CHAPTER 7 ALLOCATING COSTS OF SUPPORT DEPARTMENTS AND JOINT PRODUCTS DISCUSSION QUESTIONS 1. Stage tage one one assi ssigns servi ervice ce costs osts to producing departments. Costs are assigned using factors that reflect the consumption of the services by each producing department. Stage two allocates the costs assigned to the the prod produc ucin ing g depa depart rtme ment nts s (inc (inclu ludi ding ng serv servic ice e cost costs s and and dire direct ct cost costs) s) to the the produc products ts passi passing ng throug through h the produc producing ing departments.
department% something that the manager of the producing producing department cannot control. control. Allocating budgeted costs avoids this problem.
8. ariable ariable costs should be allocated according to usage% usage% wher whereas eas fi&ed costs costs shoul should d be allocat allocated ed accord according ing to capaci capacity ty.. ariab ariable le costs are based on usage because% as a departments usage of a service increases% the variable costs of the service department increase. increase. A service service department departments s capacity capacity and and the the asso ssociat ciate ed fi&e fi&ed d cost osts were orig origin inal ally ly set set by the the user user depa depart rtme ment nts s capaci capacitie ties s to use the servic service. e. 'hus% 'hus% each each department should receive its share of fi&ed cos costs as ori origina ginall lly y conc onceiv eived (to (to do oth otherw erwise allo allow ws one one depa deparrtmen tmentts performance to affect the amount of cost assigned to another department).
2. GAAP requires that all manufacturing costs be assi assign gned ed to prod produc ucts ts for for inve invent ntor ory y valuation. 3. Allocati Allocation on of service service costs costs aids aids in planni planning ng because it maes users pay attention to the level of service activity being consumed and also provides an incentive for them to monitor the effici efficiency ency of the servic service e depart departmen ments. ts. !t aids aids in pricing pricing becaus because e suppor supportt departm department ent cost costs s are are part part of the the cost cost of prod produc ucin ing g a product. "nowing the individual product costs is helpful helpful for developi developing ng bids bids and cost#plu cost#plus s prices.
9. *orm *ormal al or pea pea capac capacit ity y meas measur ures es the the orig origin inal al capa capaci city ty requ requir ireme ement nts s of each each producing department. !t is used when one depart departmen ment ts s spie spie in usage usage affect affects s the amount of capacity needed.
4. $ithou $ithoutt any any allo alloca cati tion on of serv servic ice e cost costs% s% users may view services as a free good and cons consum ume e mor more of the the servi ervice ce than than is opti optimal mal.. Alloc llocati ating ng servi service ce cost costs s woul would d encourage managers to use the service until such such time time as the the marg margin inal al cost cost of the the service is equal to the marginal benefit. 5. Since the user departments are charged for the services provided% they will monitor the performance of the service department. !f the serv servic ice e can can be obta obtain ined ed more more chea cheapl ply y e&ternally% then the user departments will be lie liely ly to poin pointt thi this out out to mana manage geme ment nt.. "now "nowiing thi this% a mana manage gerr of a servi ervice ce depar departme tment nt will will e&ert e&ert effor effortt to mainta maintain in a competitive competitive level of service. 6. 'he identification identification and use of causal causal factors ensures ensures that service service costs costs are accurately accurately assi assign gned ed to user users. s. 'his 'his incr increa ease ses s the the legi legiti tima macy cy of the the cont contro roll func functi tion on and and enhances product costing accuracy.
10.
+sing variable bases to allocate fi&ed costs allows allows one depart department ments s perfor performanc mance e to affect ect the costs allocated to other depart departmen ments. ts. ariab ariable le bases bases also also fail to reflect the original consumption levels that essentially caused the level of fi&ed costs.
11.
'he dual#ra dual#rate te method method separa separates tes the fi&ed and variable costs of providing services and charges them separately. !n effect% a single rate treats all service costs as variable. 'his can can give give faul faulty ty sig signal nals rega regarrding ding the the marginal cost of the service. !f all costs of the servi service ce depa depart rtmen mentt were were variab variable% le% ther there e would be no need for a dual rate. !n addition% if original original capacity equaled actual usage% the dual#rate dual#rate method and the single#rate single#rate method would give the same allocation.
12. 'he direct method allocates the direct costs of each each servic service e depar departme tment nt direct directly ly to the producing producing department departments. s. *o considerat consideration ion is given given to the fact that that other other servic service e cente centers rs
7. Allocating actual costs passes on the efficiencie efficiencies s or inefficiencies inefficiencies of the service 7-1
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14. A -oint cost is a cost incurred in the simult simultaneo aneous us produc productio tion n of two two or more more products. At least one of these -oint p roducts must be a main product. !t is possible for the -oint production process to produce a prod produc uctt of rela relati tive vely ly litt little le sal sales valu value e relative to the main product(s) this product is nown as a by#product.
may use servic services. es. 'he 'he sequen sequentia tiall method method allocates service costs sequentially. ,irst% the costs costs of the center center provid providing ing the greate greatest st service are allocated to all user departments% including including other service departments departments.. *e&t% the costs of the second greatest provider of services are allocated to all user department departments% s% e&cluding e&cluding any department department(s) (s) that that have have alre alread ady y allo alloca cate ted d cost costs. s. 'his 'his continues until all service center costs have been allocated. 'he principal difference in the two methods is the fact that the sequential sequential method considers some interactions among service centers and the direct method ignores interactions.
15.
/oin /ointt cost costs s occu occurr only only in case cases s of -oin -ointt production. A -oint cost is a common cost% but a common cost is not necessarily a -oint cost. 0any overhead costs are common to the products manufactured in a factory but do not signify a -oint production process.
13. 'he reciprocal method is more accurate be# cause it fully considers interactions among service centers.
7-2
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CORNERSTONE EERCISES C!"#$"%&!#$ E'$"()%$ 7.1 1. T! T!&*+ &*+ $',$(&$$',$(&$- (!%&% ! &/$ M*)#& M*)#&$#* $#*#($ #($ D$,*"& D$,*"&$# $#& & F)'$F)'$- (!%&% (!%&%... ...... ..... ..... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ..... ..... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ... *")* ")*+$ +$ (!%& (!%&% % 1. 1.35 35 220 22000 00 *)# *)#&$ &$#* #*#( #($ $ /"%. /"%... .... .... .... .... .... .... .... .... .... .... ..... ... T!&*+ (!%&% (!%&%... ...... ...... ...... ...... ..... ..... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ..... ..
649 64900 00 297 29700 00 946 94600 00
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
C!"#$"%&!#$ E'$"()%$ 7.2 1. *")* *")*+$ +$ "*&$ "*&$ : 1.35 ,$" ,$" *)#&$# *)#&$#*#( *#($ $ /!<" /!<" T/$ )'$- *++!(*&)!# )% (*+(<+*&$- !" $*(/ -$,*"&$#& *%$- !# <-$&$,$*> !#&/ <%*$
D$,* D$,*"& "&$ $#& #& A%%$+=..................... F*")(*&)#.................. P*(>*)#................... T!&*+.............................
P$*> N<$" ! H!< H!<"%
P$"($ $"($#& #&
390 1300 910 2600
15B 50 35 100B
@<-$&$F)'$ F)'$- C!%& C!%&
A++!(*&$F)'$ F)'$- C!%& C!%&
64900 64900 64900
9735 32450 22715 64900
P$"($#& !" A%%$+= : 390;2600 : 0.15 !" 15B
7-3
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C!"#$"%&!#$ E'$"()%$ 7.2
(!#&)#<$-
P$"($#& !" F*")(*&)# : 1300;2600 : 0.50 !" 50B P$"($#& !" P*(>*)# : 910;2600 : 0.35 !" 35B 2. D$,*"&$#& A%%$+=....... F*")(*&)#.... P*(>*)#...... T!&*+........... 3. D$,*"&$#& A%%$+=....... F*")(*&)#.... P*(>*)#...... T!&*+...........
A(&<*+ N<$" ! H!<"%
*")*+$ R*&$
*")*+$ A!<#&
F)'$A!<#&
T!&*+ C/*"$
3960 6800 10000 20760
1.35 1.35 1.35
5346 9180 13500 28026
9735 32450 22715 64900
15081 41630 36215 92926
A(&<*+ N<$" ! H!<"%
*")*+$ R*&$
*")*+$ A!<#&
F)'$A!<#&
T!&*+ C/*"$
4000 6800 10000 20800
1.35 1.35 1.35
5400 9180 13500 28080
9735 32450 22715 64900
15135 41630 36215 92980
7-4
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C!"#$"%&!#$ E'$"()%$ 7.3 1. A++!(*&)!# "*&)!% P"!,!"&)!# ! D")$" U%$- = H<*# G$#$"*+ R$%!<"($% F*(&!"= F*")(*&)# H<*# R$%!<"($% 0.32 1 G$#$"*+ F*(&!"= 0.30 3
A%%$+= 0.68 2 0.70 4
1
P"!,!"&)!# ! $,+!=$$% )# F*")(*&)# : 80;80 ? 170 : 0.32 P"!,!"&)!# ! $,+!=$$% )# A%%$+= : 170;80 ? 170 : 0.68 3 P"!,!"&)!# ! %<*"$ $$& )# F*")(*&)# : 5700;5700 ? 13300 : 0.30 4 P"!,!"&)!# ! %<*"$ $$& )# A%%$+= : 13300;5700 ? 13300 : 0.70 2
2.
D)"$(& (!%&% A++!(*&$ H<*# R$%!<"($% 1 G$#$"*+ F*(&!"= 2 T!&*+ *&$" *++!(*&)!#
S<,,!"& D$,*"&$#&% H<*# G$#$"*+ R$%!<"($% F*(&!"= 160000 340000 160000 0
340000 0
P"!-<()# D$,*"&$#&% F*")(*&)# 114600
A%%$+= 93000
51200 102000 267800
108800 238000 439800
1
F*")(*&)# : 0.32 160000 : 51200 A%%$+= : 0.68 160000 : 108800 2 F*")(*&)# : 0.30 340000 : 102000 A%%$+= : 0.70 340000 : 238000 3. S)#($ #!#$ ! &/$ H<*# R$%!<"($% (!%& )% *++!(*&$- &! G$#$"*+ F*(&!"= )& -!$% #!& *&&$" /! *#= $,+!=$$% !"> )# G$#$"*+ F*(&!"=.
7-5
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C!"#$"%&!#$ E'$"()%$ 7.4 1. A++!(*&)!# "*&)!% )&/ G$#$"*+ F*(&!"= "*#>$- )"%& P"!,!"&)!# ! D")$" U%$- = H<*# G$#$"*+ R$%!<"($% F*(&!"= F*")(*&)# H<*# R$%!<"($% 0.3200 1 G$#$"*+ F*(&!"= 0.0500 3 0.28504
A%%$+= 0.6800 2 0.6650 5
1
P"!,!"&)!# ! $,+!=$$% )# F*")(*&)# : 80;80 ? 170 : 0.32 P"!,!"&)!# ! $,+!=$$% )# A%%$+= : 170;80 ? 170 : 0.68 3 P"!,!"&)!# ! %. &. )# H<*# R$%!<"($% : 1000;1000 ? 5700 ? 13300 : 0.0500 4 P"!,!"&)!# ! %. &. )# F*")(*&)# : 5700;1000 ? 5700 ? 13300 : 0.2850 5 P"!,!"&)!# ! %. &. )# A%%$+= : 13300;1000 ? 5700 ? 13300 : 0.6650 2
2.
D)"$(& (!%&% A++!(*&$ G$#$"*+ F*(&!"= 1 H<*# R$%!<"($% 2 T!&*+ *&$" *++!(*&)!#
S<,,!"& D$,*"&$#&% H<*# G$#$"*+ R$%!<"($% F*(&!"= 160000 340000 17000 177000 0
340000 0
P"!-<()# D$,*"&$#&% F*")(*&)# 114600
A%%$+= 93000
96900 56640 268140
226100 120360 439460
1
H<*# R$%!<"($% : 0.05 340000 : 17000 F*")(*&)# : 0.285 340000 : 96900 A%%$+= : 0.665 340000 : 226100 2 F*")(*&)# : 0.32 177000 : 56640 A%%$+= : 0.68 177000 : 120360 3. T=,)(*++= "!<#-)# &/$ *++!(*&)!# "*&)!% &! %)' %)#))(*#& -))&% !<+- ,"!-<($ * !"$ ,"$()%$ *++!(*&)!# ! (!%&% *#- !<+- "$-<($ "!<#-)# $""!". I# &/)% (*%$ *++ *++!(*&)!# "*&)!% (*$ !<& (+$*#+= &! &/"$$ %)#))(*#& -))&% %! "!<#-)# &! %)' !<+- *>$ #! -)$"$#($.
7-6
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C!"#$"%&!#$ E'$"()%$ 7.5 1. A++!(*&)!# "*&)!% P"!,!"&)!# ! D")$" U%$- = H<*# G$#$"*+ R$%!<"($% F*(&!"= F*")(*&)# A%%$+= H<*# R$%!<"($% 0.1935 1 0.2581 2 0.5484 3 G$#$"*+ F*(&!"= 0.0500 4 0.2850 5 0.6650 6 1 P"!,!"&)!# ! $,+!=$$% )# G$#$"*+ F*(&!"= : 60;60 ? 80 ? 170 : 0.1935 2 P"!,!"&)!# ! $,+!=$$% )# F*")(*&)# : 80;60 ? 80 ? 170 : 0.2581 3 P"!,!"&)!# ! $,+!=$$% )# A%%$+= : 170;60 ? 80 ? 170 : 0.5484 4 P"!,!"&)!# ! %. &. )# H<*# R$%!<"($% : 1000;1000 ? 5700 ? 13300 : 0.0500 5 P"!,!"&)!# ! %. &. )# F*")(*&)# : 5700;1000 ? 5700 ? 13300 : 0.2850 6 P"!,!"&)!# ! %. &. )# A%%$+= : 13300;1000 ? 5700 ? 13300 : 0.6650 2. L$& HR : H<*# R$%!<"($% *#- GF : G$#$"*+ F*(&!"=. HR : 160000 ? 0.0500 GF GF : 340000 ? 0.1935 HR S!+)# !" H<*# R$%!<"($% HR : 160000 ? 0.05 GF : 160000 ? 0.05340000 ? 0.1935 HR : 160000 ? 17000 ? 0.009675 HR 0.990325 HR : 177000 HR : 178729 S!+)# !" G$#$"*+ F*(&!"= GF : 340000 ? 0.1935 HR : 340000 ? 0.1935178729 : 374584 3.
S<,,!"& D$,*"&$#&% H<*# G$#$"*+ R$%!<"($% F*(&!"= 160000 340000
P"!-<()# D$,*"&$#&% F*")(*&)# 114600
A%%$+= 93000
D)"$(& (!%&% A++!(*&$ H<*# R$%!<"($% 1 178729 34584 46130 98015 2 G$#$"*+ F*(&!"= 18729 374584 106756 249098 T!&*+ *&$" *++!(*&)!# 0 0 267486 440113 1 G$#$"*+ F*(&!"= : 0.1935 178729 : 34584 F*")(*&)# : 0.2580 178729 : 46130 A%%$+= : 0.5484 178729 : 98015 2 H<*# R$%!<"($% : 0.05 374584 : 18729 F*")(*&)# : 0.285 374584 : 106756 A%%$+= : 0.655 374584 : 249098 4. I F*")(*&)# /*- &/$ <+> ! &/$ %<*"$ !!&*$ )& !<+- $& &/$ +*"$%& *++!(*&)!# ! G$#$"*+ F*(&!"= (!%&%. A% * "$%<+& F*")(*&)# !<+- /*$ &/$ 7-7
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*!")&= ! %<,,!"& -$,*"&$#& (!%&% )#%&$*- ! A%%$+=.
C!"#$"%&!#$ E'$"()%$ 7.6 1. F*")(*&)# D$,&. !$"/$*- "*&$ : 267800;82000 : 3.27 ,$" *(/. /". "!<#-$- A%%$+= D$,&. !$"/$*- "*&$ : 439800;160000 : 2.75 ,$" DLH "!<#-$- F"! C!"#$"%&!#$ E'$"()%$ 73 %!+<&)!#. 2. C!%& ! J! 316 D)"$(& *&$")*+%................................................................................. D)"$(& +*!" (!%&................................................................................ A,,+)$- !$"/$*- F*")(*&)# 6 3.27................................................................. A%%$+= 4 2.75................................................................... T!&*+ (!%&........................................................................................... 3. N$ C!%& ! J! 316 D)"$(& *&$")*+%................................................................................. D)"$(& +*!" (!%&................................................................................ A,,+)$- !$"/$*- F*")(*&)# 1 3.27................................................................. A%%$+= 4 2.75................................................................... T!&*+ (!%&...........................................................................................
7-8
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120.00 80.00 19.62 11.00 230.62
120.00 80.00 3.27 11.00 214.27
C!"#$"%&!#$ E'$"()%$ 7.7 1. G"*-
%$P!<#-% 2
P$"($#& ! U#)&% 3
G"*-$ A............................. G"*-$ @............................. S+)($%................................. A,,+$%*<($....................... T!&*+..............................
1600 5000 8000 5400 20000
8.00B 25.00 40.00 27.00 100.00B
J!)#& C!%& A++!(*&)!# 3 18000 1440 4500 7200 4860 18000
P$"($#& !" G"*-$ A : 1600;20000 : 0.080 !" 8B P$"($#& !" G"*-$ @ : 5000;20000 : 0.25 !" 25B P$"($#& !" S+)($% : 8000;20000 : 0.40 !" 40B P$"($#& !" A,,+$%*<($ : 5400;20000 : 0.27 !" 27B 2. A$"*$ !)#& (!%& : 18000;20000 ,!<#-% : 0.90 ,$" ,!<#G"*-$ A !)#& (!%& *++!(*&)!# : 0.90 1600 : 1440 G"*-$ @ !)#& (!%& *++!(*&)!# : 0.90 5000 : 4500 S+)($% !)#& (!%& *++!(*&)!# : 0.90 8000 : 7200 A,,+$%*<($ !)#& (!%& *++!(*&)!# : 0.90 5400 : 4860 Note: E)&/$" $&/!- )$% &/$ %*$ *++!(*&)!# "$%<+&%. 3. I G"*-$ A /*- 2000 ,!<#-% *#- G"*-$ @ /*- 4600 ,!<#-% &/$# G"*-$ A !<+- "$($)$ 10 ,$"($#& 2000;20000 ! &/$ !)#& (!%& !" 1800 10B 18000 *#- G"*-$ @ !<+- "$($)$ 23 ,$"($#& 4600;20000 ! &/$ !)#& (!%& !" 4140 23B 18000. T/$"$ !<+- $ #! ),*(& !# &/$ *++!(*&)!# &! S+)($% *#- A,,+$%*<($ %)#($ &/$)" ,"!,!"&)!# ! &!&*+ ,!<#-% -)- #!& (/*#$.
7-9
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C!"#$"%&!#$ E'$"()%$ 7.8 1. G"*-$% G"*-$ A G"*-$ @ S+)($% A,,+$%*<($ T!&*+
N<$" ! P!<#-%
$)/& F*(&!"
1600 5000 8000 5400
4.0 2.0 1.0 0.5
$)/&$- N<$" ! P!<#-% P$"($#& 6400 10000 8000 2700 27100
A++!(*&$J!)#& C!%&
0.2362 0.3690 0.2952 0.0996
4252 6642 5314 1793 18001
Note: T/$ !)#& (!%& *++!(*&)!# -!$% #!& $<*+ 18000 -<$ &! "!<#-)#. 2. I &/$ G"*-$ A $)/& *(&!" )% -$("$*%$- &! 3.0 &/$# &/$ $)/&$- #<$" ! ,!<#-% !<+- -$("$*%$ = !#$!<"&/ *#- &/$ G"*-$ A *,,+$% !<+- "$($)$ * "$+*&)$+= %*++$" *!<#& ! !)#& (!%&. H!$$" &/$ *++!(*&)!# ! (!%& &! *++ !&/$" "*-$% )++ )#("$*%$ %)#($ &/$ -$("$*%$- $)/&$- ,!<#-% !" G"*-$ A *,,+$% )++ ),*(& *++ ,$"($#&*$%. T/$ !++!)# &*+$ %/!% /*& !<+/*,,$# G"*-$% G"*-$ A G"*-$ @ S+)($% A,,+$%*<($ T!&*+
N<$" ! P!<#-%
$)/& F*(&!"
1600 5000 8000 5400
3.0 2.0 1.0 0.5
$)/&$- N<$" ! P!<#-% P$"($#& 4800 10000 8000 2700 25500
0.1882 0.3922 0.3137 0.1059
A++!(*&$J!)#& C!%& 3388 7060 5647 1906 18001
Note: T/$ !)#& (!%& *++!(*&)!# -!$% #!& $<*+ 18000 -<$ &! "!<#-)#.
7-10
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C!"#$"%&!#$ E'$"()%$ 7.9 1. G"*-$% G"*-$ A G"*-$ @ S+)($% A,,+$%*<($ T!&*+
P")($ *& T!&*+ M*">$& P$"($#& A++!(*&$P!<#-% S,+)&O *+<$ *& ! T!&*+ J!)#& P"!-<($- ,$" ,!<#- S,+)&O M*">$& *+<$ C!%& 1600 4.00 6400 0.4015 7227 5000 1.00 5000 0.3137 5647 8000 0.50 4000 0.2509 4516 5400 0.10 540 0.0339 610 20000 15940 18000
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
G"*-$% G"*-$ A G"*-$ @ S+)($% A,,+$%*<($ T!&*+
P")($ *& T!&*+ M*">$& P$"($#& A++!(*&$P!<#-% S,+)&O *+<$ *& ! T!&*+ J!)#& P"!-<($- ,$" ,!<#- S,+)&O M*">$& *+<$ C!%& 1600 4.00 6400 0.3778 6800 5000 1.20 6000 0.3542 6376 8000 0.50 4000 0.2361 4250 5400 0.10 540 0.0319 574 20000 16940 18000
7-11
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
C!"#$"%&!#$ E'$"()%$ 7.10 1. F<"&/$" H=,!&/$&)(*+ H=,!&/$&)(*+ A++!(*&$M*">$& P"!($%%)# M*">$& N<$" M*">$& J!)#& P"!-<(& P")($ C!%& P")($ ! G*++!#% *+<$ P$"($#& C!%& 1 K 2 : 3 4 : 5 LT$# T")!+ P)!$ T!&*+
2.00 5.00 6.00
0.50 1.00 1.50
1.50 4.00 4.50
3500 4000 2500
5250 16000 11250 32500
0.1615 0.4923 0.3462
2083 6351 4466 12900
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
0.50 2.00 1.50
1.50 3.00 4.50
3500 4000 2500
5250 12000 11250 28500
0.1842 0.4211 0.3947
P$"($#& !" LT$# : 5250;28500 : 0.1842 !" 18.42B P$"($#& !" T")!+ : 12000;28500 : 0.4211 !" 42.11B P$"($#& !" P)!$ : 11250;28500 : 0.3947 !" 39.47B LT$# !)#& (!%& *++!(*&)!# : 0.1842 12900 : 2376 T")!+ !)#& (!%& *++!(*&)!# : 0.4211 12900 : 5432 P)!$ !)#& (!%& *++!(*&)!# : 0.3947 12900 : 5092
7-12
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
2376 5432 5092 12900
C!"#$"%&!#$ E'$"()%$ 7.11 1. T!&*+ "$$#<$ LT$# 2 3500.................................................... T")!+ 5 4000...................................................... P)!$ 6 2500.................................................... F<"&/$" ,"!($%%)# (!%&% LT$# 0.50 3500............................................... T")!+ 1.00 4000................................................. P)!$ 1.50 2500............................................... J!)#& ,"!($%%)# (!%&%........................................... T!&*+ "!%% *")#......................................................
7000 20000 15000
42000
1750 4000 3750
9500 12900 19600
2. G"!%% *")# ,$"($#&*$ : G"!%% *")#;T!&*+ "$$#<$ : 19600;42000 : 0.4667 !" 46.67B "!<#-$- E$#&<*+ *">$& *+<$....................... L$%% G"!%% *")# *& 46.67B......... C!%& ! !!-% %!+-....................... L$%% %$,*"*+$ (!%&%........................ A++!(*&$- !)#& (!%&.......................
LT$#
T")!+
P)!$
7000 3267 3733 1750 1983
20000 9334 10666 4000 6666
15000 7001 7999 3750 4249
Note: A++!(*&$- (!%&% *"$ "!<#-$- &! &/$ #$*"$%& -!++*" %! &/$ *++!(*&$- &!&*+ )% 12898. 3. A# )#("$*%$ )# &/$ <"&/$" ,"!($%%)# (!%& ! T")!+ )++ "$-<($ &/$ "!%% *")# ,$"($#&*$ *#- )++ -$("$*%$ &/$ !)#& (!%& *++!(*&$- &! T")!+. T!&*+ "$$#<$..................................................................................... F<"&/$" ,"!($%%)# (!%&%................................................................. J!)#& ,"!($%%)# (!%&%..................................................................... T!&*+ "!%% *")#............................................................................
42000 13500 12900 15600
G"!%% *")# ,$"($#&*$ : 15600;42000 : 0.3714 !" 37.14B "!<#-$- E$#&<*+ *">$& *+<$....................... L$%% G"!%% *")# *& 37.14B......... C!%& ! !!-% %!+-....................... L$%% %$,*"*+$ (!%&%........................ A++!(*&$- !)#& (!%&.......................
LT$# 7000 2600 4400 1750 2650
T")!+ 20000 7428 12572 8000 4572
P)!$ 15000 5571 9429 3750 5679
Note: A++!(*&$- (!%&% *"$ "!<#-$- &! &/$ #$*"$%& -!++*" %! &/$ *++!(*&$- &!&*+ )% 12901.
7-13
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
EERCISES E'$"()%$ 7.12 *. . (. -. $.
%<,,!"& ,"!-<()# %<,,!"& ,"!-<()# %<,,!"&
. . /. ). .
%<,,!"& %<,,!"& ,"!-<()# ,"!-<()# ,"!-<()#
>. +. . #. !.
%<,,!"& %<,,!"& %<,,!"& %<,,!"& %<,,!"&
$. . . /.
,"!-<()# %<,,!"& %<,,!"& ,"!-<()#
). .
,"!-<()# %<,,!"&
E'$"()%$ 7.13 *. . (. -.
%<,,!"& %<,,!"& ,"!-<()# ,"!-<()#
E'$"()%$ 7.14 *. . (. -. $. . . /. ).
N<$" ! $,+!=$$% S<*"$ !!&*$ P!<#-% ! +*<#-"= O"-$"% ,"!($%%$M*)#&$#*#($ /!<"% !">$N<$" ! $,+!=$$% N<$" ! &"*#%*(&)!#% ,"!($%%$M*(/)#$ /!<"% S<*"$ !!&*$
7-14
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
E'$"()%$ 7.15 1.
D". P!%&!# *= *#& &! (!%& &/$ (+$*#%$" !" %$$"*+ "$*%!#% &! *+<$ )#$#&!"= &! -$&$")#$ ,"!)&*)+)&= *#- &! ,+*# %*+$% *#- (!%&% !" &/$ (!)# =$*". A% +!# *% /$ %$++% "$+*&)$+= $ !&&+$% ! (+$*#%$" )& )% #!& #$($%%*"= &! *++!(*&$ *#= )#-)"$(& (!%&% &! &/$ (+$*#%$". T/$ $-)(*+ *%%)%&*#& )% ,*)- &/$ %*$ *!<#& /$&/$" %/$ )'$% &/$ (+$*#%$" !" #!&. T/$ %,*($ <%$- &! %&!"$ &/$ (+$*#%$" *&$")*+% )% %*++ *#- &/$ )#("$$#&*+ (!%& )% $"!.
2.
T/$ %)&<*&)!# /*% (/*#$- -"**&)(*++=. N! &/$ (+$*#%$" %/!<+- $ *++!(*&$- %!$ ! &/$ !)($ "$#& *% $++ *% *++ ! &/$ #$ *%%)%&*#&% %*+*"=. T/$ !)($ "$#& (!<+- $ *,,!"&)!#$- 75 ,$"($#& &! &/$ &/"$$ -!(&!"% *#- 25 ,$"($#& &! &/$ (+$*#%$" !&&+)# !,$"*&)!# )$# &/*& &/$ (+$*#%$" !,$"*&)!# &*>$% *# !)($ *#- *# $'*)#)# "!!. I& (!<+- $ *"<$- &/*& &/)% !$"%&*&$% &/$ *++!(*&)!# &! &/$ (+$*#%$" %)#($ &/$ *)&)# "!! *"$* -!$% #!& %$"$ &/$ (+$*#%$". H!$$" &/$ "$($,&)!#)%& ,"!*+= &*>$% (*++% *#!,$#% *)+ !" &/)% ,"!$(& %! !$"%&*&)# &/$ "$#& *= $ *# $*%= *= &! *-<%& !" &/)%. T/$ (!%& ,$" !&&+$ !<+- &/$# $ M*&$")*+%.......................................... L*!" 12000;40000................... O)($ "$#&...................................... T!&*+ (!%&.................................
0.50 0.30 0.38 1.18
O)($ "$#& *++!(*&)!# : 5000 12;4;40000 !&&+$% "!<#-$-.
E'$"()%$ 7.16 1.
T/$ )#("$$#&*+ $&/!- ! *++!(*&)# &/$ (!%& ! &/$ &"), !<+- "$%<+& )# * (!%& &! *++)$ ! 210 15 &)$% !<" #)/&% !" &/$ "!++**= *#- 150 !" /$" !!-.
2.
T/$ $#$)&%"$($)$- *,,"!*(/ (!<+- "$%<+& )# &/$ !++!)# (!%& *++!(*&)!# &! *++)$ M!&$+ 580 ? 15 4;3............. 213.33 F!!-................................................. 150.00 G*% 120;3.................................. 40.00 T!&*+.......................................... 403.33 T/$ &"$*&$#& ! &/$ !&$+ (!%& )% ,"!+$*&)(. T/)% (!,<&*&)!# *--% &/$ "!++**= (!%& !" !<" #)/&% &! &/$ (!%& ! &/$ -!<+$ "!! !" !<" #)/&%. H!$$" ) *++)$ %,$#-% &/$ $#&)"$ &)$ !# * +$%% (!!"&*+$ "!++**= %/$ *= $ +$%% &/*# ,+$*%$-. P$"/*,% &/$ *(*&)!#$"% (!<+- &"*-$ ! %+$$,)# !# &/$ "!++**=. 7-15
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
E'$"()%$ 7.17 1.
S)#+$ (/*")# "*&$ : 1800 ? 1500;1000 ? 1.20 : 4.50 ,$" )& 175 ? 400 ? 100 ? 75 ? 20 ? 130 ? 100 : 1000 N<$" ! G)&% : T!&*+ 160 420 240 10 50 200 450 1530
S&!"$ R*&$ T/$ S&*&)!#$"= S&*&)!#................... A"&% C!++$(&)+$%......................... )-S,!"&%....................................... J** J)%....................................... D$%)#$" S/!$%.............................. C")%&)#*% C+!%$&............................. A+*#% D"< *#- S<#-")$%.............. T!&*+.......................................... 2.
N<$" S&!"$ T/$ S&*&)!#$"= S&*&)!#................... A"&% C!++$(&)+$%......................... )-S,!"&%....................................... J** J)%....................................... D$%)#$" S/!$%.............................. C")%&)#*% C+!%$&............................. A+*#% D"< *#- S<#-")$%.............. T!&*+..........................................
! G)&% 175 400 100 75 20 130 100 1000
C/*")# 4.50 4.50 4.50 4.50 4.50 4.50 4.50
A++!(*&$P$"($#& 17.50B 40.00 10.00 7.50 2.00 13.00 10.00 100.00B
720 1890 1080 45 225 900 2025 6885
F)'$- A!<#& 577.50 1320.00 330.00 247.50 66.00 429.00 330.00 3300.00
A++!(*&$- )'$- *!<#& : P$"($#& 3300. *")*+$ "*&$ : 1.20 ,$" )& S&!"$
N<$" ! G)&%
*")*+$ A!<#& ?
T/$ S&*&)!#$"= S&*&)!#......... A"&% C!++$(&)+$%................ )-S,!"&%............................. J** J)%.............................. D$%)#$" S/!$%..................... C")%&)#*% C+!%$&................... A+*#% D"< *#- S<#-")$%.... T!&*+................................
160 420 240 10 50 200 450 1530
192 504 288 12 60 240 540 1836
F)'$T!&*+ A!<#& : C/*"$ 577.50 1320.00 330.00 247.50 66.00 429.00 330.00 3300.00
7-16
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
769.50 1824.00 618.00 259.50 126.00 669.00 870.00 5136.00
E'$"()%$ 7.17 C!#(+<-$- 3.
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
4.
D$%,)&$ &/$ (/*")# "*&$ $&/!- J$ *= $ !$"(/*")# = !$"$%&)*&)# /)% )'$- (!%&%. T/$ %,*($ <%$- = &/$ )&"*,,)# %$")($ )% !#$ ! &/"$$ *(*#& %,*($%. T/$ !,,!"&<#)&= (!%& ! <%)# )& &! "*, )&% )% $"!. U#&)+ &/$ #)#&/ %,*($ )% "$#&$- *#- &/$"$ )% *# !((<,*#& !" &/$ &$#&/ ,$"/*,% &/$ )'$- (!%& %/!<+- )#(+<-$ !#+= &/$ *$% ,*)- &! &/$ )& "*,,$"%.
E'$"()%$ 7.18 1.
A++!(*&)!# "*&)!% D$,*"&$#& A.......... D$,*"&$#& @..........
$*" 1 0.4 0.6
$*" 2 0.5 0.5
48000 72000
60000 60000
A++!(*&)!# D$,*"&$#& A.......... D$,*"&$#& @.......... 2.
T/$ *#*$" ! D$,*"&$#& @ )% #!& (!#&"!++)# /<*# "$%!<"($ (!%&% $&&$" &/*# &/$ *#*$" ! D$,*"&$#& A. T/$ *)# "$*%!# &/*& D$,*"&$#& A% *++!(*&)!# ! /<*# "$%!<"($ (!%& )#("$*%$- )% $(*<%$ D$,*"&$#& @% <%*$ -$("$*%$-.
3.
F)"%& *")*+$ *#- )'$- (!%&% %/!<+- $ *++!(*&$- %$,*"*&$+=. S$(!#- <-$&$- #!& *(&<*+ (!%&% %/!<+- $ *++!(*&$-. *")*+$ (!%&% %/!<+- $ *%%)#$- &! &/$ &! <%$" -$,*"&$#&% = <+&),+=)# &/$ <-$&$- *")*+$ (!%& ,$" /!<" = &/$ *(&<*+ /!<"% !" <-$&$- /!<"% <%$- -$,$#-)# !# /$&/$" &/$ ,<",!%$ )% ,$"!"*#($ $*+<*&)!# !" ,"!-<(& (!%&)#. F)'$(!%&% !<+- $ *%%)#$- )# ,"!,!"&)!# &! &/$ ,"*(&)(*+ !" #!"*+ *(&))&)$% ! $*(/ <%$" -$,*"&$#&.
7-17
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
E'$"()%$ 7.19 1.
P"!-<(& (!%&)# $*" 1 *#- $*" 2 *"$ )-$#&)(*+ D$,*"&$#& A *")*+$ (!%&% 0.25 20000. . . 0.25 20000. . . F)'$- (!%&% 0.5 100000. . . 0.5 100000. . . T!&*+ (!%&....................
2.
D$,*"&$#& @
5000 5000 50000 50000 55000
55000
P$"!"*#($ $*+<*&)!# $*" 1 D$,*"&$#& A D$,*"&$#& @ *")*+$ (!%&% 0.25 24000. . . 0.25 36000. . . F)'$- (!%&% 0.5 100000. . . 0.5 100000. . . T!&*+ (!%&....................
6000 9000 50000 50000
56000
59000
$*" 2 D$,*"&$#& A D$,*"&$#& @ *")*+$ (!%&% 0.25 25000. . . 0.25 25000. . . F)'$- (!%&% 0.5 100000. . . 0.5 100000. . . T!&*+ (!%&....................
6250 6250 50000 50000 56250
56250
7-18
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
E'$"()%$ 7.20 1.
A++!(*&)!# "*&)!% S<*"$ $$&.................... M*(/)#$ /!<"%.............. P<"(/*%$ !"-$"%...........
P$%&)()-$ 0.4667 0.7500 0.6667
L)<)- F$"&)+)$" 0.5333 0.2500 0.3333
C!%& *%%)#$#& P$%&)()-$ D)"$(& (!%&% P!$" 0.7500 90000............ 0.2500 90000............ G$#$"*+ F*(&!"= 0.4667 314000.......... 0.5333 314000.......... P<"(/*%)# 0.6667 167000.......... 0.3333 167000.......... T!&*+.......................................... 2.
78900
L)<)- F$"&)+)$" 107800
67500 22500 146544 167456 111339 404283
55661 353417
D$,*"&$#&*+ !$"/$*- "*&$% P$%&)()-$ 404283;24000 : 16.85 ,$" *(/)#$ /!<" L)<)- F$"&)+)$" 353417;8000 : 44.18 ,$" *(/)#$ /!<"
7-19
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
E'$"()%$ 7.21 1.
A%%<$ &/$ %<,,!"& -$,*"&$#& (!%&% *"$ *++!(*&$- )# !"-$" ! /)/$%& &! +!$%& (!%& G$#$"*+ F*(&!"= P<"(/*%)# *#- P!$".
S<*"$ $$&.................. M*(/)#$ /!<"%............ P<"(/*%$ !"-$"%.........
P!$" 0.1250 0.1000
G$#$"*+ F*(&!"=
P<"(/*%)# 0.1250
G$#$"*+ F*(&!"= P<"(/*%)# 314000 167000
P!$" D)"$(& (!%&%................. 90000 G$#$"*+ F*(&!"= 0.1250 314000 39250 39250 0.1250 314000 39250 39250 0.3500 314000 109900 0.4000 314000 125600 P<"(/*%)# 0.1000 206250 20625 20625 0.6000 206250 123750 0.3000 206250 61875 P!$" 0.7500 149875 112406 0.2500 149875 37469 T!&*+............................. 0 0 0 2.
P$%&)()-$ 0.3500 0.7500 0.6000
L)<)F$"&)+)$" 0.4000 0.2500 0.3000
P$%&)()-$ 78900
L)<)F$"&)+)$" 107800
109900 125600 123750 61875 112406 424956
37469 332744
P$%&)()-$ 424956;24000 : 17.71 ,$" *(/)#$ /!<" "!<#-$- L)<)- F$"&)+)$" 332744;8000 : 41.59 ,$" *(/)#$ /!<" "!<#-$-
7-20
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
E'$"()%$ 7.22 1.
G$#$"*+ F*(&!"= S<*"$ !!&*$............... N<$" ! "$($))# !"-$"%.......................... 0.10
R$($))# 0.20
A%%$+= 0.40
F)#)%/)# 0.40
0.56
0.34
R :
160000 ? 0.2 GF R : 160000 ? 0.2400000 ? 0.1 R R : 160000 ? 80000 ? 0.02 R 0.98R : 240000 R : 244898 G$#$"*+ F*(&!"= 400000
: 400000 ? 0.1 R GF : 400000 ? 0.1244898 GF : 400000 ? 24490 GF : 424490 GF
R$($))# 160000
A%%$+= 43000
F)#)%/)# 74000
D)"$(& !$"/$*- (!%&...... A++!(*&$ G$#$"*+ F*(&!"= *.......... 424490 84898 169796 169796 R$($))# .................... 24490 244898 137143 83265 T!&*+................................. 0 0 349939 327061 * R$($))# : 0.20 424490 : 84898 A%%$+= : 0.40 424490 : 169796 F)#)%/)# : 0.40 424490 : 169796 G$#$"*+ F*(&!"= : 0.10 244898 : 24490 A%%$+= : 0.56 244898 : 137143 F)#)%/)# : 0.34 244898 : 83265 2.
D$,*"&$#&*+ "*&$% A%%$+= 349939;25000 : 14.00 ,$" -)"$(& +*!" /!<" F)#)%/)# 327061;40000 : 8.18 ,$" -)"$(& +*!" /!<"
E'$"()%$ 7K23 1. S<*"$ !!&*$....................... N<$" ! "$($))# !"-$"% G$#$"*+ F*(&!"= 0.5000 400000......... 0.5000 400000......... R$($))# 0.6222 160000......... 0.3778 160000......... D)"$(& (!%&%............................. 2.
A%%$+= 0.5000 0.6222
F)#)%/)# 0.5000 0.3778
200000 200000 99552 43000 342552
60448 74000 334448
A%%$+= 342552;25000 : 13.70 ,$" -)"$(& +*!" /!<" F)#)%/)# 334448;40000 : 8.36 ,$" -)"$(& +*!" /!<"
7-21
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
E'$"()%$ 7.24 1. R$($))# 0.2000
S<*"$ !!&*$.................................. N<$" ! "$($))# !"-$"%.............
D)"$(& !$"/$*- (!%&...... A++!(*&$ G$#$"*+ F*(&!"= *.......... R$($))# .................... T!&*+.................................
A%%$+= 0.4000 0.6222
F)#)%/)# 0.4000 0.3778
G$#$"*+ F*(&!"=
R$($))#
A%%$+=
F)#)%/)#
400000
160000
43000
74000
400000 0 0
80000 240000 0
160000 149328 352328
160000 90672 324672
*
R$($))# : 0.2 400000 : 80000 A%%$+= : 0.4 400000 : 160000 F)#)%/)# : 0.4 400000 : 160000 A%%$+= : 0.6222 240000 : 149328 F)#)%/)# : 0.3778 240000 : 90672 2.
A%%$+= 352328;25000 : 14.09 ,$" -)"$(& +*!" /!<" F)#)%/)# 324672;40000 : 8.12 ,$" -)"$(& +*!" /!<"
E'$"()%$ 7.25 1. @*"+!#................. S$+$#$................ P+)($#$............... C!"%!+................. T!&*+..............
U#)&% 1400 2600 2500 3500 10000
2. @*"+!#........... S$+$#$........... P+)($#$.......... C!"%!+........... T!&*+.........
U#)&% 1400 2600 2500 3500
P$"($#& 0.1400 0.2600 0.2500 0.3500
J!)#& C!%& 127400 127400 127400 127400
:
A++!(*&$- J!)#& C!%& 17836 33124 31850 44590 127400
$)/& $)/&$J!)#& A++!(*&$F*(&!" : U#)&% P$"($#& C!%& :J!)#& C!%& 1.0 1400 0.0733 127400 9338 2.0 5200 0.2723 127400 34691 1.5 3750 0.1963 127400 25009 2.5 8750 0.4581 127400 58362 19100 127400
7-22
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
E'$"()%$ 7.26 @*"+!#....... S$+$#$....... P+)($#$...... C!"%!+....... T!&*+.....
U#)&% 1400 2600 2500 3500 10000
P")($ *& S,+)&O 15 20 26 35
M*">$& *+<$ *& S,+)&O 21000 52000 65000 122500 260500
J!)#& P$"($#& C!%& 0.0806 127400 0.1996 127400 0.2495 127400 0.4702 127400
A++!(*&$C!%& 10268 25429 31786 59903 127386
D!$% #!& $<*+ 127400 -<$ &! "!<#-)# ! ,$"($#&%.
E'$"()%$ 7.27 1. U#)&% O$"%....... 14000 U#-$"%..... 36000 T!&*+......
E$#&<*+ P")($ M*">$& *+<$ 2.00 28000 3.14 113040
S$,*"*+$ C!%&% 18000 23040
J!)#& (!%&............................................................ P$"($#& ! /=,!&/$&)(*+ *">$& *+<$........... A++!(*&$- !)#& (!%&............................................ 2.
H=,!&/$&)(*+ M*">$& *+<$ 10000 90000 100000
O$"% 50000 0.10 5000
*+<$ ! !$"% *& %,+)&! 14000 1.80......
25200
*+<$ ! !$"% /$# ,"!($%%$- <"&/$"........... L$%% F<"&/$" ,"!($%%)# (!%&........................ I#("$$#&*+ *+<$ ! <"&/$" ,"!($%%)#.........
28000 18000 10000
P$"($#& 0.10 0.90
U#-$"% 50000 0.90 45000
O$"% %/!<+- not $ ,"!($%%$- <"&/$" *% &/$"$ )++ $ 15200 !"$ ,"!)& ) %!+- *& %,+)&!.
7-23
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
CPATPE EERCISES E'$"()%$ 7.28 -. A++!(*&)!# "*&)!% P"!-<()# D$,*"&$#& 1 M*(/)#$ /!<"% 8000;8000 ? 2000 : 0.8 D)"$(& +*!" /!<"% 12000;12000 ? 12000 : 0.5
P"!-<()# D$,*"&$#& 2 2000;8000 ? 2000 : 0.2 12000;12000 ? 12000 : 0.5
C!%& *++!(*&$- &! P"!-<()# D$,*"&$#& 1 0.8 168000 ? 0.5 280000 : 274400
E'$"()%$ 7.29 .
E'$"()%$ 7.30 (. C/*")# "*&$ : 238000 ? 35000;14000 : 19.50 A!<#& (/*"$- &! <%)# -$,*"&$#& : 19.50 1350 : 26325
E'$"()%$ 7.31 -. F*")(*&)# !$"/$*- "*&$ : 140000;20000 : 7;*(/)#$ /!<" A%%$+= !$"/$*- "*&$ : 64000;20000 : 3.20;-)"$(& +*!" /!<" F)#)%/)# !$"/$*- "*&$ : 74880;18000 : 4.16;-)"$(& +*!" /!<" P")$ (!%& O$"/$*- *++!(*&$- "! F*")(*&)# 7 400 A%%$+= 3.20 100 F)#)%/)# 4.16 20 T!&*+ (!%& ! J! 13198
6700.00 280.00 320.00 83.20
683.20 7383.20
E'$"()%$ 7.32 *.
7-24
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
PRO@LEMS
P"!+$ 7.33 1. R*&)! !" )'$- (!%&%.......... F)'$- (!%&%........................... *")*+$ (!%&%....................
<* 0.65
@$"#*+)++! 0.35
104000 169000 273000
56000 91000 147000
<* : 2600;4000 : 0.65 @$"#*+)++! : 1400;4000 : 0.35 <* : 65 2600 @$"#*+)++! : 65 1400 2.
C!%&)# !<& %$")($% %$"$% &/$ %*$ ,<",!%$% *% (!%&)# !<& &*#)+$ ,"!-<(&% $.. ,")()# ,"!)&*)+)&= *#*+=%)% *#- ,$"!"*#($ $*+<*&)!#. O#($ &/$ (!%&% *"$ *++!(*&$- &! $*(/ "$$#<$,"!-<()# ($#&$" &/$# &/$ (!%&% <%& $ *%%)#$- &! )#-))-<*+ %$")($% &/"!</ &/$ <%$ ! *# !$"/$*- "*&$ !" "*&$%.
3. I &/$ ,<",!%$ )% &! (!%& !<& )#-))-<*+ %$")($% &/$# &/$ *++!(*&)!# )% )-$#&)(*+ &! &/*& )$# )# R$<)"$$#& 1. I &/$ ,<",!%$ )% !" ,$"!"*#($ $*+<*&)!# &/$# *")*+$ (!%&% $<*+ &/$ ,"$-$&$")#$- "*&$ <+&),+)$- = &/$ *(&<*+ <%*$. T/$ )'$- (!%&% *"$ *++!(*&$- &/$ %*$ *= *% $!"$. <* *")*+$ (!%&% 65 2580.................... 65 1600.................... F)'$- (!%&%.......................... 4.
@$"#*+)++!
167700 104000 271700
104000 56000 160000
T/$ *++!(*&$- (!%&% ! 431700 $"$ 3700 +!$" &/*# &/$ *(&<*+ (!%&% ! 435400 $(*<%$ &/$ ,"!-<()# -$,*"&$#&% *"$ (/*"$- *# *++!(*&)!# *%$- !# <-$&$- (!%&% "*&/$" &/*# *(&<*+ (!%&%. @<-$&$- (!%&% *"$ *++!(*&$- %! &/*& &/$ $)()$#()$% !" )#$)()$#()$% ! &/$ %$")($ ($#&$" *"$ #!& *%%)#$- &! &/$ <%$" -$,*"&$#&%.
7-25
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
P"!+$ 7.34 1.
A++!(*&)!# "*&)!% !" )'$- (!%&% <%$% #!"*+ +$$+% SLC H!<"% ! +)/& &)$............. 0.2500 N<$" ! ,*%%$#$"%....... 0.3333
R$#! 0.5000 0.5000
P!"&+*#0.2500 0.1667
*")*+$ "*&$% M*)#&$#*#($ 30000;8000 : 3.75 ,$" +)/& /!<" @**$ 64000;30000 : 2.1333 ,$" ,*%%$#$" SLC M*)#&$#*#($)'$- 0.2500 240000............... 0.5000 240000............... 0.2500 240000............... M*)#&$#*#($*")*+$ 3.75 2000....................... 3.75 4000....................... 3.75 2000....................... @**$)'$- 0.3333 150000............... 0.5000 150000............... 0.1667 150000............... @**$*")*+$ 2.1333 10000................. 2.1333 15000................. 2.1333 5000...................
R$#!
P!"&+*#-
60000 120000 60000 7500 15000 7500 49995 75000 25005 21333 32000 138828
242000
7-26
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
10667 103172
P"!+$ 7.34 2.
C!#(+<-$-
T/$ *++!(*&)!#% *"$ &/$ %*$ *% )# R$<)"$$#& 1 $'($,& *")*+$ (!%&% *"$ *%%)#$- <%)# *(&<*+ )#%&$*- ! <-$&$- *(&))&=. M*)#&$#*#($)'$-..................... M*)#&$#*#($*")*+$ 3.75 1800....................... 3.75 4200....................... 3.75 2500....................... @**$)'$-........................... @**$*")*+$ 2.1333 8000................... 2.1333 16000................. 2.1333 6000...................
SLC 60000
R$#! 120000
P!"&+*# 60000
6750 15750 49995
75000
9375 25005
17066 34133 133811
244883
12800 107180
$% *)#&$#*#($ *(&<*++= (!%& 315000 <& !#+= 271875 *% *++!(*&$-. @**$ *(&<*++= (!%& 189000 <& 213999 *% *++!(*&$-. A(&<*+ (!%&% *"$ #!& *++!(*&$- %! &/*& )#$)()$#()$% !" $)()$#()$% )++ #!& $ ,*%%$- !#.
P"!+$ 7.35 1. P"!,!"&)!# ! M*(/)#$ /!<"%...................................................... S<*"$ !!&*$..................................................... P!$" 0.6900 150000.............................................. 0.3100 150000.............................................. G$#$"*+ F*(&!"= 0.4000 160000.............................................. 0.6000 160000.............................................. D)"$(& (!%&%................................................................
P!&&$"= 0.6900 0.4000
R$&*)+ 0.3100 0.6000
103500 46500 64000 98000 265500
7-27
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
96000 56000 198500
P"!+$ 7.35
C!#(+<-$-
2. M*(/)#$ /!<"% S<*"$ !!&*$
P!$" 0.1667
D)"$(& (!%&%...................... 150000 G$#$"*+ F*(&!"= 0.1667 160000.... 26672 0.3333 160000.... 0.5000 160000.... P!$" 0.69 176672........ 121904 0.31 176672........ 54768 C!%& *&$" *++!(*&)!#....... 0
G$#$"*+ F*(&!"=
P!&&$"= 0.6900 0.3333
R$&*)+ 0.3100 0.5000
160000
98000
56000
26672 53328 80000
53328 80000 121904
0
273232
54768 190768
P!&&$"= 0.6273 0.3333
R$&*)+ 0.2818 0.5000
3. M*(/)#$ /!<"%................... S<*"$ !!&*$..................
G$#$"*+ F*(&!"= 0.0909
P!$" 0.1667
GF : 160000 ? 0.0909P P : 150000 ? 0.1667 GF GF : 160000 ? 0.0909150000 ? 0.1667 GF P : 150000 ? 0.1667176315 GF : 160000 ? 13635 ? 0.0152GF P : 150000 ? 29392 0.9848 GF : 173635 P : 179392 GF : 176315
P!&&$"= G$#$"*+ F*(&!"= 0.3333 176315...................... 0.5000 176315...................... P!$" 0.6273 179392...................... 0.2818 179392...................... D)"$(& (!%&%........................................ C!%& *&$" *++!(*&)!#.........................
R$&*)+
58766 88158 112533 98000 269299
7-28
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
50553 56000 194711
P"!+$ 7.36 1.
G$#$"*+ E#)#$$")# F*(&!"= M!+-)# A%%$+= D$,*"&$#& (!%&%................. 216000 370000 190000 80000 A++!(*&)!# ! E#)#$$")# 0.2 0.8 216000 0 43200 172800 G$#. F*(&!"= 0.875 0.125 0 370000 323750 46250 T!&*+ !$"/$*- (!%&.............. 0 0 556950 299050 D)"$(& +*!" /!<"%................. 40000 160000 O$"/$*- "*&$ ,$" DLH......... 13.92 1.87
2. E#)#$$")# G$#$"*+ F*(&!"= E#)#$$")# /!<"%... S<*"$ $$&................ 0.2000
M!+-)# 0.1667
A%%$+= 0.1667 0.7000
0.6667 0.1000
A+$"*)( $<*&)!#% !" "$+*&)!#%/), $&$$# %$")($ -$,*"&$#&% E : E#)#$$")# D$,*"&$#& GF : G$#$"*+ F*(&!"= D$,*"&$#& E :
216000 ? 0.2000 GF GF : 370000 ? 0.1667 E E :
216000 ? 0.2000370000 ? 0.1667 E E : 216000 ? 74000 ? 0.0333 E 0.9667 E : 290000 E : 299990 GF :
370000 ? 0.1667299990 GF : 420008
D)"$(& !$"/$*- (!%&%...... A++!(*&)!# ! E#)#$$")#..................... G$#$"*+ F*(&!"=............ T!&*+ !$"/$*- (!%&.......... 322004 D)"$(& +*!" /!<"%............. O$"/$*- "*&$ ,$" DLH....
E#)#$$")#
G$#$"*+ F*(&!"=
216000
370000
M!+-)#
A%%$+=
190000 80000
299990 50008 50008 200003 84002 420008294006 42001 12 0 534014 40000 13.35
7-29
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
160000 2.01
P"!+$ 7.36 3.
C!#(+<-$-
T/$ -)"$(& *++!(*&)!# $&/!- )#!"$% *#= %$")($ "$#-$"$- = !#$ %<,,!"& -$,*"&$#& &! *#!&/$". A++!(*&)!# ! $*(/ %<,,!"& -$,*"&$#&% &!&*+ (!%& )% *-$ -)"$(&+= &! &/$ ,"!-<(&)!# -$,*"&$#&%. T/$ "$(),"!(*+ *++!(*&)!# $&/!- "$(!#)$% &/*& %<,,!"& -$,*"&$#&% %$"$ !#$ *#!&/$" &/"!</ &/$ <%$ ! %)<+&*#$!<% $<*&)!#% !" +)#$*" *+$"*. T/)% *++!(*&)!# ,"!($-<"$ )% !"$ *((<"*&$ *#- %/!<+- +$*- &! $&&$" "$%<+&% /)(/ !<+- $ ! "$*&$" *+<$ &! *#*$$#&. H!$$" &/$ $&/!- )% )#"$<$#&+= <%$- )# *(&<*+ ,"*(&)($ $(*<%$ ! &/$ ,"!+$% *%%!()*&$- )&/ -$$+!,)# * !"$ (!,+$' !" -))(<+& !-$+ &! "$(!#)$ &/$ )#&$""$+*&)!#%/),% $&$$# %<,,!"& -$,*"&$#&%.
P"!+$ 7.37 1. T! O)+............ S)' O)+.............. D)%&)++*&$%........ T!&*+.............
@*""$+% 300000 170000 80000 550000
P$"($#& J!)#& C!%& : A++!(*&$- J!)#& C!%& 0.5455 10900000 5945950 0.3091 10900000 3369190 0.1455 10900000 1585950 10901090
D)$"$#($ -<$ &! "!<#-)#. 2. @*""$+% T! O)+...... 300000 S)' O)+....... 170000 D)%&)++*&$% 80000 T!&*+......
P")($ *& M*">$& *+<$ S,+)&O *& S,+)&O 45 13500000 25 4250000 14 1120000 18870000
P$"($#& 0.7154 0.2252 0.0594
J!)#& A++!(*&$C!%& C!%& 10900000 7797860 10900000 2454680 10900000 647460 10900000
7-30
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
P"!+$ 7.38 1.
R<)-!%! R!%$++ S*#&* R!%* E+ P*%! A+<<$"<$
2.
S/*"$ ! A((!<#&)# D$,*"&$#& )'$- (!%&% *%$- !# 2014 %*+$% R<)-!%! R!%$++ S*#&* R!%* E+ P*%! A+<<$"<$
420000;2800000 223000 588000;2800000 223000 364000;2800000 223000 728000;2800000 223000 700000;2800000 223000
405000;2700000 135000 540000;2700000 135000 432000;2700000 135000 648000;2700000 135000 675000;2700000 135000
*")*+$ C!%& R<)-!%! 20 1475 : 29500 R!%$++ 20 410 : 8200 S*#&* R!%* 20 620 : 12400 E+ P*%! 20 890 : 17800 A+<<$"<$ 20 450 : 9000 3.
? ? ? ? ? ?
: 33450 : 46830 : 28990 : 57980 : 55750
: 20250 : 27000 : 21600 : 32400 : 33750
F)'$- C!%& 20250 27000 21600 32400 33750
: : : : : :
T!&*+ 49750 35200 34000 50200 42750
T/$ $&/!- )# R$<)"$$#& 2 )% $&&$" $(*<%$ )& &)$% (!%& *++!(*&$- &! &/$ -")$" &/*& (*<%$% &/$ (!%&. T/<% *#*$"% !<+- $ !"$ +)>$+= &! <%$ A((!<#&)# D$,*"&$#& &)$ $)()$#&+=. T/$ $&/!- )# R$<)"$$#& 1 *%%)#% *((!<#&)# (!%&% !# &/$ *%)% ! * *")*+$ %*+$% /)(/ *= #!& $ (*<%*++= "$+*&$-. A+%! * !&$+ )&/ %&*+$ %*+$% "! =$*" &! =$*" *= %&)++ $',$")$#($ )+- +<(&<*&)!#% )# *++!(*&$- (!%& -<$ &! (/*#)# %*+$% ,*&&$"#% ! !&/$" !&$+%.
7-31
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
P"!+$ 7.39 1. *. R$+*&)$ %*+$%*+<$*&%,+)&! $&/!- M!#&/+= U#)& O<&,<& S&<-%....................... 75000 D$(!"*&)$ ,)$($%... 5000 P!%&%........................ 20000 T!&*+.....................
S*+$% R$+*&)$ P")($ S*+$% *+<$ ,$" U#)& *& S,+)&O 8 600000 60 300000 20 400000 1300000
P$"($#& A++!(*&$! J!)#& S*+$% C!%&% 46.15B 461500 23.08 230800 30.77 307700 100.00B 1000000
. P/=%)(*+ <#)&% !+<$ $&/!- *& %,+)&!
S&<-%....................... D$(!"*&)$ ,)$($%... P!%&%........................ T!&*+.....................
U#)&% 75000 5000 20000 100000
P$"($#& J!)#& C!%& : 0.750 1000000 0.050 1000000 0.200 1000000
A++!(*&$J!)#& C!%&% 750000 50000 200000 1000000
(. E%&)*&$- #$& "$*+)*+$ *+<$ $&/!-
S&<-%......................... D$(!"*&)$ ,)$($%.... P!%&%......................... T!&*+......................
F<++= P"!($%%$M!#&/+= U#)& O<&,<& 75000 4500 20000
S*+$% P")($
,$" U#)& 8 100 20
E%&)*&$N$& P$"($#& A++!(*&$R$*+)*+$ ! J!)#& *+<$ *+<$ C!%&% 600000 44.44B 444400 350000 25.93 259300 400000 29.63 296300 1350000 100.00B 1000000
5000 !#&/+= <#)&% ! !<&,<& K 10B #!"*+ %,!)+*$ : 4500 !!- <#)&% 4500 !!- <#)&% 100 : 450000 K F<"&/$" ,"!($%%)# (!%& ! 100000 : 350000
7-32
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
P"!+$ 7.39 2.
3.
C!#(+<-$-
M!#&/+= <#)& !<&,<&......................................................... L$%% N!"*+ <"&/$" ,"!($%%)# %/")#>*$................ U#)&% **)+*+$ !" %*+$...................................................
5000 500 4500
F)#*+ %*+$% *+<$ 4500 <#)&% 100 ,$" <#)&............ L$%% S*+$% *+<$ *& %,+)&!.......................................... D)$"$#&)*+ "$$#<$......................................................... L$%% F<"&/$" ,"!($%%)# (!%&%..................................... A--)&)!#*+ (!#&")<&)!# "! <"&/$" ,"!($%%)#.........
450000 300000 150000 100000 50000
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
7-33
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
P"!+$ 7.40 1.
C+$*"+= %!$ $',$#%$% ,$"&*)# &! !$# +))# )# &/$ /!<%$ /)+$ !&/$"% ,$"&*)# &! *++ $$"%. I#/!<%$ $$"% <%$ &/$ %$(!#- +!!" !%& ! &/$ !!- *#- !%& ! &/$ *")*+$ $',$#%$%. A++ $$"% <%$ &/$ )"%& +!!" *()+)&)$% !!- !" M!#-*= #)/& -)##$"% *#- ($"$*+ *#- )+> !" %#*(>%. HC@ <%& -$&$")#$ * *)" $&/!- ! *++!(*&)# &/$ (!%&% %)#($ &/$ %!"!")&= )% * #!#,"!)& $#&)&= *#- /!<%$ )++% )# &!&*+ <%& $<*+ /!<%$ (!%&%. I& )% -))(<+& &! *++!(*&$ &/$ (!%&% ,"$()%$+= &! &/$ &! &=,$% ! $$"% )$# &/$ %>$&(/= #*&<"$ ! &/$ -*&*.
2.
U%)# * $#$)&%"$($)$- *,,"!*(/ &/$ !++!)# (/*")# "*&$% )/& $ *,,+)$-. I#/!<%$ $$"% U%$ ! %$(!#- +!!" 240000 K 40000;2.................. U%$ ! )"%& +!!" 240000 K 40000;20.6................ F!!- 1.01602032................................................ *")*+$ $',$#%$%........................................................... T!&*+.............................................................................
100000 60000 38784 34800 233584
C/*")# "*&$ ,$" )#/!<%$ $$" ,$" =$*" 233584;60 : 3893 C!%& ,$" $*+ 40000;V40 ? 60 20 32W : 1.01 O<&!/!<%$ $$"% U%$ ! )"%& +!!" 240000 K 40000;20.4................ F!!- 1.013240...................................................... T!&*+.............................................................................
40000 1293 41293
C/*")# "*&$ ,$" !<&!/!<%$ $$" ,$" =$*" 41293;40 : 1032 C@ER RESEARCH CASE 7.41 A#%$"% )++ *"=.
T/$ C!++*!"*&)$ L$*"#)# E'$"()%$ S!+<&)!#% (*# $ !<#- !# &/$ )#%&"<(&!" $%)&$ *& /&&,;;+!)#.($#*$.(!.
T/$ !++!)# ,"!+$% (*# $ *%%)#$- )&/)# C$#*$NO *#- *"$ *<&! 7-34
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible ebsite, in hole or in part.
