Rate of Return (RoR): Meaning, Formula, and Examples

Definition

The rate of return (RoR) measures the percentage gain or loss on an investment relative to its initial cost. It shows how much the investment’s value has changed over a specified period.

Basic Formula

Rate of return = ((Current value − Initial value) / Initial value) × 100

This simple RoR (also called return on investment, ROI) does not account for the timing of cash flows or inflation.

RoR for Stocks and Bonds

• Stocks: Include price change plus any dividends.
• Example: Buy at $60, receive $10 in dividends, sell at $80.
  • RoR = ((80 − 60 + 10) / 60) × 100 = 50%
• Bonds: Include interest (coupon) plus price change.
• Example: Buy a $1,000 par bond, receive $100 total interest, sell at $1,100.
  • Gain = (1,100 − 1,000) + 100 = 200
  • RoR = (200 / 1,000) × 100 = 20%

Nominal vs. Real Rate of Return

• Nominal RoR: The simple percentage change that ignores inflation.
• Real RoR: Inflation-adjusted return that reflects changes in purchasing power.
• Exact relationship: (1 + nominal) / (1 + inflation) − 1
• Approximate when rates are low: real ≈ nominal − inflation

RoR vs. CAGR

• RoR gives total growth over the period (e.g., 34% over six years).
• Compound Annual Growth Rate (CAGR) expresses average annual growth that accounts for compounding:
• CAGR = ((Ending value / Beginning value)^(1 / number of years) − 1) × 100
• Example: Buy a house for $250,000 and sell six years later for $335,000.
  • Simple RoR = ((335,000 − 250,000) / 250,000) × 100 = 34%
  • CAGR ≈ ((335,000 / 250,000)^(1/6) − 1) × 100 ≈ 5.0% per year

Internal Rate of Return (IRR) and Discounted Cash Flow (DCF)

• Discounted cash flows (DCF) account for the time value of money by discounting each cash flow at a specified rate.
• Net Present Value (NPV) formula:
• NPV = Σ (Ct / (1 + r)^t) − C0
  • Ct = cash flow at time t
  • C0 = initial outflow
  • r = discount rate
• Internal Rate of Return (IRR) is the discount rate r that makes NPV = 0. IRR reflects an annualized return that accounts for timing and size of cash flows.
• Example concept: A $10,000 equipment purchase that generates $2,000 per year for five years can be evaluated by discounting each $2,000 back to present value and comparing the sum to $10,000. If NPV > 0 at a chosen discount rate, the investment exceeds that required rate.

Advantages and Limitations

Advantages
– Simple RoR is easy to calculate and understand.
– Useful for quick comparisons of total gains or losses.

Limitations
– Ignores timing of cash flows and the time value of money.
– Does not adjust for inflation (unless converted to real RoR).
– Does not reflect risk or variability of returns.
– Can be misleading for multi-period investments—CAGR or IRR may be more informative.

Alternatives and When to Use Them

• CAGR: Use when you want an annualized rate that accounts for compounding over multiple periods.
• IRR: Use when cash flows occur at multiple times and timing matters.
• Real RoR: Use when you need to compare returns after adjusting for inflation.

What Is a “Good” Return?

There is no universal benchmark, but long-term historical averages are often cited as a reference. One common rule of thumb is roughly 7% per year after inflation for a broadly diversified equity portfolio (often associated with long-term U.S. stock market averages). Individual goals, risk tolerance, investment horizon, and asset class should determine what constitutes a good return for a particular investor.

Conclusion

RoR is a fundamental measure of investment performance that indicates total percentage change relative to the initial cost. For a fuller assessment, complement simple RoR with metrics that adjust for time, compounding, cash-flow timing, and inflation—such as CAGR, IRR, and real RoR—depending on the nature of the investment and the question you need to answer.