The Private Equity Chronicles: The Tale of Multiples (With Formulas Explained!)

In the grand financial kingdom of Capitalia, the legendary investor Lord Ardent had launched a private equity fund, Golden Returns, investing in various merchant guilds. But he needed a way to measure how well his fund was doing.

To solve this, he called upon his four trusted financial advisors, each a master of a crucial performance metric:

1️⃣ Investment Multiple (TVPI - Total Value to Paid-In Capital)
2️⃣ Realization Multiple (DPI - Distributions to Paid-In Capital)
3️⃣ RVPI Multiple (Residual Value to Paid-In Capital)
4️⃣ PIC Multiple (Paid-In to Committed Capital)

They each explained their importance and formulas in detail.

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1️⃣ Investment Multiple (TVPI - Total Value to Paid-In Capital)

First, Sir Investus, the keeper of the Investment Multiple, stepped forward.

🔹 Formula:

$$TVPI = \frac{\text{Realized Value} + \text{Unrealized Value}}{\text{Paid-In Capital}}$$

🔹 Explanation of terms:

• Realized Value → Money already received from investments (e.g., from selling assets).
• Unrealized Value → The remaining value of investments still in the market.
• Paid-In Capital → The actual money invested so far by the fund.

🔹 Example Calculation:
Lord Ardent’s fund had:

• Realized Value = 800 gold coins
• Unrealized Value = 400 gold coins
• Paid-In Capital = 1,000 gold coins

So,

$$TVPI = \frac{800 + 400}{1,000} = 1.2$$

What it means:
👉 For every 1 gold coin invested, the fund has generated 1.2 gold coins in total value (both realized and unrealized).

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2️⃣ Realization Multiple (DPI - Distributions to Paid-In Capital)

Next, Lady Realiza, the master of Realization Multiple, spoke.

🔹 Formula:

$$DPI = \frac{\text{Realized Value}}{\text{Paid-In Capital}}$$

🔹 Explanation of terms:

• Realized Value → Cash already returned to investors.
• Paid-In Capital → The actual money invested.

🔹 Example Calculation:
Using the same numbers:

$$DPI = \frac{800}{1,000} = 0.8$$

What it means:
👉 The fund has already returned 80% of the invested capital to its investors.
👉 If DPI = 1, the fund has fully repaid the investors their original investment.

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3️⃣ RVPI Multiple (Residual Value to Paid-In Capital)

The third advisor, Sir Residus, then spoke.

🔹 Formula:

$$RVPI = \frac{\text{Unrealized Value}}{\text{Paid-In Capital}}$$

🔹 Explanation of terms:

• Unrealized Value → The value of investments still held in the market.
• Paid-In Capital → The actual money invested.

🔹 Example Calculation:

$$RVPI = \frac{400}{1,000} = 0.4$$

What it means:
👉 40% of the capital is still invested and has not yet been returned as cash.
👉 DPI + RVPI = TVPI (0.8 + 0.4 = 1.2), which makes sense since the total value is made up of both realized and unrealized portions.

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4️⃣ PIC Multiple (Paid-In to Committed Capital)

Finally, Sir Committus, the guardian of PIC Multiple, stepped forward.

🔹 Formula:

$$PIC = \frac{\text{Paid-In Capital}}{\text{Committed Capital}}$$

🔹 Explanation of terms:

• Paid-In Capital → The money actually invested so far.
• Committed Capital → The total money pledged by investors (not all of which is necessarily invested yet).

🔹 Example Calculation:
If Lord Ardent had raised 1,200 gold coins but had invested only 1,000 gold coins, then:

$$PIC = \frac{1,000}{1,200} = 0.83$$

What it means:
👉 83% of the pledged money has been invested, and 17% is still waiting to be deployed.

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The Final Verdict

Lord Ardent, pleased with his advisors’ insights, declared:

✔ TVPI (Total Value to Paid-In) → Shows how much the fund has grown overall, combining both realized and unrealized value.
✔ DPI (Distributions to Paid-In) → Shows how much cash has been returned to investors.
✔ RVPI (Residual Value to Paid-In) → Shows how much of the fund's investments are still unrealized.
✔ PIC (Paid-In to Committed) → Shows how much of the total committed capital has actually been deployed.

With this knowledge, Lord Ardent made even wiser investment decisions, ensuring Golden Returns would be the greatest fund in all of Capitalia!

[Finance]