Question

Callaghan Motors' bonds have 12 years remaining to maturity. Interest is paid annually, they have a $1,000 par value, the coupon interest rate is 7.5%, and the yield to maturity is 10%. What is the bond's current market price? Round your answer to the nearest cent.

Answer 1

Face value of the bond = $1000

Time to maturity = 12 years

Yield to maturity = 10%

Annual coupon rate = 7.5%

Annual coupon payment = Annual coupon rate*Face value = 7.5%*1000 = 75

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

Input the following values in ba ii plus calculator

N = 12

I/Y = 10

PMT = 75

FV = 1000

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

We get, PV = -829.6577044

Current market price of the bond = $829.66 (Rounded to the nearest cent)

Answer -> 829.66

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(10%,12,75,1000) = -829.66

Answer -> 829.66

Method 3: Bond's price calculation using formula

Face value of the bond = $1000

YTM = 10%

Time to maturity = 12 years

The bond will pay an annual coupon of $75 till maturity and it will also pay the face value at maturity

Year	1	2	3	4	5	6	7	8	9	10	11	12
Cashflow	75	75	75	75	75	75	75	75	75	75	75	1075

The Cash flows for the bond are:

C1 = C2 = ...... = C11 = 75 and C12 = 1075

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 = 75 and C12 = 1075

P = 487.1295754 + 342.528129 = 829.6577044

Price of the bond = $829.66 (Rounded to the nearest cent)

Answer -> 829.66