Chapter 10 Day 3

·         Yield curve ßà Term structure of interest rate

·         Upward sloping yield curve=normal yield curve

·         In order for investors to want to invest for a longer period of time, they need incentive.

Downward sloping yield curve

·         Times of high inflation

Humped Yield Curve

·         The yield curve is going from normal to inverted

Dividend yield = dividends/ current price of stock (Return from Income)

Current yield does same thing as dividend yield- but with bonds.

Current yield=return from income= annual interest/price

Problem 1

30 year, 7% coupon, Face Value= $1000, Price=$901

Current yield= 70 (annual interest)/901 (Face Value)

CY=7.78%

Problem 1 b.

Rate-35/ (1+YTM/2) +35/(1+YTM/2)^2…..35+1000/(1+YTM/2)^60

·         If it sells at a discount, the market wants a higher YTM(interest rate) then currently willing to pay)

Using Problem 1 in Excel

1)      Use the rate function

2)      Put into excel (NPR,Rate, PV, FV)

3)      =rate(60,35,-901,1000)

4)      =3.93- Remember semiannual

5)      =3.93*2= 7.86%

What is the bond price 6 months later assuming the interest rates are unchanged?

 

 

 

PV=?

FV=1000

NPR=59

Rate=3.93

PMT=35

 

HPR=Interest +CG/price=35+.43/901

HPR=3.93%

 

APR=3.93*2

APR=7.86

 

*Same as the YTM found earlier*

                                                                                                Callable

l------------------------------------------------------l----------------------------------------------l

1999 issued                                                         2009                                                       2009 Maturity                                   

7% coupon, 30 year bond

After 10 years, it is callable

They pay the call price, $1000 plus some premium

Call schedule shows each year what the premium is.

                                                                                                                                                Call Price

2009                                                                       1000+10% premium                        =$1100

2010                                                                                       + 9.5%                                   =$1095

                                                                                ( continues to decline)

 

In 2009, interest rates have fallen, only 5%.

 

Interest on old bonds=7%*1000=$70

If call, interest on new bond=5%

 

·         Further, the investors hold the bond to maturityà will make money.

·         Discount bonds go up in value-> enhance return

 

Problem 2

15 year bond, 8% coupon, $1000 Face Value

Price=$1250

Call-able in 5 years, 10%

 

YTM

PV=-1250

FV=1000

NPR=30

PMT=40

Rate=2.76

 

Annual Rate=2.76*2=5.53%

 

Yield to Call ( assume called on first call date)

 

PV (inflows)=PV (outflows)

 

40/(1+YTC/2)+40/(1+YTC/2)^2…….40+1100/(1+YTC/2)^10=1250

 

Use in Excel

 

PV=-1250

FV=1100 ( First call Price)

NPR=10

PMT=40

Rate=?

 

Rate=2.63*2

Rate=4.22%

 

Realized Yield

 

~ Sell the bond before it reaches maturity~

 

10 year bond, 12%coupon, 8%yield

 

Hold for three years and sell for 1300

 

Realized Yield

 

Pricing the Bond

-Use PV in Excel

Rate=.04

NPR=20

PMT=60

FV=1000

 

PV=1271.81=PRICE OF BOND

 

 

 

PV=-1271.81

FV=1300

NPR=20

PMT=60

Rate=

 

Rate=5.04%*2= 10.09%