The Golden Apple Tree: A Tale of the Dividend Discount Model (DDM)

In the prosperous town of Financia, there was an ancient golden apple tree standing in the center of the Royal Market. This tree was no ordinary tree—it bore magical apples that grew in value every year. The tree was owned by the wise old merchant, Master Dividen.

One day, a young investor named Theo approached Master Dividen and asked,
"Sir, I want to buy this tree, but how do I know what it’s worth?"

Master Dividen smiled and said, "The value of this tree depends on the apples it will bear for you in the future. Let me explain."

The Tree of Future Wealth (The Core Idea of DDM) 🌳

Master Dividen pointed to the tree and said:

  1. "Every year, the tree produces 10 golden apples, and I sell each for 1 gold coin. That’s 10 gold coins a year!"
  2. "But since it's a magical tree, the number of apples grows by 5% every year."
  3. "If you expect a fair return of 10% per year, how much should you pay for this tree today?"

Theo scratched his head. Master Dividen then revealed the Dividend Discount Model (DDM) formula:

P0=D1r−gP_0 = \frac{D_1}{r - g}

where:

  • P0P_0 = Present value of the tree (Stock Price)
  • D1D_1 = Next year's dividend (Golden Apples)
  • rr = Required return (Theo’s expected return)
  • gg = Growth rate of dividends (Apple growth rate)

Calculating the Value of the Tree 📊

Theo calculated:

  • Next year’s apples: 10 × 1.05 = 10.5 apples
  • Required return: 10% or 0.10
  • Growth rate: 5% or 0.05
P0=10.50.10−0.05=10.50.05=210 gold coinsP_0 = \frac{10.5}{0.10 - 0.05} = \frac{10.5}{0.05} = 210 \text{ gold coins}

Theo realized, "The tree is worth 210 gold coins today because it will generate growing dividends forever!"

What If the Growth Rate Changes? 📈📉

Master Dividen warned,
"If the tree starts producing apples at a slower rate, say 3% instead of 5%, the value would drop."

P0=10.50.10−0.03=10.50.07=150 gold coinsP_0 = \frac{10.5}{0.10 - 0.03} = \frac{10.5}{0.07} = 150 \text{ gold coins}

"And if the apples grow faster, say at 7%, the value increases!"

P0=10.50.10−0.07=10.50.03=350 gold coinsP_0 = \frac{10.5}{0.10 - 0.07} = \frac{10.5}{0.03} = 350 \text{ gold coins}

Theo nodded, understanding that dividend growth played a crucial role in valuation.

Lesson of the Golden Tree 🌟

Before buying the tree, Theo had learned three key lessons:

  1. A stock’s value comes from its future dividends.
  2. Higher growth = Higher stock price, but riskier.
  3. A lower required return makes stocks more valuable.

With this wisdom, Theo decided to buy the tree, knowing that investing is about the future cash flows, not just today’s price.

[Finance]

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