Chapter 6: Interest Rates
Slides for 12th, 13th and 14th session
Topics covered
• Cost of Money (Introduction)
• Factors affecting cost of money
– Fundamental factors
– Macroeconomic factors
•
•
•
•
Interest rate levels
Determinants of market interest rates
Term structure of interest rates
What determines the shape of the yield curve?
– Analysis of the impact of different factors (inflation risk,
maturity risk, liquidity risk, default risk) on the shape of yield
curves for treasury and corporate securities
• Risks associated with investment in overseas securities
Problems
•
•
•
•
•
•
•
•
6-2 (2.25%)
6-3 (2 yr: 6%, 3 yr: 6.33%)
6-4 (1.5%)
6-5 (0.2%)
6-9 (6.8%)
6-11 (1.55%)
6-12 (0.35%)
6-13 (1.775%)
1. INTRODUCTION
Cost of money is the rental price of borrowing
money
Suppose you go to a bank to borrow $10,000 for paying off college
fees, you won’t be able to get this money for free.
The $10,000 come with a price tag attached, i.e. some rate of
interest, consider for example a 10% rate of interest.
This 10% interest rate is the cost of obtaining $10,000. This cost is
also known as the ‘cost of money’.
In a free economy, excess funds of lenders are allocated to borrowers through a
pricing system based on the supply of and demand for funds. This pricing system is
represented by interest rates, ‘i’ or the cost of money.
EXCESS FUNDS
LENDERS
BORROWERS
PRICING SYSTEM (i)
i
Supply of funds
i
Demand of funds
$
So, Now we know!
• Supply and demand of
funds determines the
interest rates (i).
• It is by providing these
rates that the
borrowers make use of
the funds provided by
the lenders.
• Generally interest rates are believed to be the
cost of money.
• However, in case of equity capital,
– Cost of money is called ‘Cost of equity’ and it
consists of dividends and capital gains expected by
the share holders
– Cost of equity = Dividends + Capital Gains
Remember!
Cost of
Money
• Cost from fund
users’ perspective
Cost of
Money
• Return from fund
providers’
perspective
MONEY
DEBT
CAPITAL
BANK
(PROVIDER)
COST OF MONEY (i)
CORPORATION
ABC
(USER)
Return for the funds provider Cost for the user of funds
MONEY
EQUITY
CAPITAL
STOCK-HOLDERS
(PROVIDER)
COST OF MONEY (D+C.G.)
CORPORATION
ABC
(USER)
Return for the funds provider Cost for the user of funds
QUICK FLASHBACK!
• ‘i’ is the cost of obtaining money.
• Supply and demand of funds determines the
interest rates.
2. Factors affecting cost of money, ‘i’
i. Fundamental factors affecting cost of money, ‘i’
The four most fundamental factors affecting the cost of money are:
1. Production opportunities
– Rate of return that producers expect to earn on invested capital.
2.
Time preferences for consumption
– The preferences of consumers for current consumption as opposed to
saving for future consumption.
Preference for current consumption
3.
Supply of funds
Interest rate
Riskiness of loan
– The chance that an investment will provide a low or negative return.
4.
Inflation
– The amount by which prices increase over time.
Expected Inflation
Demand of funds
Interest rate
For highly risky loans
investors expect
high rate of return,
i.e. high ‘i’
ii. Macroeconomic factors affecting
cost of money, ‘i’
1. Monetary policy tools
–
–
Federal Reserve Policies
Open Market Operations
2. Business boom
3. Business recession
4. Government budget deficit and surplus
1. Federal Reserve Policies
– An increase in required reserve ratio by central
bank means reduction in volume of deposits
which raises interest rates.
RRR
Supply of funds
Interest rate
– A decrease in required reserve ratio means
availability of excess deposits which decreases
interest rates.
RRR
Supply of funds
Interest rate
2. Open Market Operations
– Central bank buys back securities from open
market thus injecting money into the system
(increasing supply of money) which decreases
interest rates.
– Central bank sells securities into open market
thus absorbs money from the system (decreasing
supply of money) which increases interest rates.
3. Business booms
Increased demand of funds
Inflationary pressures
i
4. Business recession
Decreased demand of funds
Inflationary pressures
i
5. Government budget deficit
Government needs funds which means demand for funds
i
6. Government budget surplus
Government does not need funds which means demand for funds
i
3. INTEREST RATE LEVELS
• Capital is allocated to borrowers according to interest rates, i.
– Most capital across the world is allocated through the price system (that is,
interest rate).
• As can be seen in the figure below the excess funds of lenders are
allocated to the borrowers through a price system that is the
interest rate.
INTEREST RATE LEVELS
• The firms with the most profitable investment
opportunities are willing and able to pay the most for
capital, so they tend to attract it away from inefficient firms
and firms whose products are not in demand.
• There are many different types of capital markets (for
example, market for high risk securities, market for low risk
securities etc.) and they are all interconnected.
• Interdependence of capital markets
– Capital markets are interdependent, i.e. changes in supply and
demand of funds in one market are going to produce an impact
on the supply and demand of funds in the other market/s.
4. THE DETERMINANTS OF MARKET
INTEREST RATES
• The interest rate quoted on any debt security is
composed of a real risk-free rate, r* (k *), plus
several premiums that reflect inflation, the
security’s risk, its liquidity (or marketability), and
the years to its maturity. This relationship can be
expressed as follows:
Quoted interest rate = k = k* + IP + DRP + LP + MRP
The quoted risk free rate can be written as
‘k’ or ‘r’. Similarly the real risk free rate can
also be written as ‘k*’ or ‘r*’.
Main determinants of market interest
rates
1.
2.
3.
4.
5.
K = the quoted, or nominal, rate of interest on a given security.
k* = the real risk-free rate of interest. k* is pronounced “k-star,”
and it is the rate that would exist on a riskless security in a world
where no inflation was expected.
Krf = k* x IP. It is the quoted rate on a risk-free security such as a
Treasury bill and it includes a premium for expected inflation.
IP = inflation premium. IP is equal to the average expected rate of
inflation over the life of the security.
DRP = default risk premium. This premium reflects the possibility
that the issuer will not pay the promised interest or principal at
the stated time.
DRP is zero for Treasury securities, but it rises as the riskiness of the issuer
increases.
6.
LP = liquidity (or marketability) premium. This is a premium
charged by lenders to reflect the fact that some securities cannot
be converted to cash on short notice and at a “reasonable” price.
8. MRP = maturity risk premium. Longer-term bonds, even
Treasury bonds, are exposed to a significant risk of price
declines due to increases in interest rates; and a maturity risk
premium is charged by lenders to reflect the interest rate risk.
MRP is paid to cover interest rate risk.
– Interest rate risk: The risk of capital losses to which investors are
exposed because of changing interest rates.
While long term bonds are exposed to interest rate risk, short
term bonds are exposed to reinvestment rate risk.
– Reinvestment rate risk: The risk that a decline in interest rates will
lead to lower income when bonds mature and funds are reinvested.
5. Term Structure of Interest Rates
• Describes the relationship between long term and short term interest
rates.
• The term structure is important to corporate treasurers for deciding
whether to borrow by issuing long- or short-term debt and to investors
deciding whether to buy long- or short-term bonds.
• Yield curve can best depict this relationship.
• Yield curve is actually a graph showing relationship between bond yields
and maturities.
• Three different types of Yield Curves:
– “Normal” Yield Curve
• Upward sloping yield curve
• Short term interest rates are low, long term interest rates are high.
– Inverted (“Abnormal”) Yield Curve
• Downward sloping yield curve
• Short term interest rates are high, long term interest rates are low.
– Humped yield curve
• A yield curve where interest rates on medium-term maturities are higher than rates on
both short-and long-term maturities.
6. What determines the shape of the
yield curve?
Factors affecting shape of treasury securities
• Yield on a Treasury bond that matures in t years can be expressed as follows:
–
•
•
T-bond yield = K* + IPt + MRPt
It thus emerges that expected inflation levels and bond’s maturity are the main
factors affecting shape of yield curve of treasury securities. (Value of real risk free
rate of interest, K* varies somewhat over time because of changes in the economy
and demographics, these changes are random rather than predictable, K* thus is
assumed to remain constant.)
Inflation
• Expected inflation has an important effect on the yield curve for treasury securities.
If the market expects inflation to increase in the future, the inflation premium will
be higher on a 3-year bond than on a 1-year bond. On the other hand, if the market
expects inflation to decline in the future, long-term bonds will have a smaller
inflation premium than will short-term bonds.
•
Maturity
• Since investors consider long-term bonds to be riskier than short-term bonds
because of interest rate risk, the maturity risk premium always increases with
maturity.
Factors affecting shape of Corporate bonds
• Corporate bonds include a default risk premium
(DRP) and a liquidity premium (LP). Therefore,
the yield on a corporate bond that matures in t
years can be expressed as follows:
• Corporate bond yield = K* + IP + DRP + LP + MRP
• The corporate bonds carry additional default and
liquidity risks, this is the reason they pay
premium for covering these risks which is why
the ‘i’ (interest rate) paid on corporate bond, also
called the yield, is always higher than that paid by
treasury bonds.
t
t
t
t
Because of their additional default and liquidity risk, corporate bonds yield more than treasury
bonds with the same maturity and BBB-rated bonds yield more than AA-rated bonds.
7. Risks associated with investment in
overseas securities
• Two main types of risks that an investor,
looking to invest in foreign securities, faces
are: country risk and exchange rate risk.
• Country risk
– Risk that arises from investing or doing business in
a particular country
– This risk depends on a country’s economic, social
and political environment.
– Countries with safer political, social and economic
environment have less country risk and therefore
are safe choices for overseas investment.
• Exchange rate risk
– Risk of losing money in local currency because of fluctuation
in the value of foreign currency (in which investment was
being made).
– Recall example narrated in class (Pakistani earning US dollars
and praying for weak Pakistani rupee relative to US dollar).
– Suppose a US investor purchases Japanese bond. The US
investor gets interest rate in Japanese currency (yen) which
must then be converted into US dollars whenever he wants
to make a purchase (as the investor resides in the US).
Whenever yen strengthens in comparison to dollar it means
yen can be converted into a larger number of US dollars and
the investor will be better off. On the other hand if yen
weakens relative to dollar, it would mean yen’s conversion
into dollar will give off fewer dollars and the investor will
have to suffer.
Interest rate determination
• Formula for calculation of interest rate on
short term treasury securities:
– Quoted interest rate = Real risk free rate + inflation premium
– K = K* + IP
t
• Formula for calculation of interest rate on long
term treasury securities:
– Quoted interest rate = Real risk free rate + inflation premium +
maturity risk premium
– K = K* + IP + MRP
t
t
Interest rate determination
• Formula for calculation of interest rate on
corporate securities:
– K= K* + IPt + DRPt + LPt + MRPt
– Quoted interest rate = Real risk free rate + inflation premium + default
risk premium + liquidity premium + maturity risk premium