Flashcards in Time Value Of Money Deck (13):

1

## Why is a £ worth more today than in the future

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Opportunity cost

Inflation

Uncertainty

2

## Present and future values

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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

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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

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FV=PV(1+RT)

R=interest

T= time

PV = FV / (1+RxT)

5

## Compound interest

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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)

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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

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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

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

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

9

## PV of multiple cash flows

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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

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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

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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

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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