Time Value Of Money

Question 1

Why is money worth more today than in future

Answer 1

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

Future value

Answer 2

Amount to which an investment today (PV) will grow after earning interest (r) for a time period (t)

Question 3

What does the growth of money depend on?

Answer 3

The growth depends on whether the investment earns simple interest or compound interest

Question 4

Example of simple interest - what is FV of £100 that earns for five years (t) with simple interest of 6% (r)

Answer 4

Year 1: balance =100 interest earned = 100x0.06 =6 therefore balance = 106

As simple interest - same interest earned each year

So 6 x 5 = 30

30+100 =130

Question 5

Fv with simple interest formula

Answer 5

FV=PV X (1 + r x t)

Question 6

Compound interest example - what is fv of 100 that earns for 5 years (t) at 6% with interest compounded annually

Answer 6

Year 1 100 x 0.06= 106

Year 2 106 x 0.06 = 112.36

Year 3 112.36 x 0.06 119.10

Year 4 119.10 x 0.06 = 126.25

Year 5 126.25 x 0.06 =133.82.

Question 7

Formula with annual compounding

Answer 7

FV= PV X (1+r)^t

Question 8

Fv with compound interest

Answer 8

FV = PV x (1+r)^nxt

Compounding n

Annual =1
Semi =2
Quarter = 4
Month =12
Week =52
Day =365

Question 9

Continuous Compounding

Answer 9

Continues 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^r-t

e=is known as eulers number and has a value of approx is 2.71828

Question 10

The relation between FV and PV

Answer 10

Compounding = what is the FV of £1 invested today for t years if the interest tag is r

Discounting = what is the PV of £1 that will be received after t years if the interest rate is r

Question 11

What is the PV of future cash flow on simple interest

Answer 11

FV= PV x (1+r x t)

Or

PV = FV / (1+r x t)

Question 12

What is the PV of a future cash flow with annual compounding

Answer 12

FV= PV x (1+r)^t

Or

PV= FV / (1+r) ^t

Question 13

What is PV of a future cash flow with general compounding

Answer 13

FV= PV x (1 + r/n) ^nxt

Or

PV = FV / (1 + r/n) ^n x t

Question 14

What is the PV of a future cash flow of continuing compounding

Answer 14

FV = PV x e^ r x t

Or

PV = FV / e ^ r x t