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Chapter 6

 

Annual Worth Analysis

Solutions to Problems

6.1 The estimate obtained from the three-year AW would not  be valid, because theAW calculated over one life cycle is valid only for the entire cycle, not part of thecycle. Here the asset would be used for only a part of its three-year life cycle.

6.2 -1,!A"#,1$,%& ' ( ) -1,!A"#,1$,2& ' ( * +!A",1$,2&  -1,!.211& ' ( ) -1,!.(61/& ' ( * +!.(61/&  + ) 0%66

6.%

6. AWcentrifue ) -2,!A"#,1$,6& ' %1, * ,!A",1,6&  ) -2,!.22/61& ' %1, * ,!.12/61&  ) 0-%,21

  AW belt ) -1(,!A"#,1$,& ' %, ' 26,!#",1$,2&!A"#,1$,&* 1,!A",1$,&

  ) -1(,!.%1(& ' %, ' 26,!.62&!.%1(&* 1,!.21(&

  ) 0-/%,/

  +elect centrifue.

6. AWsmall ) -1,(,!A"#,1$,12& ' 12, * 1(,!A",1$,12&  ) -1,(,!.1%& ' 12, * 1(,!.%&  ) 0-%,66

  AWlare ) -2,1,!A"#,1$,12& ' , * 21,!A",1$,12&  ) -2,1,!.1%& ' , * 21,!.%&  ) 0-%(,222

  +elect small pipeline.

6.6 AWA ) -2,,!A"#,1$,%6& ' *2,!A",1$,%6&  ) -2,,!.%%21& ' *2,!.2%21&  ) 0-66,((

  AW3 ) -2,!A"#,1$,%6& ' ,!#"A,1$,&!A"#,1$,%6&

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- 1,!#"A,1$,2&!#",1$,&!A"#,1$,%6&  ) -2,!.%%21& ' ,!(.61(&!.%%21&

- 1,!2.%16&!./2%&!.%%21&  ) 0-1/,(2%

  +elect plan 3.

6.( AW: ) -,!A"#,12$,%& ' %, * ,!A",12$,%&  ) -,!.16%& ' %, * ,!.2/6%&  ) 0-%,%6

  AW; ) -/(,!A"#,12$,%& ' 2(, * ,!A",12$,%&  ) -/(,!.16%& ' 2(, * ,!.2/6%&  ) 0-%,161

  +elect robot ; by a small marin.

6. AWA ) -2,!A"#,12$,2& ' ) -2,!./1(& ' ,

  ) 0-1,(/%

  AW3 ) -,!A"#,12$,6& ' 1  ) -,!.2%2%& ' 1  ) 0-22,

  +elect plan A.

6./

6.1 AW4 ) -,!A"#,1$,%& ' 1, * 12,!A",1$,%&  ) -,!.%(/& ' 1, * 12,!.2(/&  ) 0-2,6%

  AW< ) -6,!A"#,1$,6& ' 12, * 2,!A",1$,6&  ) -6,!.262& ' 12, * 2,!.112&  ) 0-26,%2

  +elect machine 4.

6.11 AW=  ) -16,!A"#,1$,2& ' ( * ,!A",1$,2&  ) -16,!.((& ' ( * ,!.%((&  ) 0-1%,

  AW> ) -21,!A"#,1$,& ' * 26,!A",1$,&

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  ) -21,!.26%%& ' * 26,!.16%%&  ) 0-1,1

  +elect process >.

6.12 AW? ) -2,!A"#,1$,2& ' 6  ) -2,!.(61/& ' 6  ) 0-%,2

  AW@  ) -,!A"#,1$,& ' ( * 1!A"7,1$,&B * !A",1$,&  ) -,!.%1(& ' ( * 1!1.%12&B * !.21(&  ) 0-%2,((

  +elect proCect ?.

6.1% AWland ) -11,!A"#,12$,%& '/, * 1,!A",12$,%&

  ) -11,!.16%& '/, * 1,!.2/6%&  ) 0-1%6,%%

  AWincin ) -,!A"#,12$,6& '6, * 2,!A",12$,6&  ) -,!.2%2%& '6, * 2,!.12%2%&  ) 0-22%,(((

  AWcontract ) 0-1/,

  Dse land application.

6.1 AWhot ) -!(&!%& * 2,B!A"#,$,2& '   ) -2%,!.6((& '   ) 0-1%6,22

  AWresurface ) -,!A"#,$,1& ' 2!#"A,$,&!#",$,2&!A"#,$,1&  ) -,!.1/%& ' 2!.(66&!.(%&!.1/%&  ) 0-12,1

  @esurface the road.

6.1 ind # in year 2/, move bacE to year /, and then use A" for n ) 1.

  A ) ,".1B!#",1$,2&!A",1$,1&  ) ,".1B!.16&!.62(&  ) 0 (/.(2

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6.16 AW1 ) 1,!A"#,1$,1&  ) 1,!.11&  ) 01,1

  AWF ) 1,!.1&  ) 01,

  <ifference is 01.

6.1( irst find the value of the account in year 11 and then multiply by i ) 6$.

11 ) 2,!"#,1$,11& * ,!"#,1$,/& * 1,!"A,1$,&  ) 2,!.62& * ,!%.1(/& * 1,!1%.(26&  ) 0%(1,%2

  A ) %(1,%2!.6&  ) 022,262

6.1

6.1/ AW ) -1,!.& ',!A",$,&  ) -1,!.& ',!.1(6&  ) 0-16,2%

6.2 #erpetual AW is eGual to AW over one life cycle

AW ) -6!#"A,$,2& * 1!#"7,$,2&B!#",$,2&!A"#,$,%&  ) -6!11.11& * 1!/(.6(&B!.(%&!.%&  ) 0-12,

6.21 #-1 ) 1,,!#"A,1$,11& * 1,!#"7,1$,11&  ) 1,,!6./1& * 1,!26.%/6%&  ) 0/,1%,(%

  Amt in yr 1 ) /,1%,(%!"#,1$,11&  ) /,1%,(%!2.%1&  ) 026,62,2/

  AW ) 26,62,2/!.1&  ) 02,66,2%

6.22 ind # in year '1, move to year /, and then multiply by i. Amounts are in 01.

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#-1 ) 1!#"A,12$,(& ' 1!#"7,12$,(&B!"#,12$,1&  ) 1!.6%& ' 1!11.6%&B!%.1&  ) 01.(

A ) 1.(!.12&

  ) 0126.6/

6.2% !a& AWin-house ) -%!A"#,1$,1& ' * 1 * (!A",1$,1&  ) -%!.1//2& ' * 1 * (!./2&  ) 0%.%( !0 millions&

  AWlicense ) -2!.1& '.2 * 1.  ) 01. !0 millions&

  AWcontract ) -2 * 2.  ) 0. !0 millions&

  +elect in-house option.

!b& All three options are acceptable.

FE Reie! Solutions

6.2 Answer is !b&

6.2 ind #W in year and then multiply by i.

  #W ) , * 1,!#"A,1$,1& * !2,".1&!#",1$,1&  ) , * 1,!(.661& * !2,".1&!.2%/&  ) 01(%,/1

  AW ) 1(%,/1!.1&  ) 01(,%/

  Answer is !c&

6.26 A ) ,".B!#",$,2&!A",$,%&  ) ,".B!.(%&!.%%&  ) 01%2,%(

  Answer is !d&

6.2( A ) ,".1B!#",1$,2&!A",1$,1&) ,".1B!.16&!.62(&

  ) 0662

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  Answer is !b&

6.2 9ote i ) effective 1$ per year.

  A ) 1,!"#,1$,& ' 1,!"A,1$,6&B!.1&  ) 1,!1.61& ' 1,!(.(16&B!.1&  ) 0%/

  Answer is !b&

6.2/ i"year ) !1 * .1"2&2 '1 ) 1.2$

  Answer is !d&

6.% i"year ) !1 * .1"2&2 '1 ) 1.2$

  Answer is !d&

6.%1 AW ) -,!.1& ' 1,  ) 0-/,

  Answer is !c&

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Chapter "

 

Rate o# Return Analysis$ Sin%le Alternatie

Solutions to Problems

(.1 A rate of return of '1$ means that the entire investment is lost.

(.2 3alance ) 1,!1.& ' !26%&  ) 011

(.% !a& Annual payment ) 1," * 1,!.1&B  ) 0%

!b& A ) 1,!A"#,1$,&  ) 1,!.%1(&  ) 0%1.(

(. onthly pmt ) 1,!A"#,.$,%6&  ) 1,!.6&  ) 06

  3alloon pmt ) 1,!"#,.$,6& ' 6!"A,.$,6&  ) 1,!1.%/& ' 6!6/.((&  ) 0/%,2

(.

(.6 ) -, * !1!2& * 2!& *(!1&B!#"A,i$,&  !#"A,i$,& ) %/.2

  +olve by trial and error or IJcel  i ) .$ per month !IJcel&

(.( ) -%, * !2(, ' 1,&!#"A,i$,& * !#",i$,&

  +olve by trial and error or IJcel  i ) 1(./ $ !IJcel&

(. ) -1%, ' /,!#"A,i$,& * (,!#"A,i$,& * 1!#"7,i$,&* 2%,!#",i$,&

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  +olve by trial and error or IJcel  i ) 1/.2$ !IJcel&

(./ !1, ' 1,&i ) 1,  i ) 11.1$

(.1 ) -1 ' !#"A,i$,%& - %!#"A,i$,%&!#",i$,%& * 2!#",i$,1& * %!#",i$,2&  * /!#"A,i$,&!#",i$,2&

  +olve by trial and error or IJceli ) 1.6$ !IJcel&

(.11 !a& ) -!22, * 1, * (6,&!A"#,i$,%6& * 12,!2. ' 1.& * 2  * 1,!A",i$,%6&  ) -!%11,&!A"#,i$,%6& * 1%, * 1,!A",i$,%6&

  +olve by trial and error or IJcel  i ) %.%$ per month !IJcel&

  !b& 9ominal per year ) %.%!12&  ) %/.6$ per year 

  Iffective per year ) !1 * .%/6"12&12 ' 1  ) (.6$ per year 

(.12 ) - ' 2!#"A, i$,%& * !#",i$,& * 1!#",i$,& * %!#"A,i$,&!#",i$,

  +olve by trial and error or IJceli ) .2$ per year !IJcel&

(.1% !a& ) -1,, * ,!6&!#"A,i$,%&

  +olve by trial and error or IJceli ) (.$ per year !IJcel&

!b& ) -1,, * ,!6& * 12,!/&B!#"A,i$,%& ) -1,, * !,%,&!#"A,i$,%&

+olve by trial and error or IJceli ) 1.1$ per year !IJcel&

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(.1 4ash flow tabulation is below. 9ote that both series end  at the end of month 11.

  onth %Turbo %#ower <ifference -(.// -!1.// * 1.//& -1(.//

  1 -(.// *(.//  2 -(.// -1.// - %.  % -(.// * (.//  -(.// -1.// - %.  -(.// *(.//  6 -(.// -1.// -%.  ( -(.// *(.//  -(.// -1.// -%.  / -(.// *(.//  1 -(.// -1.// - %.  11 -(.// *(.//

  !a& ) -1(.// * (.//!#",i$,1& ' %.!#",i$,2& * (.//!#",i$,%& ' %.!#",i$,&* ... * (.//!#",i$,/& ' %.!#",i$,1& * (.//!#",i$,11&

  +olve by trial and error or IJceli ) 12.2$ per month !IJcel&

  !b& 9ominal per year ) 12.2!12& ) 16.$ per year 

  Iffective ) !1 * .122&12 ' 1  ) 2/$ per year 

(.1 ) -/,!A"#,i$,2& ' .1!6& * .1!6&!1&  ) -/,!A"#,i$,2& * 1%,16

  +olve by trial and error or IJceli ) 1.%$ per month !IJcel&

(.16 ) -11, * !#"A,i$,6&!#"A,i$,6& ) 22./16(

  Dse tables or IJceli ) %./%$ per month !IJcel&

(.1( ) -21 ' 1!#",i$,1& * 1!#"A,i$,& * 6!#"7,i$,&B!#",i$,1&

  +olve by trial and error or IJceli ) 2.($ per year !IJcel&

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(.1 ) -, ' ,!#"A,i$,& '1,!#"7,i$,&B * 1,!#"A,i$,&  *1,!#"7,i$,& * ,!#"A,i$,(&!#",i$,&

  +olve by trial and error or IJcel

i ) 2.%6$ per Guarter !IJcel&  ) 2.%6!&) /.$ per year !nominal&

(.1/ ) -/, * ,!#"A,i$,& * ,!#"7,i$,&B &!#",i$,1&

  +olve by trial and error or IJceli ) .$ per year !IJcel&

(.2

(.21 !,, ' 2,&!"#, i$,& ' 2,!"A,i$,&B!i& ) 1,,  +olve by trial and error   i ) 1%.2$

(.22 8n a conventional cash flow series, there is only one sin chane in the net cash  flow. A nonconventional series has more than one sin chane.

(.2% <escartesK rule uses net cash flows while 9orstromKs criterion is based oncumulative cash flows.

(.2 !a& threeL !b& oneL !c& five

(.2 Tabulate net cash flows and cumulative cash flows.

  ?uarter IJpenses @evenue 9et 4ash low 4umulative  -2 -2 -2  1 -2 -1 -%  2 -1 1 -%  % -1 2 1 -2  -1 26 16 -  -1 2 1 *6  6 -1 1( 2 *

  ( -12 1 % *11  -1 2 -1% -2

!a& rom net cash flow column, there are two possible iM values!b& 8n cumulative cash flow column, sin starts neative but it chanes twice.

Therefore, 9orstromKs criterion is not satisfied. Thus, there may be up to two

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iM values. However, in this case, since the cumulative cash flow is neative,there is no positive rate of return value.

(.26 !a& There are two sin chanes, indicatin that there may be two real-number rate ofreturn values.

!b& ) -%, * 2,!#",i$,1& * 1,!#",i$,2& - 2!#",i$,%&  +olve by trial and error or IJcel

i ) (.%$ per year !IJcel&

(.2( !a& !b&

(.2 The net cash flow and cumulative cash flow are shown below.

  ;ear IJpenses, 0 +avins, 0 9et 4ash low, 0 4umulative, 0  -%%, -%%, -%%,

  1 -1, 1, *%, -%,  2 -, %, -2 -%2,  % -2, , *%, *%  -1%, 12, -1 *2

!a& There are four sin chanes in net cash flow, so, there are four possibleiM values.

!b& 4umulative cash flow starts neative and chanes only once. Therefore, there isonly one positive, real solution.

  ) -%%, * %!#",i$,1& - 2!#",i$,2& * %,!#",i$,%&-1!#",i$,&

  +olve by trial and error or IJceli ) 2.1$ per year !IJcel&

(.2/ 4umulative cash flow starts neative and chanes only once, so, there isonly one positive real solution.

  ) - * !#",i$,& * 2,!#",i$,& - 1,!#",i$,&

  +olve by trial and error or IJceli ) .1$ per year !IJcel&

(.% @einvestment rate refers to the interest rate that is used for funds that arereleasedfrom a proCect before the proCect is over.

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(.%1 Tabulate net cash flow and cumulative cash flow values.

  ;ear 4ash low, 0 4umulative, 0  1 - -,  2 - -1,

  % - -1,  - -2,  - -2,  6 - -%,  ( */ -21,  - -26,  / - -%1,  1 - * , *1,

!a& There are three chanes in sin in the net cash flow series, so there are three possible @N@ values. However, accordin to 9orstromKs criterion reardin

cumulative cash flow, there is only one @N@ value. !b& ove all cash flows to year 1.

  ) -!"A,i,1& * 1,!"#,i,%& * ,

  +olve for i by trial and error or IJcel

  i ) 6.%$ !IJcel&

!c& 8f IGuation (.6B is applied, all values are neative eJcept the last one. Therefore,  iK is used in all eGuations. The composite @N@ !iK& is the same as the internal

@N@ value !iM& of 6.%$ per year.

(.%2 irst, calculate the cumulative 4.

  ;ear 4ash low, 01 4umulative 4, 01  -6 -6  1 % -%  2 */  % -1 *%/  -12 *2(

  !a& The cumulative cash flow starts out neatively and chanes sin only once,  indicatin there is only one root to the eGuation.

  ) -6 * %!#",i,1& * !#",i,2& ' 1!#",i,%& ' 12!#",i,&

  +olve for i by trial and error or IJcel. 

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  i ) 2.6$ per year !IJcel&

  !b& Apply net reinvestment procedure because reinvestment rate, c, is not eGualto iM rate of 2.6$ per year

 ) -6  O L use iK  1 ) -6!1 * iK& * % 1 O L use iK  2 ) 1!1 * iK& * 2 P L use c!2 must be P because last two terms

are neative&  % ) 2!1 * .1& -1 % P L use c!% must be P because last term is

neative& ) %!1 * .1& '12

  +et  ) and solve for iK by trial and error

  1 ) -6 ' 6iK * %

  2 ) !-6 ' 6iK * %&!1 * iK& *   ) -6 - 6iK * % '6iK ' 6iK2 * %iK *  ) -6iK2 '1iK * /  % ) !-6iK2 '1iK * /&!1.1& ' 1  ) -(. iK2 '11iK * 6. ' 1  ) -(. iK2 '11iK * 6.   ) !-(. iK2 '11iK * 6.&!1.1& '12  ) -6 iK2 '1%2.%iK * %.% ' 12  ) -6 iK2 '1%2.%iK * 1.%

  +olve by Guadratic eGuation, trial and error, or spreadsheet.

  iK ) 26.6$ per year !IJcel&

(.%% Apply net reinvestment procedure.

 (.% Apply net reinvestment procedure because reinvestment rate, c, is not eGual

to iM rate of .1$ per year !from problem (.2/&

 ) -  O L use iK  1 ) -!1 * iK& *   ) - ' iK *   ) -1 ' iK 1 O L use iK  2 ) !-1 ' iK&!1 * iK&  ) -1 ' iK '1iK ' iK2

  ) -1 ' 6iK ' iK2 2 O L use iK  % ) !-1 ' 6iK ' iK2&!1 * iK&  ) -1 ' 6iK ' iK2 '1iK ' 6Ki2 ' iK%

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  ) -1 ' (iK ' 11,iK2 ' iK%  % O L use iK   ) !-1 ' (iK ' 11,iK2 ' iK%&!1 * iK& * 2,

) 1/, ' iK ' 1,iK2 ' 16,iK% - ,iK   P L use c   ) !1/, ' iK ' 1,iK2 ' 16,iK% - ,iK&!1.1& ' 1,

) 6 ' /2iK ' 2,(iK2 ' 1,iK% - ,(iK

  +et  ) and solve for iK by trial and error or spreadsheet.

  iK ) %.($ per year  (.% !a& i ) 2,!.6&"2  ) 0( every siJ months

!b& The bond is due in 22 years, so, n ) 22!2& )

(.%6 i ) 1,!.&"

  ) 02 per Guarter 

  ) -/2 * 2!#"A,i$,2& * 1,!#",i$,2&

  +olve for i by trial and error or IJcel  i ) 2.$ per Guarter !IJcel&

  9ominal i"yr ) 2.!& ) /.6$ per year 

(.%( !a& i ) ,,!.6&" ) 0(, per Guarter 

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  ) ,6, ' (,!#"A,i$,12& - ,,!#",i$,12&

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  !b& 9ominal i per year ) 1.6!&  ) 6.6$ per year 

  Iffective i per year ) !1 * .66"& '1  ) 6.(($ per year 

4hapter 6 1

PROPRIETARY MATERIAL. 5 The c7raw-Hill 4ompanies, 8nc. All rihts reserved. 9o part of this anual may bedisplayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used

 beyond the limited distribution to teachers and educators permitted by c7raw-Hill for their individual course preparation. 8f you area student usin this anual, you are usin it without permission.

8/14/2019 Ch6 and chapter 7Solutions

http://slidepdf.com/reader/full/ch6-and-chapter-7solutions 15/15

(.% i ) !.&"2) 01 per siJ months

  ) -1 * 1!#"A,i$,22& * ,!#",i$,22&

  +olve for i by trial and error or IJcel

  i ) %.1$ per siJ months !IJcel&

(.%/ ) -/2 * ,!#",i$,1&  !#",i$,1& ) .1

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(. i ) !.1&"2) 02 per siJ months

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4hapter 6 1

PROPRIETARY MATERIAL. 5 The c7raw-Hill 4ompanies, 8nc. All rihts reserved. 9o part of this anual may bedisplayed, reproduced or distributed in any form or by any means, without the prior written permission of the publisher, or used

 beyond the limited distribution to teachers and educators permitted by c7raw-Hill for their individual course preparation. 8f you area student usin this anual, you are usin it without permission.