## Multiperiod Dividend Discount Models

When you buy shares, you are essentially buying into the dividend stream. Unless you sell the shares, the only income is the dividend and therefore the value could be viewed as the present value of the future dividends. The simple perpetuity formula is the Gordon's growth model as a shortcut to present valuing a stream of cash flows. The simple formula is:

Dj = Dividend for next period i.e. Do * (1 + g) E(Ri) = Desired return g = Implied growth = Cost ofequity — Dividend yield / (1+Dividend yield)

In Figure 14.4, the dividend is 0.018 and the growth rate is 8.5 per cent. Therefore:

The simple dividend model assumes a constant rate of growth in perpetuity. It is possible to construct multi-stage models using forecast dividends and different rates of discounting. In the model above, the company forecasts a period of rapid growth over the next five years before dropping back to more modest growth. The dividend rate is 25.0 per cent and the income and dividends are shown on the Data sheet.

The forecast dividends are discounted at the cost of equity and then the final dividend is subjected to the perpetuity formula. The terminal value is:

The share value is:

Figure 14.4

Dividend model a

16 17 13

20 21 22 23"

a |
C |
D |
E |
F |
& |
H |
1 1 |

Assumed Terminal Growth |
B.50% I | ||||||

Earnings Retention Rate |
75,00% | ||||||

Cost 6f Equity |
a.25% | ||||||

' Period |
0 |
1 |
7 |
J |
t |
i |
« 1 |

Return on Equity |
3:50% |
3.41% |
4:61% |
S.67% |
6.59% |
7.36% |
3.25% |

Dividend Portion |
0.85% |
1.15% |
1.42% |
1 65% |
1.84% |
231% | |

Net Income |
3.30 |
3.50 |
4.90 |
630 |
7.70 |
S.10 | |

Dividends |
(0 titii |
iTlaui |
ft 2Ä1 |
i i sai |
raiîai | ||

Nominal Dividend |
0.Q1S |
0.01 3 |
0.025 |
0.032 |
0.039 |
0.046 |
0.049 |

Growth |
40.00% |
28.67%. |
22:22% |
18.18% |

Overall Growth Rate Terminal Value

Overall Growth Rate Terminal Value

One Stage Value >.537

### Two Stage Value per Share 4.355 Firm Value MJ.T5

The valuation by this method is 4.355 per share or 217.75 in total. The model is based on stable growth or dividends which last to infinity. This is a simplification: for example dividends cannot grow faster than earnings since it is unsustainable that dividends would become greater than earnings over a sufficient number of periods.

The model is also extremely sensitive to the growth rate. As the growth rate converges on the discount rate, the value increases rapidly and will

Figure 14.5

Sensitivity to growth rate

become negative if the growth rate exceeds the discount rate. The chart in Figure 14.5 shows a rapid increase in value followed by a dramatic fall above the growth rate of 8.5 per cent.

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