Nonconstant Growth Stock Valuation Assume that the average firm in your company\

Question

Nonconstant Growth Stock Valuation

Assume that the average firm in your company's industry is expected to grow at a constant rate of 4% and that its dividend yield is 5%. Your company is about as risky as the average firm in the industry, but it has just successfully completed some R&D work that leads you to expect that its earnings and dividends will grow at a rate of 50% [D1 = D0(1 + g) = D0(1.50)] this year and 25% the following year, after which growth should return to the 4% industry average. If the last dividend paid (D0) was $3, what is the value per share of your firm's stock? Round your answer to the nearest cent. Do not round your intermediate computations.

Explanation / Answer

Given ,

D0 = $3

G = Y1 = 50 % , Y2 = 25 % & Y3 %

R (Required rate of return) = Dividend Yield + Constant Growth Rate

R = 5 % + 4 % = 9 %

D1 = $ 3 * 1.50 = $ 4.50

D2 = 4.50 * 1.25 = $ 5.625

At constant Growth rate,

D3 = 5.625 * 1.04 = 5.85

So at constant growth Value = D3 /(R - G)

= 5.85/(.09 - 0.4) = 117

Value of Share is the PV of all the future dividends i.e PV of Dd1 + PV iof D2 + PV of D3 & onwards

PV of D1 = 4.50/1.09 = 4.128

PV of D2 = 5.625/(1.09)2 = 4.7345

PV of D3 = 117/(1.09)3= 90.3456

Value of Share = 4.128 + 4.7345 + 90.3456 = $ 99.21

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