2.24 Comparison of Single Discount Rate (YTM) and Spot Curve (Solution)
| Period | CF | YTM | PV-CF | Spot Rates | Spot Discount Rates | PV-CF |
| 1 | 4.50 | (1/1.046)1 | 4.30 | .0400 | (1/1.0400)1 | 4.33 |
| 2 | 4.50 | (1/1.046)2 | 4.11 | .0415 | (1/1.0415)2 | 4.15 |
| 3 | 4.50 | (1/1.046)3 | 3.93 | .0447 | (1/1.0447)3 | 3.94 |
| 4 | 104.50 | (1/1.046)4 | 87.30 | .0462 | (1/1.0462)4 | 87.22 |
| 118.00 | 99.64 | 99.64 |
- While the discount rates vary for each period, the two solutions yield the same dollar price.
- A bond may be thought of as a “portfolio” of (interest-only and principal-only) zero coupon bonds
- US Treasury Strips provide a direct view of the spot curve. Strips and coupons are priced differently – they have different yields.
- Strips may be created by breaking down a coupon bonds coupons and principal payments and re-packaging them as zeros.
- The YTM is the average of the spot rates.
- Some say that the YTM is derived from the spot-curve, i.e., only after the bond’s dollar value is known
- Although we do not present it herewith, the analyst may choose to add a “risk premium” of a certain percent to, or across, the spot curve to reflect the added risk over the bond yield curve embodied by the subject investment project. (“Risk premia” shall be a topic of discussion in the “Component Capital Costs / The Capital Asset Pricing Model” section following immediately below.)