Ch.11
25. a.
The tax shield definition of OCF is:
OCF = [(P – v)Q – FC](1 –
T C C)
+ T C CD
ea!!an"in" and solvin" fo! Q# $e find: (OCF – T C – T C CD)%(1 C) = (P – v)Q – FC Q = &FC + [(OCF – T C % (1 – T C % (P – v) CD) C)]'
CHAPTER 11 - 2
b.
The ash !ea*even is:
QC = &,--#--- + [(- – --#---(./0)) % (1 – ./0)]' % (-#--- – 2-#---) QC = /.,, 3nd the ao4ntin" !ea*even is: Q3 = &,--#--- + [(--#--- – --#---(./0)) % (1 – . /0)]' % (-#--- – 2-#---) Q3 = 5The finanial !ea*even is the 6oint at $hih the 7P8 is 9e!o# so: OCFF = /#,--#--- % P8F32-;#, OCFF = 1#1-#/20.<5 o: QF = [FC + (OCF – T C D)%(1 – T C )]%(P – v) QF = &,--#--- + [1#1-#/20.<5 – ./0(--#---)] % (1 – ./0)'% (-#--- – 2-#---) QF = <.
the ao4ntin" !ea*even 6oint# the net ino>e is 9e!o. Th4s 4sin" the otto> 46 definition of OCF:
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OCF = 7 + D ?e an see that OCF >4st e e@4al to de6!eiation. o# the ao4ntin" !ea*even is: Q3 = &FC + [(D – T C D) % (1 – T C)]' % (P – v) Q3 = (FC + D) % (P – v) Q3 = (FC + OCF) % (P – v) The tax !ate has anelled o4t in this ase. 26.
The DOA is ex6!essed as:
DOA = ;∆OCF % ;∆Q DOA = &[(OCF1 – OCF-)%OCF-] % [(Q1 – Q-) % Q-]' The OCF fo! the initial 6e!iod and the fi!st 6e!iod is: OCF1 = [(P – v)Q1 – FC](1 – T C) + T D OCF- = [(P – v)Q- – FC](1 – T C) + T D The diffe!ene et$een these t$o ash flo$s is: OCF1 – OCF- = (P – v)(1 – T C)(Q 1 – Q-)
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Dividin" oth sides B the initial OCF $e "et: (OCF1 – OCF-)%OCF- = (P – v)( 1–
T C )(Q1 –
Q-) % OCF-
ea!!an"in" $e "et: [(OCF1 – OCF-) % OCF-] % [(Q1 – Q-) % Q-] = [(P – v)(1 – T C)Q -] % OCF- = [OCF- – T CD + FC(1 – T C)] % OCF DOA = 1 + [FC(1 – T C) – T C D] % OCF27.
a.
sin" the tax shield a66!oah# the OCF is:
OCF = [(20- – 10,)(/,#---) – <0,#---](1 – . /0) + ./0(,#2--#--- % ,) OCF = 1#05#--3nd the 7P8 is: 7P8 = –,#2--#--- – 1-#--- + 1#05#---(P8F31/;#,) + [1-#--- + ,--#---(1 – ./0)] % 1.1/, 7P8 = 1#2/#,<5.-5 b.
n the $o!stase# the OCF is: OCF$o!st = &[(20-)(.<) – 10,](/,#---) – <0,#---' (1 – ./0) + ./0[,#2--#---(1.1,) % ,]
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OCF$o!st = 1#2<#503nd the $o!stase 7P8 is: 7P8$o!st = –,#2--#---(1.1,) – 1-#---(1.-,) + 1#2<#50-(P8F31/;#,) + [1-#---(1.-,) + ,--#---(.0,)(1 – ./0)] % 1.1/, 7P8$o!st = –1#5<#,0/.< The estase OCF is: OCF est = &[20-(1.1) – 10,](/,#---) – <0,#---'(1 – ./0) + ./0[,#2--#---(.0,) % ,] OCF est = 2#/<#/23nd the estase 7P8 is: 7P8 est = –,#2--#---(.0,) – 1-#---(.<,) + 2#/<#/2-(P8F31/;#,) + [1-#---(.<,) + ,--#---(1.1,)(1 – ./0)] % 1.1/, 7P8 est = #-15#5.- To al4late the sensitivitB to han"es in @4antitB sold# $e $ill hoose a @4antitB of /5#--- tons. The OCF at this level of sales is:
28.
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OCF = [(20- – 10,)(/5#---) – <0,#---](1 – ./0) + . /0(,#2--#--- % ,) OCF = 1#<-#<--
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The sensitivitB of han"es in the OCF to @4antitB sold is: ∆OCF%∆Q
= (1#05#--- – 1#<-#<--) % (/,#--- –
/5#---) ∆OCF%∆Q = +,0.
= (1#2/#,<5.-5 – 1#0-#5-.<0) % (/,#---
– /5#---) ∆ 7P8%∆Q = +2-.15 Eo4 $o4ldnt $ant the @4antitB to fall elo$ the 6oint $he!e the 7P8 is 9e!o. ?e *no$ the 7P8 han"es 2-.15 fo! eve!B ton sold# so $e an divide the 7P8 fo! /,#--- 4nits B the sensitivitB to "et a han"e in @4antitB. Doin" so# $e "et:
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1#2/#,<5.-5 = 2-.15( ∆Q) ∆Q = 5#10 Fo! a 9e!o 7P8# $e need to de!ease sales B 5#10 4nits# so the >ini>4> @4antitB is: QGin = /,#--- – 5#10 QGin = 20#0,2 3t the ash !ea*even# the OCF is 9e!o. ettin" the tax shield e@4ation e@4al to 9e!o and solvin" fo! the @4antitB# $e "et:
29.
OCF = - = [(20- – 10,)Q C – <0,#---](1 – ./0) + . /0(,#2--#--- % ,) QC = /#5,< The ao4ntin" !ea*even is: Q3 = [<0,#--- + (,#2--#--- % ,)] % (20- – 10,) Q3 = 21#/15 F!o> P!ole> 20# $e *no$ the finanial !ea*even is 20#0,2 tons.
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sin" the tax shield a66!oah to al4late the OCF# the DOA is:
30.
DOA = 1 + [<0,#---(1 – ./0) – ./0(,#2--#--- % ,)] % 1#05#--DOA = 1.12 Th4s a 1 6e!ent !ise in Q leads to a 1.12 6e!ent !ise in OCF. f Q !ises to /5#---# then the 6e!enta"e han"e in @4antitB is: ∆Q
= (/5#--- – /,#---) % /,#--- = .-205# o! 2.05;
o# the 6e!enta"e han"e in OCF is: ;∆OCF = 2.05;(1.12) ;∆OCF = /.1<; F!o> P!ole> 20: ∆OCF%OCF
= (1#<-#<-- – 1#05#---) % 1#05#--∆OCF%OCF = .-/1<# o! /.1<; n "ene!al# if Q !ises B 1#--- tons# OCF !ises B /.1<;.
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