USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
The WallMal Company has entered into a four-year interest rate swap, with semiannual settlement, to pay a fixed rate of 8 percent per year and receive six-month LIBOR. The notional principal is $50,000,000.
-Refer to Exhibit 15.19. Assuming that one year after the swap was initiated the fixed rate on a new three-year receive fixed pay floating LIBOR swap has fallen to 7 percent per year, calculate the market value of the 8 percent fixed rate bond based on a $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 percent fixed rate bond based on a $100 face value, we need to discount the future cash flows of the bond at the new interest rate of 7 percent per year, with semiannual settlements. The bond will pay $4 every six months (8% of $100 annually, or $4 every six months) for the next three 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.$$ PV = \frac{4}{(1+0.035)} + \frac{4}{(1+0.035)^2} + \frac{4}{(1+0.035)^3} + \frac{4}{(1+0.035)^4} + \frac{4}{(1+0.035)^5} + \frac{104}{(1+0.035)^6} \approx 102.66 $$