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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

What is the PV of a future cash flow of continuing compounding

FV = PV x e^ r x t

Or


PV = FV / e ^ r x t