1. TOPIC 4
INTEREST RATES
AND
RATES OF RETURN

2. CHAPTER PREVIEW
Objective: To develop better understanding of interest rate; its terminology and calculation. Topics include:
Measuring Interest Rates
Distinction Between Real and Nominal Interest Rates
Distinction Between Interest Rates and Returns
Interest rate – one of most closely watched variables in economy; it is imperative to know what it means exactly
In this chapter, we will see that yield to maturity (YTM) is the most accurate measure of interest rates

3. PRESENT VALUE CONCEPT (PV)
Comparing returns across debt types is difficult since timing of repayment differs
Apply the PV concept: find a common measure for funds at different times, present each in today’s dollars
The PV of $1 received n years in the future is $1/(1 + i )n
Interest rate is important in valuation of various investment instruments

4. PRESENT VALUE CONCEPT
Concept of PV (or present discounted value) is based on notion
A dollar today is better than a dollar tomorrow
A dollar of cash flow paid one year from now is less valuable than a dollar paid today.
That one dollar today could be invested in a savings account that earns interest and have more than a dollar in one year
PV analysis involves
Finding the PV of all future payments that can be received from a debt instrument
PV of a single cash flow or sum of a sequence or group of future cash flows

5. Types of Debt Instruments
Categories of bonds are used to identify variations in the timing of payments
Simple loan
Involves the principal (P) and interest ( i )
Total payment = P + iP = P(1 + i )
Fixed-payment loan
Borrower makes regular periodic payments to the lender.
Payments include both interest and principal and no lump-sum payment at maturity.
The timing of payments that bond issuers make to lenders varies across the categories of bonds.
1. With a simple loan the borrower receives from the lender an amount of funds called the principal and agrees to repay the lender the principal plus an additional amount called interest.
2. With a discount bond the borrower pays the lender the amount of the loan, called the face value or par value, at maturity, but receives less than the face value initially.
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6. Types of Debt Instruments
Coupon bond
Borrowers make multiple payments of interest at regular intervals and repay the face value at maturity
Specifies the maturity date, face value, issuer, and coupon rate (equals the yearly payment divided by face value)
Discount bond
Repays in a single payment
Repays the face value at maturity, but receives less than the face value initially
1. Borrowers issuing a coupon bond make multiple payments of interest at regular intervals and repay the face value at maturity.
2. With a fixed-payment loan the borrower makes regular periodic payments of interest and principal to the lender; at maturity there is no lump-sum payment of principal.
Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

7. PRESENT VALUE APPLICATIONS: 1. Simple Loan
Loan Principal: amount of funds lender provides to borrower
Maturity Date: date loan must be repaid; Loan Term is from initiation to maturity date
Interest Payment: cash amount that borrower must pay lender for use of loan principal
Simple Interest Rate
interest payment divided by loan principal
%of principal that must be paid as interest to the lender
conventionally expressed on an annual basis, irrespective of the loan term

8. What is the cost of borrowing?
 Loan of RM100 today requires borrower to repay the RM100 a year from now and make an additional interest payment of RM10. Calculations of interest rates:-
i = = = 10%
100
First Year
 If you give out this loan, at the end of the year, you would receive RM110, which can be rewritten as:
100 x ( ) = RM110
Second Year
110 x ( ) = RM121 OR 100 x ( ) x ( ) = 100 x ( )2 = RM121
Continuing the Loan
121 x ( ) OR RM100 x ( )3 = RM133
Today
Year 1
Year 2
Year 3
100
110
121
133

9.  Can be generalized as:
If the simple interest rate i is expressed as a decimal (0.10), then after making these loans for n years, you will receive a total payment of
RM100 x (l +i)n or
RM100 today = RM110 next year
= RM121 next 2 years
= RM133 next 3 years
 Discounting the future
Today Future
RM (I + i)3 = RM133
So that, =
(1 + i)3
 From here, we can solve for the Present Value (Present Discounted Value) – The value today of a future payment (FV) received n years from now

10. PV = FV
(1 + i)n
Q:- What is the present value of RM250 to be paid in two years if the interest rate is 15%
PV = FV
(1 + i)n
FV = 250
i = 0.15
n = number of years
PV = ?
PV = = = RM189.04
( )
Today
Yr 2
Yr 1
250
Answer = RM189.04

11. Yield to Maturity: Loans
Yield to maturity = interest rate that equates today's value with present value of all future payments
Simple Loan Interest Rate (i = 10%)

12. PRESENT VALUE APPLICATION: 2. Fixed-Payment Loan Terms
Fixed-Payment Loans are loans where the loan principal and interest are repaid in several payments, often monthly, in equal dollar amounts over the loan term.
Installment Loans, such as auto loans and home mortgages are frequently of the fixed-payment type.

13. Example:
The loan is RM1000, and the yearly payment is RM85.81 for the next 25 years.
1st Year:
2nd Year:
PV = FV
1 + i
PV =
(1 + i)2
PV =
1 + i
25th Year:
PV =
(1 + i)25

14. What makes today’s value of the loan RM1000?
= Sum of the present value of all the yearly payments gives us:-
1000 = ………………
(1 + i) (1 + i) (1 + i)25
More generally, for any fixed payment loan:-
LV = FP FP FP ……… FP
(1 + i) (1 + i) (1 + i) (1 + i)25
LV = Loan value
FP = Fixed yearly payment
n = Number of Years until maturity
 For a fixed-payment loan amount, the fixed yearly payment and the number of years until maturity are known quantities, we can then solve for yield to maturity.

15. i = annual interest rate = 0.07 n = number of years = 20
Fixed-Payment Loan
You want to purchase a house and need a $100,000 mortgage. You take up a loan from a bank that has an interest of 7%. What is the yearly payment to the bank to pay off the loan in 20 years?
LV = FP FP ……………. + FP
(1 + i) (1 + i) (1 + i)n
LV = loan value amount = 100,000
i = annual interest rate = 0.07
n = number of years =
1000,000 = FP FP ………………… FP
( ) ( ) ( )20

16. Yearly payment to bank is:- RM9,439.29
 Solving Using Finance Calculator:
n = number of years = 20
PV = amount of the loan (LV) = 100,000
FV = amount of the loan after 20 years = 0
i = annual interest rate = 0.07
Yearly payment to bank is:- RM9,439.29

17. PRESENT VALUE APPLICATION: 3. Coupon Bond
Pays owner of the bond a fixed interest payment (coupon payment) every year until maturity date, when face value/par value is repaid
Three information: Issuer; maturity date; coupon rate-the value of yearly coupon payment expressed as a % of the face value
Example: Find the price of a 10% coupon bond with a face value of $1000, a 12.25% yield-to-maturity, and 8 years to maturity
Use formula
Or use calculator

18. Find the price of a 10% coupon bond with a face value of $1,000, a 12
Find the price of a 10% coupon bond with a face value of $1,000, a 12.25% yield to maturity and eight years to maturity
Solution :
n = years to maturity = 8
FV = face value of the bond = 1000
i = annual interest rate = 12.25%
PMT = Yearly coupon payments = 100
- The price of bond is RM889.20

19. Yield to Maturity: Bonds
Coupon Bond (Coupon rate = 10% = C/F)
Consol/perpetuity: A perpetual bond with no maturity date and no repayment of principal. Fixed coupon payments of $C forever

20. PRESENT VALUE APPLICATION: 4. Discount Bond
Zero-coupon bond: a bond that is bought at a price below its face value (at a discount), and the face value is repaid at the maturity date.
Makes no interest payments-just pays off the face value
Example: A one-year TBILL paying a face value of $1,000 in 1 year’s time. If current purchase price is $900, find the yield-to-maturity
Use formula
YTM formula similar to simple loan: PV= FV/(1+i)n

21. Yield to Maturity: Bonds
One-Year Discount Bond (P = $900, F = $1000)

22. Relationship Between Price and YTM
Three observations:
When bond is at par, yield equals coupon rate
Price and yield are negatively related
Yield greater than coupon rate when bond price is below par value

23. OTHER MEASURES OF INTEREST RATE 1. Current Yield
Current yield: An approximation of YTM that equals to yearly coupon payment divided by price of a coupon bond
Two characteristics
Is better approximation to yield to maturity, nearer price is to par and longer is maturity of bond
Change in current yield always signals change in same direction as yield to maturity

24. OTHER MEASURES OF INTEREST RATE 2. Yield on a Discount Basis
One-Year Bill (P = $900, F = $1000)
Two characteristics:
Understates yield to maturity; longer the maturity, greater is understatement
Change in discount yield always signals change in same direction as yield to maturity

25. Distinction Between Real and Nominal Interest Rates
Real interest rate is the nominal interest rate adjusted for expected changes in the price level
Fisher hypothesis: change in expected inflation = change in nominal interest rate.
Real interest rate more accurately reflects true cost of borrowing
When real rate is low, greater incentives to borrow and less to lend

26. Distinction Between Real and Nominal Interest Rates (cont.)
If i = 5% and πe = 0% then
If i = 10% and πe = 20% then

27. U.S. Real and Nominal Interest Rates
Figure 3-1 Real and Nominal Interest Rates (Three-Month Treasury Bill), 1953–2004
Sample of current rates and indexes

28. Distinction Between Interest Rates and Returns
How well a person does by holding a bond over time is accurately measured by rate of return
RET is the payments to the owner plus the change in the value of the security
Rate of Return

29. Distinction Between Interest Rates and Returns
What would the rate of return be on a bond bought for $1000 and sold one year later for $800? The bond has a face value of $1000 and a coupon rate of 8%.

30. Computing Interest Rates on Money Market Assets
Formula for the actual annualized rate of return for a single year:
Investment rate (IR)
= Par value – Purchase price 
Purchase price Days to maturity
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31. Computing Interest Rates on Money Market Assets
In the money market, a different rate is quoted
Bank discount rate (DR)
Not the actual annualized rate of return
Used as trading standard
Easier to estimate than IR
Use face value in denominator instead of price
Use 360 rather than 365 days
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32. Computing Interest Rates on Money Market Assets
Formula for the bank discount rate (DR):
= Par value – Purchase price 
Par value Days to maturity
DR is always lesser than the IR: 360, par value as denominator
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