Why a $1 Million Lottery Paid Over 20 Years Isn't Worth $1 Million Today
A $1 million lottery prize paid as $50,000/year for 20 years has a present value of roughly $589,000 at a 5% discount rate — not $1 million. The reason: future dollars are worth less than present dollars because present dollars can be invested and grow. Net Present Value is the framework that makes this calculation rigorous and applicable to any investment decision.
The Time Value of Money Foundation
Present value of a single future cash flow:
PV = FV ÷ (1 + r)^t
Where r = discount rate (your required rate of return), t = years in the future
Example: $100,000 received in 5 years at 8% discount rate:
PV = $100,000 ÷ (1.08)^5 = $100,000 ÷ 1.4693 = $68,058
That future $100,000 is worth only $68,058 in today's dollars if your required return is 8%.
NPV: Summing Discounted Cash Flows
NPV = −Initial Investment + Σ [Cash Flow_t ÷ (1 + r)^t]
NPV > 0: Investment creates value; worth pursuing
NPV = 0: Investment exactly meets your required return
NPV < 0: Investment destroys value; better alternatives exist
Full NPV Worked Example: Equipment Purchase
A business considering $80,000 equipment that will generate annual cost savings of $25,000 for 5 years, with $5,000 salvage value at end of year 5. Required return: 10%.
| Year | Cash Flow | Discount Factor (10%) | Present Value |
|---|---|---|---|
| 0 (today) | −$80,000 | 1.000 | −$80,000 |
| 1 | +$25,000 | 0.9091 | +$22,727 |
| 2 | +$25,000 | 0.8264 | +$20,661 |
| 3 | +$25,000 | 0.7513 | +$18,783 |
| 4 | +$25,000 | 0.6830 | +$17,075 |
| 5 | +$30,000 | 0.6209 | +$18,628 |
| NPV | +$17,874 |
NPV of +$17,874 means this investment creates $17,874 in value above and beyond the 10% required return. It's a worthwhile investment.
IRR: The Break-Even Discount Rate
Internal Rate of Return (IRR) is the discount rate that makes NPV = 0. It represents the actual percentage return of the investment.
For the equipment example: IRR ≈ 18.5%. Since this exceeds the 10% required return, the investment is confirmed as worthwhile — and by 8.5 percentage points.
IRR calculation requires iterative solving (or =IRR() in spreadsheets). The decision rule: if IRR > required return (cost of capital), accept the investment.
Choosing the Right Discount Rate
The discount rate should reflect the risk and opportunity cost of the investment:
- Risk-free investments: Use Treasury rate (~4.5–5% currently)
- Corporate projects: Use Weighted Average Cost of Capital (WACC), typically 8–12%
- Real estate: Use your required cap rate or alternative investment return, typically 6–10%
- High-risk ventures: Use 15–25%+ to account for uncertainty
- Personal decisions: A common benchmark is the stock market expected return (~7–10%)
NPV vs. Payback Period
Many businesses use simple payback period (initial investment ÷ annual cash flow): $80,000 ÷ $25,000 = 3.2 years. This is fast to calculate but deeply flawed — it ignores the time value of money and cash flows after payback.
The discounted payback period fixes part of this by using present values of cash flows instead of nominal ones. In the equipment example, discounted payback ≈ 4.2 years (vs. 3.2 years nominal). More accurate, though still ignores post-payback cash flows.
NPV for Personal Financial Decisions
NPV applies beyond business investments:
- College education: NPV of lifetime earnings premium vs. tuition cost + forgone income
- Refinancing a mortgage: NPV of monthly savings vs. closing costs (is the break-even worthwhile?)
- Buying vs. leasing equipment: NPV of each payment stream compared
- Solar panel installation: NPV of utility savings over 25 years vs. installation cost
Bottom Line
Any time you're comparing an upfront cost against future benefits, NPV gives you the only intellectually honest answer. Pick a discount rate that reflects your required return, discount each future cash flow, sum them, and subtract your initial investment. A positive result means yes; negative means look elsewhere. Use the CalcPeek investment calculator as a starting point for modeling investment scenarios and projecting the returns on any financial decision.