Finance Chapter 6- Bonds

YTM for an n year Zero Coupon Bond

1+YTMn = (Face Value/Price) ^1/n

YTM of a coupon bond

P= CPN * 1/y (1-(1)/(1+y)^n)+ FV/ (1+y)^n Or PV of all the periodic coupon payments + PV of the FV repayment using YTM

the risk-free interest rate

The YTM for risk free bonds is

premium

a bond trades at a ____ whenever its YTM is less than its coupon rate

premium

a price greater than face value

bond

a security sold by governments and corporations to raise money from investors today in exchange for a promised future payment

coupons

additional payments that will be paid periodically until the maturity of the bond.

fall, the opposite direction

as interest rates and bond yield rise, bond prices will ____ and vise versa, so that interest rate and bond prices always move in ______

P= CPN/ (1+y) + FV+CPN/ (1+y2) 10.50/(1+0.0085)+ 1000+10.50/ (1+0.0105)^2 = 1000.02

assume that the 6 month treasury spot rate is 1.7% APR and the one year rate is 2.1% APR, both compounded semiannually. what is the price of a one year $1000 par treasury bond with 2.1% coupons?

P= CPN/(1+r)+ CPN/(1+r)^n...

assume the current treasury yield curve shows that the spot rates for 6 months, one year, and one and a half years are 1%, 1.1%, and 1.3% all quoted semiannually compounded APRs. What is the price of a $1000, par, 3.5% coupon bond maturing in one and a half years (the next coupon is exactly six months from now?)

higher

because YTM for a bond is calculated using the promised FCF's instead of the expected CF's, the yield with credit risk will be _____

junk bonds, high yield bonds, speculative bonds

bond in the bottom five categories.

investment grade bonds

bonds in the top four categories - low default risk

1000* 0.059/ 2

consider a 25 year bond with a FV of 1000 that has a coupon rate of 5.9% with semiannual payments. what is the coupon rate?

maturity date

final payment date

decrease

higher coupon payments---> effect on interest rate?

will exceed the coupon rate

if a bond trades at a discount, its YTM...

N=1 PV= -96.64 FV= 100 YTM= 3.47%

in year 1 if the price is 96.64 (per $100 face value), what is the YTM?

bond certificate

indicates the amounts and date of all payments to be made

less

investors pay ___ for bonds with credit risk than they would otherwise

increase

longer term to maturity---> effect on interest rate?

coupon bonds

pay investors their face value at maturity and coupon interest payments Ex: treasury notes which have original maturities from one to ten years and treasury bonds with more than 10 years.

CPN payment- 1000*9.2%/2 N=20 PV= -1038 PMT=46 FV= 1000 I= 4.313% x 2 = 8.626%

suppose a 10 year, 1000 bond with a 9.2% coupon rate and semiannual coupons is trading for 1,038. what is the YTM?

n=5 i=6.3 pv= -903.15 fv=1000 so PMT= 39.82 39.82/ 1000= 3.982%

suppose a five year, 1000 bond with annual coupons has a price of 903.15 and a YTM of 6.3%. whats the coupon rate?

P= CPN/y x (1-(1)/(1+y)^n)+ FV/(1+y)^n =1110.26 N=9 i= 5.70 PMT= 73 FV= 1000

suppose the GM issued a bond with 10 years until maturity, a face value of 1000 and a coupon rate of 7.3% annually. The YTM when it was issued was 5.7%. Assuming the YTM stays constant, what is the price of the bond after it makes it's first payment?

P= CPN + CPN/y x (1- 1/ (1+y)^n) + FV/ (1+Y)^n = 1183.26

suppose the GM issued a bond with 10 years until maturity, a face value of 1000 and a coupon rate of 7.3% annually. The YTM when it was issued was 5.7%. Assuming the YTM stays constant, what is the price of the bond before it makes it's first payment?

N= 30 i= 7 PMT=0 FV= 100 PV= -13.14 purchase price n=25 i=7 PMT= 0 FV=100 PV= -18.42 sale price so n=5 PV= -13.14 PMT=0 FV=18.42 so I= 7%

suppose you buy a 30 year zero coupon bond with a YTM of 7%. You hold it for 5 years before selling it. If the YTM is 7% when you sell it, what is the annualized rate of return ?

n=4 i=4.75 pmt= 40 fv= 1000 PV= -973.25

the YTM of a 1000 bond with a 8% coupon rate, semiannual coupons, and two years to maturity is 9.5% APR, CPDed semiannually. what is its price

coupon rate

the amount of each coupon payment is determined by _____ CPN= CPN Rate * Face Value / Number of Payments/ Year

credit spread

the difference between the yields of the corporate bonds and the treasury yields high for bonds with low ratings and therefore a higher likelihood of default.

the higher the yield

the longer the maturity on a zero coupon....

face value (par value or principal)

the notional amount we use to compute interest payments

Zero coupon bonds

the only cash payment an investor receives is the face value of the bond at maturity. Ex: treasury bills with a maturity up to one year

less, discount, pure discount

the price of a zero coupon bond is always ___ than the face value. that is.. they always trade at a ______ so they are called _______ bonds.

equals the price of bond

the rate of return is the discount rate at which the PV of all future CF's from the bond ___________

YTM -- sets the PV of the promise bond payments equal to the current market price of the bond

the rate of return on an investment in a bond

any difference between the purchase price and principal value and its periodic coupon payments

the return on a bond comes from two sources:

credit risk

the risk of default by the issuer of any bond that is not default free; it is an indication that the bond's cash flows are not known with certainty.

Find PV = 89.91

what is the price per $100 FV of a two year, zero coupon, risk free bond if the YTM is 5.46%

multiply, coupons per year

yields are typically quoted as APR's, so we ____ the number of _______, thereby converting the answer into an APR quote with the same compounding interval as the CPN rate

n= 20 pv= 1085 pmt- 28.75 fv= 1000 i=2.34

your company currently has 1000 par, 5.75% coupon bonds with 10 years to mature and a price of 1085. if you want to issue new 10 year coupon bonds at par, what coupon rate do you need to set? assume for both bonds, the next coupon payment is due in 6 months

1+YTMn = (Face Value/Price) ^1/n FV= PV x (1+r)^n FV= 7000000x(1+0.04)^15= 12606604.54 or N= 15, i= 4, PV= 7m FV= 12606604.54 FUTURE VALUE = FACE VALUE

your company wants to raise 7M by issuing 15-year zero coupon bonds. if YTM on the bond is 4% (annually CPD APR), what total face amount of bonds must you issue?