emgt 346 homework #2 ans 5-8

8/12/2019 EMGT 346 Homework #2 Ans 5-8

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EMGT 346 HOMEWORK #2 ANSWERS

5-3P = $50 (P/A, 10%, 4) + $50 (P/G, 10%, 4)= $50 (3.170) + $50 (4.378)

= $377.40

5-6P = A1 (P/A, q, i, n)= A1 [(1 – (1.10)4 (1.15)−4)/(0.15 – 0.10)]= $200 (3.258)= $651.60

5-15P = t! "i#t &t = $'80,000 = t! *! *! = $20,000

A = t! nn* !n!"it = $200,000!!!# &# &n!nti&n &" t! &t !in n!ti! n t! !n!"it !in&iti!. A*&, #!!!# t! P &# t ti! = 0.P = –P + A (P/A, 12%, 13) + (P/, 12%, 13)= –$'80,000 + $200,000 (6.424) + $20,000 (0.22'2)= $30',384!#!"&#!, #! t! in!, P i &iti!.

5-26i &nt = (1 + (0.045/365))30 − 1 = 0.003705P = A[((1 + i )n − 1)/(i (1 + i )n)]= $3'' [((1.003705)60 − 1)/(0.003705 (1.003705)60)]= $21,430

5-32P &" &t A = $1,300P &" &t = $100 (P/A, 6%, 5) + $100 (P/G, 6%, 5)= $100 (4.212 + 7.'34)= $1,215& inii! P &" &t, &&! .

5-35P A = –$50,000 – $2,000 (P/A, '%, 10) + $',000 (P/A, '%, 10) +$10,000 (P/, '%, 10)= –$50,000 – $2,000 (6.418) + $',000 (6.418) + $10,000 (0.4224)= –$850P = –$80,000 – $1,000 (P/A, '%, 10) + $12,000 (P/A, '%, 10) +$30,000 (P/, '%, 10)= –$80,000 – $1,000 (6.418) + $12,000 (6.418) + $30,000 (0.4224)= +$3,270() 9 :&!* !! it &iti! P.() ;!*!t n** &ti&n. ! P &" :&!* A i n!ti! t!#!"&#! it i !tt!# t& &



n&tin &# *&&< "&# &#! *t!#nti!.

5-42&t! t! P &" &t "&# 25-9!# n*9i !#i&.&t! tt in &t ! t! nn* int!nn! i $100,000 !# 9!# "t!# 25 9!#. "t!# 25 9!# ** &t #! i!nti*.

;in*! ;t! &nt#ti&nP &" &t = $22,400,000 + $100,000 (P/A, 4%, 25)= $22,400,000 + $100,000 (15.622)= $23,'62,000& ;t! &nt#ti&nP &t = $14,200,000 + $75,000 (P/A, 4%, 25) + $12,600,000 (P/, 4%, 25)= $14,200,000 + $75,000 (15.622) + $12,600,000 (0.3751)= $20,0'8,000&&! t& t! &nt#ti&n.

5-45P &" &t &" 30 9!# &" !tin&!= $45,000 + $2,700 (A/P, 10%, 30) + $42,000 (P/, 10%, 10) +$42,000 (P/, 10%, 20) − $3,000 (P/, 10%, 30)= $45,000 + $2,700 ('.427) + $42,000 (0.3855) + $42,000 (0.1486) −$3,000 (0.0573)= $'2,713

P &" &t &" 30 9!# &" >ti= $54,000 + $2,850 (P/A, 10%, 30) + $4',500 (P/, 10%, 15) −$4,500 (P/, 10%, 30)= $54,000 + $2,850 ('.427) + $4',500 (0.23'4) − $4,500 (0.0573)= $'2,45'! >ti i *it*9 *&!# &t.

5-72?! 20 9!# n*9i !#i&@

A*t. A P = $1,625 (P/A, 6%, 20) − $10,000 − $10,000 (P/, 6%, 10)= $1,625 (11.470) − $10,000 − $10,000 (0.5584)= $3,055

A*t. P = $1,530 (P/A, 6%, 20) − $15,000= $1,530 (11.470) − $15,000= $2,54'

A*t. P = $1,8'0 (P/A, 6%, 20) − $20,000= $1,8'0 (11.470) − $20,000= $1,678&&! A*t!#nti! A.

5-78?in t! P :!t& t! t9 !#i& i &&n *ti*! &" t! *i! &" t!*t!#nti!. ! ! 12 9!# n ! #!!ti*it9 &" t! "*&.



A*t!#nti! AP = $6,000 (P/A, 10%, 12) + $1,000 (P/G, 10%, 12) − $10,000 −($10,000 − $1,000) [(P/, 10%, 2) + (P/, 10%, 4) + (P/, 10%, 6) +(P/, 10%, 8) + (P/, 10%, 10)]= $40,884 + $31' − $10,000 − $26,331= $4,872

A*t!#nti! P = $10,000 (P/A, 10%, 12) − $2,000 (P/, 10%, 12) − $15,000 −($15,000 + $2,000)[(P/, 10%, 3) + (P/, 10%, 6) + (P/, 10%, ')]= $68,140 − $637 − $15,000 − $2',578= $22,'25

A*t!#nti! P = $5,000 (P/A, 10%, 12) + $3,000 (P/, 10%, 12) − $12,000 −($12,000 − $3,000) [(P/, 10%, 4) + (P/, 10%, 8)]= $34,070 + $'56 − $12,000 − $10,345= $12,681&&! A*t!#nti! .

6-3 = $60 − $15 (A/G, 12%, 4)= $60 − $15 (1.35') = $3'.62

6-26i#t, &t! A@

A = ($20,000 − $4,000) (A/P, 4%, 10) + $4,000 (0.04)= $16,000 (0.1233) + $160= $2,132.80 !# !inn* !#i&&, &t! t! !qi*!nt ni"&# nn* &t@?A = A (/A, i%, n)= $2,132.80 (/A, 4%, 2)= $2,132.80 (2.040)= $4,350.'1

6-32Gi!n@P = −$150,000

A = −$2,5004 = −$20,0005 = −$45,0008 = −$10,00010 = +$30,000?A = $150,000(A/P, 5%, 10) + $2,500 + $20,000(P/, 5%, 4)(A/P, 5%, 10) +$45,000(P/, 5%, 5)(A/P, 5%, 10) + $10,000(P/, 5%, 8) (A/P, 5%, 10) –$30,000 (A/, 5%, 10)= $1',425 + $2,500 + $2,121 + $4,566 + $876 − $2,385= $27,113



6-37() ?A = $5,000 + $35,000 (A/P, 6%, 20)= $5,000 + $35,000 (0.0872)= $8,052() ;in! t! ?A &" t! n! i!*in! i *! tn t! $5,000 nn* &t &" t!!Bitin i!*in!, it &* ! &nt#t!.

6-52?A = (P − ;) (A/P, i %, n) + ;C + Ann* &t= ($2,400 − $300) (A/P, 10%, 5) + $300 (0.10) + $1,200 + $300= $2,100 (0.2638) + $30 + $1,500= $2,084?A!*!t# = ($6,000 − $600) (A/P, 10%, 10) + $600 (0.10) + $750 + $50= $5,400 (0.1627) + $60 + $800= $1,73';!*!t t! !*!t#i &t&#.

6-54Machine A?A – ?A = − i#t &t (A/P, 12%, 7)− :int!nn! D E!#tin &t + Ann* !n!"it + ;*! F*! (A/, 12%, 7)= −$15,000 (0.21'1) − $1,600 + $8,000 + $3,000 (0.0''1)= $3,411Machine B?A – ?A = − i#t &t (A/P, 12%, 10)− :int!nn! D E!#tin &t + Ann* !n!"it + ;*! F*! (A/, 12%, 10)= −$25,000 (0.1770) − $400 + $13,000 + $6,000 (0.0570)= $8,517&&! :in! t& Bii! (?A – ?A).

7-4! #t! &" #!t#n !B!! 60% & t! int!#!t t*! #! n&t !"*. = P (1 + i)n

$25,000 = $5,000 (1 + i)3

(1 + i) = ($25,000/$5,000)1/3 = 1.71i = 0.71t! &" !t#n = 71%

7-7(/A, i, 35) = 106 / 5800 = 172.414 n i !#9 *&! t& 8% "#& t*!. (Bt = 8.003%)



7-22H!# *&0 −$2231 −$2232 −$2233 −$223

4 −$2235 −$2236 +$1,0007 +$1,0008 +$1,000' +$1,00010 +$1,000! #t! &" #!t#n 9 ! &t! 9 n9 &n!nti&n* !n. En *&!# in!ti&n &n! &!#! tt ! $223 in#!! t& $1,000 in "i! 9!#.$223 = $1,000 (P/, i%, 5)(P/, i%, 5) = $223/$1,000 = 0.2230

#& int!#!t t*!, t! &" !t#n = 35%

7-40() &# t! "*& &" t! &n ! i = 6.8% / 2 = 3.4%, & (0.034) (1000) = $34 ii !inn**9 n $1,000 i i t t! !n &" t! 10 t 9!# (20t 9!#i&).P = 0 = +1000 – 34 (P/A, i, 20) – 1000 (P/, i, 20) n int!#&*tin1000 = 34 (P/A, i, 20) + 1000( P/, i, 20)t#9 i = 3%1000 =I 34 (14.877) + 1000 (0.5537)

1000 =I 505.82 + 553.7 = 10'5.52

t#9 i = 3.5%1000 =I 34 (14.212) + 1000 (0.5026)1000 =I 483.2 + 502.6 = '85.8

int!#&*tin@

i = 3% + 3.5% [(1000 – '85.8)/(10'5.5-'85.8)] = 3% + 3.5% (0.132) = 3.46%

i = 3% + (0.5%) [59.518/(59.518 +14.192)] = 3.404% (!Bt *! = 3.400%),

# = (2) (3.404%) = 6.808%, n i = (1+ 0.03404)2

– 1 = 0.06'24 &# 6.'24%.

() ! "!! i $1,000 B 0.0075 = $7.50. ;& A &#. #!!i! $1,000 – $7.50 =$''2.50.P = 0 = ''2.5 – 34 (P/A, i, 20) – 1000 (P/, i, 20) n int!#&*tini = 3% + (0.5%) [67.018/ (67.018 + 6.692)] = 3.4546% (!Bt *! = 3.453%),# = (2) (3.4546%) = 6.'0'%, n i = (1 + 0.034546)2 – 1 = 0.0702' &# 7.02'%.



7-44;!t P &" &t = P &" !n!"it$1,845 = $50 (P/A, i%, 4) + $2,242 (P/, i%, 4)

Try i = 7%450 (3.387) + $2,242 (0.762') = $1,87' J $1,845

Try i = 8%450 (3.312) + $2,242 (0.7350) = $1,813 K $1,845t! &" !t#n = 7% + (1%) [($1,87' − $1,845)/($1,87' − $1,813)] = 7.52% "&# 6 &nt&in* nn* #t! &" #!t#n = 2 (7.52%) = 15.0%qi*!nt nn* #t! &" #!t#n = (1 + 0.0752)2 − 1 = 15.6%

Performing Linear Interpolation:

(P/A, 1%, 36) i

32.871 L%21.447 M%

i = (1/2%) + (1/4%) [(32.87 − 31.68)/(32.87 − 31.45)] = 0.71%&in* >nt!#!t t! = 12 (0.71%) = 8.5%

7-53$240,000 = $65,000 (P/A, i%, 13) − $5,000 (P/G, i%, 13)Try i = 15%$65,000 (5.583) −$5,000 (23.135) = $247,220 J $240,000Try i = 18%$65,000 (4.'10) −$5,000 (18.877) = $224,465 K $240,000t! &" !t#n = 15% + 3% [($247,220 − $240,000)/($247,220 − $224,765)]= 15.'6%

7-70H!# N H N – H0 −$100 −$50 −$501 +$35 +$16.5 +$18.52 +$35 +$16.5 +$18.53 +$35 +$16.5 +$18.54 +$35 +$16.5 +$18.5E 15.0% 12.1% 17.8%

! OE &n N – H i #!t!# tn 10%. !#!"&#!, t! in#!!nt i !i#*!.;!*!t N.



7-81

() ;*! = 0.15 B $380,000 = $57,000 n "i# int!#!t #t! = 12%.H!# P#! C!! P#! –C!!0 –$380,000 –$60,000 –$320,000

1 0 –60,000 60,0002 0 –60,000 60,0003 0 –60,000 60,0004 0 –60,000 60,0005 0 –60,000 60,0006 57,000 0 57,000

P = 0 = –320,000 + 60,000 (P/A, > , 5) + 57,000 (P/A, >, 6) n int!#&*tin> = 3% + (0.5%) [ 2538 / ( 2538 + 2730 ) ] = 3.24% (*& 3.24% "#& B!*). ! > i!** !*& t! "i# int!#!t #t! &n t! &##&! &nt ($320,000) "#&*!in, & *!! t! **&!#.

() ! "i# #!!i! $65,000 &#! tn it !n &n &!#tin n int!nn!&t.H!# P#! C!! P#! – C!!0 –$380,000 –$60,000 –$320,0001 65,000 –60,000 125,0002 65,000 –60,000 125,0003 65,000 –60,000 125,0004 65,000 –60,000 1 25,0005 65,000 –60,000 125,0006 65,000 0 122,000

57,000

P = 0 = -320,000 + 125,000 (P/A, >, 5) + 122,000 (P/, >, 6) n int!#&*tin> = 30% + (5%) [ 9778 / ( 9778 + 22346 ) ] = 31.5% (31.42% "#& B!*).

*!#*9, t! itti&n n!. ! int!#!t #t! &n t! &##&! &nt i n& !**&! t! "i# int!#!t #t!, &, 9 t! **&!#. ! #t! &" #!t#n "&# t!**&!# i** *!#*9 ! *#!t "&# ti "*& n i i!n 9

P = 0 = −380,000 + 65,000 (P/A, E, 6) + 57,000 (P/, E, 6) n int!#&*tinE = 4% + (0.5%) [ 5777 / ( 5777 + 960 ) ] = 4.43% (4.43% "#& B!*).

&t! tt t! t&# "i*! t& i! #ti* !n#i& "&# & t! $65,000!n!"it n ! #!*i! i" t! **&!# i #! int! &" *!!Q

7-85

H!# A A- 0 −$',200 −$5,000 −$4,2001 +$1,850 +$1,750 +$1002 +$1,850 +$1,750 +$1003 +$1,850 +$1,750 +$100



4 +$1,850 +$1,750 −$5,000 +$100 +$5,0005 +$1,850 +$1,750 +$1006 +$1,850 +$1,750 +$1007 +$1,850 +$1,750 +$1008 +$1,850 +$1,750 +$100

;

t! &" !t#n A@ $',200 = $1,850 (P/A, i%, 5)t! &" !t#n = 11.7%@ $5,000 = $1,750 (P/A, i%, 4)t! &" !t#n = 15%

A − @ $4,200 = $100 (P/A, i%, 8) + $5,000 (P/, i%, 4) OE A- = 8.3%;!*!t A.

8-2

Compute Rates of Return A*t!#nti! N@ $100 = $31.5 (P/A, i%, 4)(P/A, i%, 4) = $100/$31.5 = 3.17EN = '.'%

A*t!#nti! H@ $50 = $16.5 (P/A, i%, 4)(P/A, i%, 4) = $50/$16.5 = 3.03EH = 12.1%

Incremental AnalysisH!# N − H

0 −$501-4 +$15

$50 = $15 (P/A, i%, 4) O EN-H = 7.7%() At :A = 6%, t! N − H in#!!nt i !i#*!. ;!*!t N.() At :A = '%, t! N − H in#!!nt i n!i#*!. ;!*!t H.() At :A = 10%, #!R!t A*t. N EN K :A. ;!*!t H.() At :A = 14%, &t *t!#nti! ! E K :A. S& n&tin.

8-6() &# t! At* &!#, t! "*& t*! iH!# !t *& (At*)0 −$6,7001 $2,5002 $2,5003 $3,500

P = −$6,700 +$2,500 (P/A, i, 2) + $3,500 (P/, i, 3) = $0



& &*! "&# i, &nt#t t*! "&**&@

i P12% +$16i $015% −$334

?! *in!# int!#&*ti&n t& !t!#in! E@E = 12% + 3% ($16 − $0)/($16 + $334) = 12.1%

() &# t! Ti9 &!#, t! "*& t*! iH!# !t *& (Ti9)0 −$16,'001 −5 $3,3006 $6,800

P = −$16,'00 + $3,300 (P/A, i%, 5) + $6,800 (P/, i%, 6)

At :A = 8% P = −$16,'00 + $3,300 (3.''3) + $6,800 (0.6302)= +$562

;in! P i &iti! t 8%, t! E J :A.

() ! in#!!nt* "*& i

H!# !t *& !t *& Si""!#!n! (Ti9) (At*) (Ti9 –At*)

0 −$16,'00 −$6,700 −$10,2001 $3,300 $2,500 +$8002 $3,300 $2,500 +$8003 $3,300 $2,500 − $6,700 +$6,5004 $3,300 $2,500 +$8005 $3,300 $2,500 +$8006 $6,800 $3,500 +$3,300

P = −$10,200 +$800(P/A, i, 5) + $5,700(P/, i, 3) + $3,300(P/, i, 6)

&t! t! OE#9 i = 6%P = −$10,200 +$800(4.212) + $5,700(0.83'6) + $3,300(0.7050)= +$282#9 i = 7%P = −$10,200 +$800(4.100) + $5,700(0.8163) + $3,300(0.6663)= −$68?in Cin!# >nt!#&*ti&n@

OE= 6% + 1 % ($282 − $0)/($282 + $68) = 6.8%! OE K :A, & &&! t! *&!# &t *t!#nti!, t! At*.



8-15

>n#!!nt* t! &" !t#n ;&*ti&n

A S − S − A − &t $1,000 $800 $600 $500 $100 $200 $400

?ni"&# $122 $20 $'7 $122 −$25 $23 $25

Ann*!n!"it

;*! $750 $500 $500 $0 $500 $0 $250F*!

&t! 10% K 0% 1.8%>n#!!nt*t! &" !t#n

! − S in#!!nt i !i#*!. !R!t S n #!tin .! − in#!!nt i n!i#*!. !R!t n #!tin .

! A − in#!!nt i n!i#*!. !R!t A n #!tin .

&n*i&n@ ;!*!t *t!#nti! .

!t P#!!nt &#t ;&*ti&n

!t P#!!nt &#t = ?ni"&# Ann* !n!"it (P/A, 8%, 8) +;*! F*! (P/, 8%, 8) – i#t &t

PA = $122 (5.747) + $750 (0.5403) − $1,000= +$106.36P = $120 (5.747) + $500 (0.5403) − $800 = +$15'.7'

P = $'7 (5.747) + $500 (0.5403) − $600 = +$227.61PS = $122 (5.747) − $500 = +$201.13

8-27

:A = 10%,n = 10 AU>G@ 0 K &n&9 K !*# K S!*B!

Δ (Economy − 0)P = −$75,000 + ($28,000 - $8,000) (P/A, i, 10) + $3,000 (P/, i, 10)

i P0 $128,0000.15 $26,120V −$75,000

i J :A, & &n&9 i !tt!# tn &in n&tin.



Δ (Regular – Economy)

P = − ($125,000 − $75,000) + [($43,000 − $28,000)− ($13,000 − $8,000)](P/A, i, 10) + ($6,'00 − $3,000) (P/, i, 10)

i P

0 $53,'000.15 $1,154V −$50,000

i J :A, & !*# i !tt!# tn &n&9.

Δ (Deluxe – Regular)

P = − ($220,000 − $125,000) + [($7',000 - $43,000)− ($38,000 − $13,000)](P/A, i, 10) + ($16,000 − $6,'00) (P/, i, 10)

i

P0 $24,1000.15 −$37,540V −$'5,000

i K :A, & S!*B! i *! !i#*! tn !*#.! &##!t &i! i t! !*# &!*.

8-39

C!!@ P9 $267 !# &nt "&# 24 &nt.P#!@ A = $',400 (A/P, 1%, 24) = $',400 (0.0471) = $442.74;*! (#!*!) *! = $4,700

() P#! #t!# tn *!! O:&nt*9 9!nt = $442.71 − $267= $175.74 O;*! *! = $4,700 − $0 = $4,700 O t! &" #!t#nP &" &t = P &" !n!"it

$175.74 (P/A, i%, 24) = $4,700(P/A, i%, 24) = $4,700/$175.74 = 26.74i = 0.'3% !# &nt

, t! iti&n* &nt*9 9!nt &" $175.74 &* 9i!* n 11.2% #t! &" #!t#n. C!in i t!#!"&#! #!"!##! t ** int!#!t #t! &! 11.2%.

() >t! tt it <! *!in &#! !i#*!@ 1. En! &! n&t !, &# &! n&t nt t& !n, t! iti&n* $175.74 !# &nt. 2. En! n <! &#! tn 11.2% #t! &" #!t#n in &t!# in!t!nt. 3. En! &! n&t ! t& ! &n!#n! &t t! #!*! *! &" t! # t t! !n &" t& 9!#.

emgt 346 homework #2 ans 5-8

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