Time Value of Money

1 / 21

# Time Value of Money - PowerPoint PPT Presentation

Time Value of Money. TVM - Compounding \$ Today Future \$ Discounting. Future Value (FV). Definition -. FV n = PV(1 + i) n. 1. 2. 0. N. FV = ?. PV=x. Future Value Calculations.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Time Value of Money' - whitney-soto

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Time Value of Money
• TVM -

Compounding

\$ Today Future \$

Discounting

Future Value (FV)
• Definition -

FVn = PV(1 + i)n

1

2

0

N

FV = ?

PV=x

Future Value Calculations
• Suppose you have \$10 million and decide to invest it in a security offering an interest rate of 9.2% per annum for six years. At the end of the six years, what is the value of your investment?
• What if the (interest) payments were made semi-annually?
• Why does semi-annual compounding lead to higher returns?
Future Value of an Annuity (FVA)
• Definition -

0

1

2

N

A

A

A

FVA = ?

Ordinary Annuity vs. Annuity Due

Ordinary Annuity

0

1

2

N

i%

A

A

A

Annuity Due

0

1

2

N

i%

A

A

A

Future Value of an Annuity Examples
• Suppose you were to invest \$5,000 per year each year for 10 years, at an annual interest rate of 8.5%. After 10 years, how much money would you have?
• What if this were an annuity due?
Present Value (PV)
• Definition -

PV = P0 = FV / (1 + i)n

1

2

0

N

FV = x

PV= ?

Present Value Calculations
• How much would you pay today for an investment that returns \$5 million, seven years from today, with no interim cashflows, assuming the yield on the highest yielding alternative project is 10% per annum?
• What if the opportunity cost was 10% compounded semi-annually?
• Why does semi-annual compounding lead to lower present values?
Present Value of an Annuity (PVA)
• Definition -

0

1

2

N

A

A

A

PVA = ?

Present Value of an Annuity Examples
• How much would you spend for an 8 year, \$1,000, annual annuity, assuming the discount rate is 9%?
• What if this were an annuity due?
• What if you were to receive payments of \$500 every six-months instead?
TVM Properties
• Future Values
• An increase in the discount rate
• An increase in the length of time until the CF is received, given a set interest rate,
• Present Values
• An increase in the discount rate
• An increase in the length of time until the CF is received, given a set interest rate,
• Note: For this class, assume nominal interest rates can’t be negative!
Perpetuities
• Definition -

0

1

2

\$

\$

\$

PVperpetuity = ?

Perpetuity Examples
• What is the value of a \$100 annual perpetuity if the interest rate is 7%?
• What if the interest rate rises to 9%?
• Principles of Perpetuities:
Uneven Cash Flow Streams
• Description -
• Ex. Given a discount rate of 8%, how much would you be willing to pay today for an investment which provided the following cash flows:
Uneven Cash Flow Streams
• Ex. Given a discount rate of 8%, what is the future value of the following cash flows stream:
Nominal vs. Effective Rates
• Nominal Rate -
• Effective Rate -
• What’s the difference?
Nom. vs. Eff. Rate Examples
• Ex. #1: A bond pays 7% interest semi-annually, what is the effective yield on the bond?
• A credit card charges 1.65% per month (APR=19.8%), what rate of interest are they effectively charging?
• What nominal rate would produce an effective rate of 9.25% if the security pays interest quarterly?
Amortization
• Amortized Loan -
• Ex. Suppose you borrow \$10,000 to start up a small business. The loan offers a contract interest rate of 8.5%, and must be repaid in equal, annual installments over the next 4 years. How much is your annual payment?
• What percentage of your payments go toward the repayment of principal in each year?
Amortization Schedules

Year #1, Principal % =

Year #2, Principal % =

Year #3, Principal % =

Year #4, Principal % =

Continuous Compounding
• Definition/Description -
Does Compounding Matter?
• What is the present value of \$200 to be received 2 years from today, if the discount rate is 9% compounded continuously?
• How much more would the cash flow be worth if the discount rate were 9% compounded annually?
• What is the future value, in 10 years, of a \$5,000 investment today, if the interest rate is 8.75% compounded continuously?
• How much lower would the future value be if the interest rate were 8.75% compounded annually?