2. Future Value – Several Cash Flows
Concept: Compounding
Value in the future
Different cash flows paid in at different times
...
5-*
Finding FV – Several Cash Flows Example
Assumptions
Invest $100 today (compounds for 3 years)
Invest $125 at end of year 2 (compounds for 2 years)
Invest $150 at end of year 3 (compounds for 1 year)
Interest rates: 7%
...
5-*
FV Several Cash Flows Time Line Example
3. ...
Several (Different) Cash Flow Values
5-*
Future Value – Level Cash Flows
Concept: Compounding
Also called “annuities”
Value in the future
Same cash flows paid in every period
...
5-*
Finding FV – Level Cash Flows/Annuity Example
Assumptions
Invest $100 at the end of each year for 5 years
Interest rates: 8%
4. ...
5-*
Level Cash Flows Time Line Example
...
Level (same) Cash Flows Each Period
5-*
Future Value – Multiple Annuities
Concept: Compounding – annuity equation to compute future
value – two levels of cash flows
To solve for multiple annuities, compute FV for each separately
and add them together
...
5-*
Finding FV – Multiple Annuities Example
Assumptions
5. Invest $100 at end of years 1 - 3 at 8%
Invest $150 at end of years 4 - 5 at 8%
...
5-*
Future Value – Multiple Annuities
Step 1 (same as FV of Level Cash Flows Calculation)
Step 2
Add two sums together – FV of both is $690.66
Step 3
5-*
Present Value of Multiple Cash Flows
Multiple cash flows
Car loans and home mortgage loans
Determining value of business opportunities
5-*
Present Value – Several Cash Flows
6. Concept: Discounting
Value of future sum today
Different cash flows paid in at different times
...
5-*
Finding PV – Several Cash Flows Example
Assumptions
Deposit $100 today
Deposit $125 next year
Deposit $150 at end of year 2
Interest rates: 7%
...
5-*
PV Several Cash Flows Time Line Example
...
7. 5-*
Present Value – Level Cash Flows
Concept: Discounting
Value of future sum today
Level cash flows paid in at different times
Most loans set up with even payments throughout life of loan
...
5-*
Finding PV – Level Cash Flows Example
Assumptions
$100 payments at end of each year for 5 years
Interest rates: 8% per year
...
5-*
PV Level Cash Flows Time Line Example
...
8. 5-*
Present Value – Multiple Annuities
Concept: Discounting
Changing level cash flows
Ex: Alex Rodriguez’s baseball contract
...
5-*
PV – Multiple Annuities Example
Assumptions (Alex Rodriguez’s Contract)
$10 million signing bonus
$21 million per year from 2001 – 2004
$25 million per year in 2005 and 2006
$27 million per year in 2007 – 2010
Interest rates: 8% per year
...
9. 5-*
PV – Multiple Annuities Example (cont.)
5-*
Perpetuity – Special Annuity
Concept: Discounting
Stream of level cash flows paid forever
Preferred stocks are an example
Value of investment is present value of all future annuity
payments
...
5-*
Ordinary Annuities vs. Annuities Due
Ordinary Annuity
Payment occurs at the end of each period
Annuity Due
Payment occurs at the beginning of each period
5-*
Annuity Due Time Line Example
Cash flows at beginning, not at end of period
10. Five annuity-due cash flows basically same as payment today
plus 4-year ordinary annuity
Payments occur one period sooner than ordinary annuity -- earn
extra period of interest
...
5-*
Future Value of Annuity Due
Concept: Compounding
Value of future sum today
Cash flows at beginning of each period
...
5-*
Future Value of Annuity Due
Assumptions
Assumes cash flows at the beginning of each period
5 annuity-due cash flows of $100 each
First cash flow compounds for 5 years
Last cash flow compounds for 1 year
Interest rates: 8%
11. ...
5-*
Present Value of Annuity Due
Concept: Discounting
Today’s value of future sum
Cash flows at beginning of each period
...
5-*
Present Value of Annuity Due
Assumptions
Cash flows at beginning of period
5 annuity-due cash flows of $100
First cash flow paid today – not discounted
Last cash flow discounted 4 years
All cash flows discounted for one year less than ordinary
annuity
Interest rates: 8%
12. ...
5-*
Compounding Frequency
Used in situations that do not use yearly time periods
Semiannual bond payments
Quarterly stock dividends
Consumer loans – monthly payments
5-*
Effect of Compounding Frequency
Assumptions
$100 deposit today
12% annual interest rate
Bank compounds interest at six months instead of end of year
Interest is earned on interest
...
5-*
EARS and APRS
Quoted, or nominal rate called annual percentage rate (APR)
Rate that incorporates compounding called effective annual rate
(EAR)
Relationship between APR and EAR
13. ...
5-*
EARS vs. APR Example
Assumptions
Borrow $100 today
12% annual interest rate
APR: Loan compounds annually -- you pay 12.00%
EARS: Loan compounds monthly -- you pay 12.68%
...
5-*
Annuity Loans
Compares payments
Compares implied interest rate
5-*
Finding Payments on Amortized Loan
Concept
Rearrange PV of annuity formula to solve for payment
15. 6-*
Financial Markets
Manage flow of funds
Two major market dimensions
Primary versus secondary markets
Money versus capital markets
6-*
Primary Markets
Used by corporations and governments
Used to issue new financial instruments
Stocks
Bonds
6-*
Primary Market Transfer of Funds
6-*
Secondary Markets
Benefit investors and issuers
Securities traded after issue
Provide liquidity and diversification benefits for investors
Security valuation information for issuers
6-*
16. Secondary Market Transfer of Funds
6-*
Money Markets vs. Capital Markets
Money markets trade debt securities or instruments with
maturities of one year or less
Capital markets trade stocks and long-term debt with maturities
greater than one year
6-*
Money Market vs. Capital Market Maturities
6-*
Other Markets
Foreign Exchange Markets
Trade currency for immediate delivery (spot) or for some future
delivery
Subject to foreign exchange risk due to currency fluctuations
6-*
Other Markets
17. Derivatives
Highly leveraged financial securities linked to underlying
security
Potentially high-risk
Used for hedging and speculating
6-*
Financial Institutions
Banks
Thrifts
Insurance companies
Mutual funds
6-*
Financial Institutions
Perform economic functions
Monitor costs
Provide liquidity
Price risk
6-*
Funds Flow with Financial Institutions
6-*
Interest Rates
Affected by economic conditions
Nominal rate quoted most often
18. 6-*
Nominal Interest
Factors that affect rate
Inflation
Real interest rate
Default and liquidity risk
Provisions of security issuer
Time to maturity
6-*
Inflation
Percentage increase in cost of goods or services over given
period of time
Actual or Expected inflation rate
Interest rates increase in response to inflation
6-*
Inflation
Annual inflation calculation using Consumer Price Index (CPI)
6-*
Nominal Rates vs. Inflation
6-*
19. Default or Credit Risk
Risk that issuer fails to pay promised interest and principal
Investors demand higher interest with higher default risk
U.S. Treasury securities are generally considered to be free of
default risk
6-*
Default Risk Premium Calculation
DRPj = ijt - iTt
6-*
Corporate Bond Default Risk Premiums
6-*
Three Yield-Curve Theories
Unbiased Expectations
Liquidity Premium
Market Segmentation
6-*
Unbiased Expectation Yield Curves
20. 6-*
Forecasting Interest Rates
As interest rates rise, investment portfolios values fall
Forecasts important to corporate and individual financial wealth
Week 3:
Chapter 5: Time Value of Money
Saving for a Car and Car Payments
http://www.viddler.com/embed/22f775c7/?f=1&autoplay=0&pla
yer=simple&disablebranding=0
http://www.viddler.com/embed/1947f559/?f=1&autoplay=0&pla
yer=simple&disablebranding=0
Saving for the World Cup: This example can be adapted to fit
other types of games you may be interested in:
http://www.viddler.com/embed/137f7648/?f=1&autoplay=0&pla
yer=simple&disablebranding=0
Saving in a Company’s Pension Plan/Making Pension
Contribution
http://www.viddler.com/embed/b1d0741b/?f=1&autoplay=0&pla
yer=simple&disablebranding=0
http://www.viddler.com/embed/9df5a396/?f=1&autoplay=0&pla
yer=simple&disablebranding=0
Saving in IRA
http://www.viddler.com/embed/3f7d288e/?f=1&autoplay=0&pla
yer=simple&disablebranding=0
Getting a Home Mortgage:
http://www.viddler.com/embed/396f27db/?f=1&autoplay=0&pla
yer=simple&disablebranding=0
Do You Know How Credit Offers Work? Take a look at the
offers, effective interest, and paying off credit cards:
http://www.viddler.com/embed/1ec5cb18/?f=1&autoplay=0&pla
