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

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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 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 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 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!

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?

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