$. The change in net oerating income from an increase in total sales of :1!444 can be estimated by using the CM ratio as follows9 Change in total sales......................................................................... :1!444 > CM ratio........................................................................................ '4 = ; ?stimated change in net oerating income.................................... : '44 This comutation can be verified as follows9 Total sales........................................ < Total units sold.............................. ; /elling rice er unit.....................
:$44!444 4!444 units :'.44 er unit
Increase in total sales....................... < /elling rice er unit..................... ; Increase in unit sales..................... &riginal total unit sales.................... @ew total unit sales..........................
:1!444 :'.44 er unit $4 units 4!444 units 4!$4 units
Total unit sales................................. /ales................................................. Aariable exenses............................. Contribution margin......................... Fixed exenses................................. @et oerating income.......................
Original 4!444 :$44!444 1$4!444 -4!444 *!444 : 1!444
New 4!$4 :$41!444 1$4!*44 -4!'44 *!444 : 1!'44
P"o%l!& + 'Co&ut! th! B"!a,-!!n Point*
1. The euation method yields the brea"#even oint in unit sales! B! as follows9 rofit :4 :4 :%B B B
; Dnit CM > B E Fixed exenses ; (:1 E :1$) > B E :'!$44 ; (:%) > B E :'!$44 ; :'!$44 ; :'!$44 < :% ; 1!'44 bas"ets
$. The euation method can be used to comute the brea"#even oint in sales esos as follows9 14-4
Operating and Financial Leverage
CM ;
Dnit contribution margin Dnit selling rice
CM ;
:%:1 ; 4.$4
Chat!" #$
rofit ; CM ratio > /ales E Fixed exenses :4 ; 4.$4 > /ales E :'!$44 4.$4 > /ales ; :'!$44 /ales ; :'!$44 < 4.$4 /ales ; :$1!444 %. The formula method gives an answer that is identical to the euation method for the brea"#even oint in unit sales9 Dnit sales to brea" even ;
Fixed exenses Dnit CM
Dnit sales to brea" even ;
:'!$44:% ; 1!'44 bas"ets
'. The formula method also gives an answer that is identical to the euation method for the brea"#even oint in eso sales9 eso sales to brea" even ;
Fixed exenses CM ratio
eso sales to brea" even ;
:'!$444.$4 ; :$1!444
P"o%l!& / 'Co&ut! th! Ma"(in o0 Sa0!t1*
1. To comute the margin of safety! we must first comute the brea"#even unit sales. rofit :4 :4 :14B B B
; Dnit CM > B E Fixed exenses ; (:%4 E :$4) > B E :+!44 ; (:14) > B E :+!44 ; :+!44 ; :+!44 < :14 ; +4 units
14-5
Chat!" #$
Operating and Financial Leverage
/ales (at the budgeted volume of 1!444 units)............ Gess brea"#even sales (at +4 units)........................... Margin of safety (in esos)........................................
:%4!444 $$!44 : +!44
$. The margin of safety as a ercentage of sales is as follows9 Margin of safety (in esos)........................................ < /ales....................................................................... Margin of safety ercentage.......................................
1. The comany,s degree of oerating leverage would be comuted as follows9 Contribution margin................................................... < @et oerating income.............................................. 7egree of oerating leverage.....................................
:'-!444 :14!444 '.-
$. = increase in sales should result in a $'= increase in net oerating income! comuted as follows9 7egree of oerating leverage..................................... > ercent increase in sales......................................... ?stimated ercent increase in net oerating income...
'.= $'=
%. The new income statement reflecting the change in sales is9
@et oerating income reflecting change in sales..... ... &riginal net oerating income.................................... ercent change in net oerating income.....................
:$1*!444:1- ; 1$!444 units or at :%4 er unit! :%*4!444
$. The contribution margin is :$1*!444 because the contribution margin is eual to the fixed exenses at the brea"#even oint. Dnit sold to attain target rofit ;
Target rofit Fixed exenses Dnit CM
Dnit sold to attain target rofit ;
:24!444 :$1*!444 :1-
Dnit sold to attain target rofit ;
1+!444 units
%. /ales (1+!444 units > :%4 er unit)............ Aariable exenses (1+!444 units > :1$ er unit).................. Contribution margin................................... 14-7
'. Margin of safety in eso terms9 Margin of safety in esos ;
Total sales E 6rea" even sales
Margin of safety in esos ;
:'4!444 E :%*4!444 ; :24!444
Margin of safety in ercentage terms9 Margin of safety ercentage ;
Margin of safety in esos Total sales
Margin of safety ercentage ;
:24!444:'4!444 ; $4=
. The CM ratio is *4=. ?xected total contribution margin9 (:44!444 > *4=).... resent total contribution margin9 (:'4!444 > *4=)....... Increased contribution margin..........................................
:%44!444 $+4!444 : %4!444
Alternative solution:
:4!444 incremental sales > *4= CM ratio ; :%4!444 Kiven that the comany,s fixed exenses will not change! monthly net oerating income will also increase by :%4!444.
/ales of 1-!444 games reresent a $4= increase over last year,s sales. 6ecause the degree of oerating leverage is +.! net oerating income should increase by +. times as much! or by 14= (+. > $4=).
b.
The exected total amount of net oerating income for next year would be9
Gast year,s net oerating income............................. ?xected increase in net oerating income next year (14= > :$-4!444).............................. Total exected net oerating income.......................
@et oerating income.... $. The brea"#even oint for the comany as a whole is9 L:$14!444 < :'44!444 ; $.=
eso sales to brea" even ;
Fixed exenses &verall CM ratio
eso sales to brea" even ;
:1-%!+4 14-9
; :%4!444
: $*!$4
$.L
Chat!" #$
Operating and Financial Leverage
4.$ %. The additional contribution margin from the additional sales is comuted as follows9 :144!444 > $.= CM ratio ; :$!44 ssuming no change in fixed exenses! all of this additional contribution margin of :$!44 should dro to the bottom line as increased net oerating income. This answer assumes no change in selling rices! variable costs er unit! fixed exense! or sales mix. P"o%l!& 7 'B"!a,-!!n Anal1sis*
a. 6? ;
:$!444!444 :1!$44 E :+44
;
'!444 units
b. B ;
rofit FC ( E AC)
;
:1!44!444 :$!444!444 :1!$44 E :+44
B;
:%!44!444 :44
;
+!444 units
P"o%l!& 8 'B"!a,-!!n Anal1sis*
6? (before) ;
:+4!444 :'.44 E :$.*4
;
:+4!444 :1.'4
; 4!444 units
6? (after) ;
:14!444 :'.44 E :$.$
;
:14!444 :1.+
; *4!444 units
The brea"#even oint will go u. P"o%l!& #9 'D!("!! o0 L!!"a(!*
B ; $4!444! ; :*4! AC ; :%4! FC ; :'44!444! I ; :4!444 a. 7&G ;
B ( E AC) B ( E AC) E FC
; 14-10
$4!444 (:*4 E :%4) $4!444 (:*4 E :%4) E :'44!444
Operating and Financial Leverage
;
$4!444 (:%4) $4!444 (:%4) E :'44!444
7&G ;
:*44!444 :$44!444
;
b. 7FG ;
?6IT ?6IT E I
;
7FG ;
:$44!444 :14!444
;
c. 7CG ;
d. 6? ;
:*44!444 :*44!444 E :'44!444
;
%x :$44!444 :$44!444 E :4!444 1.%%x
B ( E AC) B ( E AC) E FC E I
;
$4!444 (:*4 E :%4) $4!444 (:*4 E :%4) E :'44!444 E :4!444
;
:*44!444 :*44!444 E :'44!444 E :4!444
7CG ;
:*44!444 :14!444
;
'x
:'44!444 :*4 E :%4
;
:'44!444 :%4
;
1%!%%% units
P"o%l!& ## 'B"!a,-!!n Point an) D!("!! o0 L!!"a(!*
$4!444 (:1 N :14) $4!444 (:1 E :14) E :-4!444 :144!444 :$4!444
; x
%4!444 (:1 N :14) %4!444 (:1 E :14) E :-4!444 :14!444 :+4!444
; $.1'x
Geverage goes down because we are further away from the brea"#even oint! thus the firm is oerating on a larger rofit base and leverage is reduced. ?6IT d. 7FG ; ?6IT E I First! determine the rofit or loss (?6IT) at $4!444 ieces. s indicated in part (b)! the rofit (?6IT) at %4!444 ieces is :+4!444. *&%&&& pieces :%44!444 ($44!444) (-4!444) (:$4!444)
/ales :1 er iece Gess9 Aariable costs (:14) Fixed costs rofit or Goss 7FG at $4!444 ;
:$4!444 :$4!444 E :14!444
7FG at $4!444 ;
:$4!444 :14!444
; $x
14-12
Operating and Financial Leverage
7FG at %4!444 ;
:+4!444 :+4!444 E :14!444
7FG at %4!444 ;
:+4!444 :*4!444
e. 7CG ;
; 1.1+x
B ( E AC) B ( E AC) E FC E I
7CG at $4!444 ;
$4!444 (:1 E :14) $4!444 (:1 E :14) E :-4!444 E :14!444
7CG at $4!444 ;
:144!444 :14!444
7CG at %4!444 ;
%4!444 (:1 E :14) %4!444 (:1 E :14) E :-4!444 E :14!444
7CG at %4!444 ;
:14!444 :*4!444
;
;
14x
$.4x
P"o%l!& #+ ':aan!s! ;i"& an) Co&%in!) L!!"a(!*
7CG ;
;
;
7CG ;
B ( E AC) B ( E AC) E FC E I 1$!444 (:$ E :) 1$!444 (:$ E :) E :1!-44!444 E :'44!444 1$!444 (:$4) 1$!444 (:$4) E :$!$44!444 :$!44!444 :$!44!444 E :$!$44!444
Plan D :1!$44!444 2*4!444 $ $'4!444 14-!444 1%$!444 %+!444 :.%
Plan + :1!$44!444 %44!444 % 244!444 '4!444 '2!444 1!1$!444 :.''
:*!444!444 debt 14= :*44!444 interest (:%!444!444 debt 1$=) (:*!444!444 E :%!444!444 debt retired) x 14= (:*!444!444 common euity) < (:- ar value) ; +4!444 shares
lan ? and the original lan rovide the same earnings er share because the cost of debt at 14 ercent is eual to the oerating return on assets of 14 ercent. 0ith lan 7! the cost of increased debt rises to 1$ ercent! and the firm incurs negative leverage reducing ?/ and also increasing the financial ris" to 7ream Comany. b. Oeturn on assets ; =
Plan D :*44!444 2*4!444 (%*4!444) (1*$!444) (12-!444) %+!444 (:.%)
Plan + :*44!444 %44!444 %44!444 1%!444 1*!444 1!1$!444 :.1
?6IT ; :1!-44!444
!urrent :1!-44!444 *44!444 1!$44!444 14-14
Plan D :1!-44!444 2*4!444 -'4!444
Plan + :1!-44!444 %44!444 1!44!444
Operating and Financial Leverage
Gess9 Taxes ('=) ?T Common shares ?/
'4!444 **4!444 +4!444 :.--
%+-!444 '*$!444 %+!444 :1.
%$Chat!" #$
*+!444 -$!444 1!1$!444 :.+%
If the return on assets decreases to =! lan ? rovides the best ?/! and at 1= return! lan 7 rovides the best ?/. lan 7 is still ris"y! having an interest coverage ratio of less than $.4. c.
Oeturn on assets ; 14=
?6IT ?T Common shares ?/
?6IT ; :1!$44!444
!urrent :1!$44!444 %%4!444 +4!444 :.''
Plan D :1!$44!444 1%$!444 44!444 1 :.$*
(1)
+4!444 N (:%!444!444:1$ er share) ; +4!444 N $4!444 ; 44!444
s the rice of the common stoc" increases! lan ? becomes more attractive because fewer shares can be retired under lan 7 and! by the same logic! fewer shares need to be sold under lan ?.
P"o%l!& #$ 'L!!"a(! an) S!nsitiit1 Anal1sis*
a. Oeturn on assets ; 1$=
?6IT
!urrent :1!44!444 14-15
Plan A :$!$4!444
Plan , :$!$4!444
Chat!" #$
Operating and Financial Leverage
Gess9 Interest ?6T Gess9 Taxes ('4=) ?T Common shares ?/
1!$44!444 1 %44!444 1$4!444 1-4!444 $44!444$ :.24
1!2$4!444 % %%4!444 1%$!444 12-!444 %44!444' :.**
(1)
(-4= x :14!444!444) x 1= ; :-!444!444 x 1= ; :1!$44!444
($)
($4= x :14!444!444) :14 ; :$!444!444:14 ; $44!444 shares
(%)
:1!$44!444 (current) (-4= x :!444!444) x 1-= ; :1!$44!444 :+$4!444 ; :1!2$4!444
lan 6 would continue to rovide the higher earnings er shares. The difference between lans and 6 is even greater than that indicated in part (a) d. @ot only does the rice of the common stoc" create wealth to the shareholder! which is the ma3or ob3ective of the financial manager! but it greatly influences the ability to finance ro3ects at a high or low cost of caital.