Question

Agarwal Technologies was founded 10 years ago. It has been profitable for the last 5 years, but it has needed all of its earnings to support growth and thus has never paid a dividend. Management has indicated that it plans to pay a $0.25 dividend 3 years from today, then to increase it at a relatively rapid rate for 2 years, and then to increase it at a constant rate of 8.00% thereafter. Management's forecast of the future dividend stream, along with the forecasted growth rates, is shown below. Assuming a required return of 11.00%, what is your estimate of the stock's current value? Year 0 1 2 3 4 5 6 Growth rate NA NA NA NA 30.00% 15.00% 8.00% Dividends $0.000 $0.000 $0.000 $0.250 $0.325 $0.374 $0.404 ? a. $9.21 b. $9.29 c. $8.60 d. $10.75 e. $10.50

Answer 1

Stock's current value = PV of high growth phase dividends + PV of stable growth phase dividends

PV of high growth dividends =	D1	+	D2	+	D3	+ ... +	Dn
	(1+r)		(1+r)2		(1+r)3		(1+r)n

Where r is the cost of equity and n is number of years in the high-growth phase.

PV of stable growth dividends 6th year onwards =	1	x	D5 (1 + g)
	(1+ r)5		r – g

Where,
D5 (1+g) is the dividend in the first year of the stable growth phase
r is the cost of equity
g is the constant dividend growth rate

Note: Since the PV calculated is at the end of 5th year (i.e. start of stable growth phase), it must be discounted back 5 years

D1 = $0

D2 = $0

D3 = $0.250

D4 = $0.325 [High growth]

D5 = $0.374 [High growth]

D6 = $0.404 [Constant growth]

PV of high growth dividends = 0.250 (1+0.11)3 + 0.325 (1+0.11)4 + 0.374 (1+0.11)5

PV of high growth dividends = 0.18 + 0.21 + 0.22 = $0.61

PV of stable growth dividends = 1 (1+0.11)5 x 0.374 (1 + 8%) (11% - 8%) PV of stable growth dividends = $7.99 Current Stock Value = $0.61 + $7.99 = $8.60 ---------------------------------------------------------------------------------------------------------