The Marcus Corporation plans to issue $5,000,000 of 10-year bonds at par next June, with semiannual interest payments. The company's current cost of debt is 12 percent. However, the firm's financial manager is concerned that interest rates will increase in coming months, and has decided to take a short position in U. S. government t-bond futures.Data below for t-bond futures. (Note: One standard futures contract is $100,000)
| Delivery Month |
Open |
High |
Low |
Settle |
Change |
Open Interest |
| (1) |
(2) |
(3) |
(4) |
(5) |
(6) |
(7) |
| Dec |
97'28 |
99'17 |
98'22 |
99'17 |
+5 |
387,255 |
| Mar |
98'03 |
98'21 |
97'23 |
98'01 |
+12 |
90,353 |
| June |
98'13 |
98'27 |
97'01 |
97'12 |
+7 |
9,802 |
a. Calculate the present value of the corporate bonds if rates increase by 3 percentage points
b. Calculate the gain or loss on the corporate bond position
c. Calculate the number of futures contracts required to cover the bond position. Then calculate the current value of the futures position (round up to the next whole number).
d. Calculate the implied interest rate based on the current value of the futures position
e. Interest rates increase as expected, by 3 percentage points. Calculation the present value of the futures position base don the rate calculated above.
f. Calculate the gain or loss on the futures position
g. Calculate the overall net gain or loss.