Vignette Drill: Multi-Stage Dividend Forecasting

Introduction

So, you’ve probably seen basic dividend discount models (DDM) back at Level I—like the simple Gordon Growth Model—even if you felt a bit of a headache doing the math. At Level II, though, it’s time to take that foundation and build a more robust multi-stage approach. The reality is that a company doesn’t just grow at one constant rate forever. Firms often start with rapid “supernormal” growth, then slow down to more stable rates. That’s where multi-stage models come in handy.

I remember the first time I tackled a multi-stage DDM problem on a practice exam. I was so focused on the first few years of high growth that I forgot to carefully compute the continuing (terminal) value at the end of that growth phase. Oops! Let’s try to keep you from making the same mistakes by walking through a typical vignette-style scenario step by step.

TechNova Inc. Scenario

Imagine we have a case on the exam featuring TechNova Inc. The story goes like this: TechNova is just finishing its super-charged expansion phase and is expected to continue growing quickly for five more years (though at a bit slower rate each year). After that, management projects a shift into a stable, long-term growth trend. We have to estimate the value of TechNova’s stock right now, based on future dividends.

Here’s the gist of the data you might see:

• The company has just paid a dividend (D₀).
• Over the next five years, it expects dividends to grow at specified rates, say:
– Year 1: 15% growth
– Year 2: 12% growth
– Year 3: 10% growth
– Year 4: 8% growth
– Year 5: 6% growth
• After Year 5, the stable (perpetual) growth rate is expected to be 3%.
• We’re given a required rate of return (r), which might be derived from the CAPM or another cost of equity model. Let’s call it 10% just for illustration.

Your task: Estimate today’s stock price (P₀) using a multi-stage dividend discount approach.

Step-by-Step Approach

Identify the Given Data

First, parse the vignette thoroughly. Often, you’ll get hints about:

• The dividend just paid (D₀) or about to be paid (D₁).
• High-growth (supernormal) stage assumptions: growth rates for each of the next several years.
• The stable growth rate after the high-growth phase.
• The required return on equity (r) based on beta, risk-free rate, and equity risk premium—or from a build-up approach.

Double-check if the item set references annual or quarterly dividends. The exam can slip in a detail like “quarterly dividends.” That changes your timeline and discounting.

Project Each Dividend in the High-Growth Stage

Calculate the dividend for each year using the growth rates provided. For example, if the most recent dividend (D₀) was $2.00 and the first-year growth rate is 15%, then:

D₁ = D₀ × (1 + 0.15) = $2.00 × 1.15 = $2.30

Then for the second year:

D₂ = D₁ × (1 + 0.12) = $2.30 × 1.12 = $2.576

Continue that process for each of the high-growth years, carefully applying each distinct growth rate.

Transition to the Stable Growth Stage

After you project, say, five years of dividends, the stable growth stage begins in Year 6 (which means the first stable-growth dividend is D₆). That’s the moment you typically calculate a terminal value (TV₅) that represents the present value at Year 5 of all future dividends starting in Year 6 and continuing forever.

One common formula for that perpetuity-based terminal value is:

where gₛₜₐ_bₗₑ is the long-term growth rate (e.g., 3%).

And remember, D₆ = D₅ × (1 + gₛₜₐ_bₗₑ).

Calculate the Terminal Value

Let’s say we found D₅ = $2.80, and the stable growth rate is 3%. Then:

D₆ = $2.80 × (1 + 0.03) = $2.88

So:

This $41.14 is the value of all dividends from Year 6 onward, but it’s expressed in end-of-Year-5 dollars. We still have to discount it back to Time 0.

Discount All Projected Dividends and the Terminal Value

Now that we have all the future dividends in the supernormal years (D₁, D₂, D₃, D₄, D₅) plus the terminal value at the end of Year 5, we discount each cash flow to today’s value.

The present value of each dividend Dₜ is:

And the present value of the terminal value is:

Finally, add up all those discounted cash flows:

That’s the multi-stage DDM price.

Diagram of Timelines

To keep everything clear, I often like to sketch a quick timeline:

    flowchart LR
	A["Time 0 <br/>(Today)"]
	-->B["End of Year 1 <br/>D₁"]
	-->C["End of Year 2 <br/>D₂"]
	-->D["End of Year 3 <br/>D₃"]
	-->E["End of Year 4 <br/>D₄"]
	-->F["End of Year 5 <br/>D₅ + TV₅ <br/>(Stable Growth Begins)"];

Each node shows when a dividend is paid. At Year 5, you also have that “TV₅,” which represents all dividends from Year 6 onward. Then you discount each flow back to Time 0 at the required rate r.

Practical Example

Let’s put some hypothetical numbers together:

• D₀ = $2.00 (just paid)
• Growth rates: 15%, 12%, 10%, 8%, 6% for Years 1 through 5
• Stable growth rate = 3%
• r = 10%

1. Project Dividends:
   • D₁ = $2.00 × 1.15 = $2.30
   • D₂ = $2.30 × 1.12 = $2.58 (rounded)
   • D₃ = $2.58 × 1.10 = $2.84 (approximately)
   • D₄ = $2.84 × 1.08 = $3.06 (approximately)
   • D₅ = $3.06 × 1.06 = $3.24 (approximately)

2. Next Dividend in Stable Growth:
   • D₆ = $3.24 × 1.03 = $3.34

3. Terminal Value:
   • \( TV_5 = \frac{3.34}{0.10 - 0.03} \approx \frac{3.34}{0.07} \approx $47.71 \)

4. Present Values:

   • \( \text{PV}(D_1) = \frac{2.30}{(1.10)^1} = 2.09 \)
   • \( \text{PV}(D_2) = \frac{2.58}{(1.10)^2} \approx 2.14 \)
   • \( \text{PV}(D_3) = \frac{2.84}{(1.10)^3} \approx 2.13 \)
   • \( \text{PV}(D_4) = \frac{3.06}{(1.10)^4} \approx 2.09 \)
   • \( \text{PV}(D_5) = \frac{3.24}{(1.10)^5} \approx 2.01 \)
   • \( \text{PV}(TV_5) = \frac{47.71}{(1.10)^5} \approx 29.59 \)

5. Add ’em Up:

   • Price \( P_0 = 2.09 + 2.14 + 2.13 + 2.09 + 2.01 + 29.59 = $39.05 \) (approx.)

Depending on rounding or small differences in the discount factor, you might see an answer in the range of $39.00—$39.10. On exam day, you’d check which answer choice lands near your result.

Key Exam-Day Strategies

• Watch Your Timeline: Carefully label each dividend as D₁, D₂, etc. If you accidentally label the next dividend as D₀, you’ll misplace your growth.
• Double-Check the Growth Rates: If you see a sudden drop in growth in the data, confirm that’s not your terminal growth.
• Keep an Eye on Partial-Year Dividends: Occasionally, an item set might say, “The dividend is paid mid-year.” Then you need a half-year discount factor.
• Use the Same Units: Annual rates, annual dividends. If the item set provides multiples periods (quarter, semiannual), unify them carefully.
• Look Out for a Dividend Cut: A tricky scenario might have the dividend reduce in a year before bouncing back.
• Re-Check Cost of Equity: If they mention increased risk or changes in capital structure, that might affect your discount rate.

In a timed exam environment, it’s easy to scramble. But if you methodically follow the steps—project each dividend, figure out the terminal value, discount them all—you’ll be less likely to make an error.

Advanced Techniques

Sometimes, a multi-stage dividend model can be complicated by share repurchases or new equity issuance. If the company is repurchasing shares, the effective dividend per share might be adjusted (fewer shares outstanding). Watch for signals that the question wants you to incorporate such changes.

Another twist might be if the exam references an exit multiple or market-based approach for the terminal value instead of a perpetual growth model. In that case, you’ll use something like EV/EBITDA or P/E to approximate the stock’s value at the end of Year 5. Then you discount that “exit” value back.

If you have partial information—like no direct mention of D₆ but a statement about “$3.24 is the final high-growth dividend, after which stable growth at 3% commences”—just be sure to interpret that properly: stable growth picks up from the next period.

Conclusion

I think the biggest takeaway is that multi-stage DDM is an expansion of the single-stage approach. You account for higher growth in the near term and then shift to a stable rate later. This is more realistic than assuming a single growth rate forever, especially for companies in transitional phases, like our fictional TechNova Inc. Practice is key: The more you run these calculations (with different growth patterns, discount rates, or even a mid-year convention), the faster and more confident you’ll be on exam day.

References

• Official CFA Program Curriculum for Level II, Equity Investments—Dividend Discount Models
• Investopedia, “Multistage Dividend Discount Models” (https://www.investopedia.com)
• Kaplan Schweser Practice Exams and Mock Tests
• AnalystNotes.com (for additional practice sets)

Test Your Knowledge: Multi-Stage Dividend Forecasting Quiz