Question

How to calculate the value of a bond with annual or semiannual interest payments?

Answer 1

Value of a bond is the present value of all future cash flow, discounted at the required yield rate.

The required yield rate is the market rate for such bond(of same credit rating)

Hence to calculate the value of a Bond you need the following information

• i=discount rate or market yield rate or required rate of return. If it is semi annual coupon payment, find semi-annual yield by dividing market yield by 2
• N=number of periods to maturity. If coupon payment is annual, N=number of years to maturity from the last coupon payment. If coupon payment is semi-annual, N=Number of semi annual period to maturity from the last coupon payment
• C=Amount of Coupon payment per period. If it is annual , coupon amount(C)=interest rate *Par Value. If it is semi-annual coupon, the coupon amount=C=0.5*interest rate*par value
• M=Maturity value =par value

Future cash flows of a Bond are the periodic coupon payments =C and the terminal cash flow of maturity amount M

Once , we have the above information, we can find the present value of the future cash flows by following methods:

.A Calculating present Value of each cash flow individually and adding them

.B Using Factor formula for Present value of Cash flows(P/A, i,N) and (P/F,i,N)

.C Using excel

Method A.

Bond Value=C/(1+i)+C/((1+i)^2)+ C/((1+i)^3)+ C/((1+i)^4)……..₊ C/((1+i)^N)+ M/((1+i)^N)

Method B

Factor Formula P/A,i,N=(((1+i)^N)-1)/(i*((1+i)^N))

P/A,i,N=(1-((1+i)^(-N))/i

P/F,i,N=1/((1+i)^N)

Bond value=C*((1-((1+i)^(-N))/i)+M/((1+i)^N)

Method C

Use PV function of excel with following parameters:

Rate=i, Nper=N , Pmt=-C and FV=-M

Example ,
Bond par Value	$1,000
Years to matirity	5
Coupon Rate	8%
Semiannual coupon Payment
Required Yield	9%
i=semiannual yield	0.045
N=number of periods	10	(5*2)
C=Coupon Amount	$40	(1000*0.08/2)
M=Maturity value	$1,000
Bond Value=Present Value of cash flows	$960.44	(Using PV function of excel with Rate=0.045,Nper=10, Pmt=-40, FV=-1000)