Question

Company X just made a dividend payment of $0.50 per share. Investors expect the dividend to grow by 11% per year in the first two years and then by 3% per year starting in the third year. What's the maximum price investors are willing to pay for Company X's stocks if they require an annual return rate of 13%?

Answer 1

This question is based on multiple period dividend discount model.

The company just paid a $0.50 dividend. This is D0

Re = Required rate of return

g = Growth rate

Calculation of Dividend for Year 1 and 2

For the first two years growth rate is 11%

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

= $0.50 * (1+0.11)

= $0.50 * 1.11

= $0.555

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

= $0.555 * (1+0.11)

= $0.555 * 1.11

= $0.61605

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%.

= $0.97361 * (1 + 0.03)

= $0.97361* 1.03

= $1.00282

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

= $1.00282 / (0.13 - 0.03)

= $1.00282 / 0.10

= $10.0282

Present Value of P2 = $10.0282 * 0.78315

= $7.85358

Price of Stock = Stage 1 + Stage 2

= $0.97361 + $7.85358

= $8.82719

Rounding to two decimal places (if required)

= $8.83

Maximum price the investors will be willing to pay for the stock is $8.83

Note - How did we calculate the discounting factors @13%.

Year 1 = 1/1.13

= 0.88496

Year 2 = 0.88496/1.13

= 0.78315