You purchase a bond for $875. It pays $80 a year (that is, the semiannual coupon

Question

You purchase a bond for $875. It pays $80 a year (that is, the semiannual coupon is 4%), and the bond matures after 10 years. What is the yield to maturity?

Determine the current market prices of the following $1,000 bonds if the comparable rate is 10% and answer the following questions.

XY 5.25% (interest paid annually) for 20 years AB 14% (interest paid annually) for 20 years

Which bond has a current yield that exceeds the yield to maturity?

Which bond may you expect to be called? Why?

If CD, Inc., has a bond with a 5.25% coupon and a maturity of 20 years but which was lower rated, what would be its price relative to the XY, Inc., bond? Explain.

Explanation / Answer

You purchase a bond for $875. It pays $80 a year (that is, the semiannual coupon is 4%), and the bond matures after 10 years. What is the yield to maturity?

P = price of bond = 875 $

a = annual payment = 80 $

n = period = 10 years

Let k be the yield.

we consider annual payments.

annual coupon rate = 4%*2 = 8%

F= Face value = 80/0.08 = 1000 $

P = a((1+k)^n-1)/(k(1+k)^10) + F/(1+k)^10

=> 875 = 80((1+k)^10-1)/(k(1+k)^10) + 1000/(1+k)^10

At k = 0.1004 = 10.04%, RHS = 874.87 $ = 875 $

Hence YTM = k = 10.04%

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