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Quantitative MethodsModule 2 of 11

Time Value of Money in Finance

7

Concepts

7

Formulas

2

Decisions

6

Quiz Questions

Key Concepts

7 concepts covered in this module.

Present Value (PV)

The current worth of a future cash flow discounted at the appropriate rate. Foundation of all valuation.

Future Value (FV)

The value of a current amount after earning interest over a specified period.

Annuity

A series of equal cash flows at regular intervals. Ordinary annuity: payments at END. Annuity due: payments at BEGINNING.

Perpetuity

An annuity that pays forever. PV = PMT/r. Growing perpetuity: PV = PMT/(r - g).

Cash Flow Additivity

PV of a series of cash flows equals the sum of the PVs of individual cash flows. Basis for no-arbitrage pricing.

Implied Return

The discount rate that equates the PV of future cash flows to the current market price. For bonds: YTM; for stocks: implied return from DDM.

Implied Forward Rate

Future interest rate implied by current spot rates via no-arbitrage. (1+S2)² = (1+S1)(1+f1,1).

Formulas

7 essential formulas for this module.

Future Value

FV = PV × (1 + r)n

Where: r = interest rate per period, n = number of periods

Present Value

PV = FV / (1 + r)n

Where: r = discount rate, n = periods

PV of Ordinary Annuity

PV = PMT × [(1 - (1+r)-n) / r]

Where: PMT = periodic payment

PV of Perpetuity

PV = PMT / r

Where: PMT = periodic payment, r = discount rate

PV of Growing Perpetuity

PV = PMT / (r - g)

Where: g = growth rate (must be < r)

EAR (Effective Annual Rate)

EAR = (1 + rperiodic)m - 1

Where: m = compounding periods per year

Implied Forward Rate

(1 + Sn)n = (1 + Sn-1)n-1 × (1 + fn-1,1)

Where: S = spot rate, f = forward rate

Decision Frameworks

2 decision frameworks to guide your analysis.

Ordinary Annuity vs Annuity Due?

  • Ordinary annuity: most bonds (coupons at end of period), most loans
  • Annuity due: lease payments at start, insurance premiums

When to use Cash Flow Additivity?

  • Pricing bonds by discounting each coupon separately at spot rates
  • No-arbitrage pricing of derivatives
  • Implied forward rate calculations

Mind Map

Visual overview of how concepts connect in this module.

Time Value of Money
Single Cash Flow
FV = PV(1+r)^n
PV = FV/(1+r)^n
Compounding vs Discounting
Annuities
Ordinary (end of period)
Annuity Due (beginning)
PV and FV formulas
Adjust: ×(1+r) for Due
Perpetuities
PV = PMT/r
Growing: PMT/(r-g)
Gordon Growth Model link
Cash Flow Additivity
Sum of individual PVs
No-arbitrage pricing
Forward rate derivation
EAR & Compounding
EAR = (1+r/m)^m - 1
Continuous: EAR = e^r - 1
Always > stated rate
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Present Value (PV)

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The current worth of a future cash flow discounted at the appropriate rate. Foundation of all valuation.
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Statistical Measures of Asset Returns