Question

What should be the price of a 26-year bond per $1,000 face value with a 3% annual coupon when interest rates for such bonds should be 4%?

		$840.17
		$851.02
		$862.35
		$873.53
		$884.78

Answer 1

Face value of the bond = $1000

Time to maturity = 26 years

Interest rate = Yield to maturity = 4%

Annual coupon rate = 3%

Annual coupon payment = Annual coupon rate*Face value = 3%*1000 = 30

Method 1: Bond's price calculation using ba ii plus calculator

Input the following values in ba ii plus calculator

N = 26

I/Y = 4

PMT = 30

FV = 1000

CPT -> PV [Press CPT and then press PV]

We get, PV = -840.1723082

Current market price of the bond = $840.17 (Rounded to the nearest cent)

Answer -> 840.17

Method 2: Bond's price calculation using Excel

We can calculate the price of the bond using the PV function in Excel as shown below:

=PV(4%,26,30,1000) = -840.17

Answer -> 840.17

Method 3: Bond's price calculation using formula

The bond will pay an annual coupon of $30 till maturity and it will also pay the face value at maturity

The Cash flows for the bond are:

C1 = C2 = ...... = C25 = 75 and C26= 1030

The current price of the bond is the sum of the present value of all the cashflows. Hence the current price of the bond is calculated using the formula:

where, Ci = 30 and C26 = 1030

P = 468.6623983 + 371.5099099 = 840.1723082

Price of the bond = $840.17 (Rounded to the nearest cent)

Answer -> 840.17 (1st option)