We can invest in an intelligent and disciplined manner if we know the price and the value of a company. That is because price is what we pay and value is what we get. Today we venture into Part 2 of the Dividend Discount Valuation, the Multi-stage Dividend Discount Valuation, where we discuss how to value a company with variable dividend growth rates. If you havenâ€™t had a chance, read my Valuations and Intrinsic ValueÂ and Dividend Discount Model Part 1Â posts before reading this one.

**Multiple-Stage Dividend DiscountÂ Valuation**

Growth rate estimates are usually more accurate in the near term than the longer term where there is more uncertainty. And, over time a companyâ€™s growth, and therefore the cash available for dividends, can vary. The Multi-Stage Dividend Growth Model considers variable growth stages in the valuation of a company.

In some cases, a companyâ€™s growth rate slows as it becomes larger, reducing the cash available for increasing the dividend. In other cases, cash for dividends may increase as the company matures. Less cash is needed for growth projects so it is redirected to return more cash to the shareholders, as dividends or share buybacks.

Today weâ€™ll use the Multi-Stage Dividend Discount Valuation to calculate the intrinsic value of a stock with different dividend growth rates. We estimate the dividends per share for each period and discount it back to todayâ€™s valuation date.

A stable dividend growth is often assumed after a period of rapid or variable growth. We discussed stable growth in the Constant Growth Model previously and, it now will become the last stage in the Multiple Stage Growth Model. The value calculated when the stable growth stage begins is also called the â€ś**terminal value**.â€ť The terminal value is then discounted back to the valuation date, more on this is a moment.

**Multi-Stage Dividend Growth Rate Model Formula**

The Multi-Stage considers variable growth rates reflecting different growth stages. The example below uses two stages, although any number can be used. In the BIP valuation, for example, I used a two-stage version.

**Step 1: Determine the Dividendsâ€™ Value During the Growth Stage**

The first step in this process is to calculate the present value of the multiple-stage growth using the formula below.

Where:

- D
_{1}= dividend per share to be received at the end of first year, - D
_{n}= dividend per share to be received at the end of the nth year, - r is the discount rate or required return (in this case the opportunity cost).

#### EXAMPLE:

In the case of BIP, Iâ€™ve made the following assumptions for the figures in these calculations:

- g = BIPâ€™s 7% midpoint dividend target growth rate for ten years,
- a 4% stable growth rate for the stable phase,
- r = 10% discount rate
- D
_{1}= the 2017 dividend rate of $1.74 per share.

*Note: As is often done, the long-term growth is assumed to match that of the applicable economy. In this case, the 4% stable growth rate is the World Bankâ€™s long term global GDP growth rate.*

We then apply the formula for the present value of the multiple-stage of growth to BIPâ€™s projected 7% dividend growth. We have determined the present value of the multiple growth stage to be PV = $14.01, shown here:

**Step 2: Determine the Dividendsâ€™ Value in the Stable Stage**

The next step in this valuation is to use the formula for the terminal value of the stable-stage growth:

Where:

- D
_{n+1}= dividend per share received the year the stable-stage growth starts, - r = the discount rate or required return (in this case the opportunity cost).
- g = the growth rate in the stable stage.

#### EXAMPLE:

For BIP, we apply the terminal value to this formula, shown below:

We determine the terminal value of the stable growth stage to be $57.07.

**Step 3: Determine the Present Value of the Terminal Value**

Since we calculate the terminal value in year 11, we must also discount it back to the present value in year 0. This is the formula for the present value of the terminal value:

Where:

- r = the discount rate or required return (in this case the opportunity cost),
- n = is the number of years in the growth phase.

#### EXAMPLE:

For BIP, we then calculate the present value of the terminal value. We determine the present value of the terminal value is $22.00:

**Step 4: Calculate the Intrinsic Value**

Next, we add together the present value (PV_{0}) of the high-growth-rate stage and the stable-growth stage (terminal value) to obtain the intrinsic value.

#### EXAMPLE:

When we do this for BIP, we get:

**What does this mean?**

Todayâ€™s intrinsic value of $36 per share is higher than todayâ€™s price of $35 per share, the investment appears to be attractive. This is because we pay less than we get back in todayâ€™s dollars. The value is higher than the price, *after we discount it for our 10% required rate of return.* Another way to think about this case is we get our required 10% per year return and an extra $1 per share.

In Part 1 we used Brookfield Infrastructure Partners (BIP) as an example and calculated an intrinsic value of $58 per share. In Part 2, with a seemingly small change is our assumptions, we determined the intrinsic value to be $36 per share. All we really did was change the dividend growth rate from 7% to 4% after year 10.

Sensitivity analysis is a tool used to gain insight into how different assumptions change the outcome. In the BIP example, a seemingly small change in the growth rate of the dividend ten years out, significantly changed the outcome. In the next post, we set out to simplifyÂ the Dividend Discount Valuation into Four Essential Steps and provide spreadsheet to assist with valuations andÂ sensitivity analysis.

Long: BIP

The Fine Print

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