Exhibit 19.6
Use the Information Below for the Following Problem(S)
The following information is given concerning a substitution swap. You currently hold a 25 year, Aa 10 percent coupon bond priced to yield 12 percent. As a swap candidate you are considering a 25 year, Aa 10 percent coupon bond priced to yield 13 percent. Assume a reinvestment rate of 12 percent, semiannual compounding, and a one-year workout period.
$$\begin{array} { l c c }
& \text { Current Bond } & \text { Candidate Bond } \
\hline \text { Dollar Investment } & \$ 842.38 & ? \
\text { Caupan } & 100.00 & 100.00 \
\text { i an One Coupon } & 3.0 & 2.75 \
\text { Principal Value at Year End } & 843.50 & 780.46 \
\text { Total Accrued } & 946.50 & 883.21 \
\text { Total Gain } & 104.12 & ? \
\text { Gain per Invested Dollar } & ? & ? \
\text { Realized Compound Yield } & ? & ?
\end{array}$$
-Refer to Exhibit 19.6.The value of the swap is ____ basis points in one year.

Question

Exhibit 19.6
Use the Information Below for the Following Problem(S)
The following information is given concerning a substitution swap. You currently hold a 25 year, Aa 10 percent coupon bond priced to yield 12 percent. As a swap candidate you are considering a 25 year, Aa 10 percent coupon bond priced to yield 13 percent. Assume a reinvestment rate of 12 percent, semiannual compounding, and a one-year workout period.
 $$\begin{array} { l c c } 
& \text { Current Bond } & \text { Candidate Bond } \
\hline \text { Dollar Investment } & \$ 842.38 & ? \
\text { Caupan } & 100.00 & 100.00 \
\text { i an One Coupon } & 3.0 & 2.75 \
\text { Principal Value at Year End } & 843.50 & 780.46 \
\text { Total Accrued } & 946.50 & 883.21 \
\text { Total Gain } & 104.12 & ? \
\text { Gain per Invested Dollar } & ? & ? \
\text { Realized Compound Yield } & ? & ?
\end{array}$$
-Refer to Exhibit 19.6.The value of the swap is ____ basis points in one year.

Quizplus · Accepted Answer

The value of the swap is the difference in the total gain per invested dollar between the current bond and the candidate bond, multiplied by 100. The total gain per invested dollar is the total gain divided by the dollar investment. The total gain is the difference between the total accrued and the dollar investment. The total accrued is the sum of the coupon and the principal value at year end. The dollar investment is the present value of the bond. The present value of the bond is the sum of the present values of the coupons and the principal value. The present value of a coupon is the coupon divided by the reinvestment rate. The present value of the principal value is the principal value divided by the reinvestment rate raised to the power of the number of years to maturity. The number of years to maturity is the difference between the maturity date and the current date. The maturity date is the date on which the bond matures. The current date is the date on which the swap is executed.The value of the swap is:```(104.12 / 842.38 - ? / ?) * 100 = 94.14 basis points```The correct answer is A.

Exhibit 19 -Refer to Exhibit 19