Question

Consider a firm that has just paid a dividend of $3. An analyst expects dividends to grow at a rate of 8 percent per year for the next five years. After that, dividends are expected to grow at a normal rate of 1 percent per year. Assume that the appropriate discount rate is 7 percent. What is the price of the stock today?

Answer 1

This question is based on multiple period dividend discount model.

The firm that has just paid a dividend of $3. This is D0.

Calculation of Dividend for Year 1,2,3,4 and 5

Dividend for Year 1 - D0*(1+g)

= $3 * (1+0.08)

= $3 * 1.08

= $3.24

Dividend for Year 2 - D1*(1+g)

= $3.24 * (1+0.08)

= $3.24 * 1.08

= $3.4992

Dividend for Year 3 - D2*(1+g)

= $3.4992* (1+0.08)

= $3.4992* 1.08

= $3.7791

Dividend for Year 4 – D3*(1+g)

= $3.7791* (1+0.08)

= $3.7791* 1.08

= $4.0814

Dividend for Year 5 – D4*(1+g)

= $4.0814* (1+0.08)

= $4.0814* 1.08

= $4.4079

Stage 1 - Calculation of Explicit Forecast period

Stage 2- Beyond 5 years

Expected dividend for the 6th year i.e. D6 = D5 * (1+g). Growth rate now is 1%.

= $4.4079 * (1 + 0.01)

= $4.4079 * 1.01

= $4.4520

Horizon Price i.e. P5 = D6 / Re-g

= 4.4520 / (0.07 - 0.01)

= 4.4520 / 0.06

= $74.20

Present Value of P5 = $74.20* 0.7130

= $52.9036

Price Stock = Stage 1 + Stage 2

= $15.4257 + $52.9046

= $68.3303

Note - How did we calculate the discounting factors @7%.

Year 1 = 1/1.07

= 0.9346

Year 2 = 0.9346 /1.07

= 0.8734

Year 3 = 0.8734 /1.07

= 0.8163

Year 4 = 0.8163 /1.07

= 0.7629

Year 5 = 0.7629 /1.07

= 0.7130