📘 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))

🚀 Use the JU NPV / NFV Calculator for These Questions

Recommended Tool

For the NPV / NFV questions in this chapter, use the JU calculator here:

Open JU NPV / NFV Calculator

What it helps you do

  • Compute PV today from a stream of future cash flows.
  • Compute NFV / value at a target year by compounding the PV forward.
  • Check your Excel work on questions using NPV(), FV(), and mixed cash-flow timelines.
  • See clearly how the same cash flows connect across PV today and future value later.

Use it especially for

ICE: Q1, Q2, Q3, Q4, Q5, Q8, and Q30

Idea: Enter the cash flows by year, compute the NPV/PV today, then compare that to the NFV at the target year.

Go to the calculator →

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.

🔗 NPV / NFV Sandbox: https://www.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.