Question

A T-bond is sold as STRIP. The face value per bond is $1,000. Maturity is 10 years and coupon rate is 6% APR but coupons are paid semi-annually and YTM is 7.5% APR. Use this information to answer the following:

What is the price of 6^thpayment?

If your plan is to raise $150,000 by using a) above then how many strips would you purchase?

What is the cost if you are buying principle strip and how many strips would be needed  if you want to raise $1,000,000 by buying the principle strip?

If the bond is not a strip bond then what would be your cost if you still buying the same number of strips as estimated in c.

Answer 1

Coupon rate= 6% annually, so semi-annually coupon rate= 6/2= 3%.

Semi-annual coupon payment= 3%* par value of bond = 3% * 1000= $ 30

Semi annual YTM = 7.5/2 = 3.75%

All coupon payment are sold as a STRIP bond. All coupon payments are like Zero coupon bonds.

a). 6th Payment is 6th Coupon Bond of par value of 30.

Price is PV of that bond.

PV= Par Value/(1+(YTM/2))^n  

Where n=6 ( 3 Year), YTM = 7.5%

PV= 30/1.0375^6= $ 24.054

Price= $ 24.054

b). For paymennt of $ 150,000 total STRIP bond with PV = 24.054 is

Total STRIP Bond of 3year maturity= 150000/24.054= 6236

We wil purchase 6236 STRIP bond of 3year maturity for payment of $ 150,000.

c). Principle strip's PV= 1000/1.0375^20= $ 478.892

Total Principle strip require= 1,000,000/478.892= 2089 (= 2088.15 Bond, for raising at least 1,000,000)

We wil purchase 2089 PrincipleSTRIP bond for payment of $ 1,000,000.

d).  If Bond is not a Strip bond then PV formula of Coupon Bond is

Where C= coupon payment= 30, r= semi- annual yield rate=3.75%, t= payment frequency= 10*2=20, F =face value=1000

So, Bond Value or PV= $ 895.778

Total cost for buying 2089 Bond = 895.778* 2089= $ 1,871,280.24