Time Value Of Money

Question 1

Why is a £ worth more today than in the future

Answer 1

Opportunity cost
Inflation
Uncertainty

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)

Question 3

Simple interest

Answer 3

Same increase year on year

E.g. £100 that earns 6% for 5 years

£6 increase every year
6x5=30

FV= £130

Question 4

Equation for FV with simple interest

Answer 4

FV=PV(1+RT)

R=interest
T= time

PV = FV / (1+RxT)

Question 5

Compound interest

Answer 5

Interest that builds upon the previous interest

£100 6% for 5 years

1 ) £106
2) 0.06 x 106= 6.36= £112.36
And so on

Formula - FV=PV(1+R)^T

PV= FV/(1+R)^T

Question 6

FV with compound interest (different time measurements)

Answer 6

FV=PV(1+r/n)^NT

Confounding     N
Annual.              1
Semi annual.     2
Quarter             4
Month               12
Week.               52
Day                  365

PV= FV/ (1+R/N)^NT

Question 7

continuous compounding

Answer 7

Continuous compounding means n becomes infinitely large

FV of an investment with continuous compounding is given by

FV=PV x e^RT
PV=FV/e^RT
“e” is Eulers number and has a value of approximately 2.71828

Question 8

General compounding

Answer 8

FV=PV(1+r/n)^nt

PV=FV/(1+r/n)^nt

Question 9

PV of multiple cash flows

Answer 9

PV= FV/(1+r)^t

R=discount rate e.g. 8% annually

Work out separately for each time period (e.g. year)

Add each end figure together

Question 10

PV of perpetuities

Answer 10

PV = FV/(1+r)^t
PV= cash payment/ r 

R = discount rate

Add each separate figure for each year together at end

Question 11

PV of annuities

Answer 11

PV= FV / (1+R)^T

Then add figures for each year

PV= cash payment [1/r - 1/(r(1+r)^2)]

To compute the FV multiply it’s PV by (1+r)^t

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

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

Question 12

Effective and percentage annual rates

Answer 12

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

APR= R x N

Question 13

Nominal and real interest rates

Answer 13

Nominal interest rate is the rate at which money invested grows

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

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

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