Question

Assume a par value of $1,000. Caspian Sea plans to issue a 6.00 year, semi-annual pay bond that has a coupon rate of 8.16%. If the yield to maturity for the bond is 7.60%, what will the price of the bond be?

Answer 1

Par Value of the bond = 1000

The bond pays semi-annual coupon, So we will consider semi-annual coupon rates and YTM

Time to maturity = 6 years

No. of semi-annual period = 6*2 = 12

Annual coupon rate = 8.16%

Semi-annual coupon rate = 8.16%/2 = 4.08%

Therefore, semi-annual coupon payment = 4.08%*1000 = 40.8

YTM = 7.60%

Semi-annual YTM = 7.60%/2 = 3.8%

We can calculate the price of the bond using BA ii plus calculator and using Excel

Method 1: Using ba ii plus

N = 12

I/Y = 3.8

PMT = 40.8

FV = 1000

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

We get PV = 1026.585806

Price of the bond = 1026.585806

Method 2: Using Excel

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

=PV(3.8%,12,40.8,1000) = 1026.5858063

Answer -> Price of the bond = 1026.5858063

Method 3: Using Formula

Price of the bond is the present value of the future cash payments and the present value of the par value which is received at maturity

The cash flows are:

Period	1	2	3	4	5	6	7	8	9	10	11	12
Cashflow	40.8	40.8	40.8	40.8	40.8	40.8	40.8	40.8	40.8	40.8	40.8	1040.8

C₁=C₂=.....C₁₁ = 40.8, C₁₂ = 1040.8

We can also use the below formula to calculate the price of the bond

PV = 361.3141185+665.27168785 = 1026.585806

Answer -> Price of the bond = 1026.585806