$               8.78
	Continuing value of dividends at t4 = 2.42*1.015/(0.025-0.015) =			$            245.63
	PV of continuing value = 245.63*0.90595 =			$ 222.53
	Market value of the stock today = 8.78+222.53 =			$ 231.31