Lecture 2 - Time Value Of Money

Question 1

Basic financial principle

Answer 1

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!

Question 2

Present And future values

Answer 2

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

Question 3

Simple interest

Answer 3

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..

Question 4

FV with simple interest

Answer 4

FV = PV x (1+r x t)

Question 5

Compound interest

Answer 5

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

Question 6

FV with annual compounding

Answer 6

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

Question 7

FV with compound interest

Answer 7

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

Question 8

FV with continuous compounding

Answer 8

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

Question 9

The relation between FV & PV

Answer 9

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?

Question 10

PV of annuities

Answer 10

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)

Question 11

Effective & percentage annual rates

Answer 11

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

Question 12

Nominal and real interest rates

Answer 12

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