The Cost of Money:

1
V 2.1 Aug 12

• The Cost of Money
• Learning Objectives
• Explain why lenders charge interest
• Define the components of interest rates (r
  rIPDRPLPMRP)
• Know what a term structure of interest rates is
• Define an interest rate Yield Curve
• how to read it
• what influences the shape of the yield curve
• what the shape tells us about future interest
  rates
• Make borrowing decisions using yield curve
  information
• Understand the Opportunity Cost of Capital

2
V 2 Jan 12

• The Cost of Money
• Is the interest rate you pay a lender
• Is what borrowers pay to use (rent) money
• Inflation
• Definition The decrease of the purchasing power
  of currency over time
• Cause various factors chief among them
• demand for goods services grows faster than the
  supply of goods services as time goes by,
  goods services become more valuable thus more
  expensive this reduces the purchasing power of
  currency
• An increase in the amount of money in circulation
  in an economy as quantity of currency increases,
  value of currency decreases with respect to the
  value of goods services it takes more money to
  purchase goods services, thus the purchasing
  power of currency is reduced
• What is an Interest Rate?
• When someone decides to lend money, they want
  compensation for
• the loss of the opportunity to use that money
  while its loaned out (opportunity cost)
• the loss of value over time due to inflation
• the chance that they wont get the money back
• The interest rate (r) one pays for the privilege
  of using someone elses money is the sum of these
  different compensations
• Thus r r IP RP
• r real (risk free) rate which is the
  opportunity cost
• IP the Inflation Premium which compensates for
  inflation

3

• The Cost of Money (continued)
• Interest rates are usually expressed and
  quantified as a percentage of the principle (the
  amount borrowed).
• Example A 1,000 face value bond has a coupon
  rate of 6.0000 per year. Interest is paid
  annually. How much interest is earned each year?
• Interest PMT Principle(Interest Rate)
• 1,000(0.06) 60
• Symbols r or k or i
• Two basic types of interest
• Simple Interest
• paid all at once either upon initiating or
  closing (at the end of) the loan
• no compounding
• Compound Interest
• paid in little chunks throughout the life of the
  loan, usually at the end of the period
• interest earned is reinvested thus interest
  earns interest (as discussed in Ch 4)
• The cost of money (an interest rate) is also
  referred to as

4

• The Cost of Money (continued)
• Major factors that affect the cost of money
• Opportunity Costs
• Internal investment vs. external
• Desire to consume (spend) money now versus
  investing it.
• Risk
• Expected Inflation (has the greatest influence on
  cost of money)
• Federal Reserve Policy
• Business Activity / State of the Economy
• Federal Deficits
• Foreign Trade Balance

5

• The Cost of Money (continued)
• The Components of an Interest Rate This is how
  the major factors that influence the cost of
  money are quantified and factored into interest
  rates
• Nominal Interest Rate ? r r IP
  DRP LP MRP
• r Nominal Rate in a particular market1 also
  called the Quoted Rate
• r Real Interest Rate (Real Risk-Free Rate )
• Compensates the lender for his opportunity costs,
  regardless of inflation or any other risks
• Production Opportunities
• Time Preference for Consumption
• No one really knows what the real risk-free rate
  is
• A commonly accepted value for the real risk-free
  rate can be found by subtracting current
  inflation rate from the current 30-day
  Treasury-bill rate. (See Nominal Risk-free Rate
  p. 6)
• r is not constant it changes over time
• IP Inflation Premium
• Compensates the lender for loss in value over
  time due to inflation.
• This is computed as the average expected
  inflation rate over the life of the loan (more on
  this later)

Risk Premium
6

• The Cost of Money (continued)
• DRP Default Risk Premium
• Compensates the lender for possible default.
• This is kind of like an insurance payment
• 30-day Treasury bills (T-bills 1,000 face value
  very short term bonds) have a DRP of 0 Why?
• Answer T-bills are considered riskless.
• LP Liquidity Premium
• Accounts for the ability of a borrower to repay a
  loan with the firms assets.
• If these assets are not very liquid (i.e. real
  estate, buildings, equipment, etc.), LP will be
  higher
• Although its very difficult to calculate LP, it
  tends to differ 2 to 5 percent between the most
  liquid and least liquid financial assets
• MRP Maturity Risk Premium
• Maturity is the length of the loan
• Compensates for Interest Rate Risk. The longer
  the term (time till maturity), the greater the
  interest rate risk, thus a higher MRP. (We will
  talk more about interest rate risk later in the
  semester)
• Compensates for Reinvestment (Rate) Risk.
• When a loan matures, the interest rate might be
  lower than when the loan was issued
• Therefore the lender cant reinvest the repaid
  principle at the same rate at which he originally
  loaned it.

7

• The Cost of Money (continued)
• Quoted Interest Rate ? r rRF DRP
  LP MRP
• This equation is the one most commonly used to
  compute interest rates since its easy to find
  rRF (the yield on a 30-day T-bill) just read the
  Wall Street Journal
• Example Jungle Jims Outfitters, a local outdoor
  equipment retail store, wants a 1-year, 50k loan
  from your bank. You have already determined that
  this firm warrants an DRP of 5, an LP of 1 and
  an MRP of 0.5. Todays WSJ reports 30-day
  T-bills are currently yielding 2.3. What is an
  appropriate interest rate for this loan?
• r rRF DRP LP MRP
• 2.3 5 1 0.5 8.8
• Note We assumed that the Inflation Premium (IP)
  will be the current inflation rate as implied by
  the rate on a 30-day T-bill. This usually is
  acceptable only for relatively short-term loans
  (less than 1 year maturity).

8

• The Cost of Money (continued)
• How do you compute r for loans longer than 1 year
  maturity?
• Use r r IP DRP LP MRP
• Find current inflation (what the govt reports as
  current inflation)
• Find the yield on a 30-day T-bill
• Compute r (r rRF - Current Inflation
  Rate)
• Find expected inflation for upcoming years
• Compute the average value for expected inflation
  this is IP
• IP ( I1 I2 I3 ..In) / n where n is
  the number of years of maturity and In is the
  expected inflation for a particular year
• Example Jihad Jims Travel Adventures, a new
  travel agency, wants a 3-year, 500k loan from
  your bank. You have already determined that this
  firm warrants an DRP of 10, an LP of 3 and an
  MRP of 1.5. Today is 2 January. Inflation for
  the rest of this year is expected to remain at 2
  . Next years inflation is expected to be 2.5
  and the following years inflation is expected to
  be 3. Todays WSJ reports 30-day T-bills are
  currently yielding 2.3. What is an appropriate
  interest rate for this loan?
• 1) Find r r rRF - Current Inflation
  Rate
• r 2.3 - 2 0.3
• 2) Find IP IPn ( I1 I2 I3 ..In) / n
• IP3 (2 2.5 3)/3 2.5
• 3) Find r r r IP DRP LP MRP

9

• The Cost of Money (continued)
• What factors tend to lower interest rates?
• Answer
• Everyone in the lending business wants to lend
  you (or your company) money because they want the
  cash flow from your interest payments
• Its very competitive. Lenders are always trying
  to offer more attractive rates than their
  competitors in order to get you to borrow from
  them
• This is the root cause for many banking fiascoes
  banks often enter into risky lending in pursuit
  of cash flow
• Why should you care about this interest rate
  stuff?
• Answer
• If you are a lender, it will enable you to
  determine an appropriate, competitive rate
• If you are a borrower, it will help you shop for
  money
• Related economic indicators may help you
  determine likely future interest rates (by
  examining affects on interest rate factors and
  components)
• thus helping you in deciding whether to
  lend/borrow now or wait or whether to bargain for
  higher/lower rates
• this is a form of risk management reducing
  uncertainty concerning future interest rates
• It will help you minimize your firms financing
  cost
• Just about all the other topics we will cover
  during this course involve interest rates or
  other factors that are similar in function to
  interest rates (i.e. bond valuation, stock
  valuation, required rates of return for
  individual stocks and the stock market as a
  whole, risk adjusted required rate of return,
  etc.)

10

• The Cost of Money (continued)
• Interest Rates / Investment Rates of Return (ROR)
• The interest rate that a borrower pays is exactly
  equal to the lenders ROR the lender is
  investing in the borrower
• When you invest in stock, you should expect a ROR
  that compensates for the same things associated
  with lending money
• Required ROR of stock rs r IP RP
  (Note the specific risks associated with stock
  may be different than those associated with
  lending money, but its the same idea
• When you invest in anything, you should expect
  compensation for the same things thus ranything
  r IP RP thus your Required ROR is r IP
  RP
• Even if the investment is risk-free (such as a
  short-term U.S. Treasury bill) the minimum ROR
  you should expect is compensation for opportunity
  cost and inflation
• thus rminimum r IP
• this is rRF
• thus rminimum rRF
• this is why rRF is the benchmark for all other
  rates

11

• The Opportunity Cost of Capital
• The best available expected return offered in the
  market on an investment of comparable risk and
  length (term)
• The return the investor forgoes on an alternative
  investment of equivalent risk and term when the
  investor takes on the alternative investment
• Point
• One always uses his/her Opportunity Cost of
  Capital as the discount/compound rate when
  solving TVM problems if a rate is not given
• The Opportunity Cost of Capital is your benchmark
  for comparing and choosing among options
• Capital Wealth in the form of money or property
  (real property or securities) that can be used to
  produce more wealth

12

• The Cost of Money (continued)
• The Term Structure of Interest Rates
• Term Structure the relationship between interest
  rates (yields) and different loan lengths
  (maturities).
• U.S. Treasury Bond Interest Rate Term Structure
• Term to Interest Rate
• Maturity Mar. 1980 Mar. 1999 Jan.
  2006
• 6 months 15.0 4.6
  4.16
• 1 year 14.0 4.9
  4.23
• 5 years 13.5 5.2
  4.34
• 10 years 12.8 5.5
  4.38
• 20 years 12.5 5.9
  4.46
• Why do bonds of longer maturity have higher
  interest rates?
• A graph of the term structure is called a yield
  curve. It graphically portrays the relationship
  between interest rates and maturities

13
Yield Curve Comparison (U.S. Treasury Bonds)
16 14 12 10 8 6 4 2 0
Yield Curve for March 1980 (Inflation 12)
(downward sloping or inverted)
Interest Rate ()
Yield Curve for July 2000 (flat)
Yield Curve for July 2003 (upward sloping)
1 5 10 20
Maturity
Short Term Intermediate Term Long
Term

• The yield curve is a snapshot in time it tells
  you what the relationship between maturities and
  interest rates are at a specific date
• The yield curve does not tell you what interest
  rates will be in the future (more on this later)
• Yield curves for different bond markets (i.e.
  U.S. Treasuries, investment grade, junk, etc.)
  usually have similar shapes
• Yield curves change over time due changes in the
  factors that govern interest rate components (IP,
  DRP, LP MRP).
• Historically, yield curves have mostly been
  upward sloping (i.e. interest on shorter term
  bonds were lower than longer term bonds)

14

• The Cost of Money (continued)
• The shape of the yield curve gives some
  indication about what bond markets think
  inflation (and thus, interest rates) might do in
  the future

16 14 12 10 8 6 4 2 0
Yield Curve for March 1980 (Inflation 12)
(downward sloping / inverted )
Interest Rate ()
Yield Curve for July 2000 (flat)
Yield Curve for February 2000 (concave)
Yield Curve for March 1999 (upward sloping)
Yield Curve for July 2003 (upward sloping)
Yield Curve for August 2000 (downward sloping)
1 5 10 20
Maturity
Short Term Intermediate Term Long
Term

• Expected inflation has the greatest influence on
  yield curve shape
• yield curves slope downward (Mar 1980) when debt
  markets expect inflation to decrease
• yield curves slope upward (Mar 1999) when bond
  markets expect inflation to rise
• yield curves are concave (Feb 2002) when the
  direction of inflation change is about to change

15

• Other Yield Curves
• The relative riskiness of borrowers also
  influences the shape of the yield curve

16 14 12 10 8 6 4 2 0
High-risk Firms
Interest Rate ()
Moderate-risk Firms
Spread
Low-risk Firms
U.S Treasuries
1 5 10 20
Maturity
Short Term Intermediate Term Long
Term

• The shape of the yield curve influences decisions
  on issuing debt
• Upward sloping go with l-t debt instead of s-t
  debt upward sloping means the market expects
  interest rates to rise in the future
• Downward sloping go with s-t debt instead of l-t
  debt refinance later when interest rates are
  lower
• Caution the yield curve changes over time

Expectations Theory
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20 January 2012