Solutions Manual to Accompany FAPF_Ch12

8/10/2019 Solutions Manual to Accompany FAPF_Ch12

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CHAPTER 12

CAPITAL BUDGETING UNDER CERTAINTY

1. Shareholder wealth maximization occurs when projects are chosen with a rate of

return greater than the market-determined rate of return or the cost of capital of

the firm. Stated in other words, profit maximization occurs when the firms

marginal costs equal its marginal revenue. Shareholder wealth maximization and

profit maximization are snonmous with maximizing the value of the firm.

!he relevant cash flows to examine are the expected cash inflows from the

project over time and the initial and continuing outflows or costs associated with

the project. !he future cash flows that are incremental to the project or that accrue

to the firm onl as a result of the specific project in question should "e examined.

#n addition, an decrease in cash flows to the compan caused " the project in

question, e.g., the tax depreciation "enefit when old equipment is replaced "

equipment, must "e considered as well.

$ccounting regulations attempt to adjust cash flows over several periods% e.g.,

the expense of an asset is depreciated over several time periods. &ence, project

costs associated with the project are matched with the project revenues in the

periods in which those revenues are expected to accrue. 'ecause this time frame

ma span the life of the project, accounting for cash flows at a given point in time

for capital "udgeting purposes is accomplished " using economic cash flows.

(conomic cash flows are calculated as the occur to the firm.

).a. !he incremental after-tax operating cash flow (net cash inflow in a given

period t is defined as the after tax incremental operating cash flow, *1 + tCOt

plus the incremental depreciation tax su"sid, tdept,where COtrepresents the

pretax incremental operating cash flow, trepresents the marginal tax rate, and

deptrepresents the incremental depreciation. #ncremental means the change in

a particular item as a result of the firm undertaking the project.


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". $ !"t"all# e$cl"si%eproject is one whose acceptance precludes the

acceptance of another project while an in&e'en&entproject can "e accepted

even other projects are also accepted.

c. !he o''ot"nit# cost of a new investment is the ield that is given up to

invest in the new project. !he cost of ca'ital is the rate of return required "

an investor to invest in a project which means that another investment must "e

given up. !hus, the cost of capital is the investors opportunit cost.

d. !he acco"ntin) ate of et"n (ARR !etho& is the ratio of the investments

annual net income after taxes to either total outla or average outla. *See page

/0) of text.

e. !he ein%est!ent ate is that rate at which cash flows from a project are

reinvested.

f. !he 'ofita*ilit# in&e$+ often referred to as the "enefitcost ratio, is defined as

the present value of *incremental net cash inflows over the life of the project

divided " the initial outla for the project.

g. Ca'ital ationin) refers to the scenario where a firm sets limits on the amount

of funds it will spend on fixed assets due to the large num"er of availa"le

*profita"le investments.

2. #n estimating cash flows without de"t, the following equation expresses the

necessar tax adjustments3


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45 6 #45'! *1 + ! 7 !8,

where #45'! 6 incremental 45 "efore tax,

! 6 corporate tax rate,

8 6 incremental annual change in depreciation *8(9 *i.e., 8(9 of new

8(9 of old.

#ncluded in the 45, then, are the increase in income due to the new project,

adjustments to the 45 for additional taxes due to the increased income and due to

the difference in 8(9 per ear.

:ith de"t financing we must also adjust the increased interest paments per

ear, net of tax savings. !he first and last ear 45 will include investment, set-up

costs, and salvage value, respectivel.

/. 9rofessor 9inches suggests the following process3

a. #dentification of areas of opportunit

". 8evelopment of information

c. Selection of the "est alternative or courses of action to "e implemented, and

d. 4ontrol or feed"ack of the degree of success or failure of "oth the project and

the decision process itself

;. 'oth the # have advantages relative to the $


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estimated for the projects life. !he cumulative time period is calculated at the

point where the sum of annual cash inflows equals the initial investment. !he time

period is the pa"ack period.

" !he accounting rate-of-return method averages the after-tax profit from an

investment for ever period over the initial outla.

B

$

*1 C

N

t

I=

= +

where k 6 the appropriate discount rate.

e !he profita"ilit index is calculated " dividing the discounted cash flows "

the initial investment to arrive at the present value per dollar of outla3


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=

t

tt B

459# #

*1 C==

+ .

!he project should "e undertaken if the 9# is greater than 1.

!he net present value, profita"ilit index, and internal rate-of-return methods

are theoreticall and empiricall more accepta"le than the accounting rate-of-

return and net pa"ack period methods in that the explicitl consider the cost of

capital and the time value of mone.

A.

!he net present value method assumes reinvestment of intermediate funds at a

single discount rate. #n contrast, the # and #


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"etween the =9> and #


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inflation increases. !he higher the rate of inflation, the larger the discount rate,

and thus the lower the marginal present value for successive dollars invested.

" &igh rates of inflation result in lower capitalla"or ratios and thus influence the

firms choice of technolog. !he HpriceI of la"or does not depend on the rate of

inflation, whereas the HpriceI of investment does depend on inflation. !hus the

level of inflation corresponds to different price ratios "etween la"or and capital,

and influences the chosen amount of each factor.

c #nflations impact on mutuall exclusive projects deals with depreciation in the

sense that depreciation rates are "ased on historical costs and the distri"ution of

these charges over the life span of the projects determines the net present value.

d :hen inflation is high, projects with shorter life spans will "e favored over

those with longer expected lives "ecause those with shorter life spans will have

their depreciation costs restated in current dollars more frequentl as the are

replaced.

e !his proposition relates to those projects whose lifetime is influenced "

managerial decisions a"out replacement. #n these cases, higher inflation will work

against current replacement. !his occurs "ecause the present value of the

replacement is directl influenced " the effect of inflation on future tax savings

from depreciation. !hus, although with low inflation an investment ma "e

replaced "ecause of high operating costs, with high inflation the present value of

the old project ma "e higher than that of the replacement project.

11. 9ractitioners face the pro"lem of managing uncertaint when performing capital

"udgeting. !uttle and ?itzen"erger suggest that returns on investment projects can

"e made risk-equivalent to the firms cost of equit capital " financing theprojects with the proper amount of "orrowing or lending. $ssuming a competitive

market with man small, risk-averse investors, the price of the firms common

stock *its market trade-off point is a function of its expected rate of return and

estimated standard error of return. :ith perfect correlation of projected returns,

acceptance criteria are o"vious with two exceptions. !hese occur when the

expected #


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risk inherent in the project through a specific de"t-equit ratio or through long-

term "orrowing and lending. !he risk-adjusted rate of return equals the ield to

maturit of the firms long-term de"t plus the financing mix factor multiplied "

the expected #


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$lthough in theor a projects coavariance with other projects is the relevant

risk measure, consideration must "e given to non-quantifia"le factors such as

human dedication to the project. Such factors are important in determining risk

associated with projects in real-world applications.

1). ?inear programming can "e used in capital rationing when the o"jective of the

firm is to "e maximized or minimized and the constraints limiting the firms

actions are linear functions of the decision varia"les involved. !he first step is to

model the pro"lem in linear programming form. !his is done " a identifing the

controlla"le decision varia"les and " defining the o"jective to "e maximized or

minimized and representing it as a linear function of the controlla"le decision

varia"les. !his is followed " defining the constraints and expressing them as

linear equations or inequalities of the decision varia"les. !he following

assumptions are made3

*1 the solution values of the decision varia"les are divisi"le, and

*) the constant coefficients are assumed known and deterministic. #f these

assumptions are not valid, integer and stochastic programming can "e used.

12. !raditional =9> techniques ma not "e appropriate to select a project from

mutuall exclusive investment alternatives, if the projects have different lives. !he

reason is that a short-lived project can "e replicated more quickl than a long-

lived project. #n order to compare projects with different lives, we can compute

=9> of infinite replications of the investment project. !he adjustment to

compensate for projects with unequal lives can "e carried out using either

equation *1).1) or *1).12. 'esides this infinite replication method the manager

can also use the finite replication method. !o emplo the latter approach the

following formula should "e used3

1* *1

* ,

1

tNPV N HNPV N t

H

+=

8efinitions and interpretation for this formulas components can "e found on page

/@2-/@/.

1/. =9> in "reak-even analsis uses the following model3

[ ]B

* * * t

NPV k R t C t e dt=

where =9>*k 6 net present value of the project discounted at the cost-of-capita1

rate, k.


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of various projects is determined, the values are plotted against

units sold. >arious discount rates are used to determine various "reakeven plots.

4urves are drawn on the assumptions that total nonrecurring costs are *< 7 # 6

LFBBmm, average M 6 1;.;, 2 productsmonth are produced and sold, development

and initial investment phase 6 /) months, corporate tax rate 6 ;BE, and that costs

will alwas have positive revenues. 8iscount rates are an important factor in

dnamic "reak-even analsis. &ere the "reak-even sales levels are )A@, 20B and

;1B units. #n this model, finance theor, accounting information and mathematical

tools are incorporated to make the project decision analsis more accepta"le.

1;. a =9>*$ 6 *L/,2;1*;.0;B6L)/,A;2.1; + );,BBB 6 L*1/0.A;

=9>*' 6 *L0,FFB*2.0B;6L);,1FA.F; + );,BBB 6 L 1FA.F;

" =9'*$ 6 *L/,2;1*;.)106L)),0F/.A) + );,BBB 6L),2B;.1A

=9>*' 6 *L0,FFB*2.//26L)/,B00./@ + );,BBB 6 L*F22./2

c =9>*$ 6 *L/,2;1*0.1/;6L)0,@20.AF + );,BBB 6L1,@20.AF

=9>*' 6 *L0,FFB*2.@F16L)0,/FF.BF + );,BBB 6L1,/FF.BF

Since the initial cost for "oth projects is L);,BBB, in 4ash *a, 9roject ' should

"e accepted, in 4ash *" neither project should "e accepted, and in 4ash *c

project $ should "e accepted.


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*d Nsing the information from *a, *", and *c, students can graph the =9>

profiles following the example given on page /0@of the text.

10.

9roject $

*;B ;B 0B 0B 1BB ))B.;; or ;;E

/ /BB

+ + +=

9roject '

*1B ;B 0B AB 1BB )BB.;B or ;BE

/ /BB

+ + + =

9roject 4

*1)B /B 2B 1B 1BB )BB.;B or ;BE

/ /BB

+ + +=

$ is the "est project.

1@.

9roject $3 9'9 6 ) ears

9roject '3 9'9 6 ) 7 */B0B 6 ))

2ears

9roject 43 9'9 6 1BB1)B 6;

0ears

4 is the "est project if the pa"ack method is adopted.

1A.

) 2 / ;

/B 0B ;B 1BB 1BBB)BB

*1 *1 *1 *1 *1 A A A A Ar r r r r

= + + + ++ + + + +

) 2 / ;

1BB 1BB ;B 0B /B)BB

*1 *1 *1 *1 *1 B B B B Br r r r r

= + + + +

+ + + + +


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Nsing the trial and error method, the #


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NPVAJNPVB"ut "oth projects have negative =9>s and are therefore

unaccepta"le.

)1.

)

/BB,BBB 1,)BB,BBB;BB,BBB

1.1) *1;BB, BBB 2;@,1/).A F;0, 02).0 FF

.1/

), FB./NPV + == + =

QQQ should reject this project, "ecause the =9> is negative.

)).

a. Initial Net Cash Outlay

4ost of Sstem L)BB,BBB

#nstallation (xpenses ;B,BBB

=et 4ash Kutla L);B,BBB

". Operating Cash Flows

=et Kperating 4ash 5low 6 4t6 45t*1 + T + *Td

8epreciation3 L);B,BBB; 6 L;B,BBB per ear

Savings in Kperating (xpenses

Salaries *1BL1;,BBB L1;B,BBB

9roduction 8elas A,BBB

?ost Sales 1),BBB!imel 'illing 2,BBB

L1@2,BBB

$dditional (xpenses3

Salaries of Specialists L AB,BBB

Daintenance (xpenses 1),BBB

LF),BBB

#ncremental 4ash flow *1@2,BBB + F),BBB 6 LA1,BBB

=et Kperating 4ash flow 6 LA1,BBB *1 + ./B 7 *./B*;B,BBB


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6 /A,0BB 7 )B,BBB 6 L0A,0BB

c.

;

1

0A,0BB

);B,BBB*1 .1)ttNPV == +

0A,0BB *2.0B/;- );B,BBB

L),@1B.@)

=

=

d. #3

;

1

0A,0BB);B,BBB

*1 .11;t

t=

+

6 0A,0BB *2.0/FF + );B,BBB

6 );B,2A2.1/ + );B,BBB

6 L2A2.1/

!he actual #


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g. !erminal 4ash 5low3

Sale 9rice *t 6 ; L);,BBB

!ax on gains /B E 1B,BBB

=et !45 E L1;,BBB

;

;1

1 1;,BBB0A,0BB );B,BBB

*1 .1) *1 .1)ttNPV

=

= + + +

6 0A,0BB*2.0B/; 7 1;,BBB*B.;0@/ + );B,BBB

6 )/@,)AF.)A 7 A;11 + );B,BBB

6 L;,ABB.)A

9roject is accepta"le.

h. 8epreciation 6 *);B,BBB + )B,BBB ; 6 L/0,BBB per ear

Kperating 4ash 5lows 6 A1,BBB *1 + ./ 7 *./B */0,BBB 6 L0@,BBB

!erminal 4ash 5low3

'ook >alue L )B,BBB

Darket >alue B

?oss L)B,BBB

!ax 4redit from loss on sale of asset * /BE LA,BBB

!hus, the terminal value 6 LA,BBB.

=9> 6 0@,BBB *2.0B/A 7 ABBB *B.;0@/ + );B,BBB

6 L)/1;)1.0B 7 /;2F.)B + );B,BBB

6 +L2F2F.)B

!he =9> is negative. !he project should "e rejected.

)2.


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a. Initial Net Cash Outlay:

Cashflow fo! ,ale of -l& .ehicle/

'ook >alue L 2B,BBB

Darket >alue 1/,BBB

!ax 4redit on ?oss

*2B,BBB + 1/,BBB*./B 0./BB

!otal #nflow L)B,/BB

#nitial Kutla

4ost of =ew !ruck LFB,BBB

4ash 5low 5rom Sale of Kld !ruck L)B,/BB

=et Kutla L0F,0BB

8epreciation on new 6 LFB,BBB; 6 L1A,BBB per ear

8epreciation on old 6 L2B,BBB2 6 L1B,BBB per ear

". Operating and Terminal Cash flows

Savings3

Daintenance L A,BBB

'reakdowns 1;,BBB

!otal Savings L)2,BBB

=et $nnual Kperating 4ash 5low 6 45t*1 + T+ Td

= )2,BBB*1 + ./B 7 *./B*A,BBB

6 12,ABB 7 2,)BB

6 L1@,BBB

!erminal 4ash 5low3

Sale 9rice L)B,BBB

!ax on gain /BE A,BBB


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L1),BBB

c.

;

1

1 1)BBB1@,BBB 0F,0BB

*1 .1B *1 .1Bt ttNPV

=

= + + +

1@,BBB*2.@FBA 1),BBB*B.0)BF 0F,0BB

L0/,//2.0B @/;B.AB 0F,0BB

L@1AF/./B 0F0BB

L),)F/./B

= +

= +

=

=

d. !he # T B

#


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?and L /B,BBB

'uilding AB,BBB

(quipment )B,BBB

!otal Kutla L1/B,BBB

". Kperating and !erminal 4ash flows3

8epreciation 6 *AB,BBB 7 )B,BBB1B 6 L1B,BBB per ear

4ash flow from Kperations3

$nnual aria"le 4osts )@,BBB

5ixed 4osts );,BBB

$nnual 4ash 5low L 2A,BBB

$nnual Kperating 4ash 5low 6 45t*1 + T+ dT

= 2A,BBB*1 + ./B 7 *1B,BBB*./B

6 L)),ABB 7 /,BBB

6 L)0,ABB

!erminal 4ash 5low3

Sale >alue of land and 'uilding LF;,BBB LF;,BBB

'ook >alue /B,BBB

Gain on Sale L;;,BBB

!ax on Gain * /BE )),BBB

=et !erminal 4ash 5low L@2,BBB

c.1B

1B1

1 @2,BBB)0,ABB 1/B,BBB

*1 .1B *1 .1BttNPV

=

= + + +

= )0,ABB*;.)101 7 @2,BBB*B.)0F@ + 1/B,BBB

6 L1;F,/@F.;A + 1/B,BBB

6 L1F,/@F.;A


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!he #


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adjustment onl.

)0.

$lpha *$ Gamma *'

#nitial Kutla L1B;,BBB L FB,BBB

8epreciation 1B;,BBB1B

6 L1B,;BB

FB,BBB1B

6 LF,BBB

4ash flowear +L1B,;BB +L F,BBB

$nnual =et 4ash 5lows3

9roject $3 6 +1B,;BB*1 + ./B 7 *./B*1B,;BB 6 +L),1BB

9roject '3 6 +F,BBB*1 +./B 7 *./B* F,BBB 6 +L1,ABB

1B

1

)1BB*

1)1BB 1B;,BBB

*1 .1B

0.1//0 1B;,BBB

L11@,FB2.00

A tt

NPV=

= +

=

=

NPVB6 +1ABB*0.1//0 + FB,BBB

6 +L1B1,B0B.)A

9roject Gamma should "e selected "ecause it has a lower negative =9>.

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Solutions Manual to Accompany FAPF_Ch12