Question

What is the current price of a stock that will pay a dividend of $4 at the end of Year #1, a dividend of $4.50 at the end of year #2 after which dividends will grow at a constant rate of 3% if you want 12% return?

Answer 1

Step-1 The Dividend per share for the next 2 years

Dividend in Year 1 (D1) = $4.00 per share

Dividend in Year 2 (D2) = $4.50 per share

Step-2, The Calculation of Stock Price for the Year 2 (P2)

Here, we have Dividend per share in year 2 (D2) = $4.50 per share

Dividend Growth Rate (g) = 3.00% per year

Required Rate of Return (Ke) = 12.00%

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

= $4.50(1 + 0.03) / (0.12 – 0.03)

= $4.6350 / 0.09

= $51.50 per share

Step-3, The price of the stock today

As per Dividend Discount Model, the Value of the Stock is the aggregate of the Present Value of the future dividend payments and the present value the stock price for the year 2

Year	Cash flow ($)	Present Value factor at 12.00%	Present Value of cash flows ($)
1	4.00	0.89286	3.57
2	4.50	0.79719	3.59
2	51.50	0.79719	41.06
\TOTAL			48.21

“Hence, the current price of a stock will be $48.21”

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.