Time Value

TIME VALUE

Time Value
• Interest Rates
• Compounding • Discounting

• Effective Rates
• Annuities • Perpetuities
2

Interest Rates
• Types
– Bank rate vs. Prime rate – Mortgage rates – Deposit, Loan, Credit rates

• Movement
– Demand / Supply – Inflation/ Deflation – Government intervention
3

Main Components
1. Real 2. Inflation

3. Risk
*Note:

- Risk Free (Rf) = Real + Inflation - Nominal = Rf + Risk Premium
4

Risk Free & Real Rate

• Risk Free (Rf) = Real + Inflation

• Real = [(1 + Rf) / (1 + Inflation)] - 1
• Given Rf = 10% & Inflation = 6% • Real Rate = [(1.1) / (1.06)] – 1 = 3.77%
5

Compounding
FV
r (APR) PV t

FV = PV×(1 + r)t

= Future Value
= Interest rate = Present Value = Time

Discounting

PV = FV×[1 / (1 + r)t]
6

Effective Interest Rates (EAR) m  APR  EAR  1  1 m   
Where APR = Annual Percentage Rate (Nominal) m = Rate of Compounding

Compounding “APR” for “m” times a year = Effective Rate once a year
7

Effective Interest Rate (EAR) = [1 + r/m]m -1
Compounding period (t) Number of times compounded (m) Effective annual rate (%)

Year Quarter Month Week Day Hour Minute

1 4 12 52 365 8,760 525,600

10.00 10.38 10.47 10.506 10.515 10.517 10.5171

8

Annuities & Perpetuities
11 + r )t (1 r

PV Annuity =

FV Annuity =

(1 + r)t – 1 r

C Perpetuity : PV  r

C Growing Perpetuity : PV  rg

9

Future Value Annuity
FV calculated by compounding forward one period at a time
0 1 2 3 4

5
Time (years)

$0 0

$0 2,000 x 1.1

$2,200 2,000 x 1.1 $4,200 x 1.1

$4,620 2,000 $6,620 x 1.1

$7,282 2,000 $9,282 x 1.1

$10,210.2 2,000 $12,210.2

$0

$2,000

FV calculated by compounding each cash flow separately
0 1 2 3 4 5 Time (years)

$2,000

$2,000

$2,000

$2,000 x 1.1

$2,000.0 2,200.0 2,420.0 2,662.0 2.928.2

x

1.12

Using Annuity formula: $2,000 x (1.10)5 .10 = $2,000 x 6.1051 = $12,210.2 -1 x 1.14

x

1.13

Total