Bond price formula

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Bonds essentially refer to a contract between an investor and a borrower.  It is a type of loan to be repaid at the end of the maturity period. Some bonds have annual or semi-annual coupons which are basically predetermined interest payments.  These coupons are incurred as additional cost of borrowing, and are paid to investors on a regular basis until the bond’s maturity.

This article will show us how to calculate the bond value or bond price for a zero coupon bond, an annual coupon bond and a semi-annual coupon bond.

Figure 1.  Final result:  Bond price formula

Calculate bond price

Bond price is the current discounted value of a future cash flow.  In simple terms, a bond price is the sum of the present value of the principal payment and the interest payments.  In order to calculate the bond price, we can use the PV function.

Syntax of PV function

=PV(rate, nper, pmt, [fv], [type])

• Rate  is the interest rate per period
• Nper is the total number of payment periods
• Pmt is the payment made each period and is fixed until bond maturity
• Fv is the future value at bond maturity
• Type is either 0 ((if payment is at the end of the period) or 1 (payment at the beginning of the period)

Figure 2.  Sample data to calculate bond price

Price of zero coupon bond

Our example is a ten-year bond with a face value of 10,000 and an interest rate of 5%.  In order to calculate the bond price with no coupons, we enter this formula in C8:

=PV(C6,C5,0,C3)

• Interest rate = 5%
• Number of periods = 10
• Payment made each period = 0 (zero coupons)
• Face value = 10,000

Figure 3.  Bond price formula for zero coupons

The resulting bond price is -6,139.13.  In accounting, the negative sign means it is an outgoing cash flow.

Price of annual coupon bond

There are bonds wherein the investors get a coupon each year.  In order to calculate the price of an annual coupon bond, we enter this formula in D8:

=PV(D6,D5,D3*D7,D3)

• Discount rate = 4%
• Number of periods = 10
• Payment made each period = 10,000 x 2.5%
• Face value = 10,000

Figure 4.  Bond price formula for annual coupon bond

As a result, the bond price is 8783.37.

Price of semi-annual coupon bond

There are also bonds that give out coupons twice in a year.  The formula for bond price is:

=PV(E6/2,E5,E3*E7/2,E3)

• Discount rate = 4%/2 = 2%
• Number of periods = 10×2 = 20
• Payment made each period = 10,000 x 2.5%/2
• Face value = 10,000

Figure 5.  Bond price formula for semi-annual coupon bond

Note that for semi-annual coupons, we divide the discount rate and coupon rate by 2, and the number of periods is twice the number of years.  The resulting bond price is 8773.64.