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Ms. Alumm is the portfolio manager for a large insurance company. She is considering investing $1million to purchase some bonds of Patriot Enterprises, Inc.
All of Patriot's bonds have market prices that imply a yield to maturity of 8% bond equivalent yield (that is 4% every 6-month period). Each Patriot bond is described here, based on a $1,000 face value(par value), which is the promised payment at maturity.
- Bond A matures in five years and pays a 9% coupon yield ($45 every 6 months on a $1,000 facevalue bond).
- Bond B matures in ten years, pays an 8% coupon yield ($40 seminannual payments), and is beingoffered at par.
- Bond C is a zero-coupon bond that pays no explicit interest, but will pay the face amount of$1,000 per bond at maturity in ten years.A.
A) at what price should each bond currently sell?
As an alternative, Ms. Alumm has been invited to invest $1 million in a 10-year Eurobond of a secondfirm, Nationaliste, S.A. Nationaliste bonds are similar in risk to Bond B above: they promise an 8%coupon yield for 10 years, but coupons are paid annually, not semiannually. The Nationaliste bonds are priced at a 1% discount from par, or $990 per $1,000 face value.
B.What yield to maturity is implied by the Nationaliste Eurobond? Compare this yield to the 8% bond-equivalent yield of the Patriot semiannual coupon bond (Bond B) above. In which bond should Ms. Alumm invest?
Answer:
a) at what price should each bond currently sell?
Bond A
Price of Bond = pv(rate,nper,pmt,fv)
Price of Bond = pv(4%,10,45,1000)
Price of Bond = $ 1040.55
Bond B
Price of Bond = pv(rate,nper,pmt,fv)
Price of Bond = pv(4%,20,40,1000)
Price of Bond = $ 1000
Bond C
Price of Bond = pv(rate,nper,pmt,fv)
Price of Bond = pv(4%,20,0,1000)
Price of Bond = $ 456.39
Note : Nper is semi annual period
B)
Maximum S.A. Nationaliste bonds
Implied YTM =rate(nper,pmt,pv,fv)
Implied YTM = rate(10,80,-990,1000)
Implied YTM = 8.15%
Effective Annual YTM of Bond B = (1+4%)^2 -1 =8.16%
Therefore , Ms. Alumm should invest in Bond B Which will return little higher than Nationaliste Eurobond
