Basics of Capital Budgeting

#HAPTER  THE *A+I#+ - #APITAL *.DETI!

(Difficulty Levels: Easy, Easy/Medium, Medium, Medium, Medium/Hard, and Hard)

PART I  !e" and Revised #arry$ver Pr$%lems and &uesti$ns Multi'le #$ice: Pr$%lems Pr$%lems NPV (const (constant ant cash cash flow flows; s; 3 year years) s) 1

.

Answer Answer: : a

Thom Thomso son n Elec Electr tric ic Sys Syste tems ms is is cons consid ider erin ing g a proje project ct tha that t has has the the foll follow owin ing g cash cash flo flow w and and WACC WACC dat data. a. What What is is the the proj projec ect' t's s NP! NP! Note Note tha that t a proj projec ect' t's s proj projec ecte ted d NP NP can can "e nega negati ti#e #e$ $ in whic which h case case it will will "e rejected. WACC % 1& (ear) Cash flows) a. ". c. d. e.

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1 -&&

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+ -&&

-*/+./+ -*1.*+ -*0.21 -*3*./0 -*2.+

NPV (const (constant ant cash cash flow flows; s; 4 year years) s) *

.

EASY EASY

Answer Answer: : c

EASY EASY

4la 4lanchf nchfor ord d Ente nterpri rprise ses s is cons consid ider erin ing g a proj projec ect t that that has has the the foll follow owin ing g cash cash flo flow w and and WACC WACC dat data. a. What What is is the the proj projec ect' t's s NP! NP! Note Note tha that t a proj projec ect' t's s proj projec ecte ted d NP NP can can "e nega negati ti#e #e$ $ in whic which h case case it will will "e rejected. WACC % 1& (ear) Cash flows) a. ". c. d. e.

& ,-1$&&&

1 -/3

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+ -/3

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-/*.10 -/20.+ -&.02 -12.& -*/.3*

Chapter 11: The Basics of Capital Budgeting

Page 107

NPV (const (constant ant cash cash flow flows; s; 5 year years) s) +

.

Answer Answer: : e

Tapl Tapley ey 5en 5enta tal l Asso Associ ciat ates es is is cons consid ider erin ing g a proje project ct tha that t has has the the foll follow owin ing g cash flow and WACC data. What is the project's NP! Note that a project's project's projected NP can "e negati#e$ in which case it will "e rejected. WACC % 1& (ear) Cash flows) a. ". c. d. e.

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1 -+&&

* -+&&

+ -+&&

/ -+&&

.

Answer: b

a. ". c. d. e.

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+ -/&

10.*& 10.0 13.1& 13. 1.&&

IRR (constant cash flows; 4 years) .

EA E ASY

4la 4lanchf nchfor ord d Ente nterpri rprise ses s is cons consid ider erin ing g a proj projec ect t that that has has the the foll follow owin ing g cash cash flow flow data data. . What What is the proj projec ect' t's s 677! 677! Note Note that that a proje project' ct's s projecte projected d 677 can "e less than the WACC 8and e#en negati# negati#e9$ e9$ in which which case it will "e rejected. (ear) Cash flows)



 -+&&

-110.3+ -1*+.1 -1*./3 -1+1.20 -1+3.*/

IRR (constant cash flows; 3 years) /

EASY EASY

Answer: 

EA E ASY

4la 4lanchf nchfor ord d Ente nterpri rprise ses s is cons consid ider erin ing g a proj projec ect t that that has has the the foll follow owin ing g cas cash flo flow data data. . What What is the the proj roject' ect's s 677! 677! Note Note that that a proj projec ect' t's s projecte projected d 677 can "e less than the WACC 8and e#en negati# negati#e9$ e9$ in which which case it will "e rejected. (ear) Cash flows) a. ". c. d. e.

Page 108

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13.30 12.13 *&.0 *1.0 *+.&1


IRR (constant cash flows; 5 years) 0

.

Answer: a

Smit Smithf hfie ield ld :oo :oods ds is is cons consid ider erin ing g a pro proje ject ct tha that t has has the the fol follo lowi wing ng cas cash h flow flow data. What is the the project project's 's 677! 677! Note that a project's projected 677 can "e less than the WACC 8and e#en negati#e9$ in which case it will "e rejected. (ear) Cash flows) a. ". c. d. e.

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.

Answer: c

a. ". c. d. e.

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yea year rs yea year rs yea year rs yea year rs yea year rs

Paybac! (nonconstant cash flows; 5 years) .

EASY

4la 4lanchf nchfor ord d Ente nterpri rprise ses s is cons consid ider erin ing g a proj projec ect t that that has has the the foll follow owin ing g cash flow flow data. What is the project's pay"ac;! (ear) Cash flows)



 -+&

**.11 **.3/ *+. */.1/ */.2+

Paybac! (constant cash flows; 3 years) 3

EA E ASY

Answer: e

EASY"#E$I%#

Tapl Tapley ey 5en 5enta tal l Asso Associ ciat ates es is is cons consid ider erin ing g a proje project ct tha that t has has the the foll follow owin ing g cash flow flow data. What is the project's pay"ac;! (ear) Cash flows) a. ". c. d. e.

*.11 *.11 *.& *.& *.31 *.31 +.& +.& +.*1 +.*1

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1 -+&&

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+ -+*&

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 -+/&

yea year rs yea year rs yea year rs yea year rs yea year rs


Page 109

NPV (&ne'e (&ne'en n cash cash flows; flows; 3 year years) s) 2

.

Answer Answer: : a

Edis Edison on Ele Elect ctri ric c Syst System ems s is cons consid ider erin ing g a proje project ct tha that t has has the the foll follow owin ing g cash flow and WACC data. What is the project's NP! Note that a project's project's projected NP can "e negati#e$ in which case it will "e rejected. WACC % 1& (ear) Cash flows) a. ". c. d. e.

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1 -/&

* -/0&

+ -/3&

-1/*.+3 -11.2 -100.1 -13+.*0 -12.2/

NPV (&ne'e (&ne'en n cash cash flows; flows; 3 year years) s) 1&

.

Answer Answer: : c

a. ". c. d. e.

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-  ./ - 2* 2*.* - 2 2.32 - 2 2./2 -1&*.0+

NPV (&ne'e (&ne'en n cash cash flows; flows; 4 year years) s) .

EASY"# EASY"#E$I E$I%# %#

7oc; 7oc;mo mont nt 7ec 7ecre reat atio ion n 6nc. 6nc. is is cons consid ider erin ing g a proj projec ect t that that has has the the fol follo lowi wing ng cash flow and WACC data. What is the project's NP! Note that a project's project's projected NP can "e negati#e$ in which case it will "e rejected. WACC % 1& (ear) Cash flows)

11


Answer Answer: : e


7yngaert
Page 110

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NPV (&ne'en cash flows; 5 years) 1*

.

Answer: b

7ichards Enterprises is considering a project that has the following cash flow and WACC data. What is the project's NP! Note that a project's projected NP can "e negati#e$ in which case it will "e rejected. WACC % 1& (ear) Cash flows) a. ". c. d. e.

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a. ". c. d. e.

Answer: 

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EASY"#E$I%#

+ -/2&

10.3+ 13.// 1.2 12.& *&.+3

IRR (&ne'en cash flows; 4 years) .

 -+&

Edison Electric Systems is considering a project that has the following cash flow data. What is the project's 677! Note that a project's projected 677 can "e less than the WACC 8and e#en negati#e9$ in which case it will "e rejected. (ear) Cash flows)

1/

/ -+

-/3.3/ -/*.&1 -/2.& -&3.2 -13.2+

IRR (&ne'en cash flows; 3 years) 1+

EASY"#E$I%#

Answer: a

EASY"#E$I%#

7oc;mont 7ecreation 6nc. is considering a project that has the following cash flow data. What is the project's 677! Note that a project's projected 677 can "e less than the WACC 8and e#en negati#e9$ in which case it will "e rejected. (ear) Cash flows)

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a. ,.1 ". ,+.// c. ,1.13 d. *.* e. +.3*


Page 111

IRR (&ne'en cash flows; 5 years) 1

.

Answer: c

Sam's Stores Enterprises is considering a project that has the following cash flow data. What is the project's 677! Note that a project's projected 677 can "e less than the WACC 8and e#en negati#e9$ in which case it will "e rejected. WACC % 1& (ear) Cash flows) a. ". c. d. e.

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a. ". c. d. e.

Answer: b

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years years years years years

$sco&nte aybac! (nonconstant cash flows; 4 years) .

 -*&

4lanchford Enterprises is considering a project that has the following cash flow and WACC data. What is the project's disco=nted pay"ac;! WACC % 1& (ear) Cash flows)

13

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1*.&& 1+.&& 1/.&& 1.&& 10.&&

$sco&nte aybac! (constant cash flows; 3 years) 10

EASY"#E$I%#

Answer: 

#E$I%#

7eynolds 4i;es is considering a project that has the following cash flow and WACC data. What is the project's disco=nted pay"ac;! WACC % 1& (ear) Cash flows) a. ". c. d. e.

Page 112

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#IRR (&ne'en cash flows; 3 years) 1

.

Answer: e

Edison Electric Systems is considering a project that has the following cash flow and WACC data. What is the project's <677! Note that a project's projected <677 can "e less than the WACC 8and e#en negati#e9$ in which case it will "e rejected. WACC % 1& (ear) Cash flows) a. ". c. d. e.

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#IRR (&ne'en cash flows; 4 years) 12

.

Answer: b

a. ". c. d. e.

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1+.++ 1/.&1 1.02 10.+ 13.1

NPV 's IRR (constant cash flows; 3 years) .

#E$I%#

7oc;mont 7ecreation 6nc. is considering a project that has the following cash flow and WACC data. What is the project's <677! Note that a project's projected <677 can "e less than the WACC 8and e#en negati#e9$ in which case it will "e rejected. WACC % 1& (ear) Cash flows)

*&

#E$I%#

Answer: 

#E$I%#

>ast month$ Wong Systems 6nc. decided to accept the project whose cash flows are shown "elow. ?owe#er$ "efore act=ally starting the project$ the :ederal 7eser#e too; actions that changed interest rates and Wong's WACC. 4y how m=ch did the change in the WACC affect the project's forecasted NP! Ass=me that the :ed action will not affect the cash flows$ and note that a project's projected NP can "e negati#e$ in which case it sho=ld "e rejected. @ld WACC % 1& New WACC %  (ear) & 1 * Cash flows) ,-1$&&& -&& -&& a. ". c. d. e.

+ -&&

- .03 - 2*.10 -1&/.2+ -11.12 -1*/.1


Page 113

Page 114


NPV 's IRR (nonconstant cash flows; 3 years) *1

.

Answer: a

The :ederal 7eser#e recently shifted its monetary policy$ ca=sing >asi; ision's WACC to change. >asi; had recently analyed the project whose cash flows are shown "elow. ?owe#er$ the C:@ wants to reconsider this and all other proposed projects in #iew of the :ed action. ?ow m=ch did the changed WACC ca=se the forecasted NP to change! Ass=me that the :ed action will not affect the cash flows$ and note that a project's projected NP can "e negati#e$ in which case it sho=ld "e rejected. @ld WACC % 1& New WACC %  (ear) & 1 * Cash flows) ,-1$&&& -&& -*& a. ". c. d. e.

+ -/&

-/3.// -2./ -0.3 -3/.10 -/.10

NPV 's IRR (s*e fferences) **

.

#E$I%#

Answer: c

#E$I%#"+AR$

Pettway 6nc. is considering Projects S and >$ whose cash flows are shown "elow. These projects are m=t=ally eBcl=si#e$ e=ally ris;y$ and not repeata"le. 6f the decision is made "y choosing the project with the higher 677$ how m=ch #al=e will "e forgone! Note that =nder some conditions choosing projects on the "asis of the 677 will ca=se -&.&& #al=e to "e lost. WACC % 1* (ear) C:S) C:>) a. ". c. d. e.

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1 -+3 -3&

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+ -+ -30

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-1.3 -*1./2 -*3.* -++.02 -+3.+2


Page 115

NPV 's IRR (fferent t,n- atterns) *+

.

Answer: e

#E$I%#"+AR$

Porter D Co. is considering Projects S and >$ whose cash flows are shown "elow. These projects are m=t=ally eBcl=si#e$ e=ally ris;y$ and not repeata"le. 6f the decision is made "y choosing the project with the higher 677$ how m=ch #al=e will "e forgone! Note that =nder some conditions choosing projects on the "asis of the 677 will ca=se -&.&& #al=e to "e lost. WACC % 1& (ear) C:S) C:>)

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1 -0& -1&&

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a. ,-0.2+ ". ,-*.*0 c. -&.&& d. -+.+1 e. -3.*

NPV 's IRR (fferent t,n- atterns) */

.

Answer: a

#E$I%#"+AR$

7itter 5ental E=ipment is considering Projects S and >$ whose cash flows are shown "elow. These projects are m=t=ally eBcl=si#e$ e=ally ris;y$ and are not repeata"le. 6f the decision is made "y choosing the project with the higher 677$ how m=ch #al=e will "e forgone! Note that =nder some conditions choosing projects on the "asis of the 677 will ca=se -&.&& #al=e to "e lost. WACC % 1&. (ear) C:S) C:>) a. ". c. d. e.

Page 11

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NPV 's #IRR (s*e fferences) *

.

Answer: 

Precision Prod=cts is considering Projects S and >$ whose cash flows are shown "elow. These projects are m=t=ally eBcl=si#e$ e=ally ris;y$ and not repeata"le. 6f the decision is made "y choosing the project with the higher <677$ how m=ch #al=e will "e forgone! Note that =nder some conditions choosing projects on the "asis of the <677 will ca=se -&.&& #al=e to "e lost. WACC % 1& (ear) C:S) C:>) a. ". c. d. e.

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1 -+3 -3*

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+ -+3 -3*

.

/ -+3 -3*

- 3.03 - .0/ - 2&.+2 - 22./ -1&3.+

NPV 's aybac! *0

#E$I%#"+AR$

Answer: 

#E$I%#"+AR$

Pettway 6nc. is considering Projects S and >$ whose cash flows are shown "elow. These projects are m=t=ally eBcl=si#e$ e=ally ris;y$ and not repeata"le. 6f the decision is made "y choosing the project with the shorter pay"ac;$ some #al=e may "e forgone. ?ow m=ch #al=e will "e lost in this instance! Note that =nder some conditions choosing projects on the "asis of the shorter pay"ac; will not ca=se #al=e to "e lost. WACC % 1+ (ear) C:S) C:>) a. ". c. d. e.

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+ -/&& -&&

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-.10 -00./* -3.32 -2.32 -20.10


Page 117

NPV 's IRR *3

.

Answer: a

7oss 6nc.'s C:@ thin;s the company sho=ld rely primarily on the NP method$ "=t the president prefers the 677$ so decisions are "ased on the 677. The C:@ wants yo= to show the president that at times decisions "ased on the 677 res=lt in a red=ction in the company's #al=e relati#e to its #al=e if the NP criterion were =sed. The C:@ then as;ed yo= to analye two projects that the company is now considering$ S and >$ whose cash flows are shown "elow. These projects are m=t=ally eBcl=si#e$ e=ally ris;y$ and not repeata"le. 6f the decision is made "y choosing the project with the higher 677$ how m=ch #al=e will 7oss "e forgoing! Note that at times the project with the higher 677 will also ha#e the higher NP$ and in these cases no #al=e will "y lost "y relying on the 677. WACC % 1& (ear) C:S) C:>) a. ". c. d. e.

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.

1 -0& -/&&

* -0& -/&&

+ -/&&

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- &.&& -1*./3 -1+2. -1/+.20 -13.&1

NPV an aybac! *

+AR$

Answer: e

+AR$

(o= m=st find the pay"ac; for a project$ and yo= ha#e misplaced some of the information that yo= were gi#en. (o= ;now that the project will generate positi#e cash flows of -0&$&&& per year at the end of each of the neBt  years$ that its NP is -3$&&&$ and that the companys WACC is 1&. What is the projects reg=lar pay"ac;! ?int) (o= m=st first find the project's cost$ then =se it to find the pay"ac;. a. ". c. d. e.

*.11 *.*3 *.+ *./ *./


Multi'le #$ice: #$nce'tual

Note to Professors: We designated most of these questions as being MEDIUM or HARD. Howeer! their diffi"u#t$ as seen b$ students wi## de%end on &'( what was dis"ussed in "#ass and &)( how #ong students hae to answer the questions. If time is not an issue! then man$ of the questions shou#d be "#assified as one not"h easier than our designation. *o! "onsider the amount of time students hae when se#e"ting questions for an e+am. A#so! it is E,-REME/ HEP0U for students to draw an NP1 %rofi#e when answering a number of the questions. We re"ommend %ointing this out in "#ass. Drawing these %rofi#es ta2es time! but it is a ne"essar$ ste% for man$ %eo%#e if the$ are to answer the questions "orre"t#$. Page 118


-his is true een for students who understand the "on"e%ts. Ran!n- ,ethos *2

.

Answer: b

Ass=me a project has normal cash flows. following statements is C@77ECT! a. ". c. d. e.

The The The The The

projects projects projects projects projects

All else e=al$ which of the

677 increases as the WACC declines. NP increases as the WACC declines. <677 is =naffected "y changes in the WACC. reg=lar pay"ac; increases as the WACC declines. disco=nted pay"ac; increases as the WACC declines.

Ran!n- ,ethos +&

.

EASY

Answer: 

EASY

Which of the following statements is C@77ECT! a. The internal rate of ret=rn method 86779 is generally regarded "y academics as "eing the "est single method for e#al=ating capital "=dgeting projects. ". The pay"ac; method is generally regarded "y academics as "eing the "est single method for e#al=ating capital "=dgeting projects. c. The disco=nted pay"ac; method is generally regarded "y academics as "eing the "est single method for e#al=ating capital "=dgeting projects. d. The net present #al=e method 8NP9 is generally regarded "y academics as "eing the "est single method for e#al=ating capital "=dgeting projects. e. The modified internal rate of ret=rn method 8<6779 is generally regarded "y academics as "eing the "est single method for e#al=ating capital "=dgeting projects.

Ran!n- ,ethos: +1

.

aybac!

Answer: 

EASY

Which of the following statements is C@77ECT! a. The reg=lar pay"ac; method recognies all cash flows o#er a projects life. ". The disco=nted pay"ac; method recognies all cash flows o#er a projects life$ and it also adj=sts these cash flows to acco=nt for the time #al=e of money. c. The reg=lar pay"ac; method was$ years ago$ widely =sed$ "=t #irt=ally no companies e#en calc=late the pay"ac; today. d. The reg=lar pay"ac; is =sef=l as an indicator of a projects li=idity "eca=se it gi#es managers an idea of how long it will ta;e to reco#er the f=nds in#ested in a project. e. The reg=lar pay"ac; does not consider cash flows "eyond the pay"ac; year$ "=t disco=nted pay"ac; o#ercomes this defect.


Page 119

Ran!n- ,ethos: +*

.

IRR

Answer: e

EASY

Which of the following statements is C@77ECT! a. @ne defect of the 677 method is that it does not ta;e acco=nt of cash flows o#er a projects f=ll life. ". @ne defect of the 677 method is that it does not ta;e acco=nt of the time #al=e of money. c. @ne defect of the 677 method is that it does consider the time #al=e of money. d. @ne defect of the 677 method is that it #al=es a dollar recei#ed today the same as a dollar that will not "e recei#ed =ntil some time in the f=t=re. e. @ne defect of the 677 method is that it ass=mes that the cash flows to "e recei#ed from a project can "e rein#ested at the 677 itself$ and that ass=mption is often not #alid.

Nor,al 's. nonnor,al cash flows ++

.

Answer: e

EASY

Which of the following statements is C@77ECT! a. 6f a project has FnormalG cash flows$ then its 677 m=st "e positi#e. ". 6f a project has FnormalG cash flows$ then its <677 m=st "e positi#e. c. 6f a project has FnormalG cash flows$ then it will ha#e eBactly two real 677s. d. The definition of FnormalG cash flows is that the cash flow stream has one or more negati#e cash flows followed "y a stream of positi#e cash flows and then one negati#e cash flow at the end of the projects life. e. 6f a project has FnormalG cash flows$ then it can ha#e only one real 677$ whereas a project with FnonnormalG cash flows might ha#e more than one real 677.

Nor,al 's. nonnor,al cash flows +/

.

Answer: a

EASY

Which of the following statements is C@77ECT! a. Projects with FnormalG cash flows can ha#e only one real 677. ". Projects with FnormalG cash flows can ha#e two or more real 677s. c. Projects with FnormalG cash flows m=st ha#e two changes in the sign of the cash flows$ e.g.$ from negati#e to positi#e to negati#e. 6f there are more sign changes$ then the cash flow stream is Fnonnormal.G d. The Fm=ltiple 677 pro"lemG can arise if a projects cash flows are Fnormal.G e. Projects with FnonnormalG cash flows are almost ne#er enco=ntered in the real world.

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NPV +

.

Answer: c

EASY

Which of the following statements is C@77ECT! Ass=me that the project "eing considered has normal cash flows$ with one o=tflow followed "y a series of inflows. a. A projects NP is fo=nd "y compo=nding the cash inflows at the 677 to find the terminal #al=e 8T9$ then disco=nting the T at the WACC. ". The lower the WACC =sed to calc=late it$ the lower the calc=lated NP will "e. c. 6f a projects NP is less than ero$ then its 677 m=st "e less than the WACC. d. 6f a projects NP is greater than ero$ then its 677 m=st "e less than ero. e. The NP of a relati#ely low ris; project sho=ld "e fo=nd =sing a relati#ely high WACC.

Paybac! +0

.

Answer: b

EASY

Which of the following statements is C@77ECT! Ass=me that the project "eing considered has normal cash flows$ with one o=tflow followed "y a series of inflows. a. The longer a projects pay"ac; period$ the more desira"le the project is normally considered to "e "y this criterion. ". @ne draw"ac; of the pay"ac; criterion for e#al=ating projects is that this method does not properly acco=nt for the time #al=e of money. c. 6f a projects pay"ac; is positi#e$ then the project sho=ld "e rejected "eca=se it m=st ha#e a negati#e NP. d. The reg=lar pay"ac; ignores cash flows "eyond the pay"ac; period$ "=t the disco=nted pay"ac; method o#ercomes this pro"lem. e. 6f a company =ses the same re=irement to e#al=ate all projects$ say it re=ires a pay"ac; of / years or less$ then the company will tend to reject projects with relati#ely short li#es and accept long,li#ed projects$ and this will ca=se its ris; to increase o#er time.

Paybac! +3

.

Answer: b

EASY

Which of the following statements is C@77ECT! Ass=me that the project "eing considered has normal cash flows$ with one o=tflow followed "y a series of inflows. a. The shorter a projects pay"ac; period$ the less desira"le the project is normally considered to "e "y this criterion. ". @ne draw"ac; of the pay"ac; criterion for e#al=ating projects is that this method does not ta;e acco=nt of cash flows "eyond the pay"ac; period. c. 6f a projects pay"ac; is positi#e$ then the project sho=ld "e accepted "eca=se it m=st ha#e a positi#e NP. d. The reg=lar pay"ac; ignores cash flows "eyond the pay"ac; period$ "=t the disco=nted pay"ac; method o#ercomes this pro"lem. e. @ne draw"ac; of the disco=nted pay"ac; is that this method does not consider the time #al=e of money$ while the reg=lar pay"ac; o#ercomes this draw"ac;.


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IRR

Answer: 

+

Which of the following statements is C@77ECT! Ass=me that the project "eing considered has normal cash flows$ with one o=tflow followed "y a series of inflows.

.

EASY

a. A projects reg=lar 677 is fo=nd "y compo=nding the cash inflows at the WACC to find the terminal #al=e 8T9$ then disco=nting this T at the WACC. ". A projects reg=lar 677 is fo=nd "y disco=nting the cash inflows at the WACC to find the present #al=e 8P9$ then compo=nding this P to find the 677. c. 6f a projects 677 is greater than the WACC$ then its NP m=st "e negati#e. d. To find a projects 677$ we m=st sol#e for the disco=nt rate that ca=ses the P of the inflows to e=al the P of the projects costs. e. To find a projects 677$ we m=st find a disco=nt rate that is e=al to the WACC.

IRR

Answer: 

+2

Which of the following statements is C@77ECT! Ass=me that the project "eing considered has normal cash flows$ with one o=tflow followed "y a series of inflows.

.

EASY

a. A projects reg=lar 677 is fo=nd "y compo=nding the initial cost at the WACC to find the terminal #al=e 8T9$ then disco=nting the T at the WACC. ". A projects reg=lar 677 is fo=nd "y compo=nding the cash inflows at the WACC to find the present #al=e 8P9$ then disco=nting to find the 677. c. 6f a projects 677 is less than the WACC$ then its NP will "e positi#e. d. A projects 677 is the disco=nt rate that ca=ses the P of the inflows to e=al the projects cost. e. 6f a projects 677 is positi#e$ then its NP m=st also "e positi#e.

Ran!n- ,ethos: /&

.

NPV

Answer: e

#E$I%#

Which of the following statements is C@77ECT! a. The NP method was once the fa#orite of academics and "=siness eBec=ti#es$ "=t today most a=thorities regard the <677 as "eing the "est indicator of a projects profita"ility. ". 6f the cost of capital is red=ced$ this red=ces a projects NP. c. The NP method is regarded "y most academics as "eing the "est indicator of a projects profita"ility$ hence academics recommend that firms =se only this one method. d. A projects NP depends on the total amo=nt of cash flows the project prod=ces$ "=t "eca=se the cash flows are disco=nted at the WACC$ it does not matter if the cash flows occ=r early or late in the projects life. e. The NP and 677 methods may gi#e different recommendations regarding which of two m=t=ally eBcl=si#e projects sho=ld "e accepted$ "=t they always gi#e the same recommendation regarding the accepta"ility of a

Page 122


normal$ independent project.

Ran!n- ,ethos: /1

.

NPV

Answer: b

#E$I%#

Which of the following statements is C@77ECT! a. @ne ad#antage of the NP o#er the 677 method is that NP ta;es acco=nt of cash flows o#er a projects f=ll life whereas 677 does not. ". @ne ad#antage of the NP o#er the 677 is that NP ass=mes that cash flows will "e rein#ested at the WACC whereas 677 ass=mes that cash flows are rein#ested at the 677$ and the NPs ass=mption is generally more li;ely to "e appropriate. c. @ne ad#antage of the NP o#er the <677 method is that NP ta;es acco=nt of cash flows o#er a projects f=ll life whereas <677 does not. d. @ne ad#antage of the NP o#er the <677 method is that NP disco=nts cash flows whereas the <677 is "ased on =ndisco=nted cash flows. e. Since cash flows =nder the 677 and <677 are "oth disco=nted at the same rate 8the WACC9$ these two methods always ran; m=t=ally eBcl=si#e projects in the same order.

NPV rofles /*

.

Answer: 

EASY"#E$I%#

Which of the following statements is C@77ECT! a. An NP profile graph shows how a projects pay"ac; #aries as the cost of capital changes. ". An NP profile graph for a project normally shows a positi#e 8=pward9 slope as the life of the project increases. c. An NP profile graph is designed to gi#e decision ma;ers an idea a"o=t how a projects ris; #aries with its life. d. An NP profile graph is designed to gi#e decision ma;ers an idea a"o=t how a projects contri"=tion to the firms #al=e #aries with the cost of capital. e. We cannot draw a projects NP profile =nless we ;now the appropriate WACC for =se in e#al=ating the projects NP.

Ran!n- conflcts /+

.

Answer: a

#E$I%#

Which of the following statements is C@77ECT! a. The NP method ass=mes that cash flows will "e rein#ested at the WACC$ while the 677 method ass=mes rein#estment at the 677. ". The NP method ass=mes that cash flows will "e rein#ested at the ris;, free rate$ while the 677 method ass=mes rein#estment at the 677. c. The NP method ass=mes that cash flows will "e rein#ested at the WACC$ while the 677 method ass=mes rein#estment at the ris;,free rate. d. The NP method does not consider all rele#ant cash flows$ partic=larly$ cash flows "eyond the pay"ac; period. e. The 677 method does not consider all rele#ant cash flows$ partic=larly$ cash flows "eyond the pay"ac; period.


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Paybac! ero //

.

/

.

#E$I%#

The reg=lar pay"ac; method has a n=m"er of disad#antages. Which of the following items is N@T a disad#antage of this method! a. ". c. d. e.

NPV

Answer: 

>ac; of an o"jecti#e$ mar;et,determined "enchmar; for ma;ing decisions. 6gnores cash flows "eyond the pay"ac; period. 5oes not directly acco=nt for the time #al=e of money. 5oes not pro#ide any indication regarding a projects li=idity. 5oes not directly acco=nt for differences in ris; among projects.

Answer: b

#E$I%#

Which of the following statements is C@77ECT! Ass=me that the project "eing considered has normal cash flows$ with one o=tflow followed "y a series of inflows. a. A projects NP is generally fo=nd "y compo=nding the cash inflows at the WACC to find the terminal #al=e 8T9$ then disco=nting the T at the 677 to find its P. ". The higher the WACC =sed to calc=late the NP$ the lower the calc=lated NP will "e. c. 6f a projects NP is greater than ero$ then its 677 m=st "e less than the WACC. d. 6f a projects NP is greater than ero$ then its 677 m=st "e less than ero. e. The NPs of relati#ely ris;y projects sho=ld "e fo=nd =sing relati#ely low WACCs.

NPV an IRR /0

.

Answer: e

#E$I%#

Which of the following statements is C@77ECT! Ass=me that the project "eing considered has normal cash flows$ with one o=tflow followed "y a series of inflows. a. 6f Project A has a higher 677 than Project 4$ then Project A m=st ha#e the lower NP. ". 6f Project A has a higher 677 than Project 4$ then Project A m=st also ha#e a higher NP. c. The 677 calc=lation implicitly ass=mes that all cash flows are rein#ested at the WACC. d. The 677 calc=lation implicitly ass=mes that cash flows are withdrawn from the "=siness rather than "eing rein#ested in the "=siness. e. 6f a project has normal cash flows and its 677 eBceeds its WACC$ then the projects NP m=st "e positi#e.

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NPV rofles /3

.

Answer: a

#E$I%#

Projects A and 4 ha#e identical eBpected li#es and identical initial cash o=tflows 8costs9. ?owe#er$ most of one projects cash flows come in the early years$ while most of the other projects cash flows occ=r in the later years. The two NP profiles are gi#en "elow)

NP 8-9

A

/

r 89 Which of the following statements is C@77ECT! a.
NPV rofles /

.

Answer: b

#E$I%#

Projects S and > each ha#e an initial cost of -1&$&&&$ followed "y a series of positi#e cash inflows. Project Ss =ndisco=nted net cash flows total to -*&$&&&$ while >s total =ndisco=nted flows are -+&$&&&. At a WACC of 1&$ the two projects ha#e identical NPs. Which projects NP is more sensiti#e to changes in the WACC! a. Project S. ". Project >. c. 4oth projects are e=ally sensiti#e to changes in the WACC since their NPs are e=al at all costs of capital. d. Neither project is sensiti#e to changes in the disco=nt rate$ since "oth ha#e NP profiles that are horiontal. e. The sol=tion cannot "e determined "eca=se the pro"lem gi#es =s no information that can "e =sed to determine the projects relati#e 677s.


Page 125

NPV0 IRR0 an #IRR /2

.

Answer: a

#E$I%#

Which of the following statements is C@77ECT! a. 6f a project with normal cash flows has an 677 greater than the WACC$ the project m=st ha#e a positi#e NP. ". 6f Project As 677 eBceeds Project 4s$ then A m=st ha#e the higher NP. c. A projects <677 can ne#er eBceed its 677. d. 6f a project with normal cash flows has an 677 less than the WACC$ the project m=st ha#e a positi#e NP. e. 6f the NP is negati#e$ the 677 m=st also "e negati#e.

NPV0 IRR0 an #IRR &

.

Answer: c

#E$I%#

Which of the following statements is C@77ECT! a. The <677 and NP decision criteria ne#er conflict. ". The 677 method can ne#er "e s="ject to the m=ltiple 677 pro"lem$ while the <677 method can "e. c. @ne reason why some people prefer the <677 method to the 677 method is that the <677 is "ased on a more reasona"le ass=mption a"o=t rein#estment rates than the 677 method. d. The higher the WACC$ the lower the disco=nted pay"ac; period. e. The <677 method ass=mes that cash flows are rein#ested at the crosso#er rate.

#scellaneo&s concets 1

.

Answer: a

#E$I%#

Which of the following statements is C@77ECT! a. The 677 method appeals to some managers "eca=se it gi#es an estimate of the rate of ret=rn on projects rather than a dollar amo=nt li;e the NP method pro#ides. ". The disco=nted pay"ac; method eliminates all of the pro"lems associated with the pay"ac; method. c. When e#al=ating independent projects$ the NP and 677 methods often yield conflicting res=lts. d. To find the <677$ we disco=nt the T at the 677. e. A projects NP profile m=st intersect the B,aBis at the projects WACC.

#scellaneo&s concets *

.

Answer: a

#E$I%#

Projects C and 5 are m=t=ally eBcl=si#e and ha#e normal cash flows. Project C has a higher NP if the WACC is less than 1*$ whereas Project 5 has a higher NP if the WACC eBceeds 1*. Which of the following statements is C@77ECT! a. ". c. d. e.

Page 12

Project 5 has a higher 677. Project 5 is pro"a"ly larger in scale than Project C. Project C pro"a"ly has a faster pay"ac;. Project C has a higher 677. The crosso#er rate "etween the two projects is "elow 1*.


NPV0 IRR0 an #IRR +

.

Answer: c

#E$I%#

Which of the following statements is C@77ECT! a. :or independent projects$ the NP$ 677$ <677$ and disco=nted pay"ac; 8=sing a pay"ac; re=irement of + or less years9 methods always lead to the same acceptHreject decisions for a gi#en project. ". :or m=t=ally eBcl=si#e projects$ the NP and <677 methods ne#er conflict$ "=t their res=lts co=ld conflict with the disco=nted pay"ac; and the reg=lar 677 methods. c. <=ltiple 677s can eBist$ "=t not m=ltiple <677s. This is one reason for fa#oring the <677 o#er the 677. d. 6f a firm =ses the disco=nted pay"ac; method with a re=ired pay"ac; of / years$ then it will accept more projects than if it =sed as its c=toff criterion a reg=lar pay"ac; of / years. e. The percentage difference "etween the <677 and the 677 is e=al to the projects WACC.

NPV0 IRR0 an #IRR /

.

Answer: e

#E$I%#

Which of the following statements is C@77ECT! a. :or a project with normal cash flows$ any change in the WACC will change "oth the NP and the 677. ". To find the <677$ we first compo=nd cash flows at the reg=lar 677 to find the T$ and then we disco=nt the T at the WACC to find the P. c. The NP and 677 methods "oth ass=me cash flows can "e rein#ested at the WACC. ?owe#er$ the <677 method ass=mes rein#estment at the <677 itself. d. 6f two projects ha#e the same cost$ and if their NP profiles cross$ then the project with the higher 677 pro"a"ly has more of its cash flows coming in the later years. e. 6f two projects ha#e the same cost$ and if their NP profiles cross$ then the project with the lower 677 pro"a"ly has more of its cash flows coming in the later years.

#<le IRRs 

.

Answer: 

#E$I%#

Which of the following statements is C@77ECT! a. :or a project to ha#e more than one 677$ then "oth 677s m=st "e greater than the WACC. ". 6f two projects are m=t=ally eBcl=si#e$ then they are li;ely to ha#e m=ltiple 677s. c. 6f a project is independent$ then it cannot ha#e m=ltiple 677s. d. <=ltiple 677s can only occ=r if the signs of the cash flows change more than once. e. 6f a project has two 677s$ then the one that is closest to the #ertical aBis is the one that sho=ld "e accepted.


Page 127

NPV rofles 0

.

Answer: a

Projects S and > are e=ally ris;y$ m=t=ally eBcl=si#e projects with normal cash flows. Project S has an 677 of 1$ while Project >s 677 is 1*. The two projects ha#e the same NP when the WACC is 3. Which of the following statements is C@77ECT! a. ". c. d. e.

6f the WACC 6f the WACC 6f the WACC 6f the WACC Project Ss


.

6f 6f 6f 6f 6f

NPV rofles .

is 1&$ "oth projects will ha#e positi#e NPs. is 0$ Project S will ha#e the higher NP. is 1+$ Project S will ha#e the lower NP. is 1&$ "oth projects will ha#e a negati#e NP. NP is more sensiti#e to changes in WACC than Project >s.

Answer: e

#E$I%#"+AR$

Sacramento Paper is considering two e=ally ris;y$ m=t=ally eBcl=si#e projects$ and "oth projects ha#e normal cash flows. Project A has an 677 of 11$ while Project 4 has an 677 of 1/. When the WACC is $ the projects ha#e the same NP. Ii#en this information$ which of the following statements is C@77ECT! a. ". c. d. e.



#E$I%#"+AR$

the the the the the

WACC WACC WACC WACC WACC

is 1+$ Project As NP will "e higher than Project 4s. is 2$ Project As NP will "e higher than Project 4s. is 0$ Project 4s NP will "e higher than Project As. goes o#er 1/$ Project As 677 will eBceed Project 4s. is 2$ Project 4s NP will "e higher than Project As.

Answer: b

#E$I%#"+AR$

(o= are considering two m=t=ally eBcl=si#e$ e=ally ris;y$ projects. 4oth projects ha#e 677s that eBceed the WACC that is =sed to e#al=ate "oth of them. Which of the following statements is C@77ECT! Ass=me that the projects "eing considered ha#e normal cash flows$ with one o=tflow followed "y a series of inflows. a. 6f the two projects NP profiles do not cross$ then there will "e a sharp conflict as to which one sho=ld "e selected. ". 6f the cost of capital is greater than the crosso#er rate$ then the 677 and the NP criteria will not res=lt in a conflict "etween the projects. @ne project will ran; higher "y "oth criteria. c. 6f the cost of capital is less than the crosso#er rate$ then the 677 and the NP criteria will not res=lt in a conflict "etween the projects. @ne project will ran; higher "y "oth criteria. d. :or a conflict to eBist "etween NP and 677$ the initial in#estment cost of one project m=st eBceed the cost of the other. e. :or a conflict to eBist "etween NP and 677$ one project m=st ha#e an increasing stream of cash flows o#er time while the other has a decreasing stream. 6f "oth sets of cash flows are increasing or decreasing$ then it wo=ld "e impossi"le for a conflict to eBist$ e#en if one project is larger than the other.

Page 128



.

The crosso#er rate "etween the two projects m=st "e less than 1&. The crosso#er rate "etween the two projects m=st "e greater than 1&. 6f the WACC is $ Project J will ha#e the higher NP. 6f the WACC is 1$ Project ( will ha#e the higher NP. Project J is larger in the sense that it has the higher initial cost.

NPV rofles .

+AR$

Project S m=st ha#e a higher NP than Project >. 6f Project S has a positi#e NP$ Project > m=st also ha#e a positi#e NP. 6f the WACC falls$ each projects 677 will increase. 6f the WACC increases$ each projects 677 will decrease. 6f Projects S and > ha#e the same NP at the c=rrent WACC$ 1&$ then Project >$ the one with the lower 677$ wo=ld ha#e a higher NP if the WACC =sed to e#al=ate the projects declined.

NPV rofles .

Answer: e

Ass=me that Projects S and > "oth ha#e normal cash flows$ and those cash flows are not affected "y the WACC =sed to e#al=ate them. . Which of the following statements is C@77ECT! a. ". c. d. e.

01

#E$I%#"+AR$

Project Js 677 is 12$ and Project (s 677 is 13. The projects ha#e the same ris; and the same li#es$ and their cash flows are constant o#er their li#es. 6f the WACC is 1&$ Project ( has a higher NP than Project J. Ii#en this information$ which of the following statements is C@77ECT! a. ". c. d. e.

0&

Answer: b

Answer: c

+AR$

Which of the following statements is C@77ECT! Ass=me that all projects "eing considered ha#e normal cash flows and are e=ally ris;y. a. 6f a projects 677 is e=al to its WACC$ then =nder all reasona"le conditions$ the projects NP m=st "e negati#e. ". 6f a projects 677 is e=al to its WACC$ then =nder all reasona"le conditions$ the projects 677 m=st "e negati#e. c. 6f a projects 677 is e=al to its WACC$ then =nder all reasona"le conditions$ the projects NP m=st "e ero. d. There is no necessary relationship "etween a projects 677$ its WACC$ and its NP. e. When e#al=ating m=t=ally eBcl=si#e projects$ those projects with relati#ely long li#es will tend to ha#e relati#ely high NPs when the cost of capital is relati#ely high.


Page 129

NPV rofles 0*

.

Answer: 

+AR$

A company is choosing "etween two projects. The larger project has an initial cost of -1&&$&&&$ ann=al cash flows of -+&$&&& for  years$ and an 677 of 1.*/. The smaller project has an initial cost of -&$&&&$ ann=al cash flows of -10$&&& for  years$ and an 677 of 10.0+. The projects are e=ally ris;y. Which of the following statements is C@77ECT! a. Since the smaller project has the higher 677$ the two projects NP profiles cannot cross$ and the smaller project will loo; "etter "ased on the NP at all positi#e #al=es of WACC. ". Since the smaller project has the higher 677$ the two projects NP profiles will cross$ and the larger project will loo; "etter "ased on the NP at all positi#e #al=es of WACC. c. 6f the company =ses the NP method$ it will tend to fa#or smaller$ shorter,term projects o#er larger$ longer,term projects$ regardless of how high or low the WACC is. d. Since the smaller project has the higher 677 "=t the larger project has the higher NP at a ero disco=nt rate$ the two projects NP profiles will cross$ and the larger project will ha#e the higher NP if the WACC is less than the crosso#er rate. e. Since the smaller project has the higher 677 and the larger NP at a ero disco=nt rate$ the two projects NP profiles will cross$ and the larger smaller project will loo; "etter if the WACC is less than the crosso#er rate.

#IRR 0+

.

Answer: c

+AR$

Which of the following statements is C@77ECT! Ass=me that the project "eing considered has normal cash flows$ with one o=tflow followed "y a series of inflows. a. A projects <677 is always greater than its reg=lar 677. ". A projects <677 is always less than its reg=lar 677. c. 6f a projects 677 is greater than its WACC$ then the <677 will "e less than the 677. d. 6f a projects 677 is greater than its WACC$ then the <677 will "e greater than the 677. e. To find a projects <677$ we compo=nd cash inflows at the 677 and then disco=nt the terminal #al=e at the WACC.

Page 130


#IRR 0/

.

Answer: e

+AR$

Which of the following statements is C@77ECT! Ass=me that the project "eing considered has normal cash flows$ with one cash o=tflow at t % & followed "y a series of positi#e cash flows. a. A projects <677 is always greater than its reg=lar 677. ". A projects <677 is always less than its reg=lar 677. c. 6f a projects 677 is greater than its WACC$ then its <677 will "e greater than the 677. d. To find a projects <677$ we compo=nd cash inflows at the reg=lar 677 and then find the disco=nt rate that ca=ses the P of the terminal #al=e to e=al the initial cost. e. To find a projects <677$ the teBt"oo; recommends compo=nding cash inflows at the WACC and then finding the disco=nt rate that ca=ses the P of the terminal #al=e to e=al the initial cost.

NPV an ro1ect selecton 0

.

Answer: c

+AR$

2hoosn- a,on- ,&t&ally ecl&s'e ro1ects 00

.

Answer: c

+AR$

Projects A and 4 are m=t=ally eBcl=si#e and ha#e normal cash flows. Project A has an 677 of 1 and Project 4 has an 677 of *&. Also$ the companys WACC is 1*$ and at that rate Project A has the higher NP. Which of the following statements is C@77ECT! a. The crosso#er rate for the two projects m=st "e less than 1*. ". Ass=ming the timing pattern of the two projects cash flows is the same$ Project 4 pro"a"ly has a higher cost 8and larger scale9. c. Ass=ming the two projects ha#e the same scale$ Project 4 pro"a"ly has a faster pay"ac; than Project A. d. The crosso#er rate for the two projects m=st "e 1*. e. Since 4 has the higher 677$ then it m=st also ha#e the higher NP if the crosso#er rate is less than the WACC of 1*.


Page 131

#<le IRRs 03

.

Answer: c

+AR$

(o= are on the staff of Collier Company. The C:@ "elie#es project acceptance sho=ld "e "ased on the NP$ "=t 4o" Collier$ the president$ insists that no project can "e accepted =nless its 677 eBceeds the projects ris;,adj=sted WACC. Now yo= m=st ma;e a recommendation on a project that has a cost of -1$&&& and two cash flows. -11&$&&& at the end of (ear 1 and ,-1&&$&&& at the end of (ear *. The president and the C:@ "oth agree that the appropriate WACC for this project is 1&. At 1&$ the NP is -*$+.+3$ "=t yo= find two 677s$ one at 0.++ and one at *3$ and a <677 of 11.+*. Which of the following statements "est descri"es yo=r optimal recommendation$ i.e.$ the analysis and recommendation that is "est for the company and least li;ely to get yo= in tro="le with either the C:@ or the president! a. (o= sho=ld recommend that the project "e rejected "eca=se its NP is negati#e and its 677 is less than the WACC. ". (o= sho=ld recommend that the project "e rejected "eca=se$ altho=gh its NP is positi#e$ it has an 677 that is less than the WACC. c. (o= sho=ld recommend that the project "e accepted "eca=se 819 its NP is positi#e and 8*9 altho=gh it has two 677s$ in this case it wo=ld "e "etter to foc=s on the <677$ which eBceeds the WACC. (o= sho=ld eBplain this to the president and tell him that that the firms #al=e will increase if the project is accepted. d. (o= sho=ld recommend that the project "e rejected "eca=se 819 altho=gh its NP is positi#e and 8*9 it has two 677s$ one of which is less than the WACC$ which indicates that the firms #al=e will decline if the project is accepted. e. (o= sho=ld recommend that the project "e rejected "eca=se$ altho=gh its NP is positi#e$ its <677 is less than the WACC$ and that indicates that the firms #al=e will decline if it is accepted.

PART II  &uesti$ns and Pr$%lems fr$m Pri$r Test *an0 n$t used in Part I Multi'le #$ice: Pr$%lems #E$I%# (6 thro&-h 78) Paybac! ero 0

.

Answer: b

The Seattle Corporation has an in#estment opport=nity that will yield cash flows of -+&$&&& per year in (ears 1 thro=gh /$ -+$&&& per year in (ears  thro=gh 2$ and -/&$&&& in (ear 1&. This in#estment will cost -1&$&&& today$ and the firms WACC is 1&. What is the pay"ac; period for this in#estment! a. ". c. d. e.

Page 132

.*+ /.0 /.&& 0.1* /.+




Page 133

Paybac! ero 02

.

Answer: c


$sco&nte aybac! 3&

.

Answer: e

Co=ghlin
(ear & 1 * + /

Project Cash :low ,-3&& million *&& million +3& million ** million 3&& million

6f$ the projects WACC is 1&$ what is the projects disco=nted pay"ac;! a. ". c. d. e.

+.1 /.&2 1.0* *. +.&2


$sco&nte aybac! 31

.

Answer: 

A project has the following cash flows)

(ear & 1 * + /

Project Cash :low ,-+$&&& 1$&&& 1$&&& 1$&&& 1$&&&

6f its WACC is 1&$ what is the projects disco=nted pay"ac; period! a. ". c. d.

Page 134

+.&& +.+& +.* +.3

years years years years


e. /.3 years


Page 135

NPV 3*

.

Answer: a As the capital "=dgeting director for 5en#er Corporation$ yo= are e#al=ating two m=t=ally eBcl=si#e projects with the following net cash flows) Project J Cash :low ,-1&&$&&& &$&&& /&$&&& +&$&&& 1&$&&&

(ear & 1 * + /

Project K Cash :low ,-1&&$&&& 1&$&&& +&$&&& /&$&&& 0&$&&&

6f 5en#ers WACC is 1$ which project wo=ld yo= choose! a. ". c. d. e.

Neither Project Project Project Project

project. J$ since K$ since J$ since K$ since

it it it it

has has has has

the the the the

higher higher higher higher

677. NP. NP. 677.

NPV 3+

.

Answer: a Two m=t=ally eBcl=si#e projects ha#e the following projected cash flows)

(ear & 1 * + / 

Project A Cash :low ,-&$&&& 1$0* 1$0* 1$0* 1$0* 1$0*

Project 4 Cash :low ,-&$&&& & & & & 22$&&

6f the re=ired rate of ret=rn on these projects is 1&$ which wo=ld "e chosen and why! a. ". c. d. e.

Project 4 "eca=se it has the higher NP. Project 4 "eca=se it has the higher 677. Project A "eca=se it has the higher NP. Project A "eca=se it has the higher 677. Neither$ "eca=se "oth ha#e 677s less than the cost of capital.

IRR 3/

.

Answer: c The capital "=dgeting director of Sparrow Corporation is e#al=ating a project that costs -*&&$&&&$ is eBpected to last for 1& years and prod=ces after,taB cash flows$ incl=ding depreciation$ of -//$&+ per year. 6f the firms WACC is 1/ and its taB rate is /&$ what is the projects 677! a. ". c. d. e.

Page 13

 1/ 1 , 1*


IRR 3

.

Answer: c An ins=rance firm agrees to pay yo= -+$+1& at the end of *& years if yo= pay premi=ms of -1&& per year at the end of each year for *& years. :ind the internal rate of ret=rn to the nearest whole percentage point. a. 2 ". 3 c.  d. + e. 11

IRR0 aybac!0 an ,ssn- cash flow 30

.

Answer: 

@a; :=rnishings is considering a project that has an =p,front cost and a series of positi#e cash flows. The projects estimated cash flows are s=mmaried "elow) Project Cash :low ! -&& million +&& million /&& million 0&& million

(ear & 1 * + /

The project has a reg=lar pay"ac; of *.* years. internal rate of ret=rn 86779!

What is the projects

a. *+.1 ". 1/+.2 c. 13.3 d. ++. e. /1.&

IRR an ,&t&ally ecl&s'e ro1ects 33

.

Answer: 

A company is analying two m=t=ally eBcl=si#e projects$ S and >$ whose cash flows are shown "elow) (ears

& r % 1* L

S ,1$1&& > ,1$1&&

1 L

* L

+ L

1$&&& &

+& +&&

& 1$&&

The companys WACC is 1*. What is the reg=lar 677 of the "etter project$ that is$ the project that maBimies the firms stoc; price! a. ". c. d. e.

1*.&& 1.+ 1.0* 12.& *&./0


Page 137

NPV an IRR 3

.

Answer: b

The cash flows for two non,repeata"le$ m=t=ally eBcl=si#e projects are shown "elow. 6f yo=r firms WACC is 1&$ how m=ch #al=e is sacrificed if yo=r firm selects the project with the higher 677! Project S)

& r % 1& L ,1$&&&

Project >)

& r % 1& 1 L L ,*$&&& 00.30

a. ". c. d. e.

1 L &&

* L && * L 00.30

+ L && + L 00.30

.

 L 00.30

-*/+./+ -*21.3& -++*.& -/1.1 -+.1+

NPV an IRR 32

/ L 00.30

Answer: e

A firm is analying two m=t=ally eBcl=si#e projects with the following cash flows)

(ear & 1 * + /

Project A Cash :low ,-&$&&& 1&$&&& 1$&&& /&$&&& *&$&&&

Project 4 Cash :low ,-+&$&&& 0$&&& 1*$&&& 1$&&& 1*$&&&

6f the companys WACC is 1&$ what is the NP of the project with the highest 677! a. ". c. d. e.

Page 138

- 3$&2& - $+0& -11$/& -1*$1& -1$*&&


NPV0 IRR0 an aybac! &

.

Answer: 

4ra=n 6nd=stries is following cash flows)

considering (ear & 1 * + /

The companys WACC is 1&. a. ". c. d. e.

Pay"ac; Pay"ac; Pay"ac; Pay"ac; Pay"ac;

% % % % %

*./$ *./$ *.0$ *.0$ *.0$

677 677 677 677 677

% % % % %

an

in#estment

project

that

has

the

Cash :low ,-1$&&& /&& +&& && /&& What is the projects pay"ac;$ 677$ and NP!

1&.&&$ *1.**$ *1.**$ *1.**$ */.1*$

NP NP NP NP NP

% % % % %

-0&&. -*0&. -+&&. -*0&. -+&&.

#E$I%#"+AR$ (79 thro&-h 67) Paybac! ero 1

.

Answer: c

?aig Aircraft is considering a project that has an =p,front cost paid today at t % &. The project will generate positi#e cash flows of -0&$&&& a year at the end of each of the neBt fi#e years. The projects NP is -3$&&& and the companys WACC is 1&. What is the projects reg=lar pay"ac;! a. ". c. d. e.

+.** 1.0 *./ *.+ /.10


$sco&nte aybac! *

.

Answer: 

5a#is Corporation has an in#estment policy that re=ires accepta"le projects to reco#er all costs within + years. The corporation =ses the disco=nted pay"ac; method to assess potential projects and =ses a WACC of 1&. The cash flows for two independent projects are shown "elow) (ear & 1 * + /

Project A Cash :low ,-1&&$&&& /&$&&& /&$&&& /&$&&& +&$&&&

Project 4 Cash :low ,-&$&&& &$&&& *&$&&& +&$&&& &

6n which in#estment project8s9 sho=ld the company in#est! a. Project A only. ". Neither Project A nor Project 4. c. Project A and Project 4.


Page 139

d. Project 4 only.

NPV +

.

Answer:  The Seattle Corporation has an in#estment opport=nity that will yield cash flows of -+&$&&& per year in (ears 1 thro=gh /$ -+$&&& per year in (ears  thro=gh 2$ and -/&$&&& in (ear 1&. This in#estment will cost -1&$&&& today$ and the firms WACC is 1&. What is the NP of this in#estment! a. ". c. d. e.

-1+$2/ - 1$&*+ -*12$&/ - 1$1+ - 2*$1/0

NPV /

.

Answer: b (o= are considering the p=rchase of an in#estment that wo=ld pay yo= -$&&& per year for (ears 1,$ -+$&&& per year for (ears 0,$ and -*$&&& per year for (ears 2 and 1&. 6f yo= re=ire a 1/ rate of ret=rn$ and the cash flows occ=r at the end of each year$ then how m=ch sho=ld yo= "e willing to pay for this in#estment! a. ". c. d. e.

-1$12.*3 -*1$2+3.*0 -+*$/1. -+$&&&.&& -*$1.31

NPV 

.

Answer:  4rown Irocery is The project will each of the neBt 1*. What is the a. ". c. d. e.

Page 140

considering a project that has an =p,front cost of -J. generate a positi#e cash flow of -3$&&& at the end of *& years. The project has a WACC of 1& and an 677 of projects NP!

-1$*&$&&& - 0+$13 - 0&$*& 3$+&2 - *&$&&&


NPV0 aybac!0 an ,ssn- cash flow 0

.

Answer: b

Shannon 6nd=stries is considering a project that has the following cash flows) Project Cash :low ! -*$&&& +$&&& +$&&& 1$&&

(ear & 1 * + /

The project has a pay"ac; of *. years$ and its WACC 1*. projects NP! a. ". c. d. e.

- 33.0 - 30.21 -1$&/2.& -*$301.+* -+$30.21

IRR 3

.

What is the

Answer:  Ien=ine Prod=cts 6nc. re=ires a new machine. Two companies ha#e s="mitted "ids$ and yo= ha#e "een assigned the tas; of choosing one of the machines. Cash flow analysis indicates the following)
(ear & 1 * + /

What is the 677 for each machine! a. ". c. d. e.

677A % 677A % 677A % 677A % 677A %

10M */M 1M 1M */M

6774 % 6774 % 6774 % 6774 % 6774 %

*& *& 10 */ *0


Page 141

IRR 

.

Answer: c Whitney Crane 6nc. has the following independent in#estment opport=nities for the coming year)

Project A 4 C 5

Cost -1&$&&& $&&& 1*$&&& +$&&&

Ann=al Cash 6nflows -11$&& +$&3 $020 1$&&2

>ife 8(ears9 1 * + /

677 1 1+

The 677s for Projects A and C$ respecti#ely$ are) a. ". c. d. e.

10 1 1 1 10

and and and and and

1/ 1& *& 1+ 1+

IRR 2

.

Answer: e A project has the following net cash flows) Project (ear Cash :low & ,- J 1 1& * *&& + *& / /&&  1&& At the projects WACC of 1&$ the project has an NP of -1*/.3. the projects 677! a. ". c. d. e.

1&.&& 1*.0* 1+./2 1.0* 10.+

NPV an IRR 2&

.

What is

Answer: a

A company is analying two m=t=ally eBcl=si#e projects$ S and >$ whose cash flows are shown "elow) (ears & 1 * + / S ,1$1&& 2&& +& & 1& > ,1$1&& & +&& && & The companys WACC is 1*$ and it can get an =nlimited amo=nt of capital at that cost. What is the reg=lar 677 8not <6779 of the "etter project! a. ". c. d. e.

Page 142

1+.&2 1*.&& 13./0 1+. 1*.+


IRR0 aybac!0 an ,ssn- cash flow 21

.

Answer: c

?adl.com is considering the following two projects)

(ear & 1 * + /

Project 1 Cash :low ,-1&& +& & /& &

Project * Cash :low ! /& & 0& 0&

The two projects ha#e the same pay"ac;. What is Project *s internal rate of ret=rn 86779! a. ". c. d. e.

//.*3 *+./& *&. 1/.3+ 13.0/

#IRR 2*

.

Answer:  Alyes;a Salmon 6nc is considering a new a=tomated prod=ction line project. The project has a cost of -*3$&&& and is eBpected to pro#ide after,taB ann=al cash flows of -3+$+&0 for eight years. The firms management prefers =sing the modified 677 approach. The firms WACC is 1*. What is the projects <677! a. ". c. d. e.

1.& 1/.& 1*.& 10.& 13.&

#IRR 2+

.

Answer: e
1*.1& 1/.++ 10.&& 1.* 12./


Page 143

#IRR 2/

.

Answer:  A company is considering a project with the following cash flows)

(ear & 1 * + /

Project Cash :low ,-1&&$&&& &$&&& &$&&& &$&&& ,1&$&&&

The projects WACC is estimated to "e 1&. a. ". c. d. e.

What is the <677!

11.* 11.0 1+.* 1/.* *&.+/

#IRR 2

.

Answer: e Capitol City Transfer Company is considering "=ilding a new terminal that will re=ire eBpendit=res of -1 million immediately 8at t % &9 and another -1 million at the end of (ear 1 8t % 19. 6t will then recei#e net cash flows of -&. million at the end of (ears *,$ and it eBpects to sell the property and net -1 million at the end of (ear 0. All cash inflows and o=tflows are after taBes. The companys WACC is 1*$ and it =ses the <677 criterion for capital "=dgeting decisions. What is the projects <677! a. ". c. d. e.

11.2 1*.& 11./ 11. 11.3

#IRR 20

.

Answer: e Arrington
Page 144

Cash :lows ,-*&& 1*& ,& 3&& What is the projects <677!

0./3 1./2 /. +3.** *./2


#IRR 23

.

Answer: e 5it;a 5iners is considering a project with the following eBpected cash flows 8in millions of dollars9) Project Cash :low ,-+&& ,1&& 3& 1* 3&&

(ear & 1 * + / The projects WACC is 1&. a. ". c. d. e.

What is the projects <677!

+0.2 1.1+ *3.+ *0./ *+.2+

+AR$ (66 thro&-h 88)

#IRR an ,ssn- cash flow 2

.

4elanger Constr=ction s="se=ent cash flows)

Answer:  is

considering

a

project

with

the

following

Project (ear & 1 * +

Cash :low ! -/&& && *&&

The projects pay"ac; is 1. years$ and it has a WACC of 1&. projects <677! a. ". c. d. e.

What is the

1&.&& 12.0 *1./ *+.* 1/.3


Page 145

#IRR0 aybac!0 an ,ssn- cash flow 22

.

Answer: 

Tyrell Corporation is considering a project with the following cash flows 8in millions of dollars9)

(ear & 1 * + /

Project Cash :low ! -1.& 1. *.& *.

The project has a pay"ac; of eBactly *.& years. 1*. What is the projects <677! a. ". c. d. e.

The projects WACC is

1*.& *./ 1.3 ++.0 +.1*

#&t&ally ecl&s'e ro1ects 1&&

.

Answer: b

Two m=t=ally eBcl=si#e projects ha#e the following projected cash flows)

(ear & 1 * +

Project A Cash :low ,-1&&$&&& +2$&& +2$&& +2$&&

Project 4 Cash :low ,-1&&$&&& & & 1++$&&&

4ased only on the information gi#en$ which of the two projects wo=ld "e preferred$ and why! a. ". c. d.

Project A$ "eca=se it has a higher NP. Project 4$ "eca=se it has a higher 677. 6ndifferent$ "eca=se the projects ha#e e=al 677s. 6ncl=de "oth in the capital "=dget$ since the s=m of the cash inflows eBceeds the initial in#estment in "oth cases. e. Choose neither$ since their NPs are negati#e.

/eforeta cash flows 1&1

.

Answer: b

Scott Corporations new project calls for an in#estment of -1&$&&&. 6t has an estimated life of 1& years and an 677 of 1. 6f cash flows are e#enly distri"=ted and the taB rate is /&$ what is the ann=al "efore,taB cash flow each year! 8Ass=me depreciation is a negligi"le amo=nt.9 a. ". c. d. e.

Page 14

-1$22+ -+$+*1 -1$&& -/$2+ -$&12


NPV 1&*

.

Answer: c 7et=rns on the mar;et and Ta;eda Companys stoc; d=ring the last + years are shown "elow) (ear 1 * +

Ta;eda ,1/ +1 1&

The ris;,free rate is 3$ and the mar;et ris; premi=m is . Ta;eda is considering a project whose mar;et "eta was fo=nd "y adding &.* to the companys o#erall corporate "eta. Ta;eda is 1&& e=ity financed$ all of which comes from retained earnings. The project has a cost of -1&& million$ and it is eBpected to pro#ide cash flows of -*& million per year at the end of (ears 1 thro=gh  and then -+& million per year at the end of (ears 0 thro=gh 1&. What is the projects NP 8in millions of dollars9! a. ". c. d. e.

-*&.2 -**. -*+.11 -*.30 -*.1*

NPV 1&+

.

Answer: c 7et=rns on the mar;et and Company (s stoc; d=ring the last + years are shown "elow) (ear 1 * +

Company ( ,** 1+ +0

The ris;,free rate is  percent$ and the re=ired ret=rn on the mar;et is 11 percent. (o= are considering a low,ris; project whose mar;et "eta is &. less than the companys o#erall corporate "eta. (o= finance only with e=ity$ all of which comes from retained earnings. The project has a cost of -&& million$ and it is eBpected to pro#ide cash flows of -1&& million per year at the end of (ears 1 thro=gh  and then -& million per year at the end of (ears 0 thro=gh 1&. What is the projects NP 8in millions of dollars9! a. ". c. d. e.

- 3.1& - 2.*0 -1&./* -1*.1& -1.3


Page 147

#IRR an NPV 1&/

.

Answer: c

Two m=t=ally eBcl=si#e projects$ J and ($ ha#e the following cash flows) Project J Cash :low ,-*$&&& *&& 0&& && 1$/&&

(ear & 1 * + /

Project ( Cash :low ,-*$&&& *$&&& *&& 1&& 3

The projects are e=ally ris;y$ and yo=r firms WACC is 1*. (o= m=st ma;e a recommendation$ and it m=st "e "ased on the modified 677 8<6779. What is the <677 of the "etter project! a. ". c. d. e.

1*.&& 11./0 1+.2 1*.2 1.3+

#IRR an ,ssn- cash flow 1&

.

Answer: b

Project C has the following net cash flows)

(ear & 1 * + /

Project C Cash :low ,-&& *&& ,J +&& &&

Note that the cash flow$ J$ at t % * is an o=tflow 8that is$ J O &9. Project C has a WACC of 1& and an <677 of 1*. What is the projects cash o=tflow at t % *! a. ". c. d. e.

Page 148

,-120.0 ,-*+3.2 ,-*/0.0 ,-*0*.2* ,-+1.1+


#IRR an ,ssn- cash flow 1&0

.

Answer: b

5iefen"a;er 6nc. is considering a project with the following cash flows)

(ear & 1 * + /

Project Cash :low ! -1&&$&&& *&&$&&& *&&$&&& ,1&&$&&&

The project has a pay"ac; of *.& years and a WACC of 1&. projects <677! a. ". c. d. e.

.3/ 1*.3/ 1+.+/ 10.+3 13.03

#IRR 1&3

.

What is the

Answer: e Taylor Technologies has a target capital str=ct=re that consists of /& de"t and 0& e=ity. The e=ity will "e financed with retained earnings. The companys "onds ha#e a yield to mat=rity of 1&. The companys stoc; has a "eta % 1.1. The ris;,free rate is 0$ the mar;et ris; premi=m is $ and the taB rate is +&. The company is considering a project with the following cash flows)

(ear & 1 * + /

Project A Cash :low ,-&$&&& +$&&& /+$&&& 0&$&&& ,/&$&&&

What is the projects <677! a. 0.30 ". 2.*0 c. 1&.3 d. 10.1/ e. *&.*


Page 149

#IRR 1&

.

Answer: b ?o=ston 6nc. is considering "=ilding a new refrigerated wareho=se that will cost -3$&&&$&&& at t % & and is eBpected to ha#e operating cash flows of -&&$&&& at the end of each of the neBt *& years. ?owe#er$ repairs that will cost -1$&&&$&&& m=st "e inc=rred at the end of the 1&th year. Th=s$ at the end of (ear 1& there will "e a -&&$&&& operating cash inflow and an o=tflow of ,-1$&&&$&&& for repairs. 6f ?o=stons WACC is 1*$ what is the projects <677! a. 3.3 ". .13 c. 2.1 d. 11./ e. 1*.++

PV of cash flows 1&2

.

Answer: c

A specialty shop in a local mall c=rrently has a lease that calls for payments of -1$&&& at the end of each of the neBt 0& months. The landlord has offered a new ,year lease that calls for ero rent for 0 months$ then rental payments of -1$&& at the end of each month for the neBt / months. Sallys cost of capital is 11. 4y what a"sol=te dollar amo=nt wo=ld accepting the new lease change Sallys theoretical net worth! a. ". c. d. e.

Page 150

-*$1&.&2 -+$*/+.*/ -+$&+.&0 -/$*22.3 -/$01.30


Multiple part: (The following information applies to the next five problems.)

Woodgate 6nc. is considering a project with the following after,taB operating cash flows 8in millions of dollars9)

(ear & 1 * + /

Project Cash :low ,-+&& 1* 3 *&& 1&&

The project has a WACC of 1&.

Paybac! ero 11&

.

Answer: b

What is the projects pay"ac; period! a. ". c. d. e.

*.&& *.& *.0 *.+ +.&&


$sco&nte aybac! 111

.

What is the projects disco=nted pay"ac; period! a. ". c. d. e.

*.&& *.& *.0 *.+ +.&&


IRR 11*

.

Answer:  What is the projects 677! a. ". c. d. e.

1&.&& 10.+ 12.1* *+./* *0.+*

NPV 11+

.

Answer: 

Answer: c What is the projects NP! a. ". c. d. e.

- *. - /&.21 - 2/.1 -1+3.0 -12.3+

million million million million million


Page 151

#IRR 11/

.

Answer: c What is the projects <677! a. ". c. d. e.

3.0/ 1&.+ 13.33 12.1* *3.0/

(The following information applies to the following three problems.)

Project A has a WACC of 1& and the following cash flows)

(ear & 1 * + /

NPV 11

.

Answer:  What is Project As NP! a. ". c. d. e.

- *1.+* - 00.*0 - +.&& - 22.*2 -11*.+1

IRR 110

.

Answer:  What is Project As 677! a. ". c. d. e.

1+.// 10.10 1.2* */.32 *0./

#IRR 113

.

Project A Cash :low ,-+&& 1&& 1& *&& &

Answer: e What is Project As <677! a. ". c. d. e.

Page 152

3./& 1*.1 1/./2 1./ 1.1


(The following information applies to the next two problems.)

Company A is considering a project with the following cash flows)

(ear & 1 * +

Project Cash :low ,-$&&& $&&& +$&&& ,1$&&&

The project has a WACC of 1&.

NPV 11

.

Answer: b What is the projects NP! a. ". c. d. e.

-1$13 -1$*3+ -1$1 -*$&&& -*$330

#IRR 119

.

Answer: c What is the projects <677! a. ". c. d. e.

10.0 13.& 13.0 1.& 1.0 (The following information applies to the next two problems.)

Company 4 is considering a project with the following cash flows)

(ear & 1 * +

#ssn- cash flow0 aybac! ero0 an NPV 1*&

.

Project Cash :low , J 13 13 +&&

Answer: a

Ass=me that the project has a reg=lar pay"ac; period of * years and a WACC of 1&. What is the projects NP! a. ". c. d. e.

-132.11 -*&/.11 -**2.11 -*/.11 -*32.11


Page 153

#ssn- cash flow0 IRR0 an NPV 1*1

.

Answer: c

Now instead of ma;ing an ass=mption a"o=t the pay"ac; period$ ass=me that the project has an 677 of 1. Ii#en this ass=mption$ what wo=ld "e the projects NP$ if the WACC e=als 1*! a. ". c. d. e.

- &.&& -1.& -*3./ -+3.+& -/3.+0 (The following information applies to the next three problems.)

4ell Corporation is considering two m=t=ally eBcl=si#e projects$ Project A and Project 4. The projects ha#e the following cash flows) (ear & 1 * + /

Project A Cash :low ,&& 1& *&& *& 1&&

Project 4 Cash :low ,&& +&& +&& +& ,+&&

4oth projects ha#e WACCs of 1&.

NPV 1**

.

Answer:  What is Project As NP! a. ". c. d. e.

+&.1* +/.0 /0.1+ 3.3 0*.&1

IRR 1*+

.

Answer: a What is Project As 677! a. ". c. d. e.

1.+* 1.* 10.&/ 10.0 13.&1

#IRR 1*/

.

Answer: b What is Project 4s <677! a. ". c. d. e.

Page 154

1*.& 1*.2 1+.+3 1/.&1 1/.



Page 155

#HAPTER  A!+1ER+ A!D +L.TI!+

Page 15


1.

NPV (constant cash flows; 3 years)

WACC:

10.00% 0 -$1,000

Cash flows

1 $500

Ans"er:

NPV = *.

1A##: 9ear 2:

5678378

10.00% 0 -$1,000

Cash flows

1 $475

Ans"er:

NPV =

1A##: 9ear 2:

5;2;3<=

10.00% 0 -$1,000

Cash flows

1 $300

Ans"er:

NPV =

1A##: 9ear 2:

5)8>367

3 $475

1 $450

2 $450 9ear 2:

Cash flows

1 $400

2 $400

Answer: e

EASY

)2324 5),222

3 $300

4 $300

5 $300

)2324 5),222

Answer: b

EASY

Answer: 

EASY

Answer: a

EASY

3 $450 5),222

IRR (constant cash flows; 4 years)

0 -$1,000

EASY

4 $475


0 Cash flows -$1,000 Ans"er: )<3<;4 IRR = .

2 $300

Answer: c

)2324 5),222


WACC:

/.

2 $475

EASY

3 $500


WACC:

+.

2 $500

Answer: a

3 $400

4 $400

Ans"er:

IRR =

6)3?<4

9ear 2:

5),222

0

.


0 -$1,000

Cash flows

1 $350

2 $350

3 $350

4 $350

5 $350

Ans"er:

IRR = 3.

663))4

9ear 2:

Paybac! (constant cash flows; 3 years)

5),222

Answer: c

EASY

.

Cash flows

0 -$1,000

1 $500

2 $500

3 $500

Ans"er: Cuula!"# C Pa&'a() =

-$1,000 

-$500 

$0 6322

$500 

6322

Paybac! (nonconstant cash flows; 5 years)

Cash flows Ans"er: Cuula!"# C

Pa&'a() = 2.

836)

Ans"er: NPV =

1 $300

2 $310

3 $320

4 $330

5 $340

-$1,000 

-$700 

-$3*0 

-$70 

$2+0 836)

$+00 

1 57;2

5)7638>

2 57<2

1A##:

Ans"er: NPV =

1 57;2

5=;3>=

2 5772

1A##:

Answer: a

EASY"#E$I%#

Answer: c

EASY"#E$I%#

Answer: e

EASY"#E$I%#

3 57>2

)2324

NPV (&ne'en cash flows; 3 years)

WACC: )23224 0 5),222 Cash flows

EASY"#E$I%#

0 -$1,000


WACC: )23224 0 5),222 Cash flows

1&.

Answer: e

3 5782

)2324

11

.


WACC: )23224 0 5),222 Cash flows

Ans"er: NPV 1*.

1 5722

56?=3?7


2 572;

1A##:

3 57)2

4 57);

)2324

Answer: b

EASY"#E$I%#

1A##:

)23224 0 5),222

Cash flows Ans"er: NPV = 1+.

1 5722

57?632)

2 58=;

1A##:

3 58=2

Cash flows

1 57;2

2 57>2

5 58?2

)2324

IRR (&ne'en cash flows; 3 years)

0 5),222

4 58?;

Answer: 

EASY"#E$I%#

Answer: a

EASY"#E$I%#

3 57=2

Ans"er:

IRR = 1/.

)=32;4

9ear 2:

5),222


0 5),222

Cash flows

1 56;2

2 5682

3 56)2

4 5)=2

Ans"er:

IRR = 1.

;3);4

9ear 2:

5),222


0 5),222

Cash flows

1 5822

Answer: c

2 56=;

3 56=2

4 56?;

EASY"#E$I%#

5 56?2

Ans"er:

IRR =

)73224

9ear 2:

5),222

10

.

$sco&nte aybac! (constant cash flows; 3 years)

WACC: Cash flows Ans"er: PV of Cs Cuula!"# C Pa&'a() = 13.

Answer: b

#E$I%#

Answer: 

#E$I%#

10.00%

638;

0 -$1,000

1 $500

2 $500

3 $500

-$1,000 -$1,000 

$455 -$545 

$413 -$132 

$37+ $244 638;

$sco&nte aybac! (nonconstant cash flows; 4 years)

WACC: Cash flows Ans"er: PV of Cs Cuula!"# C Pa&'a() = 1.

10.00%

638<

0 -$1,000

1 $525

2 $45

3 $445

4 $405

-$1,000 -$1,000 

$477 -$523 

$401 -$122 

$334 $212 638<

$277 $4* 

#IRR (&ne'en cash flows; 3 years) 1A##:

Cash flows

)23224 0 5),222

1 58;2

Answer: e

2 58>2

#E$I%#

3 58=2

Ans"er: T@: #$m'$unded values: 57683;2 572>322 58=2322 5),6623;2 <3?>4 fou/ as /"s(ou! a! !ha! ua!s PV of V !o (os! IRR = <3?>4 Al!a!"# (al(ula!"o, w"!h (l IRR = 12.

#IRR (&ne'en cash flows; 4 years) 1A##:

Cash flows

)23224 0 5=22

1 5822

Answer: b

2 5862

3 5872

#E$I%#

4 58<2

Ans"er: #$m'$unded values: 58==382 58?>362 58>7322 58<2322 )732)4 fou/ as /"s(ou! a! !ha! ua!s PV of V !o (os! IRR = )732)4 fou/ w"!h (l IRR =

T@: 5),;623;2

*&

.

NPV 's IRR (constant cash flows; 3 years)

l/ WACC: Cash flows Ans"er: l/ NPV = Nw NPV = Cha6 *1.

10.00% 0 -$1,000

1 $500

Nw WACC: 2 $500

Answer: 

#E$I%#

Answer: a

#E$I%#

5.00% 3 $500

5678378 58<)3<6 5))?3)=

NPV 's IRR (nonconstant cash flows; 3 years)

l/ WACC: Cash flows Ans"er: l/ NPV = Nw NPV = Cha6 **.

10.00% 0 -$1,000

1 $500

56=232) 588>37; 57>377

Nw WACC: 2 $520 ld 1A##: 1A## adder:

!e" 1A##:

.00% 3 $540 )23224 63224 ?3224

NPV 's IRR (s*e fferences) 1A##:

)63224 0 5),26; 56,);8

C C8 Ans"er: IRR, L IRR, + !P@, L !P@, + Valu los!

Answer: c

1 58>; 5>;2

2 58?2 5>;=

3 58?; 5>
4 58=2 5>>>

);3;4 )?3)4 5)<63)< 5)873<7 56>3;6



1,000 800

S L

600 400 200 0 -200 0%

*+.

#E$I%#"+AR$

5%

10%

15%

NPV 's IRR (fferent t,n- atterns)

20%

0% 2% 4% +% % 10% 12% 14% 1+% 1% 20% 22% 24% Answer: e

)873< ;2;32 78)32 8<63; 6==3) 67238 )?;3< )873< ?>3) 763> )36 8>3> >736 )2?3<

#E$I%#"+AR$

L )<636 =2)32 >;837 <)<3? 7=238 8>63= 6<83? )<636 <>38 6)36 )273) )?)3? 6;73< 8683)

1A##:

)23224 0 5),26; 5),26;


1 5<;2 5)22

2 57;2 5822

3 56;2 5;22

4 5;2 5>22

);3>4 )=3=4 5)<>3<) 5);=3>= 5>3?6

 600 500 S

400

L

300 200 100 0 -100 0%

5%

10%

15%

20%

25%

0% 2% 4% +% % 10% 12% 14% 1+% 1% 20% 22% 24%

);=3? 8>;32 86<3< 6?)32 68?36 )=>3= );=3? )683? ?=3? ;>3; 6>32 632 6=3< ;;3=

*/

.

NPV 's IRR (fferent t,n- atterns)

Answer: a

#E$I%#"+AR$

L )<>3< ;>;32 7>=36 8=)37 8)23< 68<36 )<>3< )2736 7;3; ?3= ;=37 )2<37 );23) )=23=

1A##:

)23;24 0 5),2;2 5),2;2


1 5<;2 5722

2 5<;2 5722

3

4

5722

5722

)=384 );3;4 5627387 5>23;> 52322 +

700.0 600.0 500.0 !

400.0 "

300.0 200.0 100.0 0.0 -100.0

0%

6%

12%

-200.0

18%

24%

0% 2% 4% +% % 10% 12% 14% 1+% 1% 20% 22% 24% 2+% 2%

>23< 6;232 6)632 )><32 )7)3> )2=3) >?3) 7?3; 6238 <3< 8638 ;<3= ?23; )283) )673> )7;3;

*

.

NPV 's #IRR (s*e fferences)

Answer: 

#E$I%#"+AR$

L 62738 ;;232 7>83) 72632 88<32 6>73= 6)>3= )<73= ));3; <=38 6<32 )73; ;63; ??38 )6)3= );83<

1A##:

)23224 0

C C8

5),222 56,2)2

1 58>; 5>6;

2 58>; 5>6;

3 58>; 5>6;

4 58>; 5>6;

Ans"er: MIRR, L MIRR, + !P@, L !P@, +

)83>4 )73=4 56??3); 5)??3>2

Valu los!

Pr$ect + 1A##: )2324 9ear 2: 5),222 9ear ): 58>;

Pr$ect L 1A##: )2324 9ear 2: 56,2)2 9ear ): 5>6;

5==37;



1,000 800

S L

600 400 200 0 -200 0%

5%

10%

15%

20%

0% 2% 4% +% % 10% 12% 14% 1+% 1% 20% 22% 24%

L )??3> ;2232 76>3= 8<)36 6==37 67632 )??3> )8=32 =63< 7=38 ?3? 6=36 <73= =?37

6??36 ?=232 >;23< <6)3> ;2636 8=)38 6??36 )=63) )2637 )?3> ;=3> )8836 6263) 6<<3=

*0

.

NPV 's aybac!

Answer: 

#E$I%#"+AR$

1A##:

)83224

C

0 5),222

1 5722

2 5722

3 5722

4 5722

C8

56,)22

5?22

5?22

5?22

5?22

-$1,000 -$2,100  

-$+00 -$1,300  

-$200 -$500  

$200 $300 63;2 63<8

$+00 $1,100  

Ans"er: Cuula!"# C,  Cuula!"# C, 8 Pay%ac0 + 63;2 Pay%ac0 L 63<8 !P@, L 56>=3;? !P@, + 5)?=3>= 5?=3>= Valu los!

Pr$ect + 1A##: )8324 9ear 2: 9ear ):

 0% 2% 4% +% % 10% 12% 14% 1+% 1% 20% 22% 24%

5),222 5722

Pr$ect L 1A##: )8324 9ear 2: 9ear ):

56,)22 5?22

L )?=3? <2232 ;683) 7;632 8?<32 8673= 6<>3= 6)73= )<;3; ))=38 ><32 8;3; 63; 8?38

6>=3< ),)2232 =7<36 ?283= <>63) ;7=3> 78;3= 86=3= 68)32 )8?3; ;632 6=32 )2;3) )><3<

1,200 1,000 S

800

L

600 400 200 0 0% -200

5%

10%

15%

20%

25%

*3

.

NPV 's IRR

Answer: a

+AR$

1A##:


)23224 0 5),26; 5),26;

1 5<;2 5722

2 5<;2 5722

3

4

5722

5722

623;4 )>374 56763=; 5)283)2 52322

+

700 600 500 400 300 200 100 0 0%

6%

12%

18%

24%

30%

-100 -200

*.

0% 2% 4% +% % 10% 12% 14% 1+% 1% 20% 22% 24% 2+% 2% 30%

NPV an aybac!

9a Cs

0 Cos! = 

Po;(!;,222 )2324 WACC PV of (ash "flows 8ss NPV I"!"al (os! of o;(! 9a C Cu. C Pay%ac0

0 -$152,447 -$152,447 63;7

)283) 6>;32 68>32 62)32 )<<3> )873) )283) >83; 7;38 )?37 >38 8)3= ;;3; >?3) ==3> )623; )7237

Answer: e

1 $+0,000

2 $+0,000

3 $+0,000

4 $+0,000

L 6763= ;>;32 7=?3) 76>32 8<)32 6==3= 6763= )?=3= )723; =738 ;)32 )23; 6>3; <838 =<3= )6?3< );?3;

+AR$

5 $+0,000

$227,447 = PV of Cs show o !" l" -$75,000 $152,447 1 $+0,000 -$*2,447 

2 $+0,000 -$32,447 

3 $+0,000 $27,553 63;7

4 $+0,000 $7,553 

5 $+0,000 $147,553 

*2

.

Ran!n- ,ethos

Answer: b

EASY

Statement " is tr=e$ "eca=se a projects NP increases as the WACC declines. +&.

Ran!n- ,ethos

Answer: 

EASY

Statement d is tr=e. Academics prefer NP "eca=se it indicates the amo=nt "y which a project increases the firms #al=e. +1.

Ran!n- ,ethos:

aybac!

Answer: 

EASY

Statement d is tr=e. The pay"ac; does indicate how long it sho=ld ta;e to reco#er the in#estment$ hence it is a meas=re of li=idity. +*.


IRR

Answer: e

EASY

The 677 ass=mes rein#estment at the 677$ and that is generally not as #alid as ass=ming rein#estment at the WACC$ as with the NP. ++.

Nor,al 's. nonnor,al cash flows

Answer: e

EASY

+/.

Nor,al 's. nonnor,al cash flows

Answer: a

EASY

+

.

NPV Answer: c

+0

.

Paybac! Answer: b

+3

.

.

.


EASY IRR

Answer:  /&.

EASY IRR

Answer:  +2

EASY

Paybac! Answer: b

+

EASY

NPV

Answer: e

EASY

#E$I%#

Statement e is correct. The others are all false. 6f yo= draw an NP profile for one project$ yo= will see that if the WACC is less than the 677$ the NP m=st "e positi#e. /1.

Ran!n- ,ethos: NPV

Answer: b

#E$I%#

Statement " is correct$ and the others are all false. Cash flows from a project can "e =sed to replace f=nds that wo=ld "e raised in the mar;et at the WACC$ so the WACC is the opport=nity cost for rein#ested cash flows. Since the NP ass=mes rein#estment at the WACC while the 677 ass=mes rein#estment at the 677$ NP is generally the "etter method. /*.

NPV rofles

/+.

Ran!n- conflcts

//.

Paybac! ero

/

.

Answer: 

EASY"#E$I%#

Answer: a Answer: 

#E$I%# #E$I%# NPV

/0.

NPV an IRR

/3

.

Answer: b

#E$I%#

Answer: e

#E$I%#

NPV Answer:

a

rofles #E$I%#

Statement a is tr=e and the other statements are all false. 5istant cash flows are more se#erely penalied "y high disco=nt rates$ so if the NP profile line has a steep slope$ this indicates that its cash flows occ=r relati#ely late. /.

NPV rofles

Answer: b

#E$I%#

Statement " is tr=e$ while the other statements are all false. Project > m=st ha#e the longer life$ and since distant cash flows are impacted more "y changes in the disco=nt rate$ its NP profile m=st "e steeper. /2.

NPV0 IRR0 an #IRR

Answer: a

#E$I%#

&.


Answer: c

#E$I%#

1.

#scellaneo&s concets

Answer: a

#E$I%#

*.

#scellaneo&s concets

Answer: a

#E$I%#

+.


Answer: c

#E$I%#

/.


Answer: e

#E$I%#

.

#<le IRRs

Answer: 

#E$I%#

0

.

NPV rofles

Answer: a

#E$I%#"+AR$

#P$ %&'

L

S

r %(' 0

7%

12%

15%

Statement a is tr=e$ "eca=se "oth projects ha#e an 677 greater than the WACC and th=s will ha#e a positi#e NP. Statement " is false$ "eca=se at 0$ the WACC is less than the crosso#er rate and Project > has a higher NP than S. Statement c is false$ "eca=se at 1+ the WACC is greater than the crosso#er rate and > wo=ld ha#e a higher NP than S. Statement d is false$ "eca=se of reasons mentioned for statement a. Statement e is false$ "eca=se Project Ss NP profile is flatter$ which means Project >s NP is more sensiti#e to changes in WACC. 3.

NPV rofles

Answer: e

#E$I%#"+AR$

#P$ %&'

A

B

r %(' 0

8%

11%

14%

Statement e is tr=e$ while the other statements are all false. 

.

NPV rofles

Answer: b

#E$I%#"+AR$

#P$ %&' A B

0

16% 17%

18%

30%

)iscount rate %('

Statement a is false$ "eca=se if the profiles do not cross$ then one will dominate the other$ with a higher 677 and a higher NP at e#ery disco=nt rate. Statement " is tr=e. Statement c is false. Statement d is false "eca=se a conflict can res=lt from difference in the timing of the cash flows. Statement e is false "eca=se scale differences can res=lt in profile crosso#ers and th=s conflicts. 2.

NPV rofles

Answer: b

#E$I%#"+AR$

#P$ %&' Y X

0

10%

17%

19%

)iscount rate %('

As we can see from the graph$ statement " is tr=e$ "=t the other statements are all false. 0&

.

NPV rofles

Answer: e

+AR$

7efer to the NP profile "elow. Statement a is false$ "eca=se yo= do not ;now which project has the higher NP =nless yo= ;now the WACC. Statement " is false$ "eca=se if the WACC is greater than 677> "=t less than 677S then Project S will ha#e a positi#e NP and Project >s NP will "e negati#e. Statements c and d are false$ "eca=se 677 is independent of WACC. Statement e is tr=e$ "eca=se Project

S has the higher 677$ so Project >s NP profile is a"o#e Project Ss when the WACC is "elow the crosso#er. #P$ %&'

L

S

r %(' 0

01.

10%

IRR-L

IRR-S

NPV rofles

Answer: c

+AR$

#P$ %&' A B

0

16% 17%

18%

30%

)iscount rate %('

7ecall that the #ery definition of the 677 is the disco=nt rate at which the NP is ero. Therefore$ statement c is tr=e$ while all the other statements are false. 0*

.

NPV rofles

Answer: 

50000 L S

30000

10000

-100000%

5%

10%

15%

20%

+AR$

Statement d tr=e$ "=t all the other statements are false. 0+

.

#IRR Answer: c

+AR$

7ecall that if the 677 is e=al to the WACC$ then the <677 and the 677 will "e e=al$ "=t if the 677 is greater than the WACC$ the <677 will "e less than the 677$ and #ice #ersa if the 677 is less than the WACC. This sit=ation eBists "eca=se the <677 is fo=nd "y compo=nding at the WACC while the 677 is fo=nd "y compo=nding at the 677. 6n other words$ if we compo=nd the inflows at the 677 to find the T$ we will get a larger T than if we compo=nd at the WACC. Then$ the rates that ca=se the Ps of those Ts to e=al the cost are the 677 and the <677$ respecti#ely. As a res=lt$ statement c is correctif the 677 eBceeds the WACC$ the 677 will eBceed the <677. The other statements are all false. 0/

0.

.

#IRR

NPV an ro1ect selecton

Answer: e

+AR$

Answer: c

+AR$

Statement c is tr=e$ while the other statements are all false. 6f we draw an NP profile graph$ we wo=ld see that A m=st ha#e the steeper slope. 6f the crosso#er is at $ and the WACC is at 1&$ then 4 will ha#e the higher NP. 00.

2hoosn- a,on- ,&t&ally ecl&s'e ro1ects

03.

#<le IRRs

Answer: c Answer: c

+AR$ +AR$

Statement c is tr=e$ while the other statements are all false. @ne co=ld calc=late the two 677s and the <677$ "=t the data in the pro"lem are correct$ so this is not necessary. 0

.


Answer: b

Time line 8in tho=sands9) & C:s ,1& C=m=lati#e C:s ,1&

1

*

+

/



0

3



2

1& (rs.

+&

+&

+&

+&

+

+

+

+

+

/&

,1*&

,2&

,0&

,+&



The project will completely reco#er the initial in#estment after -+&H-+ % &.0 of (ear ) Pay"ac; % /  02.


-+& -+.

% /.0 years.

Answer: c

Time line 8in tho=sands9) & C: C=m=lati#e NC:

*

+

/



0

1& (ears

• • •

,1&&

,&&

1&&

11&

1*1

1++.1

1/0./1

,1&&

,0&&

,&&

,+2&

,*02

,1+.2

1&.1

Pay"ac; %   3&.

1

-1+.2 -1/0./1

% .2* years

0 years.

≈

$sco&nte aybac!

Answer: e

The P of the o=tflows is ,-3&& million. To find the disco=nted pay"ac; yo= need to ;eep adding cash flows =ntil the c=m=lati#e Ps of the cash inflows e=al the P of the o=tflow)

(ear & 1 * + /

Cash :low ,-3&& million *&& million +3& million ** million 3&& million

5isco=nted Cash :low Q 1& ,-3&&.&&&& 11.1* +&.31 102.&/ /3.1&2/

The pay"ac; occ=rs somewhere in (ear /. To calc=late -/+.+&2H-/3.1&2/ % &.&2&3 thro=gh disco=nted pay"ac; is +.&21 years.

C=m=lati#e P ,-3&&.&&&& ,1.11 ,*1*.+203 ,/+.+&2 /+/.3 find o=t eBactly where$ we the year. Therefore$ the

31

.


(ear & 1 * + /

Answer: 

Cash :low ,-+$&&& 1$&&& 1$&&& 1$&&& 1$&&&

5isco=nted Cash :low Q 1& ,-+$&&&.&& 2&2.&2 *0./ 31.+1 0+.&1

C=m=lati#e P ,-+$&&&.&& ,*$&2&.21 ,1$*0/./0 ,1+.1 102.0

After (ear +$ yo= can see that yo= wont need all of (ear / cash flows to "rea; e#en. To find the portion that yo= need$ calc=late -1+.1H-0+.&1 % &.3. Therefore$ the disco=nted pay"ac; is +.3 years. 3*.

NPV :inancial calc=lator sol=tion 8in tho=sands9) Project J) 6np=ts) C:& % ,1&&M C:1 % &M C:* % /&M C:+ % +&M C:/ % 1&M 6H(7 % 1. @=tp=t) NPJ % ,&.++ % ,-++.

Answer: a

Project K)

6np=ts) @=tp=t)

C:& % ,1&&M C:1 % 1&M C:* % +&M C:+ % /&M C:/ % 0&M 6H(7 % 1. NPK % ,.&1/ % ,-$&1/.

At a WACC of 1$ "oth projects ha#e negati#e NPs and sho=ld "e rejected. 3+.

NPV

Answer: a

:inancial calc=lator sol=tion) Project A) 6np=ts) C:& % ,&&&&M C:1 % 10*M Nj % M 6H(7 % 1&. @=tp=t) NP % -2$*+1.&/. Project 4)

6np=ts) C:& % ,&&&&M C:1 % &M Nj % /M C:* % 22&&M 6H(7 % 1&. @=tp=t) NP % -11$31.03.

3/ NP4 R NPAM -11$31.03 R -2$*+1.&/M Choose Project 4.

.

IRR

Answer: c

:inancial calc=lator sol=tion) 6np=ts) C:& % ,*&&&&&M C:1 % //&+M Nj % 1&.

@=tp=t) 677 % 1.

3

.

IRR

Answer: c

:inancial calc=lator sol=tion) 6np=ts) C:& % &M C:1 % ,1&&M Nj % 12M C:* % +*1&.

@=tp=t)

677 % .&.

30

.

33.

IRR0 aybac!0 an ,ssn- cash flow

Answer: 

Step 1)

5etermine the cash o=tflow at t % &) The pay"ac; is *.* years$ so the cash flow will "e) C:& % ,C:1  C:*  &.*8C:+9 % ,-&&  -+&&  &.*8-/&&9 % ,-2&&.

Step *)

Calc=late the 677) C:& % ,2&&M C:1 % &&M C:* % +&&M C:+ % /&&M C:/ % 0&&M and then sol#e for 677 % ++./2 ≈ ++..

IRR an ,&t&ally ecl&s'e ro1ects

Answer: 

4eca=se the two projects are m=t=ally eBcl=si#e$ the project with the higher positi#e NP is the F"etterG project. Project S 6np=ts) C:& % ,11&&M C:1 % 1&&&M C:* % +&M C:+ % &M 6H(7 % 1*. @=tp=ts) NP % -1&3./0M 677 % *&./0. Project > 6np=ts) C:& % ,11&&M C:1 % &M C:* % +&&M C:+ % 1&&M 6H(7 % 1*. @=tp=ts) NP % -*&0.+M 677 % 12.&. Project > is the F"etterG project "eca=se it has the higher NPM its 677 %

12.&. 3.

NPV an IRR

Answer: b

Project S)

6np=ts) C:& % ,1&&&M C:1 % &&M Nj % +M 6H(7 % 1&. @=tp=ts) -*/+./+M 677 % *+.+.

Project >)

6np=ts) C:& % ,*&&&M C:1 % 00.30M Nj % M 6H(7 % 1&. @=tp=ts) -+.1+M 677 % *&.

al=e sacrificed)

-+.1+ , -*/+./+ % -*21.3&.

32

.

NPV an IRR

Answer: e

:inancial calc=lator sol=tion) Project A) 6np=ts) C:& % ,&&&&M C:1 % 1&&&&M C:* % 1&&&M C:+ % /&&&&M C:/ % *&&&&M 6H(7 % 1&. @=tp=ts) NP % -1$*&&./0 U -1$*&&M 677 % *1.+. Project 4)

6np=ts) C:& % ,+&&&&M C:1 % 0&&&M C:* % 1*&&&M C:+ C:/ % 1*&&&M 6H(7 % 1&. @=tp=ts) NP % -3$&21.3+ U -3$&2*M 677 % 12.*.

%

1&&&M

Project A has the highest 677$ so the answer is -1$*&&. &

.

NPV0 IRR0 an aybac!

Answer: 

Pay"ac; % *  -+&&H-&& % *.0 years. Vsing the cash flow register$ calc=late the NP and 677 as follows) 6np=ts) C:& % ,1&&&M C:1 % /&&M C:* % +&&M C:+ % &&M C:/ % /&&M 6H(7 % 1&. @=tp=ts) NP % -*0&./+ ≈ -*0&M 677 % *1.**. 1.

Paybac! ero Step 1)

Step *)

Step +) (ear & 1 * + / 

Answer: c

Calc=late the P of the cash flows) 6np=ts) N % M 6H(7 % 1&M P
So the pay"ac; is * 

-+*$//3 -0&$&&&

% *./ years.

*

.


Answer: 

Project A) (ear Cash :low & ,-1&&$&&& 1 /&$&&& * /&$&&& + /&$&&& / +&$&&& Project As disco=nted pay"ac; accepted.

5isco=nted Cash :low Q 1& ,-1&&$&&&.&& +0$+0+.0/ ++$&3. +&$&*.2 *&$/2&./2 period eBceeds +

C=m=lati#e P ,-1&&$&&&.&& ,0+$0+0.+0 ,+&$3.1 ,*.2* 12$20/.3 years$ so it wo=ld not "e

Project 4) 5isco=nted (ear Cash :low Cash :low Q 1& C=m=lati#e P & ,-&$&&& ,-&$&&&.&& ,-&$&&&.&& 1 &$&&& /$//. ,+/$/./ * *&$&&& 10$*.2+ ,1$&10.* + +&$&&& **$+2.// /$**.2* / & & /$**.2* (o= can see that in (ear + the c=m=lati#e cash flow "ecomes positi#e so the projects pay"ac; period is less than + years. +.

NPV

Answer: 

:inancial calc=lator sol=tion 8in tho=sands9) 6np=ts) C:& % ,1&M C:1 % +&M Nj % /M C:* % +M Nj % M C:+ % /&M 6H(7 % 1&. @=tp=t) NP % -1.1+*/ % -1$1+.*/ ≈ -1$1+. /

.

NPV

Answer: b

:inancial calc=lator sol=tion 8in tho=sands9) 6np=ts) C:& % &M C:1 % M Nj % M C:* % +M Nj % +M C:+ % *M Nj % *M 6H(7 % 1/. @=tp=t) NP % *1.2+3*0 % -*1$2+3.*0. .

NPV

Answer: 

:irst$ find the #al=e of J 8the =p,front cash flow in this project9. 677 is the rate at which yo= need to rein#est the cash flows for NP to e=al -&. 6n this case$ the 677 is 1*$ so if yo= in#est all the projects cash flows at 1*$ yo= sho=ld ha#e an NP of ero. Step 1)

Calc=late the #al=e of the initial cash flow "y sol#ing for NP at a WACC of 1*) (o= dont ha#e C:&$ so =se & as the placeholder. Enter the following data as inp=ts in yo=r calc=lator) C:& % &M C:1 % 3&&&M Nj % *&M and 6H(7 % 1*. Then sol#e for NP % -0&$*&.*3.

This is the NP when the initial cash flow is missing. The NP with the cash flow m=st "e -&$ so that initial cash flow m=st "e -0&$*&.*3. Step *)

0.

Calc=late the projects NP at its WACC of 1&) Enter the following data as inp=ts in yo=r calc=lator) C:& % ,0&*&.*3M C:1 % 3&&&M Nj % *&M and 6H(7 % 1&. Then sol#e for NP % -3$+&2.&1 ≈ -3$+&2.

NPV0 aybac!0 an ,ssn- cash flow

Answer: b

:irst$ find the missing t % & cash flow. 6f pay"ac; % *. years$ this implies t

% & cash flow m=st "e ,-*$&&& , -+$&&&  8&.9-+$&&& % ,-0$&&.

NP % ,-0$&& 

-*$&&& 1.1*



-+$&&& *

81.1*9



-+$&&& +

81.1*9



-1$&& /

81.1*9

% -30.21. :inancial calc=lator sol=tion 8in tho=sands9) 6np=ts) C:& % ,0&&M C:1 % *&&&M Nj % +&&&M C:* % 1&&M 6H(7 % 1*. @=tp=t) NP % -30.21. 3

.

IRR

Answer: 

:inancial calc=lator sol=tion)
6np=ts) C:& % ,*&&&M C:1 % +*M Nj % /. @=tp=t) 677 % */.&1 ≈ */.



.

IRR

Answer: c

:inancial calc=lator sol=tion) Project A) 6np=ts) N % 1M P % ,1&&&&M P
2.

6np=ts) @=tp=t)

N % +M P % ,1*&&&M P
IRR

Answer: e

Vsing yo=r financial calc=lator find the NP witho=t the initial cash flow) C:& % &M C:1 % 1&M C:* % *&&M C:+ % *&M C:/ % /&&M C: % 1&&M 6H(7 % 1&M and then sol#e for NP % -*/.3. This means that the initial cash flow m=st "e 3&& 8-1*/.3 , -*/.3 % ,-3&&9. Now$ we can enter all the cash flows and sol#e for the projects 677. C:& % ,3&&M C:1 % 1&M C:* % *&&M C:+ % *&M C:/ % /&&M C: % 1&&M and then sol#e for 677 % 10.+. 2&.

NPV an IRR

Answer: a

:inancial calc=lator sol=tion) Project S) 6np=ts) C:& % ,11&&M C:1 % 2&&M C:* % +&M C:+ % &M C:/ % 1&M 6H(7 % 1*. @=tp=ts) NPS % -*/.+M 677S % 1+.. Project >)

6np=ts)

C:& % ,11&&M C:1 % &M C:* % +&&M C:+ % &&M C:/ % &M 6H(7 % 1*. @=tp=ts) NP> % -+.*/M 677> % 1+.&2.

Project > has the higher NP and its 677 % 1+.&2.

21.

IRR0 aybac!0 an ,ssn- cash flow Step Step 1)

Answer: c

:ind :ind Proj Projec ect t 1s 1s pay" pay"ac ac;) ;)

(ear & 1 * + /

Project 1 Cash :low ,1&& +& & /& &

C=m=lati#e Cash :low ,1&& ,3& ,*& *& 3&

Pay"ac;Project 1 % *  -*&H-/& % *. years.

Step *)

Step Step +)

2*.

Project *s pay"ac; % *. years "eca=se were told the two projects pay"ac;s are e=al. Calc=late Calc=late Project Project *s *s initial initial o=tlay$ o=tlay$ gi#en gi#en its its pay"ac; pay"ac; % *. years) years) 6nitial o=tlay % ,C:1  C:*  8&.98C:+9 % ,-/&  -&  8&.98-0&9 % ,-1&. Calc Calc=l =lat ate e Pro Proje ject ct *s *s 677 677) ) Enter the following data in the calc=lator) C:& % ,1&M C:1 % /&M C:* % &M C:+ % 0&M C:/ % 0&M and then sol#e for 677 % *&..

#IRR

Answer: 

:inancial calc=lator sol=tion) T 6np=ts) N % M 6H(7 % 1*M 1*M P % &M P
#IRR Step Step 1)

Step Step *)

Answer: e :ind :ind the : of the cash cash inflow inflows s "y firs first t findin finding g the NP of these these inflows and then finding the : of their NP. C:& % &M C: 1,* 1,* % *&&&M C:+, +, % &&&&M 6H(7 % 1*M and then sol#e for NP % -1+3$23.+. N % M 6H(7 % 1*M P % ,1+323.+M P
2/.

#IRR

Answer: 

:irst$ calc=late the present #al=e of costs) N % /M 6H(7 % 1&M P
and

then

sol#e

for

P

%

:ind the terminal #al=e of inflows) C:& % &M C:1 % &&&&M C:* % &&&&M C:+ % &&&&M C:/ % &M 6H(7 % 1&. Sol#e for NP % -1*/$+/*.0&. Vse the T< ;eys to calc=late the f=t=re #al=e of this present #al=e. N % /M 6H(7 % 1&M P % ,1*/+/*.0&M P
#IRR

Answer: e

Calc=late T 8Terminal #al=e9 of inflows) 6np=ts) C:& % &M C:1 % &M C:* % &&&&&M Nj % /M C:+ % 1&&&&&&M 6H(7 % 1*. @=tp=t) NP % -1$0*$2&.0. 6np=ts) N % 0M 6H(7 % 1*M P % ,10*2&.0M P
#IRR

Answer: e

Time line) & L ,*&&

1*'

1

*

+

L 1*&

L ,&

L 3&&

× 81.1*9

1

×

,+ , +2.23 ,*+2.23

*

1&.*

*

81.1*9

<677 % !

&.*

Vsin Vsing g yo=r yo=r fina financ ncia ial l calc calc=l =lat ator or$ $ ente enter r the the foll follow owin ing g data data as inp= inp=ts ts) ) N % +M P % ,*+2.23M ,*+2.23M P
.

#IRR Step Step 1)

Answer: e :ind :ind the P P of the the cash cash o=tflo o=tflows ws 8in 8in millio millions ns of doll dollars ars9) 9)

Step Step *)

Step +) +)

P % ,-+&&  ,-1&&H1.1& % ,-+2&.2&21. :ind :ind the : of the cash cash infl inflows ows 8in 8in milli millions ons of of dollar dollars9) s9) * : % -3&81.1&9  -1*81.1&9  -3&& % -/.3&  -1+3.  -3&& % -2**.*&. :ind th the <6 <677) N % /M P % ,+2&.2&21M P
1

1&'

+

/

L

L

L

L

,1&&

3&

1*

3&&.&& 1+3.& /.3& 2**.*&

<677 % *+.2+'

,+2&.2&21

2.

*

#IRR an ,ssn- cash flow

Answer: 

The =p,front cost can "e calc=lated =sing the pay"ac;) -/&&  8-&&98&.9 % -0&. The terminal #al=e of the cash inflows are) 8-/&&981.19*  8-&&981.19  -*&& % -1$*+/. Vse yo=r calc=lator to o"tain the <677) Enter N % +M P % ,0&M P
#IRR0 aybac!0 an ,ssn- cash flow Step Step 1) Step Step *)

Step Step +)

Answer: 

Sol# Sol#e e fo for the the C:& "y ;nowing the pay"ac; is eBactly *.&) The C:& for the project is -1  -1. % -*. million. :ind :ind the the : : of of the the cash cash infl inflow ows) s) 1 : % -*.&  8-*.&&981.1*9  8-1.&981.1*9*  8-1.&&981.1*9+ % -*.&  -*.*/  -1.10&  -1./&/2+ % -.&*0+& million. Sol# Sol#e e for for the the <677 <677) ) Enter the following inp=t data in the calc=lator) N % /M P % ,*. ,*.M M P
for for

1&&

.

#&t&ally ecl&s'e ro1ects

Answer: b

:inancial calc=lator sol=tion) Project A) 6np=ts) C:& % ,1&&&&&M C:1 % +2&&M Nj % +. @=tp=t) 677A % .22* ≈ 2.&. Project 4)

6np=ts) @=tp=t)

C:& % ,1&&&&&M C:1 % &M Nj % *M C:* % 1++&&&. 6774 % 2.23* ≈ 1&.&.

1&1The firms cost of capital is not gi#en in the pro"lemM so =se the 677 decision r=le. Since 6774 R 677AM Project 4 is preferred.

.

/eforeta cash flows Time line) & 1 677 % 1' ,1&$&&&

P
Answer: b

*

+

/

P
P
P
1& (ears

• • •

P
:inancial calc=lator sol=tion) 6np=ts) N % 1&M 6H(7 6H(7 % 1M P % ,1&&&&M ,1&&&&M : % &. @=tp=t) P
NPV

Answer: c

Step Step 1) 1) Step *) Step Step +)

Step Step /)

1&+.

7=n a regre regressi ssion on to find find the the corpo corporat rate e "eta "eta. . 6t is is 1.10+ 1.10++. +. :ind the project projects s estimat estimated ed "eta "eta "y adding adding &.* to the the corporat corporate e "eta. "eta. The project "eta is th=s 1.+0++. :ind :ind the compa company nys s cost of of e=ity$ e=ity$ which which is its its WACC WACC "eca=se "eca=se it =ses =ses no de"t) rs % WACC % 3  891.+0++ % 1+.10 ≈ 1+.*. Now Now fin find d NP NP 8in 8in mil milli lion ons9 s9) ) C:& % ,1&&M C:1, 1, % *&M C:0,1& % +&M 6H(7 % 1+.*M and then sol#e for NP % -*+.11 million.

NPV

Answer: c

Step Step 1)

Step Step *) Step Step +)

Step Step /)

7=n a regre regressi ssion on to to find find the the corp corpora orate te "eta "eta. .
1&/

.

#IRR an NPV

Answer: c

:ind the <677 of the Projects. Time line for Project J) WACC % 1*' % !

& <677 L ,*$&&&

,*$&&&

1 L *&&

* L 0&&

<677J % ! 1+.2'

+ L &&×81.1*9

/ (ears L 1$/&&.&& 20.&& * ×81.1*9 3*.0/ + ×81.1*9 *&.22 Terminal al=e 8T9 % +$+*2.0+

Time line for Project () WACC % 1*' % !

& <677 L ,*$&&&

1 L *$&&&

* L *&&

<677( % ! 1*.2'

,*$&&&

+ L 1&&×81.1*9

/ (ears L 3.&& 11*.&& * ×81.1*9 *&. + ×81.1*9 *$&2.0 Terminal al=e 8T9 % +$*/3.3/

Calc=late NP of Projects) Project J) 6np=ts) C:& % ,*&&&M C:1 % *&&M C:* % 0&&M C:+ % &&M C:/ % 1/&&M 6H(7 % 1*. @=tp=t) NPJ % -110.&/. Project ()

6np=ts) C:& % ,*&&&M C:1 % *&&&M C:* % *&&M C:+ % 1&&M C:/ % 3M 6H(7 % 1*. @=tp=t) NP( % -0+.22.

Note that the "etter project is J "eca=se it has a higher NP. 6ts corresponding <677 % 1+.2. 8Also note that since the * projects are of e=al sie that the project with the higher <677 will also "e the project with the higher NP.9 1&.

#IRR an ,ssn- cash flow Step 1)

Step *) Step +)

1&0.

Step *)

Step +)

Step /)

1&3.

5etermine the P of cash o=tflows and the : of cash inflows. The P of all cash o=tflows is ,-&&  ,JH81.1&9*. The : of all cash + inflows is -&&  -+&&81.19  -*&&81.19 % -&&  -++&  -*00.*& % -1$&20.*&. :ind the P of the f=t=re #al=e of cash inflows =sing the <677. N % /M 6H(7 % 1*M P
#IRR an ,ssn- cash flow Step 1)

#IRR

Answer: b

Answer: b

5etermine the missing cash o=tflow) The pay"ac; is * years so the project m=st ha#e cash inflows thro=gh t % * that e=al its cash o=tflow. ,C:& % C:1  C:*M C:& % ,8-1&&$&&&  -*&&$&&&9M C:& % ,-+&&$&&&. Calc=late the present #al=e of the cash o=tflows) C:& % ,+&&&&&M C:1 % &M C:* % &M C:+ % &M C:/ % ,1&&&&&M 6H(7 % 1&M and then sol#e for NP % ,-+0$+&1.+/. Calc=late the f=t=re #al=e of the cash inflows) C:& % &M C:1 % 1&&&&&M C:* % *&&&&&M C:+ % *&&&&&M C:/ % &M 6H(7 % 1&M and then sol#e for NP % -/&0$/01.+&3+. N % /M 6H(7 % 1&M P % ,/&0/01.+&3+M P
Answer: e

:irst$ find the companys weighted a#erage cost of capital) Were gi#en the "efore,taB cost of de"t$ rd % 1&. We can find the cost of e=ity as follows) rs % &.&0  &.&81.19 % &.11 or 11.. Th=s$ the WACC is) r % &./8&.1&981 , &.+9  &.08&.119 % &.&23 or 2.3. Second$ the P of all cash o=tflows can "e calc=lated as follows) C:& % ,&&&&M C:1,+ % &M C:/ % ,/&&&&M 6H(7 % 2.3. Sol#e for NP of costs % ,-33$0*&.0*. Third$ find the terminal #al=e of the project at t % /) C:& % &M C:1 % +&&&M C:* % /+&&&M C:+ % 0&&&&M C:/ % &M 6H(7 % 2.3. Sol#e for NP % -11+$&0.30. Vse the T< ;eys to calc=late the f=t=re #al=e of this present #al=e. N % /M 6H(7 % 2.3M P % ,11+&0.30M P
.

#IRR

Answer: b

Time line 8in tho=sands9) &

% 1*'

1

1& •

•

11

*&

•

,3$&&& && ,&& ,101 ,3$101 % P of o=tflows

•

•

•

&&

&&

T of inflows)

Calc=lation of P of o=tflows) C:& % ,3&&&M C:1,2 % &M C:1& % ,&&M ,-3$10&.22 ≈ ,-3$101.

6H(7 %

Calc=lation of T of inflows) C:& % &M C:1,2 % &&M C:1& % &M C:11,*& % -+$3+.3/.

+/$/3+.+&

1*M and then sol#e for

&&M

6H(7

%

1*.

Vse T< to calc=late the f=t=re #al=e of the present #al=e. P % ,+3+.3/M P
Sol#e

for

NP %

NP

%

N % *&M 6H(7 % 1*M

Calc=lation of <677) N % *&M P % ,3101M P
677 % *.* and NP % ,-+$3$*1.

4oth are consistent with <677 less

than WACC % 1*. 1&2.

PV of cash flows

Answer: c

:inancial calc=lator sol=tion) @ld lease) 6np=ts) N % 0&M 6H(7 % 11H1* % &.2103M P

Answer: b

Pay"ac; is how long it ta;es for a firm to reco=p its initial in#estment.

(ear & 1 * + /

Project Cash :low ,-+&& 1* 3 *&& 1&&

C=m=lati#e Cash :low ,-+&& ,13 ,1&& 1&& *&&

Therefore$ the project has a pay"ac; of *  -1&&H-*&& % *. years. 111.


Answer: 

We m=st find the Ps of the cash flows =sing the firms 1& WACC.

(ear & 1 * + /

Cash :low ,-+&& 1* 3 *&& 1&&

5isco=nted Cash :low Q 1& ,-+&&.&& 1*H1.1& % 11+.0/ 3H81.1&9* % 01.2 *&&H81.1&9+ % 1&.*0 1&&H81.1&9/ % 0.+&

Therefore$ the projects disco=nted pay"ac; is * 

11*.

IRR

C=m=lati#e P ,-+&&.&& ,10.+0 ,1*/.+ *. 2/.1

-1*/ .+ -1& .*0

% *.+ years.

Answer: 

:inancial calc=lator sol=tion) C:& % ,+&&M C:1 % 1*M C:* % 3M C:+ % *&&M C:/ % 1&&M and then sol#e for 677 % *+./*. 11+.

NPV

Answer: c

:inancial calc=lator) C:& % ,+&&M C:1 % 1*M C:* % 3M C:+ % *&&M C:/ % 1&&M 6H(7 % 1&M and sol#e for NP % 2/.1 % -2/.1 million. 11/.

#IRR

Answer: c

To calc=late the <677$ we need to find the P of all the o=tflows and the : of all the inflows. The disco=nt rate that e=ates the two is the <677. P of inflows ,-+&&

-1* - 3 -*&& -1&&

: of o=tflows + × 1.1& % -100.+3 * % 2&.3& × 1.1& 1 % **&.&&& × 1.1& & % 1&&.&&& × 1.1& -33.1*

Vsing a financial calc=lator) N % /M P % ,+&&M P
NPV

Answer: 

:inancial calc=lator sol=tion) C:& % ,+&&M C:1 % 1&&M C:* % 1&M C:+ % *&&M C:/ % &M 6H(7 % 1&M and then sol#e for NP % -22.*2. 110.

IRR

Answer: 

:inancial calc=lator sol=tion) C:&% ,+&&M C:1% 1&&M C:*% 1&M C:+% *&&M C:/% &M sol#e for 677% */.32. 113.

#IRR & L

Answer: e 1&'

,+&&

1

*

+

/

L

L

L

L

1&&

1&

*&&

&.& × 1.1

× 81.19

*

× 81.19

,+&&

<677 % !

+

**&.& 11. 1++.1 /.0

All the cash o=tflows are disco=nted "ac; to the present. all cash inflows are compo=nded to (ear /.

The f=t=re #al=e of

Vsing a financial calc=lator) N % /M P % ,+&&M P
NPV

Answer: b

Vsing a financial calc=lator) C:& % ,&&&M C:1 % &&&M C:* % +&&&M C:+ % ,1&&&M 6H(7 % 1&M and then sol#e for NP % -1$*3+./ ≈ -1$*3+. 112.

#IRR Step 1) Step *) Step +)

1*&.

Answer: c The P of all cash o=tflows is) ,-$&&&  ,-1$&&&H81.1&9+ % ,-$31.+1/. The : of all cash inflows is) -$&&&81.1&9*  -+$&&&81.1&9 % -2$+&.&&. Now calc=late the <677 as follows) N % +M P % ,31.+1/M P
#ssn- cash flow0 aybac! ero0 an NPV

Answer: a

6f the project has a pay"ac; period of * years$ then J % *

-13 % -+&.

×

N=merical sol=tion) The NP is -+&  -13H81.1&9  -13H81.1&9*  -+&&H81.1&9+ % -132.11. :inancial calc=lator sol=tion) Enter the following data in yo=r calc=lator) C:& % ,+&M C:1 % 13M C:* % 13M C:+ % +&&M 6H(7 % 1&M and then sol#e for NP % -132.11.

1*1.

#ssn- cash flow0 IRR0 an NPV

Answer: c

N=merical sol=tion) To ha#e an 677 of 1$ the NP at 1 is ero. So) ,J  -13H81.19  -13H81.19*  -+&&H81.19+ % &$ or J % -/1.3+2. So$ the NP with a WACC of 1* is calc=lated as follows) NP % -/1.3+2  -13H81.1*9  -13H81.1*9*  -+&&H81.1*9+ -*3./.

%

-*3.+21

≈

:inancial calc=lator sol=tion) Step 1) :ind the missing cash flow "y entering the following data in yo=r calc=lator) C:& % &M C:1 % 13M C:* % 13M C:+ % +&&M 6H(7 % 1M and then sol#e for NP % -/1.3+2. Step *) Calc=late the NP at a WACC of 1*) C:& % ,/1.3+2M C:1 % 13M C:* % 13M C:+ % +&&M 6H(7 % 1*M and then sol#e for NP % -*3.+21 ≈ -*3./. 1**.

NPV

Answer: 

Vsing a financial calc=lator) C:& % ,&&M C:1 % 1&M C:* % *&&M C:+ % *&M C:/ % 1&&M 6H(7 % 1&M and then sol#e for NP % -3.3. 1*+.

IRR

Answer: a

Vsing a financial calc=lator) C:& % ,&&M C:1 % 1&M C:* % *&&M C:+ % *&M C:/ % 1&&M and then sol#e for 677 % 1.+*. 1*/.

#IRR

Answer: b

:irst$ find the P of all cash o=tflows) P % ,-&&  ,-+&&H81.1&9/ % ,-3&/.2&. Second$ find the : of all cash inflows) : % -+&& × 81.1&9+  -+&& × 81.1&9*  -+&

81.1&91 % -1$1/3.+&.

×

:inally$ find the <677 =sing these two #al=es "y entering the following data into yo=r financial calc=lator)

Basics of Capital Budgeting

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