Question

A company intends to pay a $1 dividend at the end of each of the next 3 years. After which it expects its dividends to increase by 3% per year forever. The required return on the company’s equity is 7%. What is the current price?

Answer 1

Calculation of Share Price

Since dividend for the 1^St 3years is constant and after 3years there is growth of dividend (i.e. increase in dividend by 3% each year).

Price of share = Present value of dividend for the 1^St 3years + Present value of dividend after 3years

1. Value of divided for 1^St 3years

Year	Dividend	present value factor @ 7%	Present value
1	$       1.00	0.9346	$       0.93
2	$       1.00	0.9074	$       0.91
3	$       1.00	0.8809	$       0.88
Total			$       2.72

2) Present value of dividend after 3years

   Formula for calculating present value of dividend in case of growth = D1/ (Re – g)

D1 = Dividend of last year + growth (1 + (1*.03) = 1.03)

Re = required rate of return of the company (i.e. 7%)

G = Growth Rate (i.e. 3%)

There for Present value of dividend after 3years = 1.03/ (.07-.03)

                                                                                    =          1.03/.04

                                                                                    =          $25.75

Since this dividends with growth will be received for end of 4^th year onwards, above present of 25.75 is present value at the end of 4^th year so we need to calculated present value as on today (i.e. year 0) = $25.75/(1.07)⁴

                                                        =$25.75/0.7628        

                                                =$19.64

Price of share = Present value of dividend for the 1^St 3years + Present value of dividend after 3years

                        =$2.72+$19.64

                      =$22.36