📘 Chapter 6: Time Value of Money Part II

📽️ Chapter 6 Slides (PPT)

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Note on solutions: For each ICE item, the solution panel lists inputs in this fixed order — Function, rate, nper, pmt, pv, fv, type — followed by the final Excel function and the numeric answer. If the Excel line solves for one of these (e.g., RATE()), that field is marked (solve). Composite formulas show inputs as — and provide the Excel line + answer.

Quick Guide: New Variables & Rates

Chapter Add-Ons

PMT (Payment): Use Excel PMT() with (rate, nper, pv, [fv], [type]). Distinguish between Ordinary Annuity (type=0) and Annuity Due (type=1).

PMT: recurring cash flow Annuity (type=0) Annuity Due (type=1)

Ordinary Annuity (type = 0)

Blue marker jumps at the end of period t ⇒ Excel type=0.

Annuity Due (type = 1)

Pink marker jumps at the beginning of period t ⇒ Excel type=1.

APR — Annual Percentage Rate

Nominal yearly rate; does not include compounding, so typically APR ≤ EAR. Monthly rate = APR/12.

Excel (APR → EAR): =EFFECT(nominal_rate, npery)

EAR — Effective Annual Rate

Right annual return incl. compounding. If APR compounded m times/yr: EAR = (1 + APR/m)^m − 1

Example: APR = 12%, monthly (m=12) → EAR = 12.68%. Excel: =EFFECT(12%, 12)

(Reverse: APR = m * ((1+EAR)^(1/m) − 1). Excel: =NOMINAL(EAR, m))

Quick Cheats: NPV, NFV, EFFECT/NOMINAL, type

  • NPV vs PV: NPV(rate, CF1..CFn) discounts t=1..n. If there’s a time-0 cash flow C0, do C0 + NPV(...). PV today = result of that expression.
  • NFV (value at year T): NFV = FV(rate, T, 0, -NPV(rate, CFs), 0) (or compound the PV to year T).
  • EFFECT/NOMINAL: EAR from APR with m compounding: =EFFECT(APR, m). APR from EAR: =NOMINAL(EAR, m).
  • Annuity timing: type=0 = END (ordinary), type=1 = BEGIN (due). Due has one extra compounding each period.

NFV sandbox: jufinance.com/nfv

Homework — Chapters 5 & 6

Answers are hidden for now — Solution coming soon. Open each “Hint” for the exact Excel function and inputs.