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What is Multi stage Dividend Discount Model ?



Multi stage growth model: In this model Company provides dividend to its shareholders at high rate in each year. And after some time the rates decreases and later the company provides constant rate of dividend in each year.

Two stage growth model: In this model Company provides dividend to its shareholders at high rate in each year. And after some time company provides constant rate of dividend in each year.


Formula:
Different dividend rate:
V = Dt *(1+ growth rate) / (1+ k) ^t
Constant Growth Dividend Discount Model:
= Dn / (k – g)
Where,
Dn = dividend amount
k = required rate of return
g = growth rate
v = value of stock

Let’s understand this model with an example:

Example: XYZ Company declares dividend Rs.1.95 per share. The dividend grows at 5% in each year for 3 years and thereafter the dividend grows at the rate of 2% constantly for infinite period. Find the share price value. The required rate of return is 12%.


Solution:
D0 = Rs. 1.95
D1 = 1.95 *(1+0.05) = 1.95*1.05 = Rs. 2.0475
D2 = 2.0475 * (1+0.05) = 2.0475*1.05 = Rs. 2.1498
D3 = 2.1498 * (1 + 0.05) = 2.1498*1.05 = Rs. 2.2572

Terminal value of constant dividend growth rate:
P3 = 2.2572 / (0.12 – 0.02) = Rs. 22.572

Present value of D1, D2, D3 and P4 value:

= 2.0475 / (1+0.12) ^1 + 2.1498 / (1+0.12) ^2 + 2.2572 / (1+0.12) ^3 + 22.572 / (1+0.12) ^3
= 1.8281 + 1.7138 + 1.6066 + 16.0666
= Rs.21.215

Example: ABC Company declares dividend Rs. 2 per share. The company has decided to raise the dividend @ 20% for next 5 years and after that the dividend growth rate will be 15% for next 4 years. After 9 years the dividend rate will be constant @ 5%. The required rate of return is 10%. Find out the share price with the help of dividend growth model.

Solution: Dividend value for first 5 years:
Dividend for 1st year (D1) = 2*(1+0.20) = 2*1.20 = Rs. 2.40
D2 = 2.40*(1+0.20) = 2.40*1.20 = Rs. 2.88
D3 = 2.88*(1+0.20) = 2.88*1.20 = Rs. 3.456
D4 = 3.456*(1+0.20) = 3.456*1.20 = Rs. 4.147
D5 = 4.147*(1+0.20) = 4.147*1.20 = Rs. 4.976
Dividend value for next 4 years:
Dividend for 6th year (D6) = 4.976*(1+0.15) = 4.976*1.15 = Rs. 5.722
D7 = 5.722*(1+0.15) = 5.722*1.15 = Rs. 6.580
D8 = 6.580*(1+0.15) = 6.580*1.15 = Rs. 7.567
D9 = 7.567*(1+0.15) = 7.567*1.15 = Rs. 8.702

Terminal value of constant dividend in 9th year:
P9 = 8.702 / 0.10 – 0.05 = 174.04

Present value of all cash outflows:
= (2.40/ (1+0.10)) + (2.88/ (1+0.10) ^2) + (3.456/ (1+0.10) ^3) + (4.147/ (1+0.10) ^4) + (4.976/ (1+0.10) ^5) + (5.722 / (1+0.10) ^6) + (6.580 / (1+0.10) ^7) + (7.567 / (1+0.10) ^8) + (8.702 / (1+0.10) ^9) + (174.04 / (1+0.10) ^9)

= (2.40/1.10) + (2.88/1.21) + (3.456/1.331) + (4.147/1.464) + (4.976/ 1.611) + (5.722/ 1.77) + (6.580 / 1.949) +(7.567 / 2.144) +(8.702/2.358) +(174.04 / 2.358)

= 2.18 + 2.38 + 2.596 + 2.832 + 3.088 + 3.232 + 3.376 + 3.529 + 3.690 + 73.808
= Rs. 100.711



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