| Ch 24-04 Build a Model Solution |
|
|
|
|
|
3/7/2001 |
|
|
|
|
|
|
|
| Chapter 24. Solution to Ch 25-04 Build a Model |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| Problem 24-4. Use the information and data from Problem 24-2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
| Problem Inputs: |
|
|
|
|
|
|
| Size of planned debt offering = |
|
|
|
$10,000,000 |
|
|
| Anticipated rate on debt offering = |
|
|
|
11% |
|
|
| Maturity of planned debt offering = |
|
|
|
10 |
|
|
| Number of months until debt offering = |
|
|
|
7 |
|
|
| Settle price on futures contract (% of par) = |
|
|
|
95.53125% |
|
|
| Maturity of bond underlying futures contract = |
|
|
|
20 |
|
|
| Coupon rate on bond underlying futures contract = |
|
|
|
6% |
|
|
| Size of futures contract (dollars) = |
|
|
|
$100,000 |
|
|
|
|
|
|
|
|
|
| a. Create a hedge with the futures contract for Zinn Company’s planned June debt offering of $10 |
|
|
|
|
|
|
| million. What is the implied yield on the bond underlying the future’s contract? |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Number of contracts needed for hedge = |
100 |
|
|
|
|
|
|
|
|
|
|
|
|
Value of contracts in hedge = |
$9,553,125 |
|
|
|
|
|
|
|
|
|
|
|
|
Implied semi-annual yield = |
It can be calculated using the RATE function in Excel
3.200% |
|
|
|
|
|
|
|
|
|
|
|
|
Implied annual yield = |
6.40% |
|
|
|
|
|
|
|
|
|
| b. Suppose interest rates fall by 300 basis points. What is the dollar savings from issuing the debt at |
|
|
|
|
|
|
| the new interest rate? What is the dollar change in value of the futures position? What is the total |
|
|
|
|
|
|
| dollar value change of the hedged position? |
|
|
|
|
|
|
|
|
|
|
|
|
|
| Change in interest rate on debt offering (basis points) = |
|
|
|
|
300 |
|
|
|
|
|
|
|
|
| New interest rate on debt = |
|
|
|
|
Start with anticipated rate and add change. Change is in basis points so devide by 10,000.
14.0% |
|
| Value of issuing at new rate interest = |
|
|
|
|
$8,410,898 |
|
| Dollar value savings or cost from issuing debt at the new rate = |
|
|
|
|
($1,589,102) |
|
|
|
|
|
|
|
|
| New yield on futures contract = |
|
|
|
|
9.40% |
|
| Value of futures contract at new yield = |
|
|
|
|
$6,959,583 |
|
| Dollar change in value of the futures position = |
|
|
|
|
$2,593,542 |
|
|
|
|
|
|
|
|
| Total dollar value change of hedge = |
|
|
|
|
$1,004,440 |
|
|
|
|
|
|
|
|
| c. Create a graph showing the effectiveness of the hedge if the change in interest rates, in basis |
|
|
|
|
|
|
| points, is: -300, -200, -100, 0, 100, 200, or 300. Show the dollar cost (or savings) from issuing the |
|
|
|
|
|
|
| debt at the new interest rates, the dollar change in value of the futures position, and the total |
|
|
|
|
|
|
| dollar value change. |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Change in rate |
Dollar change in cost/savings of issue |
Dollar change in value of futures position |
Total dollar value change of hedge |
|
|
|
Base 300 |
-$1,589,102 |
$2,593,542 |
$1,004,440 |
|
|
|
-300 |
$2,038,549 |
-$4,198,964 |
-$2,160,416 |
|
|
|
-200 |
$1,300,794 |
-$2,561,633 |
-$1,260,839 |
|
|
|
-100 |
$623,111 |
-$1,176,193 |
-$553,082 |
|
|
|
0 |
$0 |
$0 |
$0 |
|
|
|
100 |
-$573,496 |
$1,001,977 |
$428,481 |
|
|
|
200 |
-$1,101,851 |
$1,858,569 |
$756,718 |
|
|
|
300 |
-$1,589,102 |
$2,593,542 |
$1,004,440 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
