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 7%. 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 20% the following year, after which growth should return to the 4% industry average. If the last dividend paid (D0) was $2, what is the value per share of your firm's stock? Round your answer to the nearest cent. Do not round your intermediate computations.

Answer 1

Step-1, Calculation of the Required Rate of Return (Ke)

Required Rate of Return = Dividend yield + Growth rate

= 7.00% + 4.00%

= 11.00%

Step-2, Dividend for the next 2 years

Dividend in Year 0 (D0) = $2.00 per share

Dividend in Year 1 (D1) = $3.00 per share [$2.00 x 150%]

Dividend in Year 2 (D2) = $3.60 per share [$3.00 x 120%]

Step-3, Share Price in Year 2 (P2)

Dividend in Year 2 (D2) = $3.60 per share

Dividend Growth Rate after Year 2 (g) = 4.00% per year

Required Rate of Return (Ke) = 11.00%

Share Price in Year 2 (P2) = D2(1 + g) / (Ke – g)

= $3.60(1 + 0.04) / (0.11 – 0.04)

= $3.7440 / 0.07

= $53.49 per share

Step-4, The Current Stock Price

As per Dividend Discount Model, Current Stock Price the aggregate of the Present Value of the future dividend payments and the present value the share price in year 2

Year	Cash flow ($)	Present Value Factor (PVF) at 11.00%	Present Value of cash flows ($) [Cash flows x PVF]
1	3.00	0.900901	2.70
2	3.60	0.811622	2.92
2	53.49	0.811622	43.41
TOTAL			49.03

“Hence, the value per share of your firm's stock will be $49.03”

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.