V 2.1 Aug ‘12
MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
The Cost of Money:
Learning Objectives:
Explain why lenders charge interest
Define the components of interest rates (r = r*+IP+DRP+LP+MRP)
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
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V 2 Jan ‘12
MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
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 it’s loaned
out (opportunity cost)
the loss of value over time due to inflation
the chance that they won’t get the money back
The interest rate (r) one pays for the privilege of using someone
else’s 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
RP = Risk Premium which compensates for possible default
(this premium can be broken down into sub-premiums)
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
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:
The “cost of borrowed capital”
The “cost of debt”
The “cost of leverage”
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
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
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
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
Risk Premium
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)
The IP that is often applied is derived from government economic
forecasts. No one really knows what the current inflation rate is but the
one the U.S. Government reports is the commonly accepted value
No one ever really knows what the inflation rate will be in the future
(but we have some indication of what it might be; more on this later)
Note 1: we will talk about different loan markets later
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
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 firm’s
assets.
If these assets are not very liquid (i.e. real estate, buildings, equipment,
etc.), LP will be higher
Although it’s 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 can’t reinvest the repaid principle at the same rate at
which he originally loaned it.
Nominal Risk-Free Rate (rRF):
Since no one really knows what r* is, the financial world uses a commonly
accepted formula: r* ≈ rRF - Current Inflation Rate
The above equation can be re-written as rRF ≈ r* + IP This is the
“Nominal” or “Quoted” Risk-Free Rate (rRF)
The yield (interest rate) on a 30-day T-bill is usually used for rRF
See also Ch 5 pp. 144
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
The Cost of Money: (continued)
Quoted Interest Rate 
r = rRF + DRP + LP + MRP
r* + IP
This equation is the one most commonly used to compute interest
rates since it’s easy to find rRF (the yield on a 30-day T-bill); just read
the Wall Street Journal
Example: Jungle Jim’s 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%. Today’s 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).
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
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 gov’t 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 Jim’s 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 year’s inflation is expected to be
2.5% and the following year’s inflation is expected to be 3%. Today’s
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
r = 0.3% + 2.5% + 10% +3% + 1.5% = 17.3%
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
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
It’s 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 firm’s 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.)
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
The Cost of Money: (continued)
Interest Rates / Investment Rates of Return (ROR)
The interest rate that a borrower pays is exactly equal to the
lender’s 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 it’s 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
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
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
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
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
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
Yield Curve Comparison (U.S. Treasury Bonds)
16
Interest Rate (%)
14
Yield Curve for March 1980 (Inflation: 12%) (downward sloping or inverted)
12
10
8
6
Yield Curve for July 2000 (flat)
4
Yield Curve for July 2003 (upward sloping)
2
0
1
5
10
Short Term Intermediate Term
20
Long Term
Maturity
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)
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
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
Interest Rate (%)
14
12
Yield Curve for March 1980 (Inflation: 12%) (downward sloping /
inverted )
10
8
Yield Curve for July 2000 (flat)
Yield Curve for February 2000 (concave)
6
Yield Curve for March 1999 (upward sloping)
Yield Curve for July 2003 (upward sloping)
4
Yield Curve for August 2000 (downward sloping)
2
0
1
5
10
20
Short Term Intermediate Term
Long Term
Maturity
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
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
Other Yield Curves
The relative riskiness of borrowers also influences the shape of the
yield curve
16
Interest Rate (%)
14
12
10
High-risk Firms
8
Moderate-risk Firms
6
Spread
Low-risk Firms
4
U.S Treasuries
2
0
1
5
10
Short Term Intermediate Term
20
Long Term
Maturity
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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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
U.S. Treasuries Yield Curve as of 12 Sep 03
6.00
5.00
Yield (%)
4.00
3.00
2.00
1.00
0.00
0.25
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
16
17
18
19
20
Maturity (yrs)
U.S. Treasuries Yield Curve as of 16 Jan 04
6.00
5.00
Yield (%)
4.00
3.00
2.00
1.00
0.00
0.08333
0.25
0.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
18
19
20
Maturity (yrs)
U.S. Treasuries Yield Curve as of 20 Jan 2005
5.00%
Yield (%)
4.00%
3.00%
2.00%
1.00%
0.00%
0.1
0.3
0.5
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
Maturity
16
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
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MGT 326 Ch 5: Interest Rates (bdh) (The Cost of Money)
20 January 2012
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