Bond Valulation and Pricing¶
Definition of Bond Valuation¶
Bond Valuation is a financial technique used to determine the theoretical fair value of a particular bond. This process involves calculating the present value (PV) of all future cash flows associated with the bond. These cash flows include the bond's periodic interest payments (coupons) and the repayment of the principal (face value) at maturity.
Example¶
To illustrate how bond valuation works, consider a bond with the following characteristics:
- Annual Coupon Rate: 6.5%
- Face Value: $1,000
- Maturity: 3 years
- Required Return (Discount Rate): 3.9%
Calculation¶
The price of the bond can be calculated by finding the present value of the future cash flows, which are the annual coupon payments and the repayment of the face value at maturity. The formula used is:
\(PV = \frac{C}{(1+r)^1} + \frac{C}{(1+r)^2} + \frac{C + F}{(1+r)^3}\)
Where:
- C is the annual coupon payment (6.5% of $1,000 = $65),
- F is the face value of the bond ($1,000),
- r is the annual discount rate (3.9%).
Calculating each term separately:
- First year coupon payment: \(\frac{65}{1.039}\)
- Second year coupon payment: \(\frac{65}{1.039^2}\)
- Third year coupon payment and face value: \(\frac{65 + 1000}{1.039^3}\)
Adding these up gives the present value of the bond. According to the example calculation provided:
- PV = $1,072.29
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