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Nachman Industries just paid a dividend of D0 = $2.50. Analysts expect the company's dividend to...

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.

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Expert Solution

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


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