Question

Explain the multistage valuation model when applied to FCF and dividends. Also show the equation used for each

.

Answer 1

Multi-stage dividend discount model is a technique used to calculate intrinsic value of a stock by identifying different growth phases of a stock; projecting dividends per share for each the periods in the high growth phase and discounting them to valuation date, finding terminal value at the start of the stable growth phase using the Gordon growth model, discounting it back to the valuation date and adding it to the present value of the high-growth phase dividends.

The basic concept behind the multi-stage dividend discount model is the same as constant-growth model, i.e. it bases intrinsic value on the present value of expected future cash flows of a stock. The difference is that instead of assuming a constant dividend growth rate for all periods in future, the present value calculation is broken down into different phases.

Formula

Intrinsic value = PV of high growth phase dividends + PV of stable growth phase dividends

To calculate the present value of dividend payments in the high growth phase, dividend per share for each year is individually projected and then discounted.

Dividend per share in year 1 = current dividend × (1 + growth rate in year 1).

It is discounted one year back to valuation date (i.e. time=0).

Dividend per share in Year 2 = dividend per share in year 1 * (1 + growth rate in year 2).

It is discounted 2 years back to t=0.

PV of high growth dividends =	D1	+	D2	+	D3	+ ... +	Dn
	(1+r)		(1+r)2		(1+r)3		(1+r)n

Where r is the cost of equity and n is number of years in the high-growth phase.

The present value calculation of dividend payments in stable growth phase involves used of Gordon growth model, because in that phase the dividend growth rate is constant. However, since the Gordon growth model calculates present value at the end for high growth period, it is further discounted back to t=0.

PV of stable growth dividends	1	×	Dn+1
	(1+ r)n		r – g

Where,
Dn+1 is the dividend in the first year of the stable growth phase
r is the cost of equity
g is the constant dividend growth rate

Example

Flamingo Communications (FC) is fast-growing IT startup specializing in social-media marketing. You are a financial analyst at AH Ventures, a diversified conglomerate, which has 10% stake in the company.

Your in-house economist projects that FC dividends are expected to grow at 25%, 20%, 15% and 10% and 5% for the next 5 years. From 6th year onwards a stable growth rate of 5% is expected.

If FC’s current stock price is $41, its most recent dividend per share was $1.5 per share and its cost of equity is 10%, what would you recommend to your CFO regarding what to do with the investment?

Solution

In the first step, you need to project dividend expectation for each year in the high-growth phase.

The following table summarizes the calculations:

Year	Growth rate	Dividend per share	Phase	Formula
Time 0		1.50
Year 1	25%	1.88	High-growth	= 1.5 * (1 + 25%)
Year 2	20%	2.25	High-growth	= 1.88 * (1 + 20%)
Year 3	15%	2.59	High-growth	= 2.25 * (1+15%)
Year 4	10%	2.85	High-growth	= 2.59 * (1 + 10%)
Year 5	5%	2.99	High-growth	= 2.85 * (1 + 5%)
Year 6	5%	3.14	Stable growth	= 2.99 * (1 + 5%)

The first 5 years make the high-growth phase. Dividend per share expected for each of the first 5 years must be discounted back to t=0 individually as follows:

Year	Growth rate	Dividend per share	PV at t=0	Formula
Year 1	25%	1.88	1.70	= 1.88 / (1 + 10%)
Year 2	20%	2.25	1.86	= 2.25 * (1 + 10%)^2
Year 3	15%	2.59	1.94	= 2.59 * (1+10%)^3
Year 4	10%	2.85	1.94	= 2.85 * (1 + 10%)^4
Year 5	5%	2.99	1.86	= 2.99 * (1 + 5%)^5
		Sum	9.31

Year 6 onwards is the stable growth phase.

Using the Gordon growth model formula, you can arrive at the present value of perpetual dividends from 6th year onwards at the start of the stable growth phase. This value is called terminal value.

Terminal value = PV of perpetual dividends 6th year onwards = $3.14/(10% - 5%) = $62.8

Since the PV calculated above is at the end of 5th year (i.e. start of stable growth phase), it must be discounted back 5 years as follows:

PV at t=0 = $62.8/(1+10%)^5 = $39

Intrinsic value of the stock
= PV of dividends in high-growth phase + PV of terminal value
= $9.31 + $39
= $48.3

Since the current stock price is $41 and the intrinsic value is $48.3, AH Venture should keep invested in the company because it has upward potential.

Hope it helps, For Free Cash Flow, it will be on the similiar terms just like dividend.