Exhibit 14-10
USE THE FOLLOWING INFORMATION FOR THE NEXT QUESTION(S)
The WallMal Company has entered into a 4-year interest rate swap, with semiannual settlement, to pay a fixed rate of 8% per year and receive 6-month LIBOR. The notional principal is $50,000,000.
-Refer to Exhibit 14-10. Assuming that one year after the swap was initiated the fixed rate on a new 3-year receive fixed pay floating LIBOR swap has fallen to 7% per year, calculate the market value of the 8% fixed rate bond based on $100 face value. Settlement is on a semiannual basis.
A) $102.66
B) $100.00
C) $95.56
D) $89.63
E) $70.77

Question

Quizplus · Accepted Answer

To calculate the market value of the 8% fixed rate bond based on $100 face value, we need to discount the future cash flows of the bond at the new market interest rate of 7% per year, with semiannual settlements. The bond will pay $4 every six months (8% of $100 annually or $4 semiannually) for the next 3 years, plus the $100 face value at the end of the period. The present value of these cash flows, discounted at 3.5% per period (7% annual rate divided by 2 for semiannual), gives the market value of the bond. $$ PV = \frac{4}{(1+0.035)} + \frac{4}{(1+0.035)^2} + \frac{4}{(1+0.035)^3} + \frac{4}{(1+0.035)^4} + \frac{4}{(1+0.035)^5} + \frac{104}{(1+0.035)^6} $$$$ PV \approx 102.66 $$This calculation shows that the market value of the bond is approximately $102.66, which matches option A.

Exhibit 14-10 USE THE FOLLOWING INFORMATION FOR THE NEXT QUESTION(S)