Final answer:
The formula for present value of a 10 year Treasury bond with a face value of $1000 and a 3.5% coupon rate is the sum of the discounted annual coupons plus the discounted face value. A simple example using a two-year bond with a face value of $3000 and an 8% coupon illustrates how the present value calculation can change with different discount rates.
Step-by-step explanation:
When considering a 10 year Treasury bond that pays a 3.5% coupon on a $1000 face value, the formula for the present value (PV) of this security, given the discount rate r, is:
PV = C/(1+r)^1 + C/(1+r)^2 + ... + C/(1+r)^10 + FV/(1+r)^10
Where:
- C is the annual coupon payment ($1000 x 3.5% = $35)
- FV is the face value of the bond ($1000)
- r is the annual discount rate or the interest rate
The present value of a bond is equal to the present value of its coupon payments plus the present value of its face value. To illustrate this point, if we think about a simpler example of a two-year bond with a face value of $3000 and an 8% coupon rate, we can calculate the present value of such bond using the same formula:
PV = C/(1+r) + C/(1+r)^2 + FV/(1+r)^2
Here, C would be $240 (which is $3000 x 8%). If the discount rate r is also 8%, the present value would confirm to be $3000. However, if interest rates rise to 11%, the present value would decrease, reflecting the increased discount rate and thus a lower present value of the future cash flows.