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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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 Presentation

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UNDERSTANDING THE INTEREST RATES. Yield to Maturity

Frederick University2014

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

example

90 day bond, P = € 9850, F = € 10,000 YTM solves

36590

)1(

000,109850

i

36590

)1(

000,109850

i

9850

100001 365

90 i

90365

9850

100001

i

19850

10000 90365

i

yield on a discount basis

how the bond yields are actually quoted approximates the YTM

idb = F - P

Fx

360d

example

90 day bond, P = € 9850, F = € 10,000 discount yield =

%690

360

000,10

150

X

The discount yield vs. the yield to maturity

idb < YTM

why? F in denominator 360 day year

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?

i is annual rate but payments are monthly, &

compound monthly i = i/12

602 12/1

300...

12/1

300

12/1

30015000

iii

how to solve for i?

Trial and error Financial tables Financial calculator Spreadsheets

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.

Bond Yields

Yield to maturity (YTM) Current yield Holding period return

Yield to Maturity (YTM)

a measure of interest rate interest rate where

P = PV of cash flows

Current yield

approximation of YTM for coupon bonds

ic =annual coupon payment

bond price

Current yield vs. YTM

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

example

2 year bonds, F = € 10,000 P = € 9750, coupon rate = 6% current yield

ic =600

9750= 6.15%

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

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.

221

3009900

21

3009750

ii

i/2 = 3.83%i = 7.66%

why i/2? interest compounds annually not

semiannually