Flashcards in Time Value Of Money Deck (14):

1

##
Why is money worth more today than in future

###
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

## Future value

### Amount to which an investment today (PV) will grow after earning interest (r) for a time period (t)

3

## What does the growth of money depend on?

### The growth depends on whether the investment earns simple interest or compound interest

4

## Example of simple interest - what is FV of £100 that earns for five years (t) with simple interest of 6% (r)

###
Year 1: balance =100 interest earned = 100x0.06 =6 therefore balance = 106

As simple interest - same interest earned each year

So 6 x 5 = 30

30+100 =130

5

## Fv with simple interest formula

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

6

## Compound interest example - what is fv of 100 that earns for 5 years (t) at 6% with interest compounded annually

###
Year 1 100 x 0.06= 106

Year 2 106 x 0.06 = 112.36

Year 3 112.36 x 0.06 119.10

Year 4 119.10 x 0.06 = 126.25

Year 5 126.25 x 0.06 =133.82.

7

## Formula with annual compounding

### FV= PV X (1+r)^t

8

## Fv with compound interest

###
FV = PV x (1+r)^nxt

Compounding n

Annual =1

Semi =2

Quarter = 4

Month =12

Week =52

Day =365

9

## Continuous Compounding

###
Continues 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^r-t

e=is known as eulers number and has a value of approx is 2.71828

10

##
The relation between FV and PV

###
Compounding = what is the FV of £1 invested today for t years if the interest tag is r

Discounting = what is the PV of £1 that will be received after t years if the interest rate is r

11

## What is the PV of future cash flow on simple interest

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

Or

PV = FV / (1+r x t)

12

## What is the PV of a future cash flow with annual compounding

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

Or

PV= FV / (1+r) ^t

13

## What is PV of a future cash flow with general compounding

###
FV= PV x (1 + r/n) ^nxt

Or

PV = FV / (1 + r/n) ^n x t

14