3.4 Comparison of The Single Discount Rate (YTM) and the Spot Curve
Here, we will compare the dollar price of the 2-year bond (from Example II) using one observed market YTM to the price calculated by using multiple discount rates as determined from the Spot Curve.
- You have noted above that the spot curve discounts each of the bond’s cash flows at a different rate than the singular YTM.
- Alternatively, the bond’s YTM applies the same rate to each of the bond’s cash flows.
- In the end, using either method will provide the same PV, the same price.
Exercise
Using the summary data for the two-year bond on the prior page, calculate, on a period-by-period basis, the present value of the cash flows and hence the bond’s price, using alternately, the single Y-T-M discount rate, and the various spot rates. Use the template provided below. Note that “PVCF” stands for the present value of each cash flow. The sum of that column is the bond’s price.
[shaded squares are to be left blank]
| Period | CF | YTM Discount Rate | PVCF | Spot Rates | Spot Discount Rates | PVCF |
|---|---|---|---|---|---|---|
| 1 | 4.50 | |||||
| 2 | 4.50 | |||||
| 3 | 4.50 | |||||
| 4 | 104.50 | |||||
| 118.00 |
