A 15-year municipal bond was issued 5 years ago. Its coupon interest rate is 4%, interest payments are made semiannually, and its face value is $1000. If the current market interest rate is 6.09%, what should be the bond’s price? Note: The issuer of the bond (city, state, company) makes interest

Question

A 15-year municipal bond was issued 5 years ago. Its coupon interest rate is 4%, interest payments are made semiannually, and its face value is $1000. If the current market interest rate is 6.09%, what should be the bond’s price? Note: The issuer of the bond (city, state, company) makes interest payments to the bondholder (at the coupon rate), as well as a final value payment.

Accepted Answer

TABLE SOLUTION

The first 5 years are past, and there are 20 more semiannual payments. The coupon interest rate is the nominal annual rate or APR. Half that, or 2%, of $1000 or $20 is paid at the end of each 6-month period.

The bond’s price is the PW of the cash flows that will be received if the bond is purchased. The cash flows are $20 at the end of each of the 20 semiannual periods and the face value of $1000 at the end of period 20.

Since the $20 in interest is received semiannually, the market or effective annual interest rate [latex](i_{a}[/latex]) must be converted to a semiannual rate. Using Equation 3-8, we obtain

Effective annual interest rate [latex]i_{a}=(1+i)^{m}-1[/latex] (3-8)

[latex](1+i)^{2}=1+i_{a}=1.0609[/latex]

[latex](1+i)=1.03[/latex]

i=3% semiannual interest rate

[latex]PW=20(P/A,3\%,20)+1000(P/F,3\%,20)[/latex]

[latex]=20(14.877)+1000(0.5537)=\$851.24[/latex]

The $851.24 is the discounted price; that is, the PW at 6.09% of the cash flows from the $1000 bond. The $148.77 discount raises the investment’s rate of return from a nominal 4% for the face value to 6.09% on an investment of $851.24.

5-BUTTON SOLUTION

H	G	F	E	D	C	B	A
Answer	Solve for	FV	PV	PMT	n	i	Problem	1
-$851.24	PV	1000		20	20	3%	Exp. 5-14	2

This example also illustrates why it is better to separately state cash flows. At the end of period 20, there are two cash flows, $20 and $1000. The $20 is part of the 20-period uniform series, and the $1000 is a single cash flow. All of these numbers come directly from the problem statement. If the two final cash flows are combined into $1020, then the $20 uniform series has only 19 periods—and it is easy to err and forget that change.

Question 5.14: A 15-year municipal bond was issued 5 years ago. Its coupon ...

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