UNDERSTANDING THE INTEREST RATES. Yield to Maturity

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UNDERSTANDING THE INTEREST RATES. Yield to
Maturity

• Frederick University
• 2014

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Yield to Maturity

• The yield to maturity is the interest rate that
  makes the discounted value of the future payments
  from a debt instrument equal to its current value
  (market price) today.
• It is the yield bondholders receive if they hold
  a bond to its maturity.

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Bonds 4 types

• Discount bonds - zero coupon bonds
• (government bonds)
• fixed payment loans
• (mortgages, car loans)
• coupon bonds
• (government bonds, corporate bonds)
• consols

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Zero coupon bonds

• Discount bonds
• Purchased price less than face value
• P lt F
• No interest payments
• Face value on maturity

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example

• 90 day bond,
• P 9850, F 10,000
• YTM solves

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yield on a discount basis

• how the bond yields are actually quoted
• approximates the YTM

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example

• 90 day bond,
• P 9850, F 10,000
• discount yield

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The discount yield vs. the yield to maturity

• idb lt YTM
• why?
• F in denominator
• 360 day year

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fixed payment loan

• loan is repaid with equal (monthly) payments
• Each payment is a combination of principal and
  interest

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fixed payment loan

• 15,000 car loan, 5 years
• monthly payments 300
• 15,000 is price today
• cash flow is 60 pmts. of 300
• what is i?

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• i is annual rate
• but payments are monthly, compound monthly
• i i/12

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how to solve for i?

• Trial and error
• Financial tables
• Financial calculator
• Spreadsheets

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Coupon bond

• a 2-year coupon bond
• a face value F 10,000,
• a coupon rate i 6,
• a price P 9750.
• bond price PV(future bond payments)
• The coupon payments are
• face value x coupon rate/2
• 10,000 x 0.06 x 0.5 300.

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• payments are every 6 months for 2 years,
• there are a total of 2 x 2 4 payment periods.
• the yield to maturity, i, is expressed on an
  annual basis, so i/2 represents the 6 month
  discount rate
• 9750 300/(1 i/2) 300/(1 i/2)2 300/(1
  i/2)3 300/(1
• i/2)4 10000/ ( 1 i/2)4
• or
• 9750 300/(1 i/2) 300/(1 i/2)2 300/(1
  i/2)3 10 300/(1 i/2)4
• i 7.37

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3 important points

• The yield to maturity equals the coupon rate ONLY
  when the bond price equals the face value of the
  bond.
• When the bond price is less than the face value
  (the bond sells at a discount), the yield to
  maturity is greater than the coupon rate. When
  the bond price is greater than the face value
  (the bond sells at a premium), the yield to
  maturity is less than the coupon rate.
• The yield to maturity is inversely related to the
  bond price. Bond prices and market interest rates
  move in opposite directions.

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Consols (or perpetuities)

• Consols (or perpetuities) promise interest
  payments forever, but never repay principal.

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Bond Yields

• Yield to maturity (YTM)
• Current yield
• Holding period return

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Yield to Maturity (YTM)

• a measure of interest rate
• interest rate where

P
PV of cash flows
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Current yield

• approximation of YTM for coupon bonds

annual coupon payment
ic
bond price
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Current yield vs. YTM

• Better approximation when
• Maturity is shorter
• P is closer to F

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example

• 2 year bonds, F 10,000
• P 9750, coupon rate 6
• current yield

600
ic
6.15
9750
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• current yield 6.15
• true YTM 7.37
• lousy approximation
• only 2 years to maturity
• selling 2.5 below F

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Holding period return

• Holding period return the return for holding a
  bond between periods t and t1
• sell bond before maturity
• return depends on
• holding period
• interest payments
• resale price

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Holding period return
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Holding period return

• C/Pt is the current yield ic
• (Pt1 Pt)/Pt is the capital gain g
• RET ic g

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example

• 2 year bonds, F 10,000
• P 9750, coupon rate 6
• sell right after 1 year for 9900
• 300 at 6 mos.
• 300 at 1 yr.
• 9900 at 1 yr.

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i/2 3.83 i 7.66
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• why i/2?
• interest compounds annually not semiannually