2.18 What Happens When We Change a Bond’s Compounding Frequency Assumption?
As you will observe below, the compounding frequency assumption impacts the bond’s price significantly. The analyst must be certain that he utilizes the correct assumption.
- For each of the five problems below, calculate the price – given both annual (P = 1) and semi-annual (P = 2) discounting. Note how the prices change under different discounting assumptions.
- For problem five, after calculating price, recalculate it (incorrectly) using semi-annual discounting for the coupon, and annual discounting for the principal. Note how the price does not come out as Par; this solution is incorrect.
| Problem 1 | Problem 2 | Problem 3 | Problem 4 | Problem 5 |
| CPN = 0% YTM = 10% N = 20 |
CPN = 5% YTM = 10% N = 20 |
CPN = 7% YTM = 6% N = 3 |
CPN = 10% YTM = 4% N = 25 |
CPN = 10% YTM = 10% N = 25 |
Here are the solutions. Compare the indicated TVM factors against what you used. Check your calculations. Did you get ‘em right?
| Problem 1 | P = 1 | P = 2 |
| 1,000 (0.1486) = 14.86% | 1,000 (0.1420) = 14.20% |
| Problem 2 | P = 1 | P = 2 |
| 50 (8.5136) + 1,000 (0.1486) = 57.428% | 25 (17.1591) + 1,000 (0.1420) = 57.09775% |
| Problem 3 | P = 1 | P = 2 |
| 70 (2.6730) + 1,000 (.8396) = 102.671% | 35 (5.4172) + 1,000 (0.8375) = 102.7102% |
| Problem 4 | P = 1 | P = 2 |
| 100 (15.6221) + 1,000 (0.3751) = 193.731% | 50 (31.4236) + 1,000 (0.3715) = 194.268% |
| Problem 5 | P = 1 | P = 2 |
| 100 (9.0770) + 1,000 (0.0923) = 100% | 50 (18.2559) + 1,000 (0.0872) = 100% | |
| The following is incorrect: 50 (18.2559) + 1,000 (0.0923) = 100.5095% |
Notes
- Clearly, compounding frequency matters.
- There is no difference in price for a 25-year Par bond (Problem Five).
- It is not always the case that when P = 2 the result is a higher price than if P = 1
- Problems 3 and 4 are premium bonds. In that case, the dollar price increases when discounting frequency is increased from 1 to 2. Earlier – problems 1 and 2, it had decreased as per the rules of TVM.
