Personal Financial Management

1
Personal Financial Management

• Semester 2 2008 2009
• Gareth Myles g.d.myles_at_ex.ac.uk
• Paul Collier p.a.collier_at_ex.ac.uk

2
Reading

• Callaghan Chapter 4
• McRae Chapter 8

3
Interest and Interest Rates

• Some basic information on interest rates
• Bank of England base rate
• Set by Monetary Policy Committee
• Provides a basis for other rates
• No-one can trade at a lower rate (arbitrage)
• Objectives of the MPC
• To control the rate of inflation (target band)
• Increase in interest rate reduces demand
• Reduction in interest rate stimulates demand
• Base decisions on economic data

4
Other Important Rates

• LIBOR London Interbank Offered Rate
• The rate at which banks are willing to lend to
  each other
• The basis for many financial calculations
• Mortgage rates
• Mortgages are the safest form of lending to
  individual so have lowest interest rates
• Market rate is determined by competition between
  lenders

5
Other Important Rates

• Personal loans
• Loans for purchases other than property (more
  risk)
• Higher interest rate than mortgages
• More variation in interest rates than for
  mortgages
• Collateral
• Secured loan an asset is held as collateral
• Unsecured loan no collateral
• Interest rate is lower on a secured loan

6
Credit Creation

• How does the banking system function?
• Savers deposits funds
• At any time only a fraction of funds withdrawn
• The remaining fraction leant to borrowers
• The process is repeated eventually multiplying
  initial deposit
• Banks profit from the difference in interest
  rates
• So borrowing rate is higher than the saving rate
  (lack of competition, asymmetric information,
  risk)

7
Loans

• Open-ended
• An upper limit is agreed, borrower has
  flexibility
• Specific
• For the purchase of a defined item, with a clear
  payment schedule
• What determines the interest rate?
• Lowest when secured on a safe asset
• Highest when unsecured and open
• Depends also on credit worthiness of borrower

8
Profit

• Earning money from issuing loans is easy
• Lenders borrow at one rate
• Lend at a higher rate
• A loss can occur through default and poor risk
  management
• Current bank losses can be interpreted as poor
  risk management
• Bad debts increase costs
• This is why those perceived to be safe will be
  offered a lower rate of interest

9
Credit Rating Agencies

• Hold data on borrowers to advise lenders of
  previous history
• Can make mistakes
• For example assigning bad risk to an address
• If refused credit
• Can ask whether because of a credit agency report
• Can then contact agency to correct any false
  information

10
Credit Cards

• Credit Cards offer free credit if repaid
  monthly, but otherwise incur a very high interest
  rate
• Table of Rates
• Strategy carry debt from card to card to take
  advantage of introductory offers
• Store Cards usually an even higher rate
• Store Card
• The only reason to hold these is to benefit from
  card-holder discounts

11
Interest Rate Calculations

• To understand interest rates, need to go some
  through some basic calculations
• Interest is compounded at a specified interval
• The interval can make a difference
• Assume interval is one year
• Then borrowing 100 at a rate of 10 for one year
  implies a total repayment of

12
Compounding Interval

• Now consider what happens if we compound interest
  more frequently
• If every 6 months, then rate of 10 for a year
  becomes 5 for six months so
• If compounded every 3 months
• The general formula for interest at rate r
  compounded m times a year for n years on a loan
  of L is

13
Continuous Interest

• Continuous interest is the limit of more frequent
  compounding

14
Effects

• The difference between 110 and 110.52 may seem
  small
• It is equivalent to 0.52 on the
  annually-compounded interest rate of 10
• On a large loan this could be significant effect
• Compounding period
• Matters for repayment
• Needs to be clarified before alternative loans
  can be compared

15
Flat Rate Interest

• Interest can also be quoted as a flat rate
• Consider 100 borrowed for 5 years, with a flat
  rate of interest of 10
• This means 10 of interest is paid per year
• Over 5 years the total payments on the loan are
• 1010101010100 150
• The repayment structure is 5 payments of 30
• This is equivalent to an APR of 15.2 (see later
  or use mortgage calculation)

16
Annual Percentage Rate

• These compounding issues motivate the need to
  find a standard of comparison
• The government has chosen to use the Annual
  Percentage Rate (APR)
• This interest rate converts any interest schedule
  (such as the flat rate) to the annual equivalent
• Annual Percentage Rate

17
Annual Percentage Rate

• Consider receiving m payments Ak at times tk and
  making n payments Ak' at times tk '
• The interest rate that makes the present
  discounted value of both flows equal solves
• The solution r to this equation is the APR

18
Example 1

• Receive 100 at t1 0
• Pay 10 at t1' 1, pay 110 at t2' 2
• Solution is r 10
• This is just a standard loan at 10 interest

19
Example 2

• Receive 100 at t1 0, receive 50 at t2 1.5
• Pay 90 at t1' 1, pay 80 at t2' 2
• Solution is r 13.5
• How is this found?
• Draw a graph
• Trial and error

20
Example 2
21
Example 3

• Flat rate interest of 10
• 100 is received at time 0
• Five payments of 30 are made
• The APR solves
• The solution is 15.2 as claimed earlier

22
Example 3
23
Comparison

• The APR is quoted with all adverts for loans
• It is a simple means of contrasting the rates on
  loans with different structures