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Module 2 Module 2 - Time Value of Money illustration

The Time Machine Problem

Discover why €100 today is worth more than €100 tomorrow — and how to calculate exactly how much more.

Ronaldo's Money Question

Imagine Cristiano Ronaldo offers you a deal:

Option A: €1,000,000 right now, in cash, today.

Option B: €1,200,000 in exactly 5 years — guaranteed, no risk.

Which do you take?

Your gut might say "Option B! That's €200,000 more!" But your gut might be wrong. Let's figure out why.

The Big Idea: Money Today > Money Tomorrow

Here's a universal truth in finance:

€100 today is worth more than €100 in the future.

Why? Three reasons:

1. You Could Invest It

If you have €100 today and invest it at 7% return, in 5 years you'd have:

€100 × 1.07 × 1.07 × 1.07 × 1.07 × 1.07 = €140.26

So €100 today = €140 in 5 years. Flip that around: €140 in 5 years = only €100 today.

2. Inflation Eats Your Money

Things get more expensive over time. A PlayStation 5 costs €500 today. In 5 years, the PS6 might cost €600 for the same gaming power. Your €500 buys less.

3. Tomorrow Isn't Guaranteed

What if the person promising you money goes broke? Money now is certain. Money later has risk.

The Compounding Superpower

Let's see why Einstein (supposedly) called compound interest "the eighth wonder of the world."

The MrBeast Case Study

MrBeast started YouTube at 13. Let's say he made his first €1,000 at 15 and reinvested everything back into videos.

If his money compounded at 50% per year (his channel grew WAY faster than this):

AgeValue
15€1,000
16€1,500
17€2,250
18€3,375
19€5,063
20€7,594
21€11,391
22€17,086
23€25,629
24€38,443
25€57,665

By age 26 (11 years of compounding), that €1,000 became €86,498 at "only" 50% annual returns.

Key insight: Small amounts + high growth rates + long time = huge numbers.

Discount Rates: Working Backwards

If compounding takes present money and grows it forward, discounting takes future money and shrinks it back to today.

The Formula

Present Value = Future Value ÷ (1 + rate)^years

Back to Ronaldo's question:

Option B is €1,200,000 in 5 years. If you could invest money at 7% per year, what's that worth today?

Present Value = €1,200,000 ÷ (1.07)^5
Present Value = €1,200,000 ÷ 1.403
Present Value = €855,354

So Option B (€1.2M in 5 years) is really only worth €855,354 in today's money.

Option A was €1,000,000 today.

€1,000,000 > €855,354 → Option A wins. Take the money now.

What's a "Discount Rate"?

The discount rate is basically "what return could you get elsewhere?"

  • If you're a safe investor (government bonds): ~4%
  • If you're a normal investor (stock market average): ~7-10%
  • If you're an aggressive investor (risky bets): ~15%+
  • If you're MrBeast reinvesting in content: ~50%+ (historically)

Higher discount rate = future money is worth less today.

Mini-Exercise: Time Value Calculator

1. Future Value Problem

You invest €500 at 10% annual return. How much do you have in 7 years?

FV = €500 × (1.10)^7 = €500 × = €

2. Present Value Problem

Someone promises you €10,000 in 3 years. Your discount rate is 8%. What's that worth today?

PV = €10,000 ÷ (1.08)^3 = €10,000 ÷ = €

3. Real Decision

Would you rather have €5,000 today or €8,000 in 6 years? (Assume 8% annual return)

View Answer Key

1. €500 × 1.9487 = €974.36

2. €10,000 ÷ 1.2597 = €7,938.32

3. €5,000 today at 8% for 6 years = €5,000 × 1.5869 = €7,934.37. That's less than €8,000, so €8,000 in 6 years is better — but barely! If your rate was 9%, the answer would flip.

Investment Dilemma: The Epic Games Offer

Epic Games offers you two deals:

Option A: €50,000 cash today

Option B: 0.001% of Fortnite's revenue for the next 20 years

Take the Cash

€50,000 now, guaranteed

Take the Revenue Share

Potential for much more, but uncertain

How an Investor Would Think:

Step 1: Estimate Fortnite's annual revenue. Let's say €5 billion per year currently. 0.001% of €5B = €50,000/year (hey, same as Option A!)

Step 2: But will it stay at €5B? This is the hard part. Does Fortnite keep players for 20 years? Does it grow? Shrink?

Step 3: Discount it back. At an 8% discount rate, €50,000/year for 20 years ≈ €490,000 present value.

So Option B might be worth €490,000 vs. Option A's €50,000. But what if Fortnite declines 10% per year? Or shuts down in 5 years?

The lesson: The "obviously better" deal depends entirely on your assumptions about the future.

AI Lab: Compounding Calculator

Prompt Template

I want to understand compounding better. Create a table showing what happens to €[amount] invested at [X]% annual returns over [Y] years.

Then tell me:
1. How much did the initial investment multiply by?
2. What percentage of the final amount came from the original money vs. from growth?
3. What would happen if the rate was 2% higher? 2% lower?

Dinner Table Discussion

"If you could get paid your whole allowance for the year today instead of weekly/monthly, how much less would you accept? Why?"

This makes time value personal. If your allowance is €10/week (€520/year), would you take €400 today instead? €300? This reveals your personal "discount rate."

So What? The Investor Takeaway

Whenever someone talks about future money, your investor brain should immediately ask:

"What's that worth in today's money?"

This is why:

  • A company making €10M profit today is worth more than one "projected" to make €15M in 5 years
  • Investors pay more for money coming sooner vs. later
  • Growth rate expectations completely change what something is worth

You now have the foundation for the most important valuation tool in finance: the DCF.

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