7.2 Net Present Value and Internal Rate of Return

Net Present Value (NPV) and Internal Rate of Return (IRR) are crucial tools for evaluating investment opportunities. NPV calculates the present value of future cash flows, while IRR determines the rate that makes NPV zero. Both help assess project profitability.

These methods have strengths and limitations. NPV is generally more reliable, measuring absolute value in dollars. IRR provides a percentage return but can be misleading for comparing projects. Understanding both helps make informed investment decisions.

Net Present Value (NPV)

Net present value calculation

• NPV sums all future cash flows discounted to present value
  • Discounting accounts for time value of money (a dollar today is worth more than a dollar in the future)
  • Discount rate represents required rate of return or cost of capital (hurdle rate)
• NPV formula: $NPV = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t}$
  • $CF_t$ cash flow at time $t$
  • $r$ discount rate
  • $n$ number of periods
• Calculating NPV involves:
  1. Determine expected cash flows for each period (inflows and outflows)
  2. Choose appropriate discount rate (based on risk and opportunity cost)
  3. Discount each cash flow to present using discount rate
  4. Sum all discounted cash flows and subtract initial investment

NPV rule for investment decisions

• NPV rule: accept project if NPV positive, reject if NPV negative
  • Positive NPV indicates project generates returns greater than cost of capital (creates value)
  • Negative NPV suggests insufficient returns to cover cost of capital (destroys value)
• When comparing mutually exclusive projects, choose project with highest positive NPV
• NPV assumes cash flows reinvested at discount rate, which may not always be realistic (reinvestment rate assumption)

Internal Rate of Return (IRR)

Internal rate of return determination

• IRR is discount rate that makes NPV of project equal to zero
  • Represents expected rate of return generated by project (breakeven rate)
• IRR formula: $0 = \sum_{t=0}^{n} \frac{CF_t}{(1+IRR)^t}$
• Calculating IRR involves:
  1. Set NPV equation equal to zero
  2. Solve for discount rate (IRR) using trial and error or financial calculator
• IRR assumes cash flows reinvested at project's IRR, which may not always be realistic

NPV vs IRR in capital budgeting

• Both NPV and IRR evaluate financial viability of investment projects
• NPV measures absolute value in monetary terms (dollars), IRR measures rate of return (percentage)
• NPV generally considered more reliable because:
  • Accounts for time value of money
  • Assumes cash flows reinvested at cost of capital, more realistic
• IRR may give inconsistent results when comparing mutually exclusive projects with different:
  • Cash flow patterns (timing of inflows and outflows)
  • Project sizes (scale of investment)
• When NPV and IRR conflict, prioritize NPV
• Use both methods with other factors like strategic fit and risk when making capital budgeting decisions