understanding the interest rates. yield to maturity
DESCRIPTION
UNDERSTANDING THE INTEREST RATES. Yield to Maturity. Frederick University 2014. 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. - PowerPoint PPT PresentationTRANSCRIPT
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.
Bonds: 4 types
Discount bonds - zero coupon bonds(government bonds) fixed payment loans
(mortgages, car loans) coupon bonds
(government bonds, corporate bonds) consols
Zero coupon bonds
Discount bonds Purchased price less than face
value P < F No interest payments Face value on maturity
yield on a discount basis
how the bond yields are actually quoted approximates the YTM
idb = F - P
Fx
360d
fixed payment loan
loan is repaid with equal (monthly) payments
Each payment is a combination of principal and interest
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?
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.
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%
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.
Consols (or perpetuities)
Consols (or perpetuities) promise interest payments forever, but never repay principal.
current yield = 6.15% true YTM = 7.37% lousy approximation
only 2 years to maturity selling 2.5% below F
Holding period return Holding period return – the return
for holding a bond between periods t and t+1
sell bond before maturity return depends on
holding period interest payments resale price
Holding period return
C/Pt is the current yield ic (Pt+1 – Pt)/Pt is the capital gain =
g RET = ic+ g
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.