Presentation 3

Petroleum Project Economics Econ210D

Presentation 3

Interest and Time Value of MoneyWeek 3

1

• Interest remains constant each year.

• Interest is not reinvested

• Interest is calculated by the formula.

2

Simple Interest

nrPI

where: I = Interest, P = Principal, r = interest,

n = number of years.Interest and Time Value of Money

Week 3

• Interest is based on principal plus reinvested interest from

previous years

• Interest increase each successive year

3

Compound Interest

nrPA 1

where: P = Principal, r = interest, n =

number of years, A = Principal + Interest, Interest and Time Value of Money

Week 3

4

Future and Present Value

• Future Value – the value at some point in the future of a single cash flow or a series of cash flows in the future.

• Present Value – the value today of a single cash flow or a series of cash flows in the future

• Values change over time due to interest

• Interest is based on compound interestInterest and Time Value of Money

Week 3

5

where:F = Future valueI = Investment/Principalr = rate of interest (for each time period)n = number of time periods.

Future Value

nrIF 1

Interest and Time Value of Money Week 3

6

Present Value

nr

IP1

where:P = Present valueI = Investment/Principalr = rate of interest (for each time period)n = number of time periods.


7

Future Value of a Single Cash Flow

An investor deposits $100 into an account

which offers 12% p.a. compound interest.

What is the value of the investment at the

end of 3 years?


8

Present Value of a Single Cash Flow

An investor is supposed to receive $100 in

3 years time. If the rate of compound

interest is 12% p.a. what is the present

value of the amount?


9

Annuities – Series of Cash flows

• An annuity is a series of equal payments at evenly spaced intervals

• The payments occur at the beginning of each period for an annuity due while they occur at the end of each period for an ordinary annuity

• Interest is earned on amounts paid


10

Annuity Due and an Ordinary Annuity – over 3 years

• Annuity Due

• Ordinary Annuity

Jan 1st 2009

$100 $100 $100

$100$100 $100

Jan 1st 2009

Jan 1st 2010 Jan 1st 2011 Dec 31st 2011

Dec 31st 2009 Dec 31st 2010 Dec 31st 2011


11

At the beginning of each year an

investor deposits $100 into an account

which offers 12% p.a. compund

interest. What is the value of the

investment at the end of 3 years?

Future Value of an Annuity Due


12


Time Year Amount Workings Future Value

Jan 1st 2009 0 $100 $140

Jan 1st 2010 1 $100 $125

Jan 1st 2011 2 $100 $112

Dec 31st 2011 3 $0 $0

Total $300 $378


13


$0

$20

$40

$60

$80

$100

$120

$140

$160

Amount

Future Value

Amount $100 $100 $100 $0

Future Value $140 $125 $112 $0

Jan 1st 2009 Jan 1st 2010 Jan 1st 2011 Dec 31st 2012


14

Future Value of an Annuity Due using Formula

where

• I = periodic investment

• r = interest rate per period

• n = number of periods

111 1

r

rIFVA

n

DUE


15

At the end of each year an investor

deposits $100 into an account which

offers 12% p.a. compound interest.

What is the value of the investment at

the end of 3 years?

Future Value of an Ordinary Annuity


16


Time Year Amount Workings Future Value

Jan 1st 2009 0 $0 $0

Dec 31st 2009 1 $100 $125

Dec 31st 2010 2 $100 $112

Dec 31st 2011 3 $100 $100

Total $300 $337


17


$0

$20

$40

$60

$80

$100

$120

$140

Amount

Future Value

Amount $0 $100 $100 $100

Future Value $0 $125 $112 $100

Jan 1st 2009 Dec 31st 2009 Dec 31st 2010 Dec 31st 2011


18

Future Value of an Ordinary Annuity using Formula

where



• n = number of periods

r

rIFVA

n

ORDINARY

11


19


investor deposits $10,000 into an

account which offers 10% p.a.

compound interest. What is the value of

the investment at the end of 4 years?

Question 1


20

At the end of each year an investor

deposits $2,000 into an account

which offers 2% p.a. compound


investment at the end of 5 years?

Question 2


21

At the end of each quarter an investor



What is the value of the investment at

the end of 1 year?

Question 3


22

At the beginning of each month an




investment at the end of 6 months?

Question 4


23



which offers 12% p.a. compund

interest. What is the present value of

the investment?

Present Value of an Annuity Due


24


Time Year Amount Workings Present Value

Jan 1st 2009 0 $100 $100

Jan 1st 2010 1 $100 $89

Jan 1st 2011 2 $100 $80

Dec 31st 2011 3 $0 $0

Total $300 $269


25


$0

$20

$40

$60

$80

$100

$120

Amount

PresentValue

Amount $100 $100 $100 $0

Present Value $100 $89 $80 $0

Jan 1st 2009 Jan 1st 2010 Jan 1st 2011 Dec 31st 2012


26

Present Value of an Annuity Due Using the formula

11

11 1

rr

IPVAn

DUE

where



• n = number of periodsInterest and Time Value of Money

Week 3

27

At the end of each year for 3 years an



interest. What is the present value of the

investment?

Present Value of an Ordinary Annuity


28


Time Year Amount Workings Present Value

Jan 1st 2009 0 $0 $0

Dec 31st 2009 1 $100 $89

Dec 31st 2010 2 $100 $80

Dec 31st 2011 3 $100 $71

Total $300 $240


29


$0

$20

$40

$60

$80

$100

$120

Amount

PresentValue

Amount $0 $100 $100 $100

Present Value $0 $89 $80 $71

Jan 1st 2009 Dec 31st 2009 Dec 31st 2010 Dec 31st 2011


30

Present Value of an Ordinary Annuity Using the Formula

rr

IPVAn

ORDINARY

1

11

where



• n = number of periodsInterest and Time Value of Money

Week 3

31




compound interest. What is the present

value of the investment if this is done

over 4 years?

Question 5


32

At the end of each year for 5 years an



compound interest. What is the

present value of the investment?

Question 6


33

At the end of each quarter an investor



What is the present value of the

investment if this is done over 1

year?

Question 7


34

At the beginning of each month for 6

months an investor deposits $100 into

an account which offers 12% p.a.

compound interest. What is the

present value of the investment?

Question 8


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