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.)


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Corporate Finance Copyright © 2023 by Kenneth S. Bigel is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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