Time value of money
Download
1 / 21

Time Value of Money - PowerPoint PPT Presentation


  • 71 Views
  • Uploaded on

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.

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

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


An Image/Link below is provided (as is) to download presentation

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
Time Value of Money

  • TVM -

    Compounding

    $ Today Future $

    Discounting


Future value fv
Future Value (FV)

  • Definition -

FVn = PV(1 + i)n

1

2

0

N

FV = ?

PV=x


Future value calculations
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
Future Value of an Annuity (FVA)

  • Definition -

0

1

2

N

A

A

A

FVA = ?


Ordinary annuity vs annuity due
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
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?

  • What if you made payments of $2,500 every six-months instead?


Present value pv
Present Value (PV)

  • Definition -

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

1

2

0

N

FV = x

PV= ?


Present value calculations
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
Present Value of an Annuity (PVA)

  • Definition -

0

1

2

N

A

A

A

PVA = ?


Present value of an annuity examples
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
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
    Perpetuities

    • Definition -

    0

    1

    2

    $

    $

    $

    PVperpetuity = ?


    Perpetuity examples
    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
    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 streams1
    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 vs. Effective Rates

    • Nominal Rate -

    • Effective Rate -

    • What’s the difference?


    Nom vs eff rate examples
    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
    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
    Amortization Schedules

    Year #1, Principal % =

    Year #2, Principal % =

    Year #3, Principal % =

    Year #4, Principal % =


    Continuous compounding
    Continuous Compounding

    • Definition/Description -


    Does compounding matter
    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?


  • ad