Question

Variable Growth A fast growing firm recently paid a dividend of $0.50 per share. The dividend is expected to increase at a 20 percent rate for the next 3 years. Afterwards, a more stable 10 percent growth rate can be assumed. If a 12 percent discount rate is appropriate for this stock, what is its value?'

Equation:

Constant growth model = P0 = D0(1+g)

                                                 ________

                                                    I - g

Answer 1

Step-1, Dividend per share for the next 3 years

Dividend in Year 0 (D0) = $0.50 per share

Dividend in Year 1 (D1) = $0.60 per share [$0.50 x 120%]

Dividend in Year 2 (D2) = $0.72 per share [$0.60 x 120%]

Dividend in Year 3 (D3) = $0.8640 per share [$0.72 x 120%]

Step-2, Price of the Stock in 3 years (P3)

Price of the Stock in Year 3 = D3(1 + g) / (Ke – g)

= $0.8640(1 + 0.10) / (0.12 – 0.10)

= $0.9504 / 0.02

= $47.52 per share

Step-3, The Value of the stock today

As per Dividend Discount Model, the fair price of the stock today is the aggregate of the Present Value of the future dividend payments and the present value the share price in year 3

Year	Cash flow ($)	Present Value factor at 12%	Present Value of cash flows ($)
1	0.6000	0.89286	0.54
2	0.7200	0.79719	0.57
3	0.8640	0.71178	0.61
3	47.52	0.71178	33.82
TOTAL			35.55

“Therefore, the value of stock will be $35.55 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.