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A stock just paid a dividend of $2.07. The dividend is expected to grow at 27.50%...

A stock just paid a dividend of $2.07. The dividend is expected to grow at 27.50% for three years and then grow at 3.34% thereafter. The required return on the stock is 11.89%. What is the value of the stock?

Expert Solution

This question is based on multiple period dividend discount model.

Calculation of Dividend for Year 1,2 and 3.

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

= $2.07 * (1+0.2750)

= $2.6393

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

= $2.6393 * (1+0.2750)

= $3.3651

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

= $3.3651 * (1+0.2750)

= $4.2905

Stage 1 - Calculation of Explicit Forecast period

Stage 2- Beyond 3 years

Expected dividend for the 4th year i.e. D4 = D3 * (1+g). Growth rate now is 3.34%.

= $4.2905 * (1 + 0.0334)

= $4.2905 * 1.0334

= $4.4338

Horizon Price i.e. P3 = D4 / Re-g

= 4.4338 / (0.1189 - 0.0334)

= 4.4338 / 0.0855

= $51.8573

Present Value of P3 = $51.8573 * 0.7139

= $37.0226

Value of Stock = Stage 1 + Stage 2

= $8.1097 + $37.02

= $45.1297

Note - How did we calculate the discounting factor @11.89%

Year 1 = 1/1.1189

= 0.8937

Year 2 = 0.8937/1.1189

= 0.7988

Year 3 = 0.7988/1.1189

= 0.7139

Discounting Dividend factor @ Present Year ($) 11.89% Value ($) 2.6393 0.8937 2.3588 23.3651 0.7988) 2.6879 3 4.2905 0.7139 3.0629 8.1097

jeff jeffy answered 1 year ago

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