A bond is a financial asset in the form of a long-term contract under which the firm (borrower) agrees to make payments of interest and principal, on specific dates, to the holders of the bond.
The value of a bond, as of any financial asset, is the present value of the cash flows that are expected to be generated by the bond. In order to be able to calculate the present value of a bond, we need first to investigate the contractual features of a bond, which are unique for each bond. These are:
Par Value: it is the stated value of the bond which represents the amount of money the firm borrows and promises to repay on the maturity day.
Coupon Interest Rate: it is the quotient of dividing the coupon payment by the par value. For example, if par value is 1,000$ and coupon payment is 100$ per year, then the coupon interest rate is $100/$1.000 = 10%. There are cases that coupon payments vary over time and after the six first months they are adjusted to the market rate. These bonds are called floating-rate bonds. Other bonds do not pay coupons at all and they are offered at a substantial discount below their par values. These bonds are called zero coupon bonds.
Maturity Date: it is the date on which the par value should be repaid. Normally, the maturity of a bond ranges from 10 to 40 years.
Example
Assuming that firm X issues a zero-coupon bond where there are no interest payments and therefore bond pays only the par value on maturity.
Data input
M = Par value = $1,000
rd = Coupon interest rate = 8%
INT = Coupon payment = Par value x Coupon interest rate = $1,000 x 8% = $80
N = Maturity = 15 years
To calculate the present value (VB) of this zero coupon bond we apply the following equation:
VB = INT/(1+ rd)^1 + INT/(1+ rd)^2 + INT/(1+ rd)^3 + INT/(
= $80/(1+8%)^1 +$80/(1+8%)^2+$80/(1+8%)^3+$80/(1+8%)^4 ……..+$80/(1+8%)^15 =$1.000
The timeline for firm X with 8% interest rate is as follows:
Year 1 = $80 discounted by (1+8%)^1 = $74.07
Year 2 = $80 discounted by (1+8%)^2 = $68.59
Year 3= $80 discounted by (1+8%)^3 = $63.51
Year 4 = $80 discounted by (1+8%)^4 = $58.80
Year 5 = $80 discounted by (1+8%)^5 = $54.45
Year 6 = $80 discounted by (1+8%)^6 = $50.41
Year 7 = $80 discounted by (1+8%)^7 = $46.68
Year 8 = $80 discounted by (1+8%)^8 = $43.22
Year 9 = $80 discounted by (1+8%)^9 = $40.02
Year 10 = $80 discounted by (1+8%)^10 = $37.06
Year 11 = $80 discounted by (1+8%)^11 = $34.31
Year 12 = $80 discounted by (1+8%)^12 = $31.77
Year 13 = $80 discounted by (1+8%)^13 = $29.42
Year 14 = $80 discounted by (1+8%)^14 = $27.24
Year 15 = $80 discounted by (1+8%)^15 = $25.22
Year 15 = $1.000 discounted by (1+8%)^15 = $315.24
Summing up all these figures we derive $1.000 which is the present value of the expected cash flows a zero coupon bond of par value $1.000 will generate on maturity of 15 years with interest rate 8% and coupon payment $80.
Therefore, the present value of a bond is the sum of the present value of all expected coupon payments (which is an ordinary annuity as a series of fixed payments made at set intervals over a fixed period of time) plus the present value of the par value at maturity.
I work as a financial and investment advisor but my passion is writing, music and photography. Writing mostly about finance, business and music, being an amateur photographer and a professional dj, I am inspired from life.Being a strong advocate of simplicity in life, I love my family, my partner and all the people that have stood by me with or without knowing. And I hope that someday, human nature will cease to be greedy and demanding realizing that the more we have the more we want and the more we satisfy our needs the more needs we create. And this is so needless after all.
