1. UNDERSTANDING INTEREST RATES
Chapter 4 – EC311 Susanto
UNDERSTANDING INTEREST RATES

2. But first… Quiz (5 points)
Before the invention of money, people used to barter goods and services; it was difficult to match the exact needs of buyers and sellers. Money simplifies these transactions by providing an intermediate step in the buying and selling process. Additionally, we don’t have so many relative prices anymore. For example, we can say that one bottle of wine costs $8 and one loaf of bread costs $2 instead of saying that the price of a bottle of wine is 4 loaves of bread. Which two functions of money are illustrated here? (2 points)

3. Quiz (5 points) … cont’d.
True or False: A broker makes profits by charging commissions, while a dealer makes profits by buying low and selling high (1 point).
True or False: A broker is a person who executes the trade on behalf of others (his clients), whereas a dealer is a person who trades business on his own behalf. (1 point).

4. Quiz (5 points) … cont’d.
4. Vanguard pools money from many investors and invests typically in investment securities (stocks, bonds, etc). What type of financial intermediary is Vanguard? (1 point).
5. What type of financial instrument represents shares of ownership in a company that may pay out dividends periodically? (1 point).

5. Credit Instruments Debt/credit instruments:
Types of contractual agreements that require the borrower to pay the lender certain fixed dollar amounts at regular intervals until a specified time is reached.
Four Types of Credit Instruments:
1. Simple loan (principal & interest repaid at maturity)
2. Fixed-payment loan
3. Coupon bond
4. Discount (zero coupon) bond

6. Present Value
Different debt instruments have different streams of cash payments with very different timing.
To make comparisons easier: use Present Value
Concept of Present Value (Cash Flow concept)
Simple loan of $1000 at 10% interest
Year n
$1100 $1210 $ $1000x(1 + i)n
Future Value = Present Value (1 + interest)number of periods
FV = PV (1 + i)n FV
PV =
(1 + i)n

7. Present Value
Problem 1
Suppose you are depositing an amount today in an account that earns 5% interest, compounded annually. If your goal is to have $5,000 in the account at the end of six years, how much must you deposit in the account today? FV
PV =
(1 + i)n

8. Present Value Solution The following information is given:
future value (FV) = $5,000
interest rate (i) = 5%
number of periods (n) = 6
Solve for PV.
PV = FV/ (1 + i)n
PV = $5,000 / ( )6
PV = $5,000 / (1.05)6
PV = $5,000 / (1.3401)
PV = $3,731

9. Simple Loan
The borrower receives from the lender a specified amount of funds (principal) for a specified period of time (maturity). At the end of this period of time (maturity date) the borrower will repay the loan value to the lender together with an additional payment (interest payment). Real-World Examples: Standard bank deposit accounts, commercial loans to businesses.

10. Fixed-Payment Loan
The borrower receives from the lender a specified amount of funds and makes periodic fixed payments (principal + interest)until a specified maturity date. At maturity, there is no lump sum repayment of principal. Real-World Examples: Installment loans (e.g., auto loans) and home mortgages.

11. Coupon Bond
The borrower pay the lender a fixed amount of funds periodically (coupon payment) until a specified maturity date, at which time the borrower must also pay the lender the face value (or par value) of the bond.
Coupon rate: the amount of the coupon payment divided by the face value of the bond.
Example: A coupon bond has a face value of $1000, a maturity of five years, and an annual coupon payment of $60.
At the end of each year for the next five years, the borrower (bond issuer) must pay the lender (bond buyer) a coupon payment of $60.
After the five years have elapsed (maturity date), the borrower must pay the lender the face value of the bond, $1000.
The coupon rate for this coupon bond is $60/$1000 = .06, or 6 percent.
Real-World Examples: US Treasury Bonds, corporate bonds.

12. Discount Bond (Zero-Coupon Bond)
The borrower immediately receives from the lender the purchase price of the bond, which is typically less than the face value of the bond.
At the bond's maturity date, the borrower will pay the lender the face value of the bond.
It does not pay interest payments; just the face value at maturity.
Real-World Examples: US Treasury Bills, savings bonds.

13. Comparisons of Debt Instruments

14. Yield to Maturity: Loans
Yield to maturity = interest rate that equates today’s value with present value of all future payments (YTM representation of interest rate)
What is the “today’s value”?
1. Simple Loan (i = 10%)
$100 = $110/(1 + i) 
$110 – $100 $10
i = = = 0.10 = 10%
$100 $100
For simple loans
YTM = the simple interest rate
Present value is the sum of present values of all cash flow payments from the beginning until the end of the loan.
2. Fixed Payment Loan (i = 12%)
$126 $126 $126 $126
$ =
(1+i) (1+i)2 (1+i) (1+i)25
FP FP FP FP
LV =
(1+i) (1+i)2 (1+i)3 (1+i)n
LV – loan value, FP – fixed payment

15. Yield to Maturity: Bonds
3. Coupon Bond (Coupon rate = 10% = C/F) , C – coupon payment, F – face value, P - price
$100 $100 $100 $100 $1000
P =
(1+i) (1+i)2 (1+i)3 (1+i)10 (1+i)10
C C C C F
P =
(1+i) (1+i)2 (1+i)3 (1+i)n (1+i)n
Consol (Perpetuity): Fixed coupon payments of $C forever
C C
P = i =
i P
Present value is the sum of present values of all coupon payments, plus the present value of the final payment (i.e., face value) of the bond.
4. Discount Bond (P = $900, F = $1000), one year
$1000
$900 =
(1+i)
$1000 – $900
i = = = 11.1%
$900
F – P
i = P 
Coupon’s bond YTM = the increase in price over time divided by the initial price.

16. YTM Calculation Examples
Problem 2 You purchased a consol (perpetuity) with annual coupon payments of $50 for $833. What is the yield to maturity?
Solution
Coupon payments (C) = $50
Price of consol (P) = $833
Solve for YTM (i)
i = C / P
= 50 / 833
= = 6%
The yield to maturity is 6%
Note:
Coupon bonds with long term maturity (> 20 years) behave much like a consol (perpetuity). Thus, YTM for these coupon bonds is calculated just like a perpetuity would, and it is called current yield.
Thus, current yield = C / P.

17. YTM Calculation Examples
Problem 3 You purchased a one-year US treasury bill with the face value of $1000 at a discount (zero-coupon) for $950. What is the yield to maturity?
Solution
Face value (F) = $1000
Current/purchase price (P) = $950
Solve for YTM (i)
i = (F – P) / P
= ( ) / 950
= 50 / 950 = .0526
The yield to maturity is 5.26%

18. Zero Coupon Bond Present Value
Problem 4 Calculate the price of a zero-coupon bond that is maturing in five years, has a par value of $1,000 and a required yield of 6%, compounded annually.
Solution
Face value (F) = $1000 Yield (i) = .06 Number of years = 5
Solve for PV.
PV = FV / (1+i)n
= 1000 / (1+.06)5
= 1000 / (1.338)
= $747.38

19. Relationship Between Price and Yield to Maturity
Three Interesting Facts in Table 1
1. When bond is at par, yield equals coupon rate
2. Price and yield are negatively related
3. Yield greater than coupon rate when bond price is below par value

20. Key Facts about Relationship Between Interest Rates and Returns

21. Distinction Between Interest Rates and Returns
Rate of Return: is not necessarily equal to the interest rate.
The return takes into account any capital gains or losses, in addition to payments received during the holding period.
C + Pt+1 – Pt
RET = = ic + g Pt C
where: ic = = current yield Pt
Pt+1 – Pt
g = = capital gain

22. Rate of Return Calculation
Problem 5 You purchased a consol with annual coupon payments of $50, the interest rate is 6%. One year later the interest rate has changed to 5% and you decide to sell the consol. What is your one-year holding period return?
Solution
Return = i + g
= (Coupon payment/Price Paid) + (Change in Price/Price Paid)
Pthis year = C / i = 50 / 0.06 =
Pnext year = C / i = 50 / 0.05 = 1000
* Change in price = 1000 – = (Gain)
* There will be one coupon payment of $50 in one year and the payments are still going to continue infinitely in the future.
The holding period return is therefore:
Return = (50 / ) + (166.67/833.33) =
= 0.26 (26%)

23. Maturity and the Volatility of Bond Returns
Key Findings from Table 2
1. Only bond whose return = yield is one with maturity = holding period
2. For bonds with maturity > holding period, i  P implying capital loss
3. Longer is maturity, greater is % price change associated with interest rate change
4. Longer is maturity, more return changes with change in interest rate
5. Bond with high initial interest rate can still have negative return if i 
Conclusion from Table 2 Analysis
Prices and returns more volatile for long-term bonds because have higher interest-rate risk:
The uncertainty regarding return rates that bond holders face due to possible changes in yields to maturity.
2. No interest-rate risk for any bond whose maturity equals holding period

24. Distinction Between Real and Nominal Interest Rates
Real Interest Rate
Interest rate that is adjusted for expected changes in the price level
ir = i – e
1. Real interest rate more accurately reflects true cost of borrowing
2. When real rate is low, greater incentives to borrow and less to lend
if i = 5% and e = 3% then:
ir = 5% – 3% = 2%
if i = 8% and e = 10% then
ir = 8% – 10% = –2%
e can be obtained from TIPS (inflation indexed bonds):
Treasury Inflation Protection Securities