NET PRESENT VALUE (NPV) & INTERNAL RATE OF RETURN (IRR)
Calculation for one period:
- FV=PV + PV. r -> FV=PV(1+r) -> PV=FV/(1+r)
Calculation for multiple periods:
- PV=[FCF1/(1+r) + FCF2/(1+r)'2 + ... + FCFn/(1+r)'n]
Calculation of NPV:
- NPV = PV – Initial Investment
Calculation of IRR:
- Solve “r” (the discount rate) that gives an NPV of zero
NOTES:
- FCF1, FCF2, FCFn – Projected Yearly Free Cash Flows
- r – Interest Rate or Cost of Capital (carefully use the project’s WACC, not the company’s one bc risks are different)
- I – Initial Investment
- n – Project Life (years, months, etc, but put r according to period specified)
Mathematical Problems with the IRR
(a) Negative Cash Flows and Multiple Rates of Return; e.i. when cash flows are +-+, gives multiple IRR, and thus mathematical calculation gives an error.
(b) The Re-investment Problem: bc when you borrow, WACC can change due to different risks.
(c) Ranking Differences: cannot decide in terms of size of projects and timing of cash.
Investment Appraisal and Inflation
(a) Adjust projected cash flows, to account for anticipated fall in value of money
(b) Re-state the discount rate, to allow for anticipated impact of expected inflation
APPENDIX – Future Values and Discount Rate Table
Tags: calculate irr, calculate npv, calculate wacc, fv, IRR, NPV, pv, wacc, Weighted Average Cost of Capital