Question

Question: A two-year bond with par value \(1,000 making annual coupon payments of \)100 is priced at $1,000. What is the yield to maturity of the bond? What will be the realized compound yield to maturity if the one-year interest rate next year turns out to be:

( a ) 8%,

( b ) 10%,

( c ) 12%?

Short answer

Answer

a. 9.91%

b. 10.00%

c. 10.09%

Step-by-step solution

Given information

The bond is selling at par value.

Its yield to maturity equals the coupon rate, 10%.

If the first-year coupon is reinvested at an interest rate of r percent, then total proceeds at the end (1 + r) + 1100].

Calculation of the realized compound YTM

Therefore, realized compound yield to maturity of the second year will be a function of r as given below:

r	Total proceeds	Realized YTM = √Proceeds / 1000 -1
8%	$1208	√1208/1000 - 1 = 0.0991 = 9.91 %
10%	$ 1210	√1210/1000 - 1 = 0.1000 = 10.00 %
12%	$ 1212	√1212/1000 - 1 = 0.1009 = 10.09 %