Question

Biarritz Corp. is growing quickly. Dividends are expected to grow at a rate of 31 percent for the next three years, with the growth rate falling off to a constant 6.1 percent thereafter. The required return is 12 percent and the company just paid a dividend of $2.80. What are the dividends each year for the next four years? What is the share price in three years? What is the current share price?

Answer 1

This question is based on multiple period dividend discount model.

Calculation of Dividend for Year 1,2 and 3.

For years 1,2 and 3 the growth rate is 31%

Step 1- Calculation of dividends

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

= $2.80 * (1+0.31)

= $2.80 * 1.31

= $3.668

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

= $3.668 * (1+0.31)

= $3.668 * 1.31

= $4.80508

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

= $4.80508 * (1+0.31)

= $4.80508 * 1.31

= $6.2946548

After year 3 the growth rate will fall to 6.1%.

Dividend for Year 4 - D3*(1+g)

= $6.2946548 * (1+0.061)

= $6.2946548 * 1.061

= $6.6786287428

Step 2 - Explicit forecast period (First three years)

Years Discounting Dividend ($) factor @ 12% Present Value ($) 3.668 0.8928571429 3.275000000 1 2 4.80508 0.7971938776 3.830580357 3 6.2946548 0.7117802478 4.480410953 11.58599131

Step 3 - Horizon value

Beyond 3 years (The growth rate is now 6.1%)

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

=$6.6786287428 / (0.12 - 0.061)

= $6.6786287428 / 0.059

= $113.197097335

Rounding to two decimal places (if required)

= $113.20

This is the share price in three years

Calculation of Current share price

Present Value of P3 = $113.197097335 * 0.7117802478

= $80.5714579913

Current share price = Step 2 + Stage 3

= $11.58599131 + $80.5714579913

= $92.1574493013

Rounding to two decimal places (if required)

= $92.16

This is the current share price.

Note - How did we calculate the discounting factors @12%

Year 1 = 1/1.12

= 0.89285714285

Year 2 = 0.89285714285 /1.12

= 0.7971938776

Year 3 = 0.7971938776 /1.12

= 0.7117802478

Intermediate calculations are not rounded off in the solution above.