3.5 Comparison of Single Discount Rate (YTM) and Spot Curve (Solution)
| Period | CF | YTM Discount Rate | PVCF | Spot Rates | Spot Discount Rates | PVCF |
|---|---|---|---|---|---|---|
| 1 | 4.50 | (1/1.046) 1 | 4.3 | .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 | 3.5 | 99.64 | 3.5 | 99.64 |
The Spot Curve can be used to illustrate future reinvestment rates.
While the discount rates vary for each period, the two solutions yield the same dollar price.
- The Law of One Price assures that the two alternatives are equivalent.
The observed YTM is the average of the implied spot rates.
- Add up both the YTM and “Spot Discount Rate” columns and find that they are equal, i.e., approximately 3.5.
A bond may be thought of as a “portfolio” of (interest-only and principal-only) zero coupon bonds (“Zeros”).
US Treasury Strips may be created by breaking down a coupon bond’s coupons and principal payments and re-packaging them as zeros. Imagine paying $3.94 and receiving in three six-month periods $4.50 – with no interim cash payments.
US Treasury Strips provide a direct view of the spot curve. Strips and coupons are priced differently – they have different yields.
You may say that the YTM is derived from the “unobserved” 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.)
