Chapter 7 Asset Investment Decisions and Capital Rationing

8/10/2019 Chapter 7 Asset Investment Decisions and Capital Rationing

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Chapter 7 Asset Investment Decisions and Capital Rationing

Answer Test your understanding 1

The ratio of NPV at 10% to outlay in year 0 (the year of capital rationing) is as follows.

Project Outlay in

Year 0 ()

PV

()

NPV

()

!atio !an"ing

# $0000 $$&00 $&00 1.11' r

* +,000 1+-0 +-0 1.11, +n

0000 ',0 ',0 1.1'/ 1st

The optial inestent policy is as follows.

!an"ing Project Year 0 outlay () NPV ()

1st 0000 ',0

+n * +,000 +-0

r # (2alance) +000 ('% of $&00) ++,

&,-,

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Answer 1

(a) Purchase outright

+00, +00- +010 +011 +01+ +01 Mar

s

Outlay4resiual alue(/0000) +0000

5aintenance (1$000) (1$000) (1$000) (1$000) !1"

!esulting reuction in

ta6'$00 '$00 '$00 '$00 !1"

Ta6 effect of 78#s

(71)+&000 +0+$0 1$1,, 11-1 !#"

Ta6 effect of 2alancing

allowance (7+)+,1&+ !1"

ash flow (/0000) 1+000 -&$0 '/,, +0,-1 +/&+

8iscount factor at 10% 1.000 0.-0- 0.,+/ 0.&$1 0./, 0./+1

Present alue (/0000) 10-0, ,0$' +$1 1'+/- +0+,-

NPV of cost 9 (0+-$-) !1 mar"

71 7riting own allowanceYear Ta6 written own

alue 24

7riting own

allowance (78#)

+$%

Ta6 effect at 0% 3

ta6 reuction

+00, /0000 -0000 +&000

+00- +&0000 /&$00 +0+$0

+010 +0+$00 $0/+$ 1$1,,

+011 1$1,&$ &-/- 11-1+01+ 11-0/

The ta6 effect is one year in arrears so the reuction relating to +00, affects cash flows in

+00- an so on.

7+ *alance allowance4charge an its ta6 effect

Ta6 written own alue at start of year of sale 11-0/

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:ale procees +0000

*alancing allowance --0/

;ffect on ta6< reuction in ta6 at 0% +,1&+

The cash flow effect is one year in arrears.

$inance lease

#nnuity factor (#=) at 10% for ' years is .1&

Thus PV outflows 9 (1$000 > 1$000) 6 .1& 9 ('&$$00) !1 mar"

PV of ta6 relief 9 ?(1$0000 6 0. 6 .1&)41.1@ 9 1+-/,+ !1 mar"

Net present cost 9 ('$,1,) !1 mar"

%perating lease

#nnuity factor at 10% for years is +.',&

Thus PV of outflows 9 1'0000 6 (+.',& > 1) 9 (',,1,0) !1 mar"

PV of ta6 relief 9 ?(1'0000 6 0.) 6 (+.',& > 1)@ 4 1.1 9 11'0 !1 mar"

Net present cost 9 ($$0'0) !1 mar"

On the 2asis of NPV purchasing outright appears to 2e the lease cost etho.

(2)

;ach 1 of outlay 2efore 1 8ece2er +00- woul ean a loss in NPV on the alternatie

project of 0.+0. There is thus an opportunity cost of using funs in +00,. !1 mar"

Purchasing

Net present alue of cost (0+-$-)

Opportunity cost (0.+ 6 /0000) (&+000)Net PV of cost (&'-$-)

!1 mar"

$inance lease

Net present cost 9 ('$,1,)

There is no cash flow 2efore 1 8ece2er +00- in this case an thus no opportunity cost.

!1 mar"

%perating lease

Net present alue of cost ($$0'0)

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Opportunity cost (0.+ 6 1'0000) (+,000)

Net PV of cost (,0'0)

!1 mar"

Thus the finance lease is now the lowest cost option. &1 mar'

#ll the a2oe assue that the alternatie project cannot 2e elaye.

(c)

Report

To( The Directors o) A*D Co

$rom( A +usiness advisor

Date( ,,-,,-,,

.u+/ect( Ac0uiring the tur+ine machine

Introduction

An financial ters an with capital rationing outright purchase is the preferre etho of

financing as it has the lowest NPV of cost. 7ith capital rationing a finance lease arrangeent

2ecoes the least3cost etho. There are howeer a nu2er of other factors to 2e

consiere 2efore a final ecision is ta"en.

(1) Af capital rationing persists into )urther periods the value o) cash used in leasing

+ecomes more signi)icantan so purchasing woul 2ecoe relatiely less attractie.

(+) ;en without capital rationing leasing has a shortterm cash )low advantage oer

purchasing which ay 2e signi)icant )or li0uidity.

() The use of a 123 cost o) capital may +e inappropriate as these are financing issues

an are unli"ely to 2e su2ject to the aerage 2usiness ris". #lso they ay alter the

capital structure an thus the )inancial ris o) the +usinessan thus the cost o) capital

itsel). This ay alter the optial ecision in the face of capital rationing.

(') The actual cash inflows generate 2y the tur2ine are constant for all options e6cept thatuner an operating lease the lessor may re)use to lease the tur+ine at the en of any

annual contract thus a"ing it unaaila2le fro this particular source. On top of capital

rationing we nee to consider the continuing availa+ility o) )inance under the

operating lease.

($) onersely howeer with the operating lease #B8 o can cancel if 2usiness

conitions change (e.g. technologically iproe asset ay 2ecoe aaila2le). This is

not the case with the other )inancing options . On the other han if the ar"et is

2uoyant then the lessor ay raise lease rentals whereas the cost is fi6e uner the other

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Answer #

(a)

4,planation o) ARR(

#ccounting rate of return (#!!) is a measure o) the return on an investment where the

annual pro)it +e)ore interest and ta, is e,pressed as a percentage o) the capital sum

invested. There are a num+er o) alternative )ormulaewhich can 2e use to calculate #!!

which iffer in the way in which they efine capital cost. The ore alternatie easures

aaila2le are222 >222 >222

Purchase an sale (+0) $0 !#"

# ta6 2enefits +' 1, - !:"

5aintenance costs (+$) (+$) (+$) !1"

5ain. osts 2enefits , , , !1"

Net cash flow (+0) (+$) & $1 '&

8iscount factor (&%) 1.000 0.-$ 0.,& 0.,1/ 0.&/

Present alue (+0) (+) / '+ /

PV of 2orrowing to 2uy 9 IL+$-000 !1 mar"

7or"ings< apital allowance ta6 2enefits

*alancing allowance 9 (+0000 I $0000) I (,0000 > /0000) 9 L10000

Measing ealuation

=ear 2 1 # : < Mars

>222 >222 >222 >222 >222

Mease rentals (1+0) (1+0) (1+0) !1"

Mease rentals ta6

2enefits/ / / !1"

Net cash flows (1+0) (1+0) (,') / /

8iscount factors (&%) 1.000 0.-$ 0.,& 0.,1/ 0.&/

Present alues (1+0) (11+) (&) +- +&

PV of leasing 9 IL+'-000 !1 mar"

On financial grouns leasing is to 2e preferre as it is cheaper 2y L10000. Note that the first

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lease rental is ta"en as 2eing pai at year 0 as it is pai in the first onth of the first year of

operation. !1 mar"

#n alternatie for of ealuation co2ines the cash flows of the a2oe two ealuations.

*ecause this ealuation is ore cople6 it is ore li"ely to lea to coputational errors.

The PV of IL1+000 inicates that leasing woul 2e L1+000 cheaper than 2orrowing. The

ifference 2etween this an the preious ealuation is ue to rouning.

(2)

$inance lease(

1. # finance lease e6ists when the su+stance of the lease is that the lessee en/oys

su+stantially all o) the riss and rewards o) ownership een though legal title to the

lease asset oes not pass fro lessor to lessee.

+. # finance lease is therefore characterised +y one lessee )or most if not all o) its

use)ul economic li)e with the lessee eeting aintenance an siilar regular costs.

. # finance lease cannot +e cancelled once entere into without incurring seere

financial penalties. # finance lease therefore acts as a ind o) medium to longterm

source o) de+t )inancewhich in su2stance allows the lessee to purchase the esire

asset.'. This ownership iension is recognise in the stateent of financial position where a

)inanceleased asset must +e capitalised (as a non3current asset) together with the

aount of the o+ligationsto a"e lease payents in future perios (as a lia2ility).

!< ? mars"

%perating lease(

$. An contrast an operating lease is a rental agreementwhere seeral lessees are e6pecte

to use the lease asset an so the lease perio is much shorter than the asset9s use)ul

economic li)e.

/. Maintenance and similar costs are +orne +y the lessor with this cost 2eing reflecte

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in the lease rentals charge.

&. #n operating lease can usually 2ecancelled without penalty at short notice. This

allows the lessee to ensure that only up3to3ate assets are lease for use in 2usiness

operations avoiding the o+solescence pro+lem associate with the rapi pace of

technological change in assets such as personal coputers an photocopiers.

,. *ecause the su2stance of an operating lease is that of a short3ter rental agreeent

operating leases do not re0uire to +e capitalisedin the stateent of financial position

allowing copanies to ta"e aantage of this for of off32alance sheet financingC.

!< ? mars"

(c)(i)

The offer of 10% per year with interest paya2le eery si6 onths eans that the 2an" will

reJuire $% eery si6 onths. This is eJuialent to an annual percentage rate of 10+$% (100

6 (10$+I 1)) 2efore ta6. !# mars"

(c)(ii)

To calculate the repayent scheule use 1,& > &, 9 $0000

Total epreciation 9 +$0000 I $000 9 +'$000

#erage annual accounting profit 9 ($0 I +'$)4 ' 9 &1+$0 !# mars"

#erage inestent 9 (+$0000 > $000)4 + 9 1+&$00 !# mars"

!eturn on capital eploye 9 100 6 &1+$04 1+&$00 9 $/% !1 mar"

Bien the target return on capital eploye of Trecor o is +0% an the !O; of the

inestent is $/% the purchase of the achine is recoene.

(c).trengths(

1. One of the strengths of internal rate of return (A!!) as a etho of appraising capital

inestents is that it is a iscounte cash flow (8=) etho an so taes account o)

the time value o) money

+. At also considers cash )lows over the whole o) the pro/ect li)ean is sensitie to 2oth

the aount an the tiing of cash flows.

. At is preferre 2y soe as it o))ers a relative measure o) the value of a propose

inestent ie the etho calculates a percentage that can 2e copare with the

copanyCs cost of capital an with econoic aria2les such as inflation rates an

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interest rates.

!# : mars"

;eanesses(

1. :ince it is a relatie easureent of inestent worth it does not measure the

a+solute increase in company value(an therefore shareholer wealth) which can 2e

foun using the net present alue (NPV) etho.

+. # further pro+lem arises when evaluating nonconventional pro/ects (where cash

flows change fro positie to negatie uring the life of the project). A!! ay offer as

any A!! alues as there are changes in the alue of cash flows giing rise to

ealuation ifficulties.

. There is a potential con)lict +etween IRR and 6P in the evaluation o) mutually

e,clusive pro/ects where the two methods can o))er con)licting adviceas which of

two projects is prefera2le. 7here there is conflict 6P always o))ers the correct

investment advice< A!! oes not although the aice offere can 2e aene 2y

consiering the A!! of the increental project. There are therefore a nu2er of reasons

why A!! can 2e seen as an inferior inestent appraisal etho copare to its 8=

alternatie NPV.

!? B mars"

ACCA Maring .cheme

Answer B

(a)

Net present alue ealuation of inestent

#fter3ta6 weighte aerage cost of capital 9 (11 6 0.,) > (,./ 6 (1 I 0.) 6 0.+) 9 10%

!# mars"

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=ear 1 # : < ? Mars

@222 @222 @222 @222 @222

ontri2ution ''0 $$0 //0 //0 !#"

=i6e costs (+'0) (+/0) (+,0) (00) !1"

Ta6a2le cash flow +00 +-0 ,0 /0

Ta6ation 3 (/0) (,&) (11') (10,) !1"

# ta6 2enefits 3 /0 '$ ' -+ !:"

:crap alue 3 3 3 0 3 !1"

#fter3ta6 cash flows +00 +-0 , 10 (1/)

8iscount at 10% 0.-0- 0.,+/ 0.&$1 0./, 0./+1 !1"

Present alues 1,+ +'0 +$' +1+ (10)

@222 Mars

PV of future 2enefits ,&,

Mess< initial inestent (,00)

NPV &, !1"

The net present value is positivean so the inestent is )inancially accepta+le. Koweer

ean 2ecoes greater than prouction capacity in the fourth year of operation an so

further inestent in new achinery ay 2e neee after three years. The new achine will

itself nee replacing after four years if prouction capacity is to 2e aintaine at an increase

leel. At ay 2e necessary to inclue these e6pansion an replacement considerationsfor a

ore coplete appraisal of the propose inestent.

# ore coplete appraisal of the inestent coul address issuessuch as the assuption of

constant selling price and varia+le cost per ilogram and the a+sence o) any

consideration o) in)lation the linear increase in fi6e costs of prouction oer tie an the

linear increase in ean oer tie. Af these issues are not addressed the appraisal of

inesting in the new achine is li"ely to possess a signi)icant degree o) uncertainty.

!1 # mars"

7or"ings

#nnual contri2ution

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apital allowance (#) ta6 2enefits

(2)

Anternal rate of return ealuation of inestent

=ear 1 # : < ? Mars

@222 @222 @222 @222 @222

#fter3ta6 cash flows +00 +-0 , 10 (1/)

8iscount at +0% 0., 0./-' 0.$&- 0.',+ 0.'0+

Present alues 1/& +01 1-/ 1'- (/)

@222 Mars

PV of future 2enefits &0&

Mess< initial inestent (,00)NPV (-) !1"

A!! 9 %/.1'%)10%+0(-&,

&,%10 =

+

+ !# mars"

The inestent is )inancially accepta+lesince the internal rate o) return is greater than

the cost o) capital usedfor inestent appraisal purposes. Koweer the appraisal su))ers

)rom the limitations discussed inconnection with net present alue appraisal in part &a'.

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!1 # mars"

(c)

Ris and uncertainty

1. Risrefers to the situation where pro+a+ilities can +e assignedto a range of e,pected

outcomes arising fro an inestent project an the li"elihoo of each outcoe

occurring can therefore 2e 0uanti)ied.

+. ncertainty refers to the situation where pro+a+ilities cannot +e assigned to

e,pected outcomes.

. Anestent project ris therefore increases with increasing varia+ility o) returns

while uncertainty increaseswith increasing pro/ect li)e. The two ters are often use

interchangea2ly in financial anageent 2ut the istinction 2etween the is a useful

one.

!# : mars"

.ensitivity analysis

1. :ensitiity analysis assesses how the net present valueof an inestent project is

a))ected +y changes in pro/ect varia+les.

+. onsiering each project aria2le in turn the change in the varia+le re0uired to mae

the net present value 8ero is determined or alternatiely the change in net present

alue arising fro a fi6e change in the gien project aria2le. An this way the ey or

critical pro/ect varia+les are determined.

. Koweer sensitiity analysis does not assess the pro+a+ility o) changes in pro/ect

varia+lesan so is often isisse as a way of incorporating ris" into the inestent

appraisal process.

!# : mars"

Pro+a+ility analysis

1. Pro2a2ility analysis refers to the assessment o) the separate pro+a+ilities o) a

num+er o) speci)ied outcomes of an inestent project. =or e6aple a range ofe6pecte ar"et conitions coul 2e forulate an the pro2a2ility of each ar"et

conition arising in each of seeral future years coul 2e assesse.

+. The net present alues arising fro com+inations o) )uture economic conditions

coul then 2e assessed and lined to the /oint pro+a+ilitiesof those co2inations.

The e,pected net present value (;NPV) coul 2e calculated together with the

pro2a2ility of the worst3case scenario an the pro2a2ility of a negatie net present

alue. An this way the downside ris o) the investment could +e determined an

incorporate into the inestent ecision.

!# : mars"

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ACCA Maring .cheme

Answer 7

(a)

#fter3ta6 cost of 2orrowing 9 ,./ 6 (1 I 0%) 9 /% per year

;aluation of leasing

Year ash flow #ount () /% 8= PV Mars

03 Mease rental (,0000) 1 > +./& 9 ./& (1-$&'0) !#"

+3$ Ta6 saings 11'000 '.+1+ I 0.-' 9 .+/- &+/// !1"

(10+0&')

Present alue of cost of leasing 9 10+0&' !1 mar"

;aluation of 2orrowing to 2uy

=ear 2 1 # : < ? Mars

@ @ @ @ @ @

Anestent R scrap (1000000

)

100000 !1"

Micence fee (10'000

)

(10,1/0

)

(11+',/

)

(11/-,/

)

!1"

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Ta6 2enefits 10/+00 ,,/-, &$-' 11/$- !:"

Net cash flow (1000000

)

(10'000

)

(1-/0) (+&,,) $,-', 11/$-

8= Q /% 1.000 0.-' 0.,-0 0.,'0 0.&-+ 0.&'&

Present alue (1000000

)

(-,0&+) (1&'') (1--,+) '//,& -,'-

Present alue of cost of 2orrowing to 2uy 9 -&'&/+ !1 mar"

#:OP shoul 2uy the new technology since the present alue of cost of 2orrowing to 2uy is

lower than the present alue of cost of leasing. !1 mar"

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(2)

Noinal ters net present alue analysis

=ear 1 # : < ? Mars

@ @ @ @ @

ost saings /$'00 '&-+$0 /&'$0 $/'000 !#"

Ta6 lia2ilities (10-/+0

)

(1'&&$

)

(1-1+$

)

(1/-+00) !1"

Net cash flow /$'00 /-/0 '-/&$ &+&/$ (1/-+00)

8iscount at 11% 0.-01 0.,1+ 0.&1 0./$- 0.$-

Present alue +-++$ 001'0 /0,&/ +'$/$+ (100/) !1"

Present alue of 2enefits 11$$$

&

Present cost of financing (-&'&/+

)

Net present alue 1/0&-$ !1"

The inestent in new technology is accepta2le on financial grouns as it has a positie net

present alue of 1/0&-$. !1 mar"

(c)

The e0uivalent annual cost or +ene)it method can 2e used to calculate the e0ual annualamount o) cost or +ene)it which when discounted at the appropriate cost o) capital

produces the same present value o) cost or net present value as a set of arying annual

costs or 2enefits.

!1 mar"

=or e6aple the net present alue (NPV) of inesting in the new technology of 1/0&-$ in

part (2) was calculate using a weighte aerage cost of capital (7#) of 11% oer an

e6pecte life of four years. The annuity factor for 11% an four years is 10+. The eJuialent

annual 2enefit (;#*) is therefore 1/0&-$410+ 9 $1,$- per year. This can 2e chec"e 2y

ultiplying the ;#* 2y the annuity factor i.e. $1,$- 6 10+ 9 1/0&-$.

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!1 mar"

Af an alternatie inestent in siilar technology oer fie years ha a lower ;#* the four3

year inestent woul 2e preferre as it has the higher ;#*. !1 mar"

()

7hen capital is rationed the optimal investmentscheule is the one that ma,imises the

return per dollar invested. The capital rationing pro+lem is therefore concerned with

limiting )actor analysis 2ut the approach aopte is slightly ifferent depending on

whether the investment pro/ects +eing evaluated are divisi+le or indivisi+le.

!1 # mars"

7ith divisi+le pro/ects the assumption is ae that a proportionrather than the whole

inestent can +e undertaen with the net present alue (NPV) 2eing proportional to the

aount of capital ineste. Af &0% of a project is unerta"en for e6aple the resulting NPV

is assue to 2e &0% of the NPV of inesting in the whole project. !1 mar"

=or each divisi+le pro/ect a pro)ita+ility inde, can +e calculated efine either as the net

present alue of the project iie 2y its initial inestent or as the present alue of the

future cash flows of the project iie 2y its initial inestent. The profita2ility ine6

represents the return per dollar invested and can +e used to ran the investment

pro/ects. The liite inestent funs can then 2e invested in the pro/ects in the order o)

their pro)ita+ility inde,es with the final inestent selection 2eing a proportionate one if

there is insufficient finance for the whole project. This represents the optiu inestent

scheule when capital is ratione an projects are iisi2le. !1 # mars"

7ith indivisi+le pro/ects ran"ing 2y profita2ility ine6 will not necessarily inicate the

optiu inestent scheule since it will not 2e possi2le to inest in part of a project. An this

situation the 6P o) possi+le com+inations o) pro/ects must +e calculated . The ost

li"ely co2inations are often inicate 2y the profita2ility ine6 ran"ing. The com+inationo) pro/ects with the highest aggregate 6P will then +e the optimum investment

schedule. !1 # mars"

#&3+,


29/31

ACCA Maring .cheme

Answer

(a)

The profita2ility ine6 (PA) will 2e calculate as the ratio of the PV of net cash inflows to the

year 0 capital outlay.

Year ash flow 8= (1+%) PV PA

Project # 1 I $ &0000 ./0$ +$+$0

0 (+'/000) 1.000 (+'/000)

NPV 9 /$0 1.0+/

Project * 1 &$000 0.,- //-&$

+ ,&000 0.&-& /--

/'000 0.&1+ '$$/,

1,1,,+

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0 (1,0000) 1.000 (1,0000)

NPV 9 1,,+ 1.010

Project 1 ',000 0.,- '+,/'+ ',000 0.&-& ,+$/

/000 0.&1+ '',$/

' &000 0.// '/'+,

1&+'0'

0 (1&$000) 1.000 (1&$000)

NPV 9 (+$-/) 0.-,$

Project 8 1 I ' /+000 .0& 1,,+-'

0 (1,0000) 1.000 (1,0000)

NPV 9 ,+-' 1.0'/

!an"ing NPV PA

1st 8 8

+n # =

r ; ;

'th = #

$th * *

/th

The ran"ing iffer 2ecause the projectCs capital outlays iffer. NPV shows the a2solute 2enefit

fro a project while profita2ility ine6 scales that 2enefit accoring to the projectCs siDe.

(2)

Project coes si6th an last in the ran"ing accoring to 2oth NPV an PA. At has a negatie

NPV an shoul not 2e unerta"en.

*anen cannot affor to unerta"e ore than three projects gien the a6iu aaila2le

capital of /+0000. At shoul not unerta"e project an it cannot unerta"e # an ;

siultaneously. The arious feasi2le options are as follows.

Project An total NPV in total

8 = ; $10000 1,&&&

8 = # $&/000 1-/&

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31/31

8 = * $10000 1$1/-

8 ; * $'0000 1$///

8 # * /0/000 1/$+/

= # * $&/000 1++$

= ; * $10000 1+/$

*anen shoul not inest any funs in the oney ar"ets 2ecause the return woul only 2e

-% pa an the cost of capital for *anen is higher at 1+% pa.

At is assue that the copany oes not hae to use ore funs than it nees to an so there

will not 2e any surplus funs which hae to 2e ineste soewhere.

Recommendation. The copany shoul use $&/000 an inest in projects 8 = an #.

(c)

7hen there is capital rationing there is not enough capital to inest in all projects which hae

a positie NPV when their NPVs are calculate 2y iscounting the estiate cash flows at

the copanyCs cost of capital. The financial irector is correct in theory to say that the

copanyCs cost of capital is inappropriate. The arginal cost of capital which will 2e higher

than the copanyCs cost of capital woul 2e ore appropriate for calculating project NPVs

an eciing which projects woul yiel the 2est returns gien the shortage of capital.

Koweer the arginal cost of capital cannot 2e calculate easily an a practical way of

a"ing ecisions in a capital rationing situation is to calculate the NPV of each project using

the copanyCs noral cost of capital an then to ran" the projects in orer of esira2ility as

in parts (a) an (2) of this solution.

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Chapter 7 Asset Investment Decisions and Capital Rationing

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