Use the zero-coupon bond prices given in the following table to answer the questions that follow.
-Consider a three-year swap receiving fixed paying floating with principal of $10 million dollars,receiving a fixed rate of 2 percent per year,and paying the one-year floating spot rate yearly.What is the value of the swap when it is issued?

Question

Use the zero-coupon bond prices given in the following table to answer the questions that follow. 
-Consider a three-year swap receiving fixed paying floating with principal of $10 million dollars,receiving a fixed rate of 2 percent per year,and paying the one-year floating spot rate yearly.What is the value of the swap when it is issued?

Quizplus · Accepted Answer

To calculate the value of the swap at the time of issuance, we need to determine the fixed rate that makes the present value of the fixed payments equal to the present value of the floating payments. 
The fixed payments are $200,000 per year (2% of $10 million). 
The floating payments are based on the one-year spot rate, which is currently 4% according to the table. 
To determine the fixed rate that makes the present value of the fixed payments equal to the present value of the floating payments, we can use the following formula: 
PV(fixed payments) = PV(floating payments) 
$200,000/(1+r) + $200,000/(1+r)^2 + $200,000/(1+r)^3 = $10,000,000 - $10,000,000/(1+0.04) 
Solving for r, we get r = 0.051 or 5.1%. 
Therefore, the swap is issued at a value of $448,000, which is the present value of the fixed payments calculated using the fixed rate of 5.1%.

Use the Zero-Coupon Bond Prices Given in the Following Table