Question

Blossom, Inc., is a fast-growing technology company. Management projects rapid growth of 30 percent for the next two years, then a growth rate of 17 percent for the following two years. After that, a constant-growth rate of 8 percent is expected. The firm expects to pay its first dividend of $2.25 a year from now. If dividends will grow at the same rate as the firm and the required rate of return on stocks with similar risk is 15 percent, what is the current value of the stock? (Round all intermediate calculations and final answer to 2 decimal places, e.g. 15.20.)

Answer 1

Step-1, Calculation of Dividend per share for the next 5 years

Dividend in Year 1 (D1) = $2.25 per share

Dividend in Year 2 (D2) = $2.9250 per share [$2.25 x 130%]

Dividend in Year 3 (D3) = $3.8025 per share [$2.9250 x 130%]

Dividend in Year 4 (D4) = $4.4489 per share [$3.9025 x 117%]

Dividend in Year 5 (D5) = $5.2052 per share [$4.4489 x 117%]

Step-2, Calculation of Stock Price for the Year 5

Stock Price for the Year 5 = D5(1 + g) / (Ke – g)

= $5.2052(1 + 0.08) / (0.15 – 0.08)

= $5.6217 / 0.07

= $80.31 per share

Step-3, Value of the Stock

As per Dividend Discount Model, the Value of the Stock is the Present Value of the future dividend payments and the present value the stock price for the year 5

Year	Cash flow ($)	Present Value factor at 15%	Present Value of cash flows ($)
1	2.2500	0.86957	1.96
2	2.9250	0.75614	2.21
3	3.8025	0.65752	2.50
4	4.4489	0.57175	2.54
5	5.2052	0.49718	2.59
5	80.31	0.49718	39.93
TOTAL			51.73

“Hence, the Current Value of the stock = $51.73 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.