Debt Adds Value: The Derivation of Dt
Topic 42 explores the mechanics of deriving and fully understanding the benefit of debt and provides the background for applying the methodology in doing levered merger and acquisition transactions.
The reader is encouraged to take the time to read the text in conjunction with the referenced Appendices to gain the appropriate level of understanding of the subject matter discussed in the narrative. Appendices are either presented at the end of this Topic or are available for review and download on the companion Web site noted at the end of this Topic.
DERIVATION OF DT AND TAX ADVANTAGE OF A FIXED LEVEL OF DEBT
- The present value (PV) of the taxes saved by assuming a level amount of debt is equal to Dt and is derived as:
- The PV of the stream of interest payments paid out in perpetuity on a fixed amount of debt plus the eventual debt repayment will equal the fixed amount of debt if discounted at the pretax nominal interest rate on the debt.
- The reason is that the ultimate debt repayment that is presumed to occur at the end of the interest stream takes place so far into the future—the end of perpetuity (whether by terms or as multiple refinancings)—that its PV is effectively zero. Therefore, the only outflow entering into the PV of the cost of a permanent debt level is the interest stream.
- Illustration 42.1 presents the derivation of this conclusion.
Illustration 42.1 Derivation of Dt
The PV of the total cash stream (TCSPV) of interest ...