Present Value

Present value is the foundation of all financial decision-making. It answers the question: "What is a future amount of money worth today?" This concept helps you compare investments, evaluate loans, and make smart financial choices.

The Core Formula: Present Value = Future Value ÷ (1 + Interest Rate)^Number of Periods

Simple Example:

• You're offered $1,000 in 1 year
• Interest rate is 5%
• Present Value = $1,000 ÷ (1 + 0.05)^1 = $952.38
• Translation: $1,000 in one year is worth $952.38 today

Real-World Applications:

Investment Decisions:

• Stock A: Pays $100 dividend in 1 year

• Stock B: Pays $100 dividend in 2 years

• At 7% discount rate:

• Stock A PV: $93.46

• Stock B PV: $87.34

• Stock A is worth more today

Loan Evaluation:

• Loan A: $10,000 today, pay back $12,000 in 2 years

• Loan B: $10,000 today, pay back $11,500 in 1 year

• At 10% discount rate:

• Loan A cost: $12,000 ÷ (1.10)^2 = $9,917

• Loan B cost: $11,500 ÷ (1.10)^1 = $10,455

• Loan A is actually cheaper

Retirement Planning:

• Need $1,000,000 in 30 years
• Expected 7% return
• Present Value = $1,000,000 ÷ (1.07)^30 = $131,366
• Translation: You need to save $131,366 today to have $1,000,000 in 30 years

Key Factors:

1. Time

• Longer time = lower present value

2. Interest Rate

• Higher rate = lower present value

3. Risk

• Riskier investments need higher discount rates

Common Uses:

• Net Present Value (NPV)
• Evaluating business investments
• Bond Pricing
• Determining fair bond prices
• Annuity Valuation
• Calculating pension values
• Insurance Decisions
• Comparing lump sum vs. payments

The Bottom Line: Present value helps you make apples-to-apples comparisons between different financial options. A dollar today is always worth more than a dollar tomorrow because you can invest today's dollar and earn returns. Understanding present value prevents you from making costly financial mistakes.