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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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