Question

Assume that the average firm in your company's industry is expected to grow at a constant rate of 5% and that its dividend yield is 8%. Your company is about as risky as the average firm in the industry and just paid a dividend (D0) of $2. You expect that the growth rate of dividends will be 50% during the first year (g0,1 = 50%) and 30% during the second year (g1,2 = 30%). After Year 2, dividend growth will be constant at 5%. What is the estimated value per share of your firm’s stock? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Step-1, Required rate of return on your company's stock

Required rate of return on your company's stock = Dividend Growth Rate + Dividend Yield

= 5.00% + 8.00%

= 13.00%

Step-2, Dividend per share for the next two 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) = $3.90 per share [$3.00 x 130%]

Step-3, Calculation of Stock Price in Year 2 (P2)

Dividend Growth Rate (g) = 5.00% per year

Required Rate of Return (Ke) = 13.00%

Therefore, the Stock Price in Year 2 (P2) = D2(1 + g) / (Ke – g)

= $3.90 (1 + 0.05) / (0.13 – 0.05)

= $4.0950 / 0.08

= $51.19

Step-4, Value per share of the firm’s stock

The Value per share is the present value of future dividend plus the present value of the share price in year 2

Year	Cash flow ($)	Present Value factor at 13%	Present Value of cash flows ($)
1	3.00	0.88496	2.65
2	3.90	0.78315	3.05
2	51.19	0.78315	40.10
TOTAL			$45.80

“Therefore, the estimated value per share of the firm’s stock would be $45.80 per share”

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.