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Learning Objectives

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Learning Objectives

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Now · 1. Time Value of Money

Learning Objectives

Understand the time value of money
Calculate present and future values
Apply TVM to business decisions

1. Time Value of Money

Intuition: A dollar today is worth more than a dollar tomorrow because it can be invested to earn interest. Future Value:

FV = PV(1 + r)^n

Present Value:

PV = \frac{FV}{(1 + r)^n}

Worked Example: If you invest

1,000 at 8% for 5 years: FV = 1000(1.08)^5 = 1000 x 1.4693 =

1,469.33

2. Compounding Frequency

Annual: FV = PV(1 + r)^n Semi-annual: FV = PV(1 + r/2)^(2n) Continuous: FV = PV(e^(rn)) Effective Annual Rate:

EAR = (1 + r/m)^m - 1

3. Annuities and Perpetuities

Ordinary Annuity: Payments at end of each period.

PV_{annuity} = PMT \times \frac{1 - (1+r)^{-n}}{r}

Perpetuity: Infinite stream of equal payments.

PV_{perpetuity} = \frac{PMT}{r}

Growing Perpetuity:

PV = \frac{PMT}{r - g}

Concept	Formula
FV	FV = PV(1+r)^n
PV	PV = FV/(1+r)^n
Annuity PV	PV = PMT x [1-(1+r)^(-n)]/r
Perpetuity	PV = PMT/r

Q1: PV of $10,000 received in 3 years at 6%?

PV = 10000/(1.06)^3 = 10000/1.191 = $8,396.19 **Q2:$ 200/month for 5 years at 6% annual. PV?**

r = 0.06/12 = 0.005, n = 60. PV = 200 x [1-(1.005)^(-60)]/0.005 = 200 x 51.7256 = $10,345.12 **Q3: A perpetuity pays$ 500/year, r=8%. What is PV?**

PV = 500/0.08 = $6,250 **Q4:$ 100 growing at 3%/year, r=10%. PV of growing perpetuity?**

PV = 100/(0.10-0.03) = 100/0.07 = $1,428.57 Q5: What is EAR if nominal rate is 12% compounded monthly?

EAR = (1+0.12/12)^12 - 1 = (1.01)^12 - 1 = 12.68% Join Discord NextNPV, IRR & Capital Budgeting