A bond is a debt security issued by a company or public entity that gives its holder the right to repayment of the capital loaned to the issuer (usually € 1000) at the maturity of the bond, plus periodically paid interest (usually every six months or annually) on this sum. To calculate the present value follow these steps.
Steps
Step 1. Determine the coupon of the bond
This is the interest paid periodically. For example, a bond with a face value of € 1000 and a coupon of 6% will pay € 60 each year.
Step 2. Divide the annual interest by the number of times the interest is paid per year to get to l
For example, if the bond pays semi-annual interest, it will pay I = $ 30 per term (every 6 months).
Step 3. Determine the minimum gain percentage required
What is an acceptable payout percentage for investing in the bond? Take into account the inflation rate (historically equal to 3-4% per year), the quality of the bond (a higher percentage of return is required to compensate for riskier financial products), the interest rate of bonds of similar quality, and the return rates offered by other types of investments. Divide the required percentage by the periods in a year to arrive at k, the required percentage of earnings. For example, if l requires a minimum interest rate of 5% per annum for a bond that pays semiannually, then k = 5% / 2 = 2.5%.
Step 4. Determine the number n of periods in which interest is paid by multiplying the number of years to maturity by the number of times the interest is paid
For example, if the aforementioned bond has a maturity of 10 years and pays semi-annual interest it will have n = 10 * 2 = 20 number of periods.
Step 5. Insert the values of I, k and into the formula for the present value of an annuity PVA = I [1- (1 + k) ^ - n] / k
In our example, the present value is $ 30 [1- (1 + 0.025) ^ - 20] /0.025 = $ 467.67.
Step 6. Enter the values of k and n into the formula PV = FV / (1 + k) ^ n to arrive at the present principal value of the bond of € 1000 (FV) at maturity
For example, PV = $ 1000 / (1 + 0.025) ^ 20 = $ 610.27.
Step 7. Add the present value of the interest to the present value of the principal to arrive at the present value of the entire bond
In our case = $ 467.67 + $ 610.27 = $ 1077.94.
