This preview shows page 1. Sign up to view the full content.
Unformatted text preview: ly for growing perpetuities. 22  IESE Business SchoolUniversity of Navarra FCFt + Dt1 [RF t – Kdt (1T)] –
– (Et1 + Dt1) (Kut – RF t) Appendix 2 (continued) Equations common to all methods:
WACC t = E t 1 Ke t + D t 1 Kd t (1  T)
E t 1 + D t 1 WACC BT t = E t 1 Ke t + D t 1 Kd t
E t 1 + D t 1 Relationships between cash flows:
ECFt = FCFt +(DtDt1) Dt1Kdt (1T) CCFt = FCFt + Dt1 Kdt T CCFt = ECFt (DtDt1)+ Dt1Kdt Cash flows\\Ku: ECF\\Ku = ECFt  Et1 (Ket  Ku t) FCF\\Ku = FCFt  (Et1 + Dt1)(WACCt  Ku t) = CCF\\Ku = CCFt  (Et1 + Dt1)(WACCBTt  Ku t)
Cash flows\\ RF: ECF\\RF = ECFt  Et1 (Ket  RF t) FCF\\RF = FCFt  (Et1 + Dt1)(WACCt  RF t) = CCF\\RF = CCFt  (Et1 + Dt1)(WACCBTt  RF t)
ECF\\RF = ECF\\Ku  Et1 (Kut  RF t) FCF\\RF = FCF\\Ku  (Et1 + Dt1)(Kut  RF t) FCF\\Ku  ECF\\Ku = Dt1 Ku t  (Dt  Dt1) FCF\\RF  ECF\\RF = Dt1 RF t  (Dt  Dt1) IESE Business SchoolUniversity of Navarra  23 Appendix 3
Valuation Equations According to the Main Theories when the Debt’s Market Value (D) Is Not Equal
to Its Nominal or Book Value (N) This appendix contains the expressions of the basic methods for valuing companies by
discounted cash flows when the debt’s market value (D) is not equal to its nominal value (N). If
the debt’s market value (D) is not equal to its nominal value (N), it is because the required
return on debt (Kd) is different from the cost of the debt (r).
The interest paid in a period t is: It = Nt1 rt The increase in debt in period t is: ∆Nt = Nt  Nt1.
Consequently, the debt cash flow in period t is: CFd = It  ∆ Nt = Nt1 rt  (Nt  Nt1 ).
Consequently, the value of the debt at t=0 is: D 0 = ∞ ∑ Nt1 rt − (Nt  N t1 ) t=1 t ∏ (1 + Kd t )
1 It is easy to show that the relationship between the debt’s market value (D) and its nominal
value (N) is:
Dt  Dt1= Nt  Nt1 + Dt1 Kdt  Nt1 rt
Consequently: ∆Dt = ∆Nt + Dt1 Kdt  Nt1 rt
The fact that the debt’s market value (D) is not equal to its nominal value (N) affects several
equations given in Section 1 of this paper. Equations [1], [3], [4], [6], [7], [9] and [10] continue
to be valid, but the other equatio...
View Full
Document
 Fall '11
 MBA
 Business

Click to edit the document details