# Abacus Inc. has asked you price a 5 year bullet bond

2 Year 3.80% 3.25%

3 Year 4.5% 3.5%

4 Year 5% 4%

5 Year 6% 4.5%

You can assume that coupon payments are annual and that you are pricing on a coupon day (no accrued interest) and you may ignore basis conventions. You should make your process and methodology clear with explanations at each stage. Assignment hint: You will need to use the T-Note data to bootstrap a zero coupon treasury curve and apply the Z-spread to price the Abacus bond. You might find it easier to use the PV and RATE functions in Excel rather than PRICE and YIELD (but both will work).

Step 1:Calculate the Price of Bonds (We will use the EXCEL FUNCTION PV)

Assume Face Value of bonds as $ 1000 (it does not matter whether we select $100, $1000, $10,000 or any number)

Face Value$1,000.00

YearCouponYTMAnnual Coupon PaymentPrice

13.25%3%$32.50 =3.25% x $1,000.$1,002.43 = -PV(3.%,1,32.5,1000) 23.80%3.25%$38.00 =3.8% x $1,000.$1,010.49 = -PV(3.25%,2,38,1000) 34.50%3.50%$45.00 =4.5% x $1,000.$1,028.02 = -PV(3.5%,3,45,1000) 45%4%$50.00 =5.% x $1,000.$1,036.30 = -PV(4.%,4,50,1000) 56%4.50%$60.00 =6.% x $1,000.$1,065.85 = -PV(4.5%,5,60,1000)

Please Note:

We have put a negative sign before PV so that we get a positive number; If you purchase a bond, PV is the price you pay- a negative number since there is a cash outflow PV function is written as =PV(RATE,NPER,PMT,FV)

RATE= Discount Rate per period = Yield to Maturity; since coupon payments are annual we have taken discount rate per year NPER= Number of periods= Maturity

PMT= Periodic payments= Annual Coupon payments

FV= Cash flow at maturity= Redemption Value of the bond= Face Value of the bond

Step 2 :Calculate Zero coupon bond rare

We will use zero-coupon bond rate to calculate the price of the bond

Price= C/(1+y1)^1 + C/(1+y2)^2 + -----------+ C/(1+yn-1)^(n-1) + (FV+C)/(1+yn)^n where C= annual coupon payment

FV= Redemption value at maturity= Face Value

y1,y2,------,yn-1,yn ate zero coupon bond rates for 1,2,----,n-1,n years ^ means raised to the power of

Start with 1year coupon bond

MaturityCouponFVYTMAnnual Coupon PaymentPrice

13.25%$1,000.00 3.00%$32.50 $1,002.43

Substituting the values

$1,002.43 =(32.5+1000)/(1+ y1)^1

Solving y1=3.00%

Next2year coupon bond

MaturityCouponFVYTMAnnual Coupon PaymentPrice

23.80%$1,000.00 3.25%$38.00 $1,010.49

YearCash flowZero Coupon rateDiscounted Cash flow 1$38.00 3.00%36.89=38/ (1+0.03)^1(Zero coupon rate calculated above)

36.89

2$1,038.00 y2?

$1,010.49

or 1038/(1+...

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