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Flashcards in Time Value Of Money Deck (13):
1

Why is a £ worth more today than in the future

Opportunity cost
Inflation
Uncertainty

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)


3

Simple interest

Same increase year on year

E.g. £100 that earns 6% for 5 years

£6 increase every year
6x5=30

FV= £130

4

Equation for FV with simple interest

FV=PV(1+RT)

R=interest
T= time



PV = FV / (1+RxT)

5

Compound interest

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

6

FV with compound interest (different time measurements)

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

7

continuous compounding

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

8

General compounding

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

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

9

PV of multiple cash flows

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

10

PV of perpetuities

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

R = discount rate

Add each separate figure for each year together at end

11

PV of annuities

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)

12

Effective and 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

APR= R x N

13

Nominal and real interest rates

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