In: Finance
Nachman Industries just paid a dividend of D0 = $2.50. Analysts expect the company's dividend to grow by 30% this year, by 10% in Year 2, and at a constant rate of 5% in Year 3 and thereafter. The required return on this low-risk stock is 9.00%. What is the best estimate of the stock’s current market value? Do not round intermediate calculations.
Let D1, D2, D3 be the expected dividends in the next year years
respectively.
Dn = Dn-1 * (1 + growth rate)
We have D0 = $2.50
Using the formula,
D1 = 2.50 * 1.30 = 3.25
D2 = $3.25 * 1.10 = 3.575
After 2 years dividend will grow at a growth rate of 5%.
So D3 = D2 (1+g)
D3 = $3.575 * 1.05 =3.75375
Let V0 be the stock price today.
R = 9%
g = 5%
As per the multiperiod dividend discount model,
V0 = (D1/(1+R)1) + (D2/(1+R)2) + ……….. + (Dn/(1+R)n) +
(Pn/(1+R)n)
where,
V0 = Value of stock today
Dn = Dividend payment for nth period
Pn = Stock price for nth period from now
R = Required rate of return.
Pn is calculated at [Dn * (1+g)]/R – g
P2 = [D2 * (1+g)]/R – g
P2 = 3.75375/.09 – .05
P2 = 3.75375/.04
P2 = 93.84375
Using the formula
V0 = (D1/(1+R)1) + (D2/(1+R)2) + P2
V0 = ($3.25/(1+0.09)1) + ($3.575/(1+0.09)2) + 93.84375
V0 = ($3.25/1.09) + ($3.575/(1.09)2) + 93.84375
V0 = 2.9817 + 3.0090 + 93.84375
V0 = $99.83445
Stock’s current market value is $99.83445