1. Chapter 4 Understanding Interest Rates

2. Learning Objectives 1. Detail terms present value and interest rate
2. Discern measurments of interest rates: YTM, Current Yield, Yield on Discount basis
3. Illustrate inverse relationship of bond prices and interest rates
4. Explain difference between nominal and real interest rates
5. Explain difference between interest rates and rates of return

3. Contents Present Value and Interest Rates
Subprime Mortgages and Interest Rates
Measuring Interest Rates
Bond Prices and Interest Rates
International Interest Rates
Nominal vs Real Interest Rates
Interest Rates vs Rates of Return

4. Present Value and Interest Rates
PV = FV / (1+i) ^ t
A dollar paid to you 1 year from now is worth less than one dollar paid to you today
Ex. PV of $250 paid in 2 years, i=15%
PV = 250 / ( ) ^ 2
= $189.04

5. Credit Market Instruments
1 – Simple Loan
2 – Fixed-Payment Loan
3 – Coupon Bond
4 – Discount Bond

6. Simple Loan
Lender provides borrower funds, borrower repays at maturity date plus additional interest amount
$500 loan with 10% interest:
1 year: $500 * ( ) = $550
2 years: $550 * ( ) = $605
P = F (1 + i) ^ t
P = Total payment
F = Face Value
i = interest rate
t = number of periods

7. Coupon Bond
Face value amount is paid to issuer for ownership of bond, then issuer pays owner of bond fixed interest payment every period until maturity, then pays face value to owner
Three pieces of information: Issuer of bond, maturity date of bond, coupon rate of bond

8. Coupon Bond
P = C * (1 – (1 / (1 + i) ^ t)) / r + F / (1 + i) ^ t
P = bond price
C = Coupon rate
i = interest rate
t = number of periods
F = face value
Ex. $1000, 5% coupon, annual bond with 15 year maturity. What would the price be if the interest rate was 6.5%?
A. $858.96

9. Discount Bond Like a coupon bond, but without coupons
No interest payments, is issued at a discount of face value
Ex. Face value of $1000 may be bought for $900 and in one years time the owner will be paid $1000
Examples include Canadian government treasury bills and long term zero-coupon bonds

10. Discount Bond
Similar formula as Coupon Bond, just missing the coupon section:
P = F / (1 + i) ^ t
P = price of bond
F = face value
i = interest rate
t = number of periods
$10,000, zero-coupon bond maturing in 7 years, interest rate is 4%. Selling price?
A. $7,599.18

11. Fixed Payment Loan
Lender provides borrower funds, borrower pays back lender in fixed payments every period until the loan is paid off (ie. Mortgage or auto loan)
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12. Subprime Loans
“A mortgage granted to a borrower considered subprime, that is, a person with a less-than-perfect credit report. Subprime borrowers have either missed payments on a debt or have been late with payments. Lenders charge a higher interest rate to compensate for potential losses from customers who may run into trouble or default.”

13. Subprime Meltdown Background:
U.S. housing bubble began in early 2000’s
Low interest rates and new “mania” for buying houses caused housing prices to skyrocket
Some banks and newly-formed lending institutions took advantage of the situation by offering long term mortgages to people who could normally not afford them – subprime borrowers
These borrowers relied on the capital value of their new homes to pay off the mortgage, rather than their earning power

14. Subprime Meltdown Outcome
The rapid rise in housing prices created a bubble, which burst in late 2005
Housing prices began to fall and, eventually, many subprime borrowers began to default on their loans
This caused the collapse and bankruptcy of many of these institutions, and has hurt the financial industry substantially

15. Subprime Meltdown

16. Subprime Meltdown Outcome
This meltdown has depressed the US economy, causing the Federal Reserve to lower it’s benchmark rate
Has caused a weakening of the US dollar, and billions of dollars of losses for investment funds

17. Subprime Meltdown International
All of this has caused Canada to be affected as well
Canadian dollar has risen against US dollar and is now at parity
Depressed US housing market and high dollar has resulted in a crisis for the forestry industry (ie. Canfor mill closures)

18. Subprime Meltdown
Initially, it was all caused by extremely low interest rates in the early 2000’s in order to stimulate the economy after the dot-com crash

19. Measuring Interest Rates
Yield to Maturity
Current Yield
Yield on a Discount Basis

20. Yield to Maturity
Interest rate that equates PV of cash flow payments received with its value today
Most accurate measure of interest rates
1. Simple Loans
2. Fixed-Payment Loans
3. Coupon Bonds
4. Perpetuity
5. Discount Bonds

21. Yield to Maturity Simple Loans
Q. Pete borrows $100 from Bob and Bob wants back $110 from him next year. YTM?
A. PV = FV / ( 1 + i ) ^ t
100 = 110 / (1+ i ) ^ 1
r = 0.1 = 10%
In a simple loan, i = YTM

22. Yield to Maturity Fixed Payment Loan
Q. $100,000 loan, payments of $ for next 20 years. YTM?
LV = FP / (1 + i) + FP / (1 + i)^ FP / (1 + i) ^ n
LV = Loan Value
FP = Fixed Yearly Payment
n = number of years until maturity
A. 0.7 = 7%

23. Yield to Maturity Coupon Bond PP = C ((1-(1/(1+i)^n)/i) + FV/ (1+i)^n
PP = Value of Bond
C = Coupon Payment
i = YTM
N = number of periods
FV = Face value of bond

24. YTM
Price of 8% coupon bond is $1122, FV of $1000, 12 years to maturity, paid annually, what is YTM?
PP = C ((1-(1/(1+i)^n)/i) + FV/ (1+i)^n
PP = Value of Bond
C = Coupon Payment
i = YTM
N = number of periods
FV = Face value of bond
A = 6.5%

25. Yield to Maturity Perpetuity
Coupon bond with no maturity date (goes on forever)
P = C / i
P = Price of perpetuity
C = Yearly Payment
i = YTM
Q. Bond with price of $2000 and pays $100 annually forever, what is YTM?
Answer: 100 / 2000 = 0.05 = 5%

26. Yield to Maturity Discount Bond i = (F – P) / P
F = Face Value
P = Current Price
Ex. Treasury Bills that pays a FV of $1000 in 1 year. Purchase Price is $900. YTM?
A. i = (1000 – 900) / 900 = = 11.1%

27. Yield to Maturity
Yield to Maturity for bonds is the actual interest rate
Bond prices and interest rates are negatively related

28. Current Yield Yield of a bond at a point in time
Does not reflect total return
Used as approximation to describe interest rates for long term bonds
CY = C / P
C = Coupon payment
P = Current price

29. Current Yield
Q. What is the current yield of a $1000, 8% coupon bond maturing in 3 years and selling for a price of $1200?
A. CY = C / P
= 80 / 1200
= = 6.66%

30. Yield on a Discount Basis
Most accurate measure of interest rates for short term bonds
Yield of bills with a maturity of less than one year
i = (F – P) / P * 365 / Days to Maturity
i = Yield on a discount basis
F = Face Value
P = Purchase Price

31. Yield on a Discount Basis
Q. 91 day treasury bill selling for $988 with FV of $1000
A. i = (F – P) / P * 365 / Days to Maturity
i = (1000 – 988) / * 365 / 91 = = 4.87%

32. Central Banks and Interest Rates
Very important in determining interest rates
Central banks determine lending rates and heavily influence market interest rates
Lending rate is the rate that the central bank will lend to other banks, thereby insuring that all lending rates (inter-bank or otherwise) are above this rate

33. Central Banks
Can be government controlled, or independent of government (Bank of Canada, Federal Reserve)
Determine countries monetary policy
Sole issuer of the countries' currency
Supervises banking industry
“Lender of last resort” and governments banker
Manages gold reserves
Sets interest rate

34. International Interest Rates
Canada %
United States %
United Kingdom %
Europe %
Japan %
Australia %
China %
India %

35. Canada
Determined by the Bank of Canada

36. United States
Determined by the Federal Reserve

37. United Kingdom
Determined by the Bank of England

38. Japan
Determined by Bank of Japan

39. Japan
Island nation with no natural resources and very high population, and yet has the second largest economy in the world with the highest life expectancy, and very technologically advanced
For past 15 years has been in prolonged stagnation due to many factors

40. Japan
As a result, the interest rate has been very low (0.1% for past 5 years) in order to stimulate the economy
Extremely low compared to Canada (4.5%)
Low interest rate has resulted in negative inflation

41. Interest Rates vs Returns
Rate of return on a bond not necessarily the yield to maturity of the bond
Rate of return is dependant on behaviour of market interest rates over the holding period of the bond
If a bond is held for its entire life, then yield to maturity is equal to the return of the bond
RET = (C / Pt) + (Pt+1 – Pt) / Pt
RET = Return
Pt = Initial Price of Bond
Pt+1 = Selling Price of Bond
C = Coupon Payment

42. Interest Rates vs Returns
Q. What is the rate of return on a bond bought for $988 and sold one year later for $1200? The coupon rate is 5%, and face value is $1000.
A. (C / Pt) + (Pt+1 – Pt) / Pt
= ( 50 / 988) + (1200 – 988) / 988 =
= = 26.5%

43. Volatility of Bonds Longer term = larger risk/more volatility
Known as interest rate risk

44. Real vs Nominal Rates So far, i = nominal interest rate
Real interest rate is a more accurate rate that is adjusted for inflation
i = real interest rate + expected inflation OR
Real interest rate = i – expected inflation
i = nominal rate
Actual inflation is not known until later

45. Real vs Nominal Rates
When real interest rate is low, there are greater incentives to borrow and fewer to lend
Measured by indexed bonds
Interest and principal payments are adjusted for price levels by indexing to the Consumer Price Index (CPI)

46. Real vs Nominal Rates
Real rate is lower than nominal rate because of inflation

47. Learning Objectives 1. Detail terms present value and interest rate
2. Discern measurements of interest rates: YTM, Current Yield, Yield on Discount basis
3. Illustrate inverse relationship of bond prices and interest rates
4. Explain difference between nominal and real interest rates
5. Explain difference between interest rates and rates of return

48. The End
Questions?