Lecture: Financing Based on Market Values II

Transcription

1 Lectre: Fnancng Based on Market Vales II Ltz Krscwtz & Andreas Löler Dsconted Cas Flow, Secton ,

2 Otlne Mles-Ezzell- and Modglan-Mller Mles-Ezzell adjstment Modglan-Mller adjstment Example Te nte example Te nnte example Smmary,

3 Mles-Ezzell: te problem 1 Up to now we know tree procedres to evalate Ẽt (or Ṽ l t ). In case o nancng based on market vales tese procedres concde, oterwse not. Bt wat can we tell abot te relaton between WACC and te nlevered cost o captal,.e. k E,? Ts s te topc o adjstment ormlas. And ts tme we wll need te assmpton o weak atoregressve cas lows Mles-Ezzell- and Modglan-Mller,

4 Mles-Ezzell adjstment 2 Teorem 2.11 (Mles-Ezzell 1980): I cas lows o te nlevered rm are weak atoregressve, te levered rm s nanced based on market vales and WACC s determnstc, ten ( 1 + WACC t and k E, s determnstc. 1 + k E, t ) ( 1 τr l t ) Mles-Ezzell- and Modglan-Mller, Mles-Ezzell adjstment

5 Remarks 3 Te orgnal artcle o Mles-Ezzell reqred a constant leverage rato l t : we do not! Ts adjstment ormla nally sows wy WACC mgt be sel (remember apples and oranges?). Te assmpton o weak atoregressve cas lows s necessary (we come back to ts). Te proo s not an easy task. Wat s te connecton to te Modglan-Mller (1963) adjstment ormla? Later Mles-Ezzell- and Modglan-Mller, Mles-Ezzell adjstment

6 Proo (part I) 4 E Q ev l ev t l t+1 + FCF g t+1 + τe It+1 F t E Q ev l ev t l t+1 + FCF g t+1 Ft t+1 F t + t+1 Ft E Q ev l ev t l t+1 + FCF g E Q ev l ev t l t+1 + FCF g e ev t l τr Dt E Q ev l t+1 + FCF g + E Q τe It+1 F t + τr Dt e 1 + r t+1 Ft 1 + r E Q ev l ev t l t+1 + FCF g t+1 F t 1 τr l t. (1 + r 1+r ) E Q τr e Dt F t Mles-Ezzell- and Modglan-Mller, Mles-Ezzell adjstment

7 Proo (part II) 5 1 τr l t E Q ev l ev t l t+1 + FCF g t+1 F t 1 τr l t (1 + r 1+r ) TX E Q gfcf ev t l s Ft st+1 1 τr l 1+r s 1 1 τr l 1+r t ( ) s t TX E gfcf ev t l s Ft st+1 1 τr l 1+r s 1 1 τr l 1+r t 1 + k E, s t E ev l ev t l t+1 + FCF g t+1 F t 1 τr l t 1+r 1 + k E, t+1 Ft E ev l t+1 + g FCF 1 E, + k ev t l 1 τr l t 1 E, + k 1 + WACC t Mles-Ezzell- and Modglan-Mller, Mles-Ezzell adjstment

8 Modglan-Mller: te problem 6 Ts eqaton s te rst (1963) adjstment ormla. Two assmptons are necessary: constant amont o debt (atonomos nancng!) and nnte letme. Clams a nce ormla: [ ] E FCF WACC k E, (1 τl) compare to MoM: V l 0 (1 τl 0 )k E,. Bt ts does not seem to relate to te Mles-Ezzell adjstment?! Teorem 2.12 (Modglan-Mller): I te WACC type 2 (WACC) and te nlevered rm s cost o eqty (k E, ) are determnstc, ten te rm s nanced based on market vales. Ts s a contradcton to atonomos nancng, ence te Modglan-Mller ormla s not applcable! Mles-Ezzell- and Modglan-Mller, Modglan-Mller adjstment

9 Contradcton to Modglan-Mller 7 Smmary: In order to apply MoM two costs o captal mst be determnstc: WACC and k E,, oterwse te (nce) ormla does not make sense. Bt ten te rm s nanced based on market vales (see above teorem). Ts contradcts te assmpton o MoM (constant debt)! Hence, tere s no connecton to Mles-Ezzell, snce te nce ormla s not applcable nder any crcmstances! Mles-Ezzell- and Modglan-Mller, Modglan-Mller adjstment

10 Modglan-Mller agan 8 Is te orgnal paper Modglan-Mller (1963) lawed? No, snce or bot (as or Mles-Ezzell as well) costs o captal were not condtonal expected retrns (bt dscont rates... )! Altog yo can se MoM teorem (Teorem 2.5), yo cannot se MoM adjstment ormla. Pt derently: dscont rates and expected retrns cover derent economc concepts Mles-Ezzell- and Modglan-Mller, Modglan-Mller adjstment

11 Proo 9 (1 τ l t ) T (1 + g t )... (1 + g s ) FCF t (1 + WACC st+1 t )... (1 + WACC s 1 ) }{{} e V l t T (1 + g t ) (1 + g s ) FCF ( ) ( t). st kt E, k E, s 1 }{{} e V t Mles-Ezzell- and Modglan-Mller, Modglan-Mller adjstment

12 Te nte example 10 Consder nancng based on market vales l 0 55%, l 1 10%, l 2 10%. WACC reslts rom Mles-Ezzell adjstment (Teorem 2.11), ( WACC k E,) ( 1 τr ) l 0 1 ( ) ( ) % WACC % WACC % Example, Te nte example

13 Te nte example 11 Te rm vale s [ ] [ ] E FCF V0 l 1 E FCF WACC 0 (1 + WACC 0 )(1 + WACC 1 ) [ ] E FCF 3 + (1 + WACC 0 )(1 + WACC 1 )(1 + WACC 2 ) Example, Te nte example

14 Te nnte example 12 Te leverage rato s l 20% and constant trog letme. Wt Mles-Ezzell adjstment te WACC s ( WACC (1 + k E, ) 1 τr ) l % and te rm vale s V l 0 t1 t1 [ ] E FCF t F 0 (1 + WACC) t FCF 0 (1 + WACC) t FCF 0 WACC Example, Te nnte example

15 Smmary 13 Te connecton between costs o captal o a levered rm and an nlevered rm are gven by adjstment ormlas. In partclar a relaton between WACC and k E, can be proven, ence WACC s ndeed sel. Te adjstment by Mles-Ezzell s applcable (bt ts reqres nancng based on market vales!). Te adjstment by Modglan-Mller s not applcable, altog te Modglan-Mller Teorem can be sed. Smmary,