Jawaban Biaya Ch 7

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 departments usage of a service increases% the variable costs of the service department increase. increase. A service service department departments 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 tmentts 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 maes 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 ts s spie spie 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 lie liely 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 ments 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


CORNERSTONE EERCISES C!"#$"%&!#$ E'$"()%$ 7.1 1. T! T!&*+ &*+ $',$(&$$',$(&$- (!%&% ! &/$ M*)#& M*)#&$#* $#*#($ #($ D$,*"& D$,*"&$# $#& & F)'$F)'$- (!%&% (!%&%... ...... ..... ..... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ..... ..... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ... *")* ")*+$ +$ (!%& (!%&% % 1. 1.35 35  220 22000 00 *)# *)#&$ &$#* #*#( #($ $ /"%. /"%... .... .... .... .... .... .... .... .... .... .... ..... ... T!&*+ (!%&% (!%&%... ...... ...... ...... ...... ..... ..... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ...... ..... ..

649 64900 00 297 29700 00 946 94600 00

S)#+$ (/*")# "*&$ : 94600;22000 : 4.30 ,$" *)#&$#*#($ /!<" 2. C/*"$ *%$*%$- !# *(&<*+ *(&<*+ <%*$ : C/*")# C/*")# "*&$ "*&$  A(&<*+ A(&<*+ *)#&$#*#($ *)#&$#*#($ /!<"% /!<"% A%%$+= D$,*"&$#& (/*"$ : 4.30  3960 : 17028 F*")(*&)# D$,*"&$#& (/*"$ : 4.30  6800 : 29240 P*(>*)# D$,*"&$#& (/*"$ : 4.30  10000 : 43000 T!&*+ *!<#& (/*"$- : 17028 ? 29240 ? 43000 : 89268 3. A%%$ A%%$+= += D$,*"& D$,*"&$#& $#& (/*" (/*"$ $ : 4.30  4000 4000 : 17200 17200 F*")(*&)# D$,*"&$#& (/*"$ : 4.30  6800 : 29240 P*(>*)# D$,*"&$#& (/*"$ : 4.30  10000 : 43000 T!&*+ *!<#& (/*"$- : 17200 ? 29240 ? 43000 : 89440

C!"#$"%&!#$ E'$"()%$ 7.2 1. *")* *")*+$ +$ "*&$ "*&$ : 1.35 ,$" ,$" *)#&$# *)#&$#*#( *#($ $ /!<" /!<" T/$ )'$- *++!(*&)!# )% (*+(<+*&$- !" $*(/ -$,*"&$#& *%$- !# <-$&$,$*> !#&/ <%*$

D$,* D$,*"& "&$ $#& #& A%%$+=..................... F*")(*&)#.................. P*(>*)#................... T!&*+.............................

P$*> N<$" ! H!< H!<"%

P$"($ $"($#& #&

390 1300 910 2600

15B 50 35 100B

@<-$&$F)'$ F)'$- C!%& C!%&

A++!(*&$F)'$ F)'$- C!%& C!%&

64900 64900 64900

 9735 32450 22715  64900

P$"($#& !" A%%$+= : 390;2600 : 0.15 !" 15B

7-3


C!"#$"%&!#$ E'$"()%$ 7.2

(!#&)#<$-

P$"($#& !" F*")(*&)# : 1300;2600 : 0.50 !" 50B P$"($#& !" P*(>*)# : 910;2600 : 0.35 !" 35B 2. D$,*"&$#& A%%$+=....... F*")(*&)#.... P*(>*)#...... T!&*+........... 3. D$,*"&$#& A%%$+=....... F*")(*&)#.... P*(>*)#...... T!&*+...........

A(&<*+ N<$" ! H!<"%

*")*+$ R*&$

*")*+$ A!<#&

F)'$A!<#&

T!&*+ C/*"$

3960 6800 10000 20760

1.35 1.35 1.35

 5346 9180 13500 28026

 9735 32450 22715 64900

15081 41630 36215 92926

A(&<*+ N<$" ! H!<"%

*")*+$ R*&$

*")*+$ A!<#&

F)'$A!<#&

T!&*+ C/*"$

4000 6800 10000 20800

1.35 1.35 1.35

 5400 9180 13500 28080

 9735 32450 22715 64900

15135 41630 36215 92980

7-4


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%%$+= : 170;80 ? 170 : 0.68 3 P"!,!"&)!# ! %<*"$ $$& )# F*")(*&)# : 5700;5700 ? 13300 : 0.30 4 P"!,!"&)!# ! %<*"$ $$& )# A%%$+= : 13300;5700 ? 13300 : 0.70 2

2.

D)"$(& (!%&% A++!(*&$ H<*# R$%!<"($% 1 G$#$"*+ F*(&!"= 2 T!&*+ *&$" *++!(*&)!#

S<,,!"& D$,*"&$#&% H<*# G$#$"*+ R$%!<"($% F*(&!"=  160000  340000 160000   0

 340000  0

P"!-<()# D$,*"&$#&% F*")(*&)# 114600

A%%$+=  93000

51200 102000 267800

108800 238000 439800

1

F*")(*&)# : 0.32  160000 : 51200 A%%$+= : 0.68  160000 : 108800 2 F*")(*&)# : 0.30  340000 : 102000 A%%$+= : 0.70  340000 : 238000 3. S)#($ #!#$ ! &/$ H<*# R$%!<"($% (!%& )% *++!(*&$- &! G$#$"*+ F*(&!"= )& -!$% #!& *&&$" /! *#= $,+!=$$% !"> )# G$#$"*+ F*(&!"=.

7-5


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%%$+= : 170;80 ? 170 : 0.68 3 P"!,!"&)!# ! %. &. )# H<*# R$%!<"($% : 1000;1000 ? 5700 ? 13300 : 0.0500 4 P"!,!"&)!# ! %. &. )# F*")(*&)# : 5700;1000 ? 5700 ? 13300 : 0.2850 5 P"!,!"&)!# ! %. &. )# A%%$+= : 13300;1000 ? 5700 ? 13300 : 0.6650 2

2.

D)"$(& (!%&% A++!(*&$ G$#$"*+ F*(&!"= 1 H<*# R$%!<"($% 2 T!&*+ *&$" *++!(*&)!#

S<,,!"& D$,*"&$#&% H<*# G$#$"*+ R$%!<"($% F*(&!"=  160000  340000 17000 177000  0

340000   0

P"!-<()# D$,*"&$#&% F*")(*&)# 114600

A%%$+=  93000

96900 56640 268140

226100 120360 439460

1

H<*# R$%!<"($% : 0.05  340000 : 17000 F*")(*&)# : 0.285  340000 : 96900 A%%$+= : 0.665  340000 : 226100 2 F*")(*&)# : 0.32  177000 : 56640 A%%$+= : 0.68  177000 : 120360 3. T=,)(*++= "!<#-)# &/$ *++!(*&)!# "*&)!% &! %)' %)#))(*#& -))&% !<+- ,"!-<($ * !"$ ,"$()%$ *++!(*&)!# ! (!%&% *#- !<+- "$-<($ "!<#-)# $""!". I# &/)% (*%$ *++ *++!(*&)!# "*&)!% (*$ !<& (+$*#+= &! &/"$$ %)#))(*#& -))&% %! "!<#-)# &! %)' !<+- *>$ #! -)$"$#($.

7-6


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%%$+= : 170;60 ? 80 ? 170 : 0.5484 4 P"!,!"&)!# ! %. &. )# H<*# R$%!<"($% : 1000;1000 ? 5700 ? 13300 : 0.0500 5 P"!,!"&)!# ! %. &. )# F*")(*&)# : 5700;1000 ? 5700 ? 13300 : 0.2850 6 P"!,!"&)!# ! %. &. )# A%%$+= : 13300;1000 ? 5700 ? 13300 : 0.6650 2. L$& HR : H<*# R$%!<"($% *#- GF : G$#$"*+ F*(&!"=. HR : 160000 ? 0.0500 GF GF : 340000 ? 0.1935 HR S!+)# !" H<*# R$%!<"($% HR : 160000 ? 0.05 GF : 160000 ? 0.05340000 ? 0.1935 HR  : 160000 ? 17000 ? 0.009675 HR 0.990325 HR : 177000 HR : 178729 S!+)# !" G$#$"*+ F*(&!"= GF : 340000 ? 0.1935 HR : 340000 ? 0.1935178729 : 374584 3.

S<,,!"& D$,*"&$#&% H<*# G$#$"*+ R$%!<"($% F*(&!"=  160000  340000

P"!-<()# D$,*"&$#&% F*")(*&)# 114600

A%%$+=  93000

D)"$(& (!%&% A++!(*&$ H<*# R$%!<"($% 1 178729 34584 46130 98015 2 G$#$"*+ F*(&!"= 18729 374584 106756 249098 T!&*+ *&$" *++!(*&)!#  0  0 267486 440113 1 G$#$"*+ F*(&!"= : 0.1935  178729 : 34584 F*")(*&)# : 0.2580  178729 : 46130 A%%$+= : 0.5484  178729 : 98015 2 H<*# R$%!<"($% : 0.05  374584 : 18729 F*")(*&)# : 0.285  374584 : 106756 A%%$+= : 0.655  374584 : 249098 4. I F*")(*&)# /*- &/$ <+> ! &/$ %<*"$ !!&*$ )& !<+- $& &/$ +*"$%& *++!(*&)!# ! G$#$"*+ F*(&!"= (!%&%. A% * "$%<+& F*")(*&)# !<+- /*$ &/$ 7-7


*!")&= ! %<,,!"& -$,*"&$#& (!%&% )#%&$*- ! A%%$+=.

C!"#$"%&!#$ E'$"()%$ 7.6 1. F*")(*&)# D$,&. !$"/$*- "*&$ : 267800;82000 : 3.27 ,$" *(/. /". "!<#-$- A%%$+= D$,&. !$"/$*- "*&$ : 439800;160000 : 2.75 ,$" DLH "!<#-$- F"! C!"#$"%&!#$ E'$"()%$ 73 %!+<&)!#. 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


 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!&*+..............................

1600 5000 8000 5400 20000

8.00B 25.00 40.00 27.00 100.00B

J!)#& C!%& A++!(*&)!# 3  18000  1440 4500 7200 4860 18000

P$"($#& !" G"*-$ A : 1600;20000 : 0.080 !" 8B P$"($#& !" G"*-$ @ : 5000;20000 : 0.25 !" 25B P$"($#& !" S+)($% : 8000;20000 : 0.40 !" 40B P$"($#& !" A,,+$%*<($ : 5400;20000 : 0.27 !" 27B 2. A$"*$ !)#& (!%& : 18000;20000 ,!<#-% : 0.90 ,$" ,!<#G"*-$ A !)#& (!%& *++!(*&)!# : 0.90  1600 : 1440 G"*-$ @ !)#& (!%& *++!(*&)!# : 0.90  5000 : 4500 S+)($% !)#& (!%& *++!(*&)!# : 0.90  8000 : 7200 A,,+$%*<($ !)#& (!%& *++!(*&)!# : 0.90  5400 : 4860 Note: E)&/$" $&/!- )$% &/$ %*$ *++!(*&)!# "$%<+&%. 3. I G"*-$ A /*- 2000 ,!<#-% *#- G"*-$ @ /*- 4600 ,!<#-% &/$# G"*-$ A !<+- "$($)$ 10 ,$"($#& 2000;20000 ! &/$ !)#& (!%& !" 1800 10B  18000 *#- G"*-$ @ !<+- "$($)$ 23 ,$"($#& 4600;20000 ! &/$ !)#& (!%& !" 4140 23B  18000. T/$"$ !<+- $ #! ),*(& !# &/$ *++!(*&)!# &! S+)($% *#- A,,+$%*<($ %)#($ &/$)" ,"!,!"&)!# ! &!&*+ ,!<#-% -)- #!& (/*#$.

7-9


C!"#$"%&!#$ E'$"()%$ 7.8 1. G"*-$% G"*-$ A G"*-$ @ S+)($% A,,+$%*<($ T!&*+

N<$" ! P!<#-%

$)/& F*(&!"

1600 5000 8000 5400

4.0 2.0 1.0 0.5

$)/&$- N<$" ! P!<#-% P$"($#& 6400 10000 8000 2700 27100

A++!(*&$J!)#& C!%&

0.2362 0.3690 0.2952 0.0996

 4252 6642 5314 1793 18001

Note: T/$ !)#& (!%& *++!(*&)!# -!$% #!& $<*+ 18000 -<$ &! "!<#-)#. 2. I &/$ G"*-$ A $)/& *(&!" )% -$("$*%$- &! 3.0 &/$# &/$ $)/&$- #<$" ! ,!<#-% !<+- -$("$*%$ = !#$!<"&/ *#- &/$ G"*-$ A *,,+$% !<+- "$($)$ * "$+*&)$+= %*++$" *!<#& ! !)#& (!%&. H!$$" &/$ *++!(*&)!# ! (!%& &! *++ !&/$" "*-$% )++ )#("$*%$ %)#($ &/$ -$("$*%$- $)/&$- ,!<#-% !" G"*-$ A *,,+$% )++ ),*(& *++ ,$"($#&*$%. T/$ !++!)# &*+$ %/!% /*& !<+/*,,$# G"*-$% G"*-$ A G"*-$ @ S+)($% A,,+$%*<($ T!&*+

N<$" ! P!<#-%

$)/& F*(&!"

1600 5000 8000 5400

3.0 2.0 1.0 0.5

$)/&$- N<$" ! P!<#-% P$"($#& 4800 10000 8000 2700 25500

0.1882 0.3922 0.3137 0.1059

A++!(*&$J!)#& C!%&  3388 7060 5647 1906  18001

Note: T/$ !)#& (!%& *++!(*&)!# -!$% #!& $<*+ 18000 -<$ &! "!<#-)#.

7-10


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!%& 1600 4.00  6400 0.4015  7227 5000 1.00 5000 0.3137 5647 8000 0.50 4000 0.2509 4516 5400 0.10 540 0.0339 610 20000  15940 18000

M*">$& *+<$ *& %,+)&! !" G"*-$ A : 1600  4.00: 6400 M*">$& *+<$ *& %,+)&! !" G"*-$ @ : 5000  1.00 : 5000 M*">$& *+<$ *& %,+)&! !" S+)($% : 8000  0.50 : 4000 M*">$& *+<$ *& %,+)&! !" A,,+$%*<($ : 5400  0.10 : 540 P$"($#& !" G"*-$ A : 6400;15940 : 0.4015 !" 40.15B P$"($#& !" G"*-$ @ : 5000;15940 : 0.3137 !" 31.37B P$"($#& !" S+)($% : 4000;15940 : 0.2509 !" 25.09B P$"($#& !" A,,+$%*<($ : 540;15940 : 0.0339 !" 3.39B G"*-$ A !)#& (!%& *++!(*&)!# : 0.4015  18000 : 7227 G"*-$ @ !)#& (!%& *++!(*&)!# : 0.3137  18000 : 5647 S+)($% !)#& (!%& *++!(*&)!# : 0.2509  18000 : 4516 A,,+$%*<($ !)#& (!%& *++!(*&)!# : 0.0339  18000 : 610 2. I &/$ ,")($ ! G"*-$ @ *,,+$% )#("$*%$% &! 1.20 ,$" ,!<#- &/$# G"*-$ @ !<+- /*$ * /)/$" *">$& *+<$ *#- !<+- "$($)$ * /)/$" ,$"($#&*$ ! !)#& (!%&. T/$ !&/$" &/"$$ "*-$% !<+- /*$ %!$/*& +!$" !)#& (!%& *++!(*&)!#%. R$%<+&% ! &/)% (/*#$ !++!

G"*-$% G"*-$ A G"*-$ @ S+)($% A,,+$%*<($ T!&*+

P")($ *& T!&*+ M*">$& P$"($#& A++!(*&$P!<#-% S,+)&O *+<$ *& ! T!&*+ J!)#& P"!-<($- ,$" ,!<#- S,+)&O M*">$& *+<$ C!%& 1600 4.00  6400 0.3778  6800 5000 1.20 6000 0.3542 6376 8000 0.50 4000 0.2361 4250 5400 0.10 540 0.0319 574 20000 16940 18000

7-11


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 LT$# T")!+ P)!$ T!&*+

2.00 5.00 6.00

0.50 1.00 1.50

1.50 4.00 4.50

3500 4000 2500

 5250 16000 11250 32500

0.1615 0.4923 0.3462

 2083 6351 4466 12900

P$"($#& !" LT$# : 5250;32500 : 0.1615 !" 16.15B P$"($#& !" T")!+ : 16000;32500 : 0.4923 !" 49.23B P$"($#& !" P)!$ : 11250;32500 : 0.3462 !" 34.62B LT$# !)#& (!%& *++!(*&)!# : 0.1615  12900 : 2083 T")!+ !)#& (!%& *++!(*&)!# : 0.4923  12900 : 6351 P)!$ !)#& (!%& *++!(*&)!# : 0.3462  12900 : 4466 2. I )& (!%& 2 &! ,"!($%% $*(/ *++!# ! T")!+ &/$ /=,!&/$&)(*+ *">$& ,")($ !<+- $ +$%% &/$ /=,!&/$&)(*+ *">$& *+<$ !<+- $ +$%% *#- T")!+ !<+"$($)$ * %*++$" *++!(*&)!# ! !)#& (!%&. T/$ !++!)# &*+$ %/!% &/$ "$%<+&% F<"&/$" H=,!&/$&)(*+ H=,!&/$&)(*+ A++!(*&$M*">$& P"!($%%)# M*">$& N<$" M*">$& J!)#& P"!-<(& P")($ C!%& P")($ ! G*++!#% *+<$ P$"($#& C!%& 1 K 2 : 3  4 : 5 LT$# 2.00 T")!+ 5.00 P)!$ 6.00 T!&*+

0.50 2.00 1.50

1.50 3.00 4.50

3500 4000 2500

 5250 12000 11250 28500

0.1842 0.4211 0.3947

P$"($#& !" LT$# : 5250;28500 : 0.1842 !" 18.42B P$"($#& !" T")!+ : 12000;28500 : 0.4211 !" 42.11B P$"($#& !" P)!$ : 11250;28500 : 0.3947 !" 39.47B LT$# !)#& (!%& *++!(*&)!# : 0.1842  12900 : 2376 T")!+ !)#& (!%& *++!(*&)!# : 0.4211  12900 : 5432 P)!$ !)#& (!%& *++!(*&)!# : 0.3947  12900 : 5092

7-12


 2376 5432 5092 12900

C!"#$"%&!#$ E'$"()%$ 7.11 1. T!&*+ "$$#<$ LT$# 2  3500.................................................... T")!+ 5  4000...................................................... P)!$ 6  2500.................................................... F<"&/$" ,"!($%%)# (!%&% LT$# 0.50  3500............................................... T")!+ 1.00  4000................................................. P)!$ 1.50  2500............................................... J!)#& ,"!($%%)# (!%&%........................................... T!&*+ "!%% *")#......................................................

 7000 20000 15000

 42000

 1750 4000 3750

9500 12900  19600

2. G"!%% *")# ,$"($#&*$ : G"!%% *")#;T!&*+ "$$#<$ : 19600;42000 : 0.4667 !" 46.67B "!<#-$- E$#&<*+ *">$& *+<$....................... L$%% G"!%% *")# *& 46.67B......... C!%& ! !!-% %!+-....................... L$%% %$,*"*+$ (!%&%........................ A++!(*&$- !)#& (!%&.......................

LT$#

T")!+

P)!$

7000 3267 3733 1750 1983

20000 9334  10666 4000  6666

15000 7001  7999 3750  4249

Note: A++!(*&$- (!%&% *"$ "!<#-$- &! &/$ #$*"$%& -!++*" %! &/$ *++!(*&$- &!&*+ )% 12898. 3. A# )#("$*%$ )# &/$ <"&/$" ,"!($%%)# (!%& ! T")!+ )++ "$-<($ &/$ "!%% *")# ,$"($#&*$ *#- )++ -$("$*%$ &/$ !)#& (!%& *++!(*&$- &! T")!+. T!&*+ "$$#<$..................................................................................... F<"&/$" ,"!($%%)# (!%&%................................................................. J!)#& ,"!($%%)# (!%&%..................................................................... T!&*+ "!%% *")#............................................................................

 42000 13500 12900  15600

G"!%% *")# ,$"($#&*$ : 15600;42000 : 0.3714 !" 37.14B "!<#-$- E$#&<*+ *">$& *+<$....................... L$%% G"!%% *")# *& 37.14B......... C!%& ! !!-% %!+-....................... L$%% %$,*"*+$ (!%&%........................ A++!(*&$- !)#& (!%&.......................

LT$# 7000 2600 4400 1750 2650

T")!+ 20000 7428  12572 8000  4572

P)!$ 15000 5571  9429 3750  5679

Note: A++!(*&$- (!%&% *"$ "!<#-$- &! &/$ #$*"$%& -!++*" %! &/$ *++!(*&$- &!&*+ )% 12901.

7-13


EERCISES E'$"()%$ 7.12 *. . (. -. $.

%<,,!"& ,"!-<()# %<,,!"& ,"!-<()# %<,,!"&

. . /. ). .

%<,,!"& %<,,!"& ,"!-<()# ,"!-<()# ,"!-<()#

>. +. . #. !.

%<,,!"& %<,,!"& %<,,!"& %<,,!"& %<,,!"&

$. . . /.

,"!-<()# %<,,!"& %<,,!"& ,"!-<()#

). .

,"!-<()# %<,,!"&

E'$"()%$ 7.13 *. . (. -.

%<,,!"& %<,,!"& ,"!-<()# ,"!-<()#

E'$"()%$ 7.14 *. . (. -. $. . . /. ).

N<$" ! $,+!=$$% S<*"$ !!&*$ P!<#-% ! +*<#-"= O"-$"% ,"!($%%$M*)#&$#*#($ /!<"% !">$N<$" ! $,+!=$$% N<$" ! &"*#%*(&)!#% ,"!($%%$M*(/)#$ /!<"% S<*"$ !!&*$

7-14


E'$"()%$ 7.15 1.

D". P!%&!# *= *#& &! (!%& &/$ (+$*#%$" !" %$$"*+ "$*%!#% &! *+<$ )#$#&!"= &! -$&$")#$ ,"!)&*)+)&= *#- &! ,+*# %*+$% *#- (!%&% !" &/$ (!)# =$*". A% +!# *% /$ %$++% "$+*&)$+= $ !&&+$% ! (+$*#%$" )& )% #!& #$($%%*"= &! *++!(*&$ *#= )#-)"$(& (!%&% &! &/$ (+$*#%$". T/$ $-)(*+ *%%)%&*#& )% ,*)- &/$ %*$ *!<#& /$&/$" %/$ )'$% &/$ (+$*#%$" !" #!&. T/$ %,*($ <%$- &! %&!"$ &/$ (+$*#%$" *&$")*+% )% %*++ *#- &/$ )#("$$#&*+ (!%& )% $"!.

2.

T/$ %)&<*&)!# /*% (/*#$- -"**&)(*++=. N! &/$ (+$*#%$" %/!<+- $ *++!(*&$- %!$ ! &/$ !)($ "$#& *% $++ *% *++ ! &/$ #$ *%%)%&*#&% %*+*"=. T/$ !)($ "$#& (!<+- $ *,,!"&)!#$- 75 ,$"($#& &! &/$ &/"$$ -!(&!"% *#- 25 ,$"($#& &! &/$ (+$*#%$" !&&+)# !,$"*&)!# )$# &/*& &/$ (+$*#%$" !,$"*&)!# &*>$% *# !)($ *#- *# $'*)#)# "!!. I& (!<+- $ *"<$- &/*& &/)% !$"%&*&$% &/$ *++!(*&)!# &! &/$ (+$*#%$" %)#($ &/$ *)&)# "!! *"$* -!$% #!& %$"$ &/$ (+$*#%$". H!$$" &/$ "$($,&)!#)%& ,"!*+= &*>$% (*++% *#!,$#% *)+ !" &/)% ,"!$(& %! !$"%&*&)# &/$ "$#& *= $ *# $*%= *= &! *-<%& !" &/)%. T/$ (!%& ,$" !&&+$ !<+- &/$# $ M*&$")*+%.......................................... L*!" 12000;40000................... O)($ "$#&...................................... T!&*+ (!%&.................................

0.50 0.30 0.38 1.18

O)($ "$#& *++!(*&)!# : 5000  12;4;40000 !&&+$% "!<#-$-.

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


E'$"()%$ 7.17 1.

S)#+$ (/*")# "*&$ : 1800 ? 1500;1000 ? 1.20 : 4.50 ,$" )& 175 ? 400 ? 100 ? 75 ? 20 ? 130 ? 100 : 1000 N<$" ! G)&% : T!&*+ 160 420 240 10 50 200 450 1530

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 1000

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 1890 1080 45 225 900 2025 6885

F)'$- A!<#&  577.50 1320.00 330.00 247.50 66.00 429.00 330.00 3300.00

A++!(*&$- )'$- *!<#& : P$"($#&  3300. *")*+$ "*&$ : 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 1530

 192 504 288 12 60 240 540 1836

F)'$T!&*+ A!<#& : C/*"$  577.50 1320.00 330.00 247.50 66.00 429.00 330.00 3300.00

7-16


 769.50 1824.00 618.00 259.50 126.00 669.00 870.00 5136.00

E'$"()%$ 7.17 C!#(+<-$- 3.

T/$ %/!,% &/*& *(&<*++= <%$ &/$ )&"*,,)# %$")($ +$%% &/*# *#&)(),*&$!<+- +)>$ &/$ %)#+$ (/*")# "*&$. T/$ %)#+$ (/*")# "*&$ *%%)#% +$%% ! &/$ )'$- (!%& &! &/$ %/!,% <%)# +$%% ! &/$ %$")($. J** J)% !"))#*++= *#&)(),*&$- /*)# 75 )&% "*,,$- ,$" !#&/ <& *(&<*++= /*- !#+= 10 )&% "*,,$-. U#-$" &/$ %)#+$ (/*")# "*&$ J** J)% ,*=% 45 <#-$" &/$ -<*+ (/*")# "*&$ )& ,*=% 259.50. T/$ -<*+ (/*")# "*&$ $&/!- )% ,"$$""$- = %/!,% &/*& <%$ &/$ %$")($ *% <(/ *% !" !"$ &/*# *#&)(),*&$-. A+*#% D"< *#- S<#-")$% /*- * <(/ "$*&$" <%$ !" &/$ %$")($ *#- !<+- $ (/*"$- 870 <#-$" &/$ -<*+ "*&$ <& 2025 <#-$" &/$ %)#+$ "*&$.

4.

D$%,)&$ &/$ (/*")# "*&$ $&/!- J$ *= $ !$"(/*")# = !$"$%&)*&)# /)% )'$- (!%&%. T/$ %,*($ <%$- = &/$ )&"*,,)# %$")($ )% !#$ ! &/"$$ *(*#& %,*($%. T/$ !,,!"&<#)&= (!%& ! <%)# )& &! "*, )&% )% $"!. U#&)+ &/$ #)#&/ %,*($ )% "$#&$- *#- &/$"$ )% *# !((<,*#& !" &/$ &$#&/ ,$"/*,% &/$ )'$- (!%& %/!<+- )#(+<-$ !#+= &/$ *$% ,*)- &! &/$ )& "*,,$"%.

E'$"()%$ 7.18 1.

A++!(*&)!# "*&)!% D$,*"&$#& A.......... D$,*"&$#& @..........

$*" 1 0.4 0.6

$*" 2 0.5 0.5

48000 72000

60000 60000

A++!(*&)!# D$,*"&$#& A.......... D$,*"&$#& @.......... 2.

T/$ *#*$" ! D$,*"&$#& @ )% #!& (!#&"!++)# /<*# "$%!<"($ (!%&% $&&$" &/*# &/$ *#*$" ! D$,*"&$#& A. T/$ *)# "$*%!# &/*& D$,*"&$#& A% *++!(*&)!# ! /<*# "$%!<"($ (!%& )#("$*%$- )% $(*<%$ D$,*"&$#& @% <%*$ -$("$*%$-.

3.

F)"%& *")*+$ *#- )'$- (!%&% %/!<+- $ *++!(*&$- %$,*"*&$+=. S$(!#- <-$&$- #!& *(&<*+ (!%&% %/!<+- $ *++!(*&$-. *")*+$ (!%&% %/!<+- $ *%%)#$- &! &/$ &! <%$" -$,*"&$#&% = <+&),+=)# &/$ <-$&$- *")*+$ (!%& ,$" /!<" = &/$ *(&<*+ /!<"% !" <-$&$- /!<"% <%$- -$,$#-)# !# /$&/$" &/$ ,<",!%$ )% ,$"!"*#($ $*+<*&)!# !" ,"!-<(& (!%&)#. F)'$(!%&% !<+- $ *%%)#$- )# ,"!,!"&)!# &! &/$ ,"*(&)(*+ !" #!"*+ *(&))&)$% ! $*(/ <%$" -$,*"&$#&.

7-17


E'$"()%$ 7.19 1.

P"!-<(& (!%&)# $*" 1 *#- $*" 2 *"$ )-$#&)(*+ D$,*"&$#& A *")*+$ (!%&% 0.25  20000. . . 0.25  20000. . . F)'$- (!%&% 0.5  100000. . . 0.5  100000. . . T!&*+ (!%&....................

2.

D$,*"&$#& @

 5000  5000 50000 50000 55000

55000

P$"!"*#($ $*+<*&)!# $*" 1 D$,*"&$#& A D$,*"&$#& @ *")*+$ (!%&% 0.25  24000. . . 0.25  36000. . . F)'$- (!%&% 0.5  100000. . . 0.5  100000. . . T!&*+ (!%&....................

 6000  9000 50000 50000 

56000

59000

$*" 2 D$,*"&$#& A D$,*"&$#& @ *")*+$ (!%&% 0.25  25000. . . 0.25  25000. . . F)'$- (!%&% 0.5  100000. . . 0.5  100000. . . T!&*+ (!%&....................

 6250  6250 50000 50000 56250

56250

7-18


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  90000............ 0.2500  90000............ G$#$"*+ F*(&!"= 0.4667  314000.......... 0.5333  314000.......... P<"(/*%)# 0.6667  167000.......... 0.3333  167000.......... T!&*+.......................................... 2.

 78900

L)<)- F$"&)+)$" 107800

67500 22500 146544 167456 111339 404283

55661  353417

D$,*"&$#&*+ !$"/$*- "*&$% P$%&)()-$ 404283;24000 : 16.85 ,$" *(/)#$ /!<" L)<)- F$"&)+)$" 353417;8000 : 44.18 ,$" *(/)#$ /!<"

7-19


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<"(/*%)#  314000  167000

P!$" D)"$(& (!%&%.................  90000 G$#$"*+ F*(&!"= 0.1250  314000 39250 39250 0.1250  314000 39250 39250 0.3500  314000 109900 0.4000  314000 125600 P<"(/*%)# 0.1000  206250 20625 20625 0.6000  206250 123750 0.3000  206250 61875 P!$" 0.7500  149875 112406 0.2500  149875 37469 T!&*+.............................  0  0  0 2.

P$%&)()-$ 0.3500 0.7500 0.6000

L)<)F$"&)+)$" 0.4000 0.2500 0.3000

P$%&)()-$  78900

L)<)F$"&)+)$" 107800

109900 125600 123750 61875 112406 424956

37469 332744

P$%&)()-$ 424956;24000 : 17.71 ,$" *(/)#$ /!<" "!<#-$- L)<)- F$"&)+)$" 332744;8000 : 41.59 ,$" *(/)#$ /!<" "!<#-$-

7-20


E'$"()%$ 7.22 1.

G$#$"*+ F*(&!"= S<*"$ !!&*$...............  N<$" ! "$($))# !"-$"%.......................... 0.10

R$($))# 0.20

A%%$+= 0.40

F)#)%/)# 0.40



0.56

0.34

R :

160000 ? 0.2 GF R : 160000 ? 0.2400000 ? 0.1 R  R : 160000 ? 80000 ? 0.02 R 0.98R : 240000 R : 244898 G$#$"*+ F*(&!"=  400000

: 400000 ? 0.1 R GF : 400000 ? 0.1244898 GF : 400000 ? 24490 GF : 424490 GF

R$($))#  160000

A%%$+=  43000

F)#)%/)#  74000

D)"$(& !$"/$*- (!%&...... A++!(*&$ G$#$"*+ F*(&!"= *.......... 424490 84898 169796 169796  R$($))# .................... 24490 244898 137143 83265 T!&*+.................................  0  0 349939 327061 * R$($))# : 0.20  424490 : 84898 A%%$+= : 0.40  424490 : 169796 F)#)%/)# : 0.40  424490 : 169796  G$#$"*+ F*(&!"= : 0.10  244898 : 24490 A%%$+= : 0.56  244898 : 137143 F)#)%/)# : 0.34  244898 : 83265 2.

D$,*"&$#&*+ "*&$% A%%$+= 349939;25000 : 14.00 ,$" -)"$(& +*!" /!<" F)#)%/)# 327061;40000 : 8.18 ,$" -)"$(& +*!" /!<"

E'$"()%$ 7K23 1. S<*"$ !!&*$....................... N<$" ! "$($))# !"-$"% G$#$"*+ F*(&!"= 0.5000  400000......... 0.5000  400000......... R$($))# 0.6222  160000......... 0.3778  160000......... D)"$(& (!%&%............................. 2.

A%%$+= 0.5000 0.6222

F)#)%/)# 0.5000 0.3778

200000 200000 99552 43000 342552

60448 74000 334448

A%%$+= 342552;25000 : 13.70 ,$" -)"$(& +*!" /!<" F)#)%/)# 334448;40000 : 8.36 ,$" -)"$(& +*!" /!<"

7-21


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)#)%/)#

 400000

 160000

 43000

 74000

400000 0  0

80000 240000  0

160000 149328 352328

160000 90672 324672

*

R$($))# : 0.2  400000 : 80000 A%%$+= : 0.4  400000 : 160000 F)#)%/)# : 0.4  400000 : 160000  A%%$+= : 0.6222  240000 : 149328 F)#)%/)# : 0.3778  240000 : 90672 2.

A%%$+= 352328;25000 : 14.09 ,$" -)"$(& +*!" /!<" F)#)%/)# 324672;40000 : 8.12 ,$" -)"$(& +*!" /!<"

E'$"()%$ 7.25 1. @*"+!#................. S$+$#$................ P+)($#$............... C!"%!+................. T!&*+..............

U#)&% 1400 2600 2500 3500 10000

2. @*"+!#........... S$+$#$........... P+)($#$.......... C!"%!+........... T!&*+.........

U#)&%  1400 2600 2500 3500

P$"($#& 0.1400 0.2600 0.2500 0.3500

 J!)#& C!%& 127400 127400 127400 127400

:

A++!(*&$- J!)#& C!%&  17836 33124 31850 44590 127400

$)/& $)/&$J!)#& A++!(*&$F*(&!" : U#)&% P$"($#&  C!%& :J!)#& C!%& 1.0 1400 0.0733 127400  9338 2.0 5200 0.2723 127400 34691 1.5 3750 0.1963 127400 25009 2.5 8750 0.4581 127400 58362 19100 127400

7-22


E'$"()%$ 7.26 @*"+!#....... S$+$#$....... P+)($#$...... C!"%!+....... T!&*+.....

U#)&% 1400 2600 2500 3500 10000

P")($ *& S,+)&O 15 20 26 35

M*">$& *+<$ *& S,+)&O  21000 52000 65000 122500 260500

J!)#& P$"($#& C!%& 0.0806 127400 0.1996 127400 0.2495 127400 0.4702 127400

A++!(*&$C!%&  10268 25429 31786 59903  127386

D!$% #!& $<*+ 127400 -<$ &! "!<#-)# ! ,$"($#&%.

E'$"()%$ 7.27 1. U#)&% O$"%....... 14000 U#-$"%..... 36000 T!&*+......

E$#&<*+ P")($ M*">$& *+<$ 2.00  28000 3.14 113040

S$,*"*+$ C!%&% 18000 23040

J!)#& (!%&............................................................  P$"($#& ! /=,!&/$&)(*+ *">$& *+<$........... A++!(*&$- !)#& (!%&............................................ 2.

H=,!&/$&)(*+ M*">$& *+<$  10000 90000 100000

O$"% 50000  0.10  5000

*+<$ ! !$"% *& %,+)&! 14000  1.80......

25200

*+<$ ! !$"% /$# ,"!($%%$- <"&/$"........... L$%% F<"&/$" ,"!($%%)# (!%&........................ I#("$$#&*+ *+<$ ! <"&/$" ,"!($%%)#.........

28000 18000 10000

P$"($#& 0.10 0.90

U#-$"% 50000  0.90  45000

O$"% %/!<+- not $ ,"!($%%$- <"&/$" *% &/$"$ )++ $ 15200 !"$ ,"!)& ) %!+- *& %,+)&!.

7-23


CPATPE EERCISES E'$"()%$ 7.28 -. A++!(*&)!# "*&)!% P"!-<()# D$,*"&$#& 1 M*(/)#$ /!<"% 8000;8000 ? 2000 : 0.8 D)"$(& +*!" /!<"% 12000;12000 ? 12000 : 0.5

P"!-<()# D$,*"&$#& 2 2000;8000 ? 2000 : 0.2 12000;12000 ? 12000 : 0.5

C!%& *++!(*&$- &! P"!-<()# D$,*"&$#& 1 0.8  168000 ? 0.5  280000 : 274400

E'$"()%$ 7.29 .

E'$"()%$ 7.30 (. C/*")# "*&$ : 238000 ? 35000;14000 : 19.50 A!<#& (/*"$- &! <%)# -$,*"&$#& : 19.50  1350 : 26325

E'$"()%$ 7.31 -. F*")(*&)# !$"/$*- "*&$ : 140000;20000 : 7;*(/)#$ /!<" A%%$+= !$"/$*- "*&$ : 64000;20000 : 3.20;-)"$(& +*!" /!<" F)#)%/)# !$"/$*- "*&$ : 74880;18000 : 4.16;-)"$(& +*!" /!<" P")$ (!%& O$"/$*- *++!(*&$- "! F*")(*&)# 7  400 A%%$+= 3.20  100 F)#)%/)# 4.16  20 T!&*+ (!%& ! J! 13198

6700.00 280.00 320.00 83.20

683.20 7383.20

E'$"()%$ 7.32 *.

7-24


PRO@LEMS

P"!+$ 7.33 1. R*&)! !" )'$- (!%&%.......... F)'$- (!%&%........................... *")*+$ (!%&%....................

<* 0.65

@$"#*+)++! 0.35

104000 169000 273000

 56000 91000 147000

<* : 2600;4000 : 0.65 @$"#*+)++! : 1400;4000 : 0.35 <* : 65  2600 @$"#*+)++! : 65  1400 2.

C!%&)# !<& %$")($% %$"$% &/$ %*$ ,<",!%$% *% (!%&)# !<& &*#)+$ ,"!-<(&% $.. ,")()# ,"!)&*)+)&= *#*+=%)% *#- ,$"!"*#($ $*+<*&)!#. O#($ &/$ (!%&% *"$ *++!(*&$- &! $*(/ "$$#<$,"!-<()# ($#&$" &/$# &/$ (!%&% <%& $ *%%)#$- &! )#-))-<*+ %$")($% &/"!</ &/$ <%$ ! *# !$"/$*- "*&$ !" "*&$%.

3. I &/$ ,<",!%$ )% &! (!%& !<& )#-))-<*+ %$")($% &/$# &/$ *++!(*&)!# )% )-$#&)(*+ &! &/*& )$# )# R$<)"$$#& 1. I &/$ ,<",!%$ )% !" ,$"!"*#($ $*+<*&)!# &/$# *")*+$ (!%&% $<*+ &/$ ,"$-$&$")#$- "*&$ <+&),+)$- = &/$ *(&<*+ <%*$. T/$ )'$- (!%&% *"$ *++!(*&$- &/$ %*$ *= *% $!"$. <* *")*+$ (!%&% 65  2580.................... 65  1600.................... F)'$- (!%&%.......................... 4.

@$"#*+)++!

167700 104000 271700

104000 56000 160000

T/$ *++!(*&$- (!%&% ! 431700 $"$ 3700 +!$" &/*# &/$ *(&<*+ (!%&% ! 435400 $(*<%$ &/$ ,"!-<()# -$,*"&$#&% *"$ (/*"$- *# *++!(*&)!# *%$- !# <-$&$- (!%&% "*&/$" &/*# *(&<*+ (!%&%. @<-$&$- (!%&% *"$ *++!(*&$- %! &/*& &/$ $)()$#()$% !" )#$)()$#()$% ! &/$ %$")($ ($#&$" *"$ #!& *%%)#$- &! &/$ <%$" -$,*"&$#&%.

7-25


P"!+$ 7.34 1.

A++!(*&)!# "*&)!% !" )'$- (!%&% <%$% #!"*+ +$$+% SLC H!<"% ! +)/& &)$............. 0.2500 N<$" ! ,*%%$#$"%....... 0.3333

R$#! 0.5000 0.5000

P!"&+*#0.2500 0.1667

*")*+$ "*&$% M*)#&$#*#($ 30000;8000 : 3.75 ,$" +)/& /!<" @**$ 64000;30000 : 2.1333 ,$" ,*%%$#$" SLC M*)#&$#*#($)'$- 0.2500  240000............... 0.5000  240000............... 0.2500  240000............... M*)#&$#*#($*")*+$ 3.75  2000....................... 3.75  4000....................... 3.75  2000....................... @**$)'$- 0.3333  150000............... 0.5000  150000............... 0.1667  150000............... @**$*")*+$ 2.1333  10000................. 2.1333  15000................. 2.1333  5000...................

R$#!

P!"&+*#-

 60000 120000  60000 7500 15000 7500 49995 75000 25005 21333 32000 138828

242000

7-26


10667  103172

P"!+$ 7.34 2.

C!#(+<-$-

T/$ *++!(*&)!#% *"$ &/$ %*$ *% )# R$<)"$$#& 1 $'($,& *")*+$ (!%&% *"$ *%%)#$- <%)# *(&<*+ )#%&$*- ! <-$&$- *(&))&=. M*)#&$#*#($)'$-..................... M*)#&$#*#($*")*+$ 3.75  1800....................... 3.75  4200....................... 3.75  2500....................... @**$)'$-........................... @**$*")*+$ 2.1333  8000................... 2.1333  16000................. 2.1333  6000...................

SLC  60000

R$#! 120000

P!"&+*# 60000

6750 15750 49995

75000

9375 25005

17066 34133 133811

244883

12800 107180

$% *)#&$#*#($ *(&<*++= (!%& 315000 <& !#+= 271875 *% *++!(*&$-. @**$ *(&<*++= (!%& 189000 <& 213999 *% *++!(*&$-. A(&<*+ (!%&% *"$ #!& *++!(*&$- %! &/*& )#$)()$#()$% !" $)()$#()$% )++ #!& $ ,*%%$- !#.

P"!+$ 7.35 1. P"!,!"&)!# ! M*(/)#$ /!<"%...................................................... S<*"$ !!&*$..................................................... P!$" 0.6900  150000.............................................. 0.3100  150000.............................................. G$#$"*+ F*(&!"= 0.4000  160000.............................................. 0.6000  160000.............................................. D)"$(& (!%&%................................................................

P!&&$"= 0.6900 0.4000

R$&*)+ 0.3100 0.6000

 103500  46500 64000 98000 265500

7-27


96000 56000 198500

P"!+$ 7.35

C!#(+<-$-

2. M*(/)#$ /!<"% S<*"$ !!&*$

P!$"  0.1667

D)"$(& (!%&%......................  150000 G$#$"*+ F*(&!"= 0.1667  160000.... 26672 0.3333  160000.... 0.5000  160000.... P!$" 0.69  176672........ 121904 0.31  176672........ 54768 C!%& *&$" *++!(*&)!#.......  0

G$#$"*+ F*(&!"=  

P!&&$"= 0.6900 0.3333

R$&*)+ 0.3100 0.5000

160000

 98000

 56000

26672 53328 80000

53328 80000 121904



0

273232

54768 190768

P!&&$"= 0.6273 0.3333

R$&*)+ 0.2818 0.5000

3. M*(/)#$ /!<"%................... S<*"$ !!&*$..................

G$#$"*+ F*(&!"= 0.0909 

P!$"  0.1667

GF : 160000 ? 0.0909P P : 150000 ? 0.1667 GF GF : 160000 ? 0.0909150000 ? 0.1667 GF  P : 150000 ? 0.1667176315 GF : 160000 ? 13635 ? 0.0152GF P : 150000 ? 29392 0.9848 GF : 173635 P : 179392 GF : 176315

P!&&$"= G$#$"*+ F*(&!"= 0.3333  176315...................... 0.5000  176315...................... P!$" 0.6273  179392...................... 0.2818  179392...................... D)"$(& (!%&%........................................ C!%& *&$" *++!(*&)!#.........................

R$&*)+

 58766  88158 112533 98000 269299

7-28


50553 56000 194711

P"!+$ 7.36 1.

G$#$"*+ E#)#$$")# F*(&!"= D$,*"&$#& (!%&%.................  216000  370000 A++!(*&)!# ! E#)#$$")# 0.2 0.8......... 216000 0 G$#. F*(&!"= 0.875 0.125 0 370000 T!&*+ !$"/$*- (!%&..............  0  0 D)"$(& +*!" /!<"%................. O$"/$*- "*&$ ,$" DLH.........

M!+-)# 190000

A%%$+=  80000

43200 323750 556950  40000  13.92

172800 46250 299050 160000  1.87

A%%$+= 0.1667 0.7000

0.6667 0.1000

2. E#)#$$")# G$#$"*+ F*(&!"= E#)#$$")# /!<"%...  S<*"$ $$&................ 0.2000

M!+-)# 0.1667 

A+$"*)( $<*&)!#% !" "$+*&)!#%/), $&$$# %$")($ -$,*"&$#&% E : E#)#$$")# D$,*"&$#& GF : G$#$"*+ F*(&!"= D$,*"&$#& E :

216000 ? 0.2000 GF GF : 370000 ? 0.1667 E E :

216000 ? 0.2000370000 ? 0.1667 E  E : 216000 ? 74000 ? 0.0333 E 0.9667 E : 290000 E : 299990 GF :

370000 ? 0.1667299990 GF : 420008

D)"$(& !$"/$*- (!%&%...... A++!(*&)!# ! E#)#$$")#..................... G$#$"*+ F*(&!"=............ T!&*+ !$"/$*- (!%&.......... D)"$(& +*!" /!<"%............. O$"/$*- "*&$ ,$" DLH....

E#)#$$")#

G$#$"*+ F*(&!"=

M!+-)#

A%%$+=

 216000

 370000

190000

 80000

299990 84002  12

50008 420008  0

50008 294006 534014  40000  13.35

200003 42001 322004 160000  2.01

7-29


P"!+$ 7.36 3.

C!#(+<-$-

T/$ -)"$(& *++!(*&)!# $&/!- )#!"$% *#= %$")($ "$#-$"$- = !#$ %<,,!"& -$,*"&$#& &! *#!&/$". A++!(*&)!# ! $*(/ %<,,!"& -$,*"&$#&% &!&*+ (!%& )% *-$ -)"$(&+= &! &/$ ,"!-<(&)!# -$,*"&$#&%. T/$ "$(),"!(*+ *++!(*&)!# $&/!- "$(!#)$% &/*& %<,,!"& -$,*"&$#&% %$"$ !#$ *#!&/$" &/"!</ &/$ <%$ ! %)<+&*#$!<% $<*&)!#% !" +)#$*" *+$"*. T/)% *++!(*&)!# ,"!($-<"$ )% !"$ *((<"*&$ *#- %/!<+- +$*- &! $&&$" "$%<+&% /)(/ !<+- $ ! "$*&$" *+<$ &! *#*$$#&. H!$$" &/$ $&/!- )% )#"$<$#&+= <%$- )# *(&<*+ ,"*(&)($ $(*<%$ ! &/$ ,"!+$% *%%!()*&$- )&/ -$$+!,)# * !"$ (!,+$' !" -))(<+& !-$+ &! "$(!#)$ &/$ )#&$""$+*&)!#%/),% $&$$# %<,,!"& -$,*"&$#&%.

P"!+$ 7.37 1. T! O)+............ S)' O)+.............. D)%&)++*&$%........ T!&*+.............

@*""$+% 300000 170000 80000 550000

P$"($#&  J!)#& C!%& : A++!(*&$- J!)#& C!%& 0.5455 10900000  5945950 0.3091 10900000 3369190 0.1455 10900000 1585950 10901090

D)$"$#($ -<$ &! "!<#-)#. 2. @*""$+% T! O)+...... 300000 S)' O)+....... 170000 D)%&)++*&$% 80000 T!&*+......

P")($ *& M*">$& *+<$ S,+)&O *& S,+)&O 45 13500000 25 4250000 14 1120000 18870000

P$"($#& 0.7154 0.2252 0.0594

J!)#& A++!(*&$C!%& C!%& 10900000 7797860 10900000 2454680 10900000 647460 10900000

7-30


P"!+$ 7.38 1.

R<)-!%! R!%$++ S*#&* R!%* E+ P*%! A+<<$"<$

2.

S/*"$ ! A((!<#&)# D$,*"&$#& )'$- (!%&% *%$- !# 2014 %*+$% R<)-!%! R!%$++ S*#&* R!%* E+ P*%! A+<<$"<$

420000;2800000  223000 588000;2800000  223000 364000;2800000  223000 728000;2800000  223000 700000;2800000  223000

405000;2700000  135000 540000;2700000  135000 432000;2700000  135000 648000;2700000  135000 675000;2700000  135000

*")*+$ C!%& R<)-!%! 20  1475 : 29500 R!%$++ 20  410 : 8200 S*#&* R!%* 20  620 : 12400 E+ P*%! 20  890 : 17800 A+<<$"<$ 20  450 : 9000 3.

? ? ? ? ? ?

: 33450 : 46830 : 28990 : 57980 : 55750

: 20250 : 27000 : 21600 : 32400 : 33750

F)'$- C!%& 20250 27000 21600 32400 33750

: : : : : :

T!&*+ 49750 35200 34000 50200 42750

T/$ $&/!- )# R$<)"$$#& 2 )% $&&$" $(*<%$ )& &)$% (!%& *++!(*&$- &! &/$ -")$" &/*& (*<%$% &/$ (!%&. T/<% *#*$"% !<+- $ !"$ +)>$+= &! <%$ A((!<#&)# D$,*"&$#& &)$ $)()$#&+=. T/$ $&/!- )# R$<)"$$#& 1 *%%)#% *((!<#&)# (!%&% !# &/$ *%)% ! * *")*+$ %*+$% /)(/ *= #!& $ (*<%*++= "$+*&$-. A+%! * !&$+ )&/ %&*+$ %*+$% "! =$*" &! =$*" *= %&)++ $',$")$#($ )+- +<(&<*&)!#% )# *++!(*&$- (!%& -<$ &! (/*#)# %*+$% ,*&&$"#% ! !&/$" !&$+%.

7-31


P"!+$ 7.39 1. *. R$+*&)$ %*+$%*+<$*&%,+)&! $&/!- M!#&/+= U#)& O<&,<& S&<-%....................... 75000 D$(!"*&)$ ,)$($%... 5000 P!%&%........................ 20000 T!&*+.....................

S*+$% R$+*&)$ P")($ S*+$% *+<$ ,$" U#)& *& S,+)&O  8  600000 60 300000 20 400000 1300000

P$"($#& A++!(*&$! J!)#& S*+$% C!%&% 46.15B  461500 23.08 230800 30.77 307700 100.00B 1000000

. P/=%)(*+ <#)&% !+<$ $&/!- *& %,+)&!

S&<-%....................... D$(!"*&)$ ,)$($%... P!%&%........................ T!&*+.....................

U#)&% 75000 5000 20000 100000

P$"($#&  J!)#& C!%& : 0.750 1000000 0.050 1000000 0.200 1000000

A++!(*&$J!)#& C!%&%  750000 50000 200000 1000000

(. E%&)*&$- #$& "$*+)*+$ *+<$ $&/!-

S&<-%......................... D$(!"*&)$ ,)$($%.... P!%&%......................... T!&*+......................

F<++= P"!($%%$M!#&/+= U#)& O<&,<& 75000 4500 20000

S*+$% P")($

,$" U#)&  8 100 20

E%&)*&$N$& P$"($#& A++!(*&$R$*+)*+$ ! J!)#& *+<$ *+<$ C!%&%  600000 44.44B  444400 350000 25.93 259300 400000 29.63 296300 1350000 100.00B  1000000

5000 !#&/+= <#)&% ! !<&,<& K 10B #!"*+ %,!)+*$ : 4500 !!- <#)&% 4500 !!- <#)&%  100 : 450000 K F<"&/$" ,"!($%%)# (!%& ! 100000 : 350000

7-32


P"!+$ 7.39 2.

3.

C!#(+<-$-

M!#&/+= <#)& !<&,<&......................................................... L$%% N!"*+ <"&/$" ,"!($%%)# %/")#>*$................ U#)&% **)+*+$ !" %*+$...................................................

5000 500 4500

F)#*+ %*+$% *+<$ 4500 <#)&%  100 ,$" <#)&............ L$%% S*+$% *+<$ *& %,+)&!.......................................... D)$"$#&)*+ "$$#<$......................................................... L$%% F<"&/$" ,"!($%%)# (!%&%..................................... A--)&)!#*+ (!#&")<&)!# "! <"&/$" ,"!($%%)#.........

450000 300000 150000 100000  50000

A%%<)# S!#)*- S*)++ I#(. *##!<#($% &/*& )# %)' !#&/% )& )++ %$++ &/$ "!</(<& ,"!-<(& *& %,+)&! -<$ &! )#("$*%)# (!,$&)&)$ ,"$%%<"$ *& +$*%& &/"$$ &=,$% ! +)>$+= $/*)!" &/*& )++ $ -$!#%&"*&$- = &/$ %>)++$- +*!" )# &/$ ,+*#)# *#- %))# ,"!($%% )#(+<-$ &/$ !++!)# P!!"$" <*+)&= R$-<($- !&)*&)!# *#- !"*+$ J! )#%$(<")&= +$*-)# &! #!#,"!-<(&)$ $,+!=$$ &)$ %,$#& +!!>)# !" !% $+%$/$"$ M*#*$$#& *(&)!#% &/*& (!<+- ),"!$ &/)% $/*)!" )#(+<-$ &/$ !++!)# T/$ (!,*#= (!<+- ),"!$ (!<#)(*&)!# = ))# &/$ !">$"% * !"$ (!,"$/$#%)$ $',+*#*&)!# !" /= &/$ !"-$" *% (/*#$- *#- = !<&+)#)# * ,+*# !" <&<"$ !,$"*&)!# ! &/$ "$%& ! &/$ ,+*#&. T/$ (!,*#= (*# !$" )#($#&)$ !#<%$% &! *)#&*)# <*+)&= *#,"!-<(&)!# *#- *+)# "$*"-% )&/ !*+%. T/$ (!,*#= (!<+- ,"!)-$ ! "$+!(*&)!# *#- )#&$"#*+ ! &"*#%$"%.

7-33


P"!+$ 7.40 1.

C+$*"+= %!$ $',$#%$% ,$"&*)# &! !$# +))# )# &/$ /!<%$ /)+$ !&/$"% ,$"&*)# &! *++ $$"%. I#/!<%$ $$"% <%$ &/$ %$(!#- +!!" !%& ! &/$ !!- *#- !%& ! &/$ *")*+$ $',$#%$%. A++ $$"% <%$ &/$ )"%& +!!" *()+)&)$% !!- !" M!#-*= #)/& -)##$"% *#- ($"$*+ *#- )+> !" %#*(>%. HC@ <%& -$&$")#$ * *)" $&/!- ! *++!(*&)# &/$ (!%&% %)#($ &/$ %!"!")&= )% * #!#,"!)& $#&)&= *#- /!<%$ )++% )# &!&*+ <%& $<*+ /!<%$ (!%&%. I& )% -))(<+& &! *++!(*&$ &/$ (!%&% ,"$()%$+= &! &/$ &! &=,$% ! $$"% )$# &/$ %>$&(/= #*&<"$ ! &/$ -*&*.

2.

U%)# * $#$)&%"$($)$- *,,"!*(/ &/$ !++!)# (/*")# "*&$% )/& $ *,,+)$-. I#/!<%$ $$"% U%$ ! %$(!#- +!!" 240000 K 40000;2.................. U%$ ! )"%& +!!" 240000 K 40000;20.6................ F!!- 1.01602032................................................ *")*+$ $',$#%$%........................................................... T!&*+.............................................................................

100000 60000 38784 34800 233584

C/*")# "*&$ ,$" )#/!<%$ $$" ,$" =$*" 233584;60 : 3893 C!%& ,$" $*+ 40000;V40 ? 60  20  32W : 1.01 O<&!/!<%$ $$"% U%$ ! )"%& +!!" 240000 K 40000;20.4................ F!!- 1.013240...................................................... T!&*+.............................................................................

40000 1293  41293

C/*")# "*&$ ,$" !<&!/!<%$ $$" ,$" =$*" 41293;40 : 1032 C@ER RESEARCH CASE 7.41 A#%$"% )++ *"=.

T/$ C!++*!"*&)$ L$*"#)# E'$"()%$ S!+<&)!#% (*# $ !<#- !# &/$ )#%&"<(&!" $%)&$ *& /&&,;;+!)#.($#*$.(!.

T/$ !++!)# ,"!+$% (*# $ *%%)#$- )&/)# C$#*$NO *#- *"$ *<&! 7-34


Jawaban Biaya Ch 7

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