Lecture 2 - Time Value Of Money Flashcards Preview

Business Finance > Lecture 2 - Time Value Of Money > Flashcards

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

Nominal and real interest rates

Nominal interest rate is the rate at which money invested grow

Real interest rate is the rate at which the purchasing power of an investment grows

1 + real investment rate = 1 + nominal interest rate / 1 + inflation rate

Nominal (real) cash flows must be discounted at the nominal (real) rate