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Kut rf t fcft et 1 ku ku gvts et 1 dt 1kut

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Unformatted text preview: ly for growing perpetuities. 22 - IESE Business School-University of Navarra FCFt + Dt-1 [RF t – Kdt (1-T)] – – (Et-1 + Dt-1) (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 +(Dt-Dt-1)- Dt-1Kdt (1-T) CCFt = FCFt + Dt-1 Kdt T CCFt = ECFt -(Dt-Dt-1)+ Dt-1Kdt Cash flows\\Ku: ECF\\Ku = ECFt - Et-1 (Ket - Ku t) FCF\\Ku = FCFt - (Et-1 + Dt-1)(WACCt - Ku t) = CCF\\Ku = CCFt - (Et-1 + Dt-1)(WACCBTt - Ku t) Cash flows\\ RF: ECF\\RF = ECFt - Et-1 (Ket - RF t) FCF\\RF = FCFt - (Et-1 + Dt-1)(WACCt - RF t) = CCF\\RF = CCFt - (Et-1 + Dt-1)(WACCBTt - RF t) ECF\\RF = ECF\\Ku - Et-1 (Kut - RF t) FCF\\RF = FCF\\Ku - (Et-1 + Dt-1)(Kut - RF t) FCF\\Ku - ECF\\Ku = Dt-1 Ku t - (Dt - Dt-1) FCF\\RF - ECF\\RF = Dt-1 RF t - (Dt - Dt-1) IESE Business School-University 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 = Nt-1 rt The increase in debt in period t is: ∆Nt = Nt - Nt-1. Consequently, the debt cash flow in period t is: CFd = It - ∆ Nt = Nt-1 rt - (Nt - Nt-1 ). Consequently, the value of the debt at t=0 is: D 0 = ∞ ∑ Nt-1 rt − (Nt - N t-1 ) 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 - Dt-1= Nt - Nt-1 + Dt-1 Kdt - Nt-1 rt Consequently: ∆Dt = ∆Nt + Dt-1 Kdt - Nt-1 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...
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