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

Topics: Bond, Zero-coupon bond, Bond duration Pages: 9 (1096 words) Published: March 24, 2014
Abacus Inc. has asked you price a 5 year bullet bond issue for them, with Price, Yield to Maturity and Modified Duration. There are no comparable existing issues in the secondary market either by Abacus or a competitor and so you will need to price the issue from scratch. You have the following set of US Treasury bond data and consultations with your Bank Equity Analyst and Debt Analyst suggest that a Z-spread for Abacus of 200 bps over Treasuries and a coupon rate of 6.5% should be appropriate to attract investors. US Treasury Notes Coupon Yield to Maturity Zero coupon rate 1 Year 3.25% 3% 3%

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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