Determination of interest Rate

1. CHAPTER TWO
Determination
of Interest
Rates
1

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3. DEFINITION of Interest Rate
• The amount charged, expressed as a
percentage of principal, by a lender to a
borrower for the use of assets.
• Interest is charged by lenders as
compensation for the loss of the asset's
use.
• Interest rates are among the most closely
watched variables in the economy.

4. MEASURING INTEREST
RATES
Present Value
• The concept of present value (or present
discounted value) is based on the
commonsense notion that a birr paid to
you one year from now is less valuable to
you than a birr paid to you today:
PV = FV
• (1 + i) n

5. • In terms of the timing of their payments, there
are four basic types of credit market
instruments.
1. A simple loan. the lender provides the
borrower with an amount of funds, which
must be repaid to the lender at the maturity
date along with an additional payment for the
interest. Many money market instruments are
of this type: for example, commercial loans to
businesses.

6. 2. A fixed-payment loan (which is also
called a fully amortized loan).
• the lender provides the borrower with an
amount of funds, which must be repaid by
making the same payment every period
(such as a month), consisting of part of the
principal and interest for a set number of
years.
• For example, if you borrowed Br. 1,000, a
fixed-payment loan might require you to
pay Br. 126 every year for 25 years.

7. 3. A coupon bond. In which pays the
owner of the bond a fixed interest payment
(coupon payment) every year until the
maturity date, when a specified final
amount (face value or par value) is repaid.

8. 4. A discount bond (also called a zero-
coupon bond) is bought at a price below
its face value (at a discount), and the face
value is repaid at the maturity date. Unlike
a coupon bond, a discount bond does not
make any interest payments; it just pays
off the face value.

9. Yield to Maturity
• Of the several common ways of
calculating interest rates, the most
important is the yield to maturity, the
interest rate that equates the present
value of payments received from a debt
instrument with its value today. It is also
called the internal rate of return.

10. • Lets now look at how YTM is calculated for
the four types of credit market instruments.
• i. YTM on Simple Loan-For example, if you
made your friend, Almaz, a simple loan of Br.
100 for one year, and you would require her
to repay the principal of Br. 100 in one year’s
time along with an additional payment for
interest; say, Br. 10, the payments in one
year’s time would be Br. 110 (the repayment
of Br. 100 plus the interest payment of Br.
10).

11. Br. 100 = Br. 110
1 + i
i = Br. 110 - Br. 100 = Br.10 = 0.10 = 10%
Br. 100 Br. 100
ii. YTM ON Fixed-Payment Loan
LV= FP + FP + …… + FP
(1 + i) (1 + i) 2 (1 + i) n
Where LV = loan value
FP = fixed yearly payment
n = number of years until maturity

12. iii. YTM ON Coupon Bond
P = C + C + …… + C + F
(1 + i) (1 + i) 2 (1 + i) n (1 + i) n
Where P= price of coupon bond
C = yearly coupon payment
F = face value of the bond
n = years to maturity date

13. • The present value of a $1,000-face-value
bond with ten years to maturity and
yearly coupon payments of $100 (a 10%
coupon rate) can be calculated as follows:
•

14. iv. YTM ON Discount Bond
• Let us consider a discount bond such as a
one-year Treasury bill, which pays off a
face value of Br. 1,000 in one year’s time.
If the current purchase price of this bill is
Br. 900

15. Br. 900 = Br. 1,000
1+ i
And solving for i,
(1+ i) * Br. 900 = Br. 1,000
Br. 900 + Br. 900 i= Br. 1,000
Br. 900 i= Br. 1,000 - Br. 900
i= Br. 1,000 - Br. 900 = 0.111= 11.1%
Br. 900
More generally, for any one-year discount bond, the yield to
maturity can be written bas:
i = F - P
P
Where: F=facevalueofthediscount bond and P=current priceofthediscount bond

16. Real and nominal interest rates
• The distinction b/n Real and nominal
interest rates is that real interest rate is
the interest rate that is adjusted by
subtracting expected changes in the price
level (inflation) so that it more accurately
reflects the true cost of borrowing but in
nominal interest we have ignored the
effects of inflation on the cost of
borrowing.

17. • The Fisher equation states that the
nominal interest rate i equals the real
interest rate Ir plus the expected rate of
inflation π e
• Rearranging terms, we find that the real
interest rate equals the nominal interest rate
minus the expected inflation rate:

18. • From the above equation we can say
that “When the real interest rate is low,
there are greater incentives to borrow
and fewer incentives to lend.”

19. Changes of equilibrium interest
rates
1. Shifts in the Demand for Bonds
These factors cause the demand curve for
bonds to shift. These factors include
changes in four parameters:
– Wealth
– Expected returns on bonds relative to
alternative assets
– . Risk of bonds relative to alternative assets
– Liquidity of bonds relative to alternative
assets

20. A. Wealth
• When the economy is growing rapidly in a
business cycle expansion and wealth is
increasing, the quantity of bonds demanded
at each bond price (or interest rate) increases
and another factor that affects wealth is the
public’s propensity to save. If households
save more, wealth increases and the demand
for bonds rises and the demand curve for
bonds shifts to the right.

21. Where P= Price of Bonds
i= Interest Rate
B=Quantity of Bonds

22. B. Expected Returns
• For bonds with maturities of greater than
one year, the expected return may differ
from the interest rate. if people begin to
think that interest rates will be higher next
year than they had originally anticipated,
the expected return today on long-term
bonds would fall, and the quantity
demanded would fall at each interest rate

24. C. Risk
• An increase in the riskiness of bonds
causes the demand for bonds to fall and
the demand curve to shift to the left.
• Conversely, an increase in the volatility of
prices in another asset market, such as
the stock market, would make bonds more
attractive.

26. D. Liquidity
• If more people started trading in the bond
market, and as a result it became easier to
sell bonds quickly, the increase in their
liquidity would cause the quantity of bonds
demanded at each interest rate to rise.

28. Shifts in the Supply of Bonds
• Certain factors can cause the supply
curve for bonds to shift, among them
these:
A. Expected profitability of investment
opportunities
B. Expected inflation
C. Government activities

29. A. Expected profitability of investment
opportunities
• When the economy is growing rapidly, as
in a business cycle expansion,
investment opportunities that are
expected to be profitable abound, and the
quantity of bonds supplied at any given
bond price and interest rate will increase.

31. B. Expected inflation
• For a given interest rate, when expected
inflation increases, the real cost of
borrowing falls; hence the quantity of
bonds supplied increases at any given
bond price and interest rate.

33. C. Government activities
• The government Treasury issues bonds to
finance government deficits, the gap
between the government’s expenditures
and its revenues. When these deficits are
large, the Treasury sells more bonds, and
the quantity of bonds supplied at each
bond price and interest rate increases.