Flashcards in Lecture 2 - Time Value Of Money Deck (12):

1

## Basic financial principle

###
A £ today is worth more than a £ in the future

Why?

- opportunity cost

- inflation

- uncertainty

Cash flows occurring in different time periods are not directly comparable. They need to be adjusted for the time value of money!

2

## Present And future values

###
Future value (FV) is the amount to which an investment today - present value (PV) - will grow after earning interest (r) for a time period (t)

The growth depends on whether the investment earns:

- simple interest

Or

- compound interest

3

## Simple interest

###
What is the future value of £100 that earns for 5 years 6% simple interest:

Year1) £100. 0.06 x 100= £6. £106

Year2) £106. 0.06 x 100 =£6. £112

Etc..

4

## FV with simple interest

### FV = PV x (1+r x t)

5

## Compound interest

###
What is the future value of £100 that earns for 5 years 6% compound interest ?

Year1) £100. 0.06 x £100 =£6. £106

Year2) £106. 0.06 x £100 =£6.36. £112.36

Year3) £112.36. 0.06x£100=£6.74. £119.10

Etc

6

## FV with annual compounding

### FV = PV x (1 + r)power of t

7

## FV with compound interest

###
FV = PV x (1 + r/n) power of n x t

Compounding N

- annual 1

- semi-annual. 2

- quarter. 4

- month 12

- week. 52

- day 365

8

## FV with continuous compounding

###
Continuous compounding means that n becomes infinitely large. It turns out that the FV of an investment with continuous compounding is given by:

FV = PV x e (power of r x t)

E is known as Euler’s number & has a value of approximately 2.71828

9

## The relation between FV & PV

###
Compounding:

- what is the future value of £1 invested today for t years if the interest rate is r?

Discounting:

- what is the present value of £1 that will be received after t year if the interest rate is r?

10

## PV of annuities

###
PV = cash Payment x [1/r - 1/r x (1+r) t ]

For computing the FV of an annuity simply multiply its PV by (1 + r)t

If the first cash payment is today, the annuity is called ‘annuity due’

The PV (FV) of an annuity due is simply the PV (FV) of an ordinary annuity multiplied by (1+r)

11

## Effective & percentage annual rates

###
Effective annual interest rate (EAR) is an interest rate annualised using compound interest

- 1 + EAR = (1 + r/n)n

Annual percentage rate (APR) is a short term rate annualised by multiplying the rate per period with the number of periods in a year

12