Calculate the present value of future money, annuities, and cash flows. Understand the time value of money and make informed financial decisions with accurate present value calculations.
Present Value (PV) is a fundamental financial concept that calculates the current worth of a future sum of money or stream of cash flows, given a specified rate of return. This calculation is based on the principle that money available today is worth more than the same amount in the future due to its potential earning capacity.
Present value calculations are essential for investment decisions, loan evaluations, retirement planning, and any financial scenario where you need to compare money received or paid at different times.
FV = Future Value, r = Interest Rate, n = Number of Periods
PMT = Periodic Payment, payments made at end of period
Payments made at beginning of each period
| Scenario | Future Value | Rate/Time | Present Value | Interest Saved |
|---|---|---|---|---|
| $1,000 in 10 years at 6% | $1,000 | 6% / 10 years | $558.39 | $441.61 |
| $5,000 in 5 years at 8% | $5,000 | 8% / 5 years | $3,402.92 | $1,597.08 |
| $100/month for 20 years at 7% | $52,397 | 7% / 20 years | $12,675 | $39,722 |
| $10,000 in 25 years at 4% | $10,000 | 4% / 25 years | $3,751.34 | $6,248.66 |
| Future Value: $1,000 in 10 Years | 3% Rate | 6% Rate | 9% Rate | 12% Rate |
|---|---|---|---|---|
| Present Value | $744.09 | $558.39 | $422.41 | $321.97 |
| Discount Amount | $255.91 | $441.61 | $577.59 | $678.03 |
| Discount Percentage | 25.6% | 44.2% | 57.8% | 67.8% |
| Future Value: $1,000 at 6% | 5 Years | 10 Years | 20 Years | 30 Years |
|---|---|---|---|---|
| Present Value | $747.26 | $558.39 | $311.80 | $174.11 |
| Value Lost to Time | $252.74 | $441.61 | $688.20 | $825.89 |
| Percentage of FV | 74.7% | 55.8% | 31.2% | 17.4% |
Annuity due has higher present value due to earlier payments
Ordinary Annuity: Payments made at the end of each period (most common).
Annuity Due: Payments made at the beginning of each period (rent, insurance).
Example: $100/month for 5 years at 6% has PV of $5,323 (ordinary) vs. $5,643 (due).
When payments grow at rate 'g' each period
When to Use: Salary projections, inflation-adjusted cash flows, growing dividends.
Requirement: Growth rate (g) must be less than discount rate (r).
Measures total value creation from an investment
Decision Rule: Accept projects with NPV > 0, reject if NPV < 0.
Advantage: Considers all cash flows and provides absolute dollar value.
Sum of present values of all future cash flows
Coupon PV: Present value of regular interest payments (annuity).
Face Value PV: Present value of principal repayment (lump sum).
Yield to Maturity: The discount rate that makes bond price equal to PV.
| Discount Rate Type | Rate Range | Use Case | Risk Level |
|---|---|---|---|
| Risk-free Rate | 2-5% | Government bonds, certain cash flows | Very Low |
| Cost of Debt | 4-12% | Corporate borrowing costs | Low-Medium |
| Cost of Equity | 8-15% | Expected stock returns | Medium-High |
| WACC | 6-12% | Company-wide projects | Company-specific |
| Opportunity Cost | Variable | Alternative investment returns | Variable |
Adjusts for inflation to show purchasing power
Nominal PV: Present value in current dollars without inflation adjustment.
Real PV: Present value adjusted for inflation, shows true purchasing power.
When to Use: Long-term financial planning, retirement calculations.
Wrong Discount Rate: Using inappropriate rate for the risk level of cash flows.
Ignoring Inflation: Not considering purchasing power erosion over time.
Timing Errors: Confusing ordinary annuity with annuity due timing.
Tax Neglect: Using pre-tax instead of after-tax cash flows.
Compounding Frequency: Not matching compounding periods with payment periods.
| Aspect | Present Value | Future Value | Usage |
|---|---|---|---|
| Time Direction | Future → Present | Present → Future | Different perspectives |
| Purpose | What to invest today | What investment will be worth | Planning vs. projection |
| Decision Making | Compare options today | Set future goals | Current vs. future focus |
| Risk Consideration | Built into discount rate | Usually ignored | Risk assessment timing |
Perpetuity PV: PV = Payment ÷ Interest Rate (infinite payments).
Growing Perpetuity: PV = Payment ÷ (Interest Rate - Growth Rate).
Variable Cash Flows: Calculate PV of each cash flow separately and sum.
Continuous Compounding: PV = FV ÷ e^(r×t) where e is Euler's number.