Question

A company just paid a $2 dividend per share. The dividend growth rate is expected to be 10% for each of the next 2 years, after which dividends are expected to grow at a rate of 3% forever. If the company’s required return (r_s) is 11%, what is its current stock price?

Answer 1

This question is based on multiple period dividend discount model.

The company just paid a $2 dividend. This is D0

Calculation of Dividend for Year 1 and 2

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

= $2 * (1+0.10)

= $2 * 1.10

= $2.20

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

= $2.20 * (1+0.10)

= $2.20 * 1.10

= $2.42

Stage 1 - Calculation of Explicit Forecast period

Stage 2- Beyond 2 years

Expected dividend for the 3th year i.e. D3 = D2 * (1+g). Growth rate now is 3%.

= $2.42 * (1 + 0.03)

= $2.42 * 1.03

= $2.4926

Horizon Price i.e. P2 = D3 / (Re-g)

= $2.4926 / (0.11 - 0.03)

= $2.4926 / 0.08

= $31.1575

Present Value of P2 = $31.1575 * 0.8116

= $25.2874

Price of Stock = Stage 1 + Stage 2

= $3.9461 + $25.2874

= $29.2335

The current stock price is $29.2335.

Note - How did we calculate the discounting factors @11%.

Year 1 = 1/1.11

= 0.9009

Year 2 = 0.9009 /1.11

= 0.8116