Module 5: The Time Value of Money (TVM)

The Time Value of Money (TVM) is the central theorem of modern finance . The axiom is absolute: A sum of money today is worth more than the exact same sum in the future.

1. The Three Drivers of TVM

Why must you demand a premium to delay gratification?

1. Opportunity Cost: Capital held today can be invested. By waiting a year for $10,000, you forfeit the risk-free interest you could have generated in US Treasury bills .
2. Inflation: Macroeconomic inflation continually erodes purchasing power. $100 buys less utility in 2030 than it does today .
3. Risk: The future is uncertain. A debtor may default. Cash in hand removes counterparty risk .

2. Compounding and Discounting

• Compounding (Future Value): Moving present capital into the future. It calculates what an investment today will grow into at a specific interest rate .
  • Formula: FV = PV * (1 + r)^n
• Discounting (Present Value): Moving future capital into the present. It calculates what a promised future sum is worth to you today .
  • Formula: PV = FV / (1 + r)^n

Case Study: The Lottery Payout

A lottery winner in California is offered $5 Million today (Lump Sum) or $6 Million paid out over 10 years (Annuity).

• Analysis: Using TVM, if the winner can secure a safe 5% return in the bond market, the Present Value of the 10-year annuity is less than $5 Million. Mathematically, the winner should take the $5 Million upfront and invest it immediately.

Self-Assessment Quiz

1. Based on the TVM formula, what happens to the Present Value of a future cash flow if the central bank raises interest rates?
2. Define "Opportunity Cost" in the specific context of receiving a delayed payment.