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Chapter 4

Chapter 4. Understanding Interest Rates. Measuring Interest Rates. Discount rate – the rate used to weigh a stream of future payments Most choices require decision-makers to trade-off costs and benefits at different points in time (e.g., savings , work effort, education, projects…)

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Chapter 4

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  1. Chapter 4 Understanding Interest Rates

  2. Measuring Interest Rates Discount rate – the rate used to weigh a stream of future payments Most choices require decision-makers to trade-off costs and benefits at different points in time (e.g., savings, work effort, education, projects…) As the payment gets further and further into the future people place less and less weight on it People who are more worried about Right Now discount the future more than people who are more concerned with the future In economics, the discount rate is determined by market rate of interest i one’s time preference

  3. Present Value — The Schooling Decision Dollars/year 40,000 Goes to College (24,000/year)(43 years) = $1,032,000 Only High School 16,000 Age 0 18 22 65 $20,000 + = $84,000 $64,000 -5,000 • A person gets only a HS diploma earns $16,000 a year from age 18 until he retires. • If the person goes to college, • she pays $20,000 in tuition • foregoes earning $64,000, • but earns $1,032,000 more by graduation from college from age 22 to age 64.

  4. Present Value — The Schooling Decision • The previous model ignores the discount rate • Swann (2003) estimates the annual discount rate of women at 20% • Keane and Wolpin (1997) estimate the discount rate of young men at 28%

  5. Present Value — The Schooling Decision • The slope indicates earnings increase in years of education, and the wage-schooling locus in concave • The worker makes $33,600 graduating from JHS • The worker makes $41,600 graduating from HS • The worker makes $46,400 graduating from Univ (41,600-33,600)/33,600 = 6% (46,400-41,600)/41,600 = 3%

  6. Present Value — The Schooling Decision 24 18 15 12 9 6 3 • The Marginal Rate of Return (to an additional year of schooling) is the percent change in w given a one-year increase in s • Finishing 12th grade increases earnings by 6% • Finishing college (rather than dropping out after your junior year) increases earnings by 3%

  7. Present Value — The Schooling Decision 24 18 15 12 9 6 3 r s* • A worker maximizes the present value of lifetime earnings by going to school until the marginal rate of return to schooling equals the discount rate. • A worker with discount rate r = 3% goes to school for s* = 12 years.

  8. Present Value — The Schooling Decision Individuals with different discount rates Rate of Interest Dollars 50 17 30 9 mrr 12 Years of Schooling 12 16 16 Years of Schooling • John and Jill have the same wage-schooling locus because they have the same ability • For this reason they have the same mrr • They have different discount rates • Jill graduates from college but John goes to high school only.

  9. Present Value — The Schooling Decision Individuals with different abilities Rate of Interest Dollars Bob 60 Ace 40 30 8 mrrBob mrrAce 12 Years of Schooling 16 12 16 Years of Schooling • Ace and Bob have the same discount rate • They have a different wage-schooling and mrr schedules because Bob is more able. • Ace doesn’t go to college since his mrr = 8 after graduating HS, • Bob graduates from college, and earns 30. and earns 60.

  10. Present Value — The Schooling Decision Individuals with different abilities Ability is not accounted for Dollars Bob 60 Ability is accounted for Ace 40 30 12 Years of Schooling Years of Schooling 16 • The wage differential between Bob and Ace overstates the gain from college • Bob is more able • We don’t observe either wage-schooling schedule • The difference does not tells us how much Ace’s earnings rise by if he gets a BS

  11. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity coupon bond P = price of bond when auctioned/issued F = face value of bond c = annual coupon rate (in percent) C = dollar value of annual coupon payment = cF n = years to maturity date

  12. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity coupon bond 100 100 100 1000 100 c = 10%, n = 10, F = $1,000 M&B_bond_prices.xlsx

  13. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity coupon bond 100 100 100 1000 100 c = 10%, n = 10, F = $1,000 M&B_yields.xlsx

  14. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity fixed payment loan 0 P = payment to borrower after loan is signed C = annual cash payment n = years to maturity date M&B_loan.xlsx

  15. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity perpetuity (or consol) bond P = price of bond when auctioned/issued C = dollar value of annual coupon payment n = infinity F = face value of bond

  16. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity perpetuity (or consol) bond P = price of bond when auctioned/issued C = dollar value of annual coupon payment n = infinity

  17. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity perpetuity (or consol) bond P = price of bond when auctioned/issued C = dollar value of annual coupon payment n = infinity

  18. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity perpetuity (or consol) bond P = price of bond when auctioned/issued C = dollar value of annual coupon payment n = infinity

  19. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity perpetuity (or consol) bond P = price of bond when auctioned/issued C = dollar value of annual coupon payment n = infinity

  20. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity perpetuity (or consol) bond P = price of bond when auctioned/issued C = dollar value of annual coupon payment n = infinity

  21. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity perpetuity (or consol) bond P = price of bond when auctioned/issued C = dollar value of annual coupon payment n = infinity

  22. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity perpetuity (or consol) bond P = price of bond when auctioned/issued C = dollar value of annual coupon payment n = infinity

  23. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity perpetuity (or consol) bond P = price of bond when auctioned/issued C = dollar value of annual coupon payment n = infinity

  24. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity perpetuity (or consol) bond c P = price of bond when auctioned/issued C = dollar value of annual coupon payment n = infinity ic= current yield to maturity

  25. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity coupon bond P = price of bond when auctioned/issued F = face value of bond C = dollar value of annual coupon payment n = years to maturity date

  26. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity discount bond 0 0 0 0 P = price of bond when auctioned/issued F = face value of bond C = 0 n = years to maturity date

  27. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity discount bond P = price of bond when auctioned/issued F = face value of bond n = years to maturity date

  28. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity simple loan C P = payment to borrower after the loan is signed C = cash payoff of loan’s principal and interest n = years to maturity date C

  29. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity discount bond P = price of bond when auctioned/issued F = face value of bond n = 1

  30. Measuring Interest Rates • Discount rate (continued) • In Money & Banking, it is • market rate of interest i on a loan: • called the Yield to Maturity simple loan C P = payment to borrower after the loan is signed C = cash payoff of loan’s principal and interest n = 1 C

  31. Properties of bonds as interest rates rise. • The price of a bond falls

  32. Properties of bonds as interest rates rise. • The price of a bond falls • The rate of return(R) is the return on a bond held for a given period of time • R =yield to maturity only if it is held for all n periods no Interest-Rate Risk

  33. Properties of bonds as interest rates rise. • The price of a bond falls • The rate of return (R) is the return on a bond held for a given period of time • R =yield to maturity only if it is held for all n periods • R ≠ yield to maturity if the bond is held less than nperiods • If a coupon bond is purchased and held for its final year,

  34. Properties of bonds as interest rates rise. • The price of a bond falls • The rate of return(R) is the return on a bond held for a given period of time • R =yield to maturity only if it is held for all n periods • R ≠ yield to maturity if the bond is held less than nperiods • If a coupon bond is purchased and held for its final year,

  35. Properties of bonds as interest rates rise. • The price of a bond falls • The rate of return(R) is the return on a bond held for a given period of time • R =yield to maturity only if it is held for all n periods • R ≠ yield to maturity if the bond is held less than n periods • If a coupon bond is purchased and held for its final year,

  36. Properties of bonds as interest rates rise. • The price of a bond falls • The rate of return(R) is the return on a bond held for a given period of time • R =yield to maturity only if it is held for all n periods • R ≠ yield to maturity if the bond is held less than n periods • If a coupon bond is purchased and held for its final year,

  37. Properties of bonds as interest rates rise. • The price of a bond falls • The rate of return(R) is the return on a bond held for a given period of time • R =yield to maturity only if it is held for all n periods • R ≠ yield to maturity if the bond is held less than n periods • If a coupon bond is purchased and held for its final year,

  38. Properties of bonds as interest rates rise. • The price of a bond falls • The rate of return(R) is the return on a bond held for a given period of time • R =yield to maturity only if it is held for all n periods • R ≠ yield to maturity if the bond is held less than n periods • If a coupon bond is purchased and held for its final year,

  39. Properties of bonds as interest rates rise. • The price of a bond falls • The rate of return(R) is the return on a bond held for a given period of time • R =yield to maturity only if it is held for all n periods • R ≠ yield to maturity if the bond is held less than n periods • If a zero-coupon bond is purchased and held for its final year, 0

  40. Properties of bonds as interest rates rise. • The price of a bond falls • The rate of return(R) is the return on a bond held for a given period of time • R =yield to maturity only if it is held for all n periods • R ≠ yield to maturity if the bond is held less than n periods • If a coupon bond is purchased and held for its final year, and its purchase price equals its face value, F F F

  41. Properties of bonds as interest rates rise. • The price of a bond falls • The rate of return(R) is the return on a bond held for a given period of time • R =yield to maturity only if it is held for all n periods • R ≠ yield to maturity if the bond is held less than n periods • If a coupon bond is purchased and held for its final year, and its purchase price equals its face value, c F F

  42. Properties of bonds as interest rates rise. • The price of a bond falls • The rate of return(R) is the return on a bond held for a given period of time • R =yield to maturity only if it is held for all n periods • R ≠ yield to maturity if the bond is held less than n periods • If a coupon bond is held for one yearand sold before it matures, P t t+1 t t

  43. Properties of bonds as interest rates rise. • The price of a bond falls • The rate of return(R) is the return on a bond held for a given period of time • R =yield to maturity only if it is held for all n periods • R ≠ yield to maturity if the bond is held less than n periods • If a zero-coupon bond is held for one yearand sold before it matures, P t t+1 t t

  44. Properties of bonds as interest rates rise. • The price of a bond falls • The rate of return(R) is the return on a bond held for a given period of time • R =yield to maturity only if it is held for all n periods • R ≠ yield to maturity if the bond is held less than n periods • If a coupon bond is held for one year, and sold before it matures for the same price it was purchased,

  45. Properties of bonds • A rise in interest rates is associated with a fall in bond prices, resulting in a capital loss if time to maturity is longer than the holding period • The more distant a bond’s maturity, the greater the size of the percentage price change associated with an interest-rate change • The more distant a bond’s maturity, the lower the rate of return the occurs as a result of an increase in the interest rate • Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise

  46. Properties of bonds • A rise in interest rates is associated with a fall in bond prices, resulting in a capital lossif time to maturity is longer than the holding period • The more distant a bond’s maturity, the greater the size of the percentage price change associated with an interest-rate change • The more distant a bond’s maturity, the lower the rate of return the occurs as a result of an increase in the interest rate • Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise c = 10%, n = 5, F = $1,000 100 100 100 1000 100 100 = 1000

  47. Properties of bonds • A rise in interest rates is associated with a fall in bond prices, resulting in a capital lossif time to maturity is longer than the holding period • The more distant a bond’s maturity, the greater the size of the percentage price change associated with an interest-rate change • The more distant a bond’s maturity, the lower the rate of return the occurs as a result of an increase in the interest rate • Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise c = 10%, n = 5, F = $1,000 100 100 100 1000 100 100 = 741 = 1000 M&B_bond_properties.xlsx

  48. Properties of bonds • A rise in interest rates is associated with a fall in bond prices, resulting in a capital lossif time to maturity is longer than the holding period • The more distant a bond’s maturity, the greater the size of the percentage price change associated with an interest-rate change • The more distant a bond’s maturity, the lower the rate of return the occurs as a result of an increase in the interest rate • Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise • Prices and returns for long-term bonds are more volatile than those for shorter-term bonds Interest-Rate Risk

  49. Figure 1 Interest Rates (3-Month Treasury Bill), 1953–2011 Real vs. Nominal Interest Rates • When the real rate is low, there are • greater incentives to borrow • fewer incentives to lend • The real rate is a better indicator of the incentives to borrow & lend

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