Chapter 12 Cash Flow Estimation and Risk Analysis Learning Objectives
After reading this chapter, students should be able to: Analyze an expansion project and make a decision whether the project should be accepted on the basis of standard capital budgeting techniques. Discuss diculties and rele!ant considerations in estimating net cash "ows, and explain how project cash "ow di#ers from accounting income.
De$ne the following following terms: terms: incre incremen mental tal cash cash "ow, "ow, repla replacem cement ent analysis, analysis, sunk sunk cost, cost, De$ne opportunity cost, externalities, and cannibalization e#ect. %dentify and brie"y explain three separate and distinct types of risk. Demonstrate sensiti!ity and scenario analyses and explain &onte 'arlo simulation. (xplain why con!entional D') techniques do not always lead to proper capital budgeting decisions.
abandonment*shutdown option, and option !alue. (xplain the following terms: real option, abandonment*shutdown +ist the steps a $rm goes through when establishing its optimal capital budget in practice, and explain what capital rationing is.
Chapter 12 Cash Flow Estimation and Risk Analysis
Learning Objectives
!"
Lect#re $#ggestions
his chapter chapter co!ers some some important important but relati!ely relati!ely technical technical topics. topics. -ote too that this chapter chapter is more modular than most, i.e., the major sections are discrete, hence they can be omitted without without loss of continuity continuity. herefore herefore,, if you are experiencin experiencing g a time crunch, crunch, you could skip sections of the chapter. chapter. hat we co!er, and the way we co!er it, can be seen by scanning the slides and %ntegrated %ntegrated 'ase solution for 'hapter 'hapter /0, which appears at the end of this chapter solution. )or other suggestions about the lecture, please see the 1+ecture 2uggestions3 in 'hapter 0, where we describe how we conduct our classes. %A&$ %A&$ O' C(A)*ER ! OF +, %A&$ %A&$ -+./min#te periods0
!,
Lecture Suggestions
Chapter 12 Cash Flow Estimation and Risk Analysis
Lect#re $#ggestions
his chapter chapter co!ers some some important important but relati!ely relati!ely technical technical topics. topics. -ote too that this chapter chapter is more modular than most, i.e., the major sections are discrete, hence they can be omitted without without loss of continuity continuity. herefore herefore,, if you are experiencin experiencing g a time crunch, crunch, you could skip sections of the chapter. chapter. hat we co!er, and the way we co!er it, can be seen by scanning the slides and %ntegrated %ntegrated 'ase solution for 'hapter 'hapter /0, which appears at the end of this chapter solution. )or other suggestions about the lecture, please see the 1+ecture 2uggestions3 in 'hapter 0, where we describe how we conduct our classes. %A&$ %A&$ O' C(A)*ER ! OF +, %A&$ %A&$ -+./min#te periods0
!,
Lecture Suggestions
Chapter 12 Cash Flow Estimation and Risk Analysis
Answers to End/o/Chapter #estions
12/1
4nly cash can be spent or rein!ested, and since accounting pro$ts do not represent cash, they are of less fundamental fundamental importance than cash "ows "ows for in!estment analysis. analysis. 5ecall 5ecall that in the stock !aluation chapter we focused on di!idends, which represent cash "ows, rather than on earnings per share.
12/2
'apital budgeting analysis should only include those cash "ows that will be a#ected by the decision. 2unk costs are unreco!erable unreco!erable and cannot cannot be changed, so they ha!e no bearing on the capital budgeting decision. 4pportunity costs represent the cash "ows the $rm gi!es up by in!esting in this project rather than its next best alternati!e, and externalities are the cash "ows 6both positi!e and negati!e7 to other projects that result from the $rm taking on this project. project. hese cash "ows "ows occur only because because the $rm took on the capital capital budgeting project8 therefore, they must be included in the analysis.
12/3
hen a $rm takes on a new capital budgeting project, it typically must increase its in!estment in recei!ables and in!entories, o!er and abo!e the increase in payables and accrua accruals, ls, thus thus incre increasi asing ng its net operat operating ing working working capita capitall 6-4'7. 6-4'7. 2ince 2ince this this increase must be $nanced, it is included as an out"ow in 9ear 9ear of the analysis. At the end of the project;s life, in!entories are depleted and recei!ables are collected. hus, there is a decrease in -4', which is treated as an in"ow in the $nal year of the project;s life.
12/! he costs costs assoc associat iated ed with with $nanci $nancing ng are are re"ect re"ected ed in the the weight weighted ed a!erag a!erage e cost cost of capital capital.. o o inc includ lude e int inter eres estt exp expens ense e in in the the capita capitall bud budget geting ing analy analysis sis would would 1doubl 1double e coun count3 t3 the the cost cost of debt $nancing. 12/+
Daily cash "ows would be theoretically best, but they would be costly to estimate and probably no more accurate than annual estimates because we simply cannot forecast accurately accurately at a daily le!el. herefor herefore, e, in most cases we simply assume assume that all cash "ows occur at the end of the year. year.
? since both re!en re!enues ues and costs costs are are being being recognized at the end of the year. year. @nless re!enues and costs are distributed radically di#erent throughout the year, there should be no bias.
12/4
%n repla replacem cement ent proje projects cts,, the bene$ bene$ts ts are are genera generally lly cost cost sa!ing sa!ings, s, althou although gh the the new machiner machinery y may also permit permit additional additional output. output. he data for replace replacement ment analysis analysis are generally easier to obtain than for new products, but the analysis itself is somewhat more 'ew E6pansion complicated because almost all of the cash "ows are incremental, found by subtracting the )roject A new new cost numbers from from the old numbers. 2imilarly, di#erences di#erences in depreciat depreciation ion and any in!estment designed Replacement other factor that a#ects cash "ows must also be determined. to increase )roject Ansales. in!estment12/" to replace 2tand=alone 2tand=alone risk is the project;s project;s risk if it is held as a lone asset. %t disregards disregards the fact old equipment andthat it is but one asset within the $rm;s portfolio of assets and that the $rm is but one thereby reduce costs, stock in a typical in!estor;s in!estor;s portfolio portfolio of stocks. 2tand=alone 2tand=alone risk is measured measured by the increase output, or!ariabi !ariabilit lity y of the project project;s ;s expect expected ed retur returns. ns. 'orporat 'orporate, e, or within within=$r =$rm, m, risk risk is the im ro!e ualit . proje project;s ct;s risk to the corporat corporation ion,, gi!ing gi!ing consid considerat eration ion to the fact fact that that the proje project ct represents only one in the $rm;s portfolio of assets, hence some of its risk will be elimin eliminated ated by di!ers di!ersi$c i$cati ation on within within the $rm. $rm. 'orpor 'orporate ate risk risk is measur measured ed by the project;s impact on uncertainty uncertainty about the $rm;s future earnings. &arket, or beta, risk Chapter 12 Cash Flow Estimation and Risk Analysis
Answers and Solution Solutions s
!5
is the riskiness of the project as seen by well=di!ersi$ed stockholders who recognize that the project is only one of the $rm;s assets and that the $rm;s stock is but one small part of their total portfolios. &arket risk is measured by the project;s e#ect on the $rm;s beta coecient. 12/,
%t is often dicult dicult to quantify quantify market market risk. 4n the other hand, we can usually get a good idea of a project;s stand=alone risk, and that risk is normally correlated with market risk: he higher the stand=alone risk, the higher higher the market risk is likely to be. be. herefore herefore,, $rms tend tend to focus focus on stand=alon stand=alone e risk, then then deal with with corporate corporate and marke markett risk by making subjecti!e, judgmental modi$cations to the calculated stand=alone risk.
12/5
2imulation analysis in!ol!es working with continuous probability distributions, and the output of a simulation analysis is a distribution of net present !alues or rates of return. 2cen 2cenar ario io anal analys ysis is in!o in!ol! l!es es pick pickin ing g se!e se!era rall poin points ts on the the !ari !ariou ous s prob probab abil ilit ity y distributions and determining cash "ows or rates of return for these points. 2ensiti!ity analysis in!ol!es determining the extent to which cash "ows change, gi!en a change in one particular particular input input !ariable. !ariable. 2imulation 2imulation analysis analysis is is expensi! expensi!e. e. herefor herefore, e, it would more than likely be employed in the decision for the B million in!estment in a satellite system than in the decision for the C, truck.
12/1. 2cenario analyses, and especially simulation analyses, would probably be reser!ed for !ery important important 1make=or 1make=or=br =break3 eak3 decisions decisions.. hey would not be used used for e!ery e!ery project project decision because it is costly 6in terms of money and time7 to perform the necessary calculations and it is challenging to gather all the required information for a full analysis. 2imulation analysis, in particular, requires data from many di#erent departments about costs costs and project projections ions,, includin including g the probabi probability lity distribu distribution tions s corres correspond ponding ing to those those estimates and the correlation coecients between !arious !ariables. 12/11 here here are se!eral types of real options. options. All increase increase the expected expected ->? of the project and lower its risk. he abandonment abandonment option option allows a project project to be shut down if it has low cash "ows. he timing option allows a project to be delayed delayed until more information about demand demand and*or costs can be obtained. obtained. rowth rowth options permit permit a project to be expanded if demand turns out to be stronger than expected. expected. )inally, "exibility options permit the output to be changed if market conditions change change 6output "exibility7. "exibility7. Also an input input "exib "exibili ility ty option option allows allows a proje project;s ct;s inputs inputs in its produ producti ction on proce process ss to be changed if input prices and*or a!ailability change. 12/12 %t might be necessary for the $rm to arrange things so that it has the possibility of abandonment, or "exibility, or timing, or growth options when it is making the initial decision. his might require contractual arrangements with suppliers, customers, and its union, and there there might be some costs to getting getting the ad!ance permissi permissions. ons. 2uch costs could be compared with the !alue of the option as calculated, and this could enter into into the initial decision. decision. %f the cost is greater greater than the option option !alue, then the option would not be done. 12/13 )or planning purposes, managers must also forecast the total capital budget, because the amount of capital raised a#ects the A'' A'' and thus in"uences projects; projects; ->?s. he $rm must think carefully about each di!ision;s relati!e risk, about the risk of each project within the di!isions, and about the relationship between the total amount of capital capital raised and the cost of that capital. capital. he process process forces forces the $rm to adjust adjust its capital budget to re"ect capital market conditions. %f the costs of debt and equity equity rise, this fact will be re"ected in the cost of capital used to e!aluate projects, and projects that would be marginally acceptable when capital costs were low would 6correctly7 be +. Answers and Solutions Solutions
Chapter 12 Cash Flow Estimation and Risk Analysis
ruled unacceptable when capital costs become high. 12/1! 'apital rationing is the situation where a $rm can raise only a speci$ed, limited amount of capital regardless of how many good projects it has. %n such situations capital is limited, so it should be used in the most ecient way possible.
Chapter 12 Cash Flow Estimation and Risk Analysis
Answers and Solutions
+1
$ol#tions to End/o/Chapter )roblems
12/1
a7 (quipment -4' %n!estment %nitial in!estment outlay
E,, C,, /0,,
b7 -o, last year;s B, expenditure is considered a sunk cost and does not represent an incremental cash "ow.
a7 4perating cash "ows: t F / 2ales re!enues 4perating costs Depreciation 4perating income before taxes axes 6HI7 4perating income after taxes Add back depreciation 4perating cash "ow
/,, G,, 0,, /,, H, J, 0,, 0,J,
b7 he cannibalization of existing sales needs to be considered in this analysis on an after=tax basis, because the cannibalized sales represent sales re!enue the $rm would realize without the new project but would lose if the new project is accepted. hus, the after=tax e#ect would be to reduce the $rm;s operating cash "ow by /,,6/ K 7 F /,,6.J7 F J,. hus, the $rm;s 4') would now be 0,, rather than 0,J,. c7 %f the tax rate fell to CI, the operating cash "ow would change to: 4perating income before taxes axes 6CI7 4perating income after taxes Add back depreciation 4perating cash "ow
/,, C, G, 0,, 0,G,
hus, the $rm;s operating cash "ow would increase by /,. 12/3
(quipment;s original cost Depreciation 6LI7 Mook !alue
0,, /J,, H,,
ain on sale F B,, K H,, F /,,. ax on gain F /,,6.H7 F H,.
+2 Answers and Solutions
Chapter 12 Cash Flow Estimation and Risk Analysis
A net sal!age !alue F B,, K H, F H,J,.
12/!
a7 he applicable depreciation !alues are as follows for the two scenarios: 9ear / 0 C H
2cenario / 62traight=+ine7 0, 0, 0, 0,
2cenario 0 6&A'527 0JH, CJ, /0, BJ,
b7 o $nd the di#erence in net present !alues under these two methods, we must determine the di#erence in incremental cash "ows each method pro!ides. he depreciation expenses cannot simply be subtracted from each other, as there are tax rami$cations due to depreciation expense. he full depreciation expense is subtracted from 5e!enues to get operating income, and then taxes due are computed hen, depreciation is added to after=tax operating income to get the project;s operating cash "ow. herefore, if the tax rate is HI, only JI of the depreciation expense is actually subtracted out during the after=tax operating income calculation and the full depreciation expense is added back to calculate operating income. 2o, there is a tax bene$t associated with the depreciation expense that amounts to HI of the depreciation expense. herefore, the di#erences between depreciation expenses under each scenario should be computed and multiplied by .H to determine the bene$t pro!ided by the depreciation expense.
9ear / 0 C H
Depreciation (xpenseDepreciation (xpense Di#erence 60 K /7 Di#. × .H 6&A'527 JH, 0B,J /J, JH, =L, =C0, =/HH, =BG,J
-ow to $nd the di#erence in ->? to be generated under these scenarios, just enter the cash "ows that represent the bene$t from depreciation expense and sol!e for net present !alue based upon a A'' of /I. ') F 8 ')/ F 0BJ8 ')0 F JH8 ')C F =C08 ')H F =BGJ8 and %*95 F /. 2ol!e for ->? F /0,GL/.JH 2o, all else equal the use of the accelerated depreciation method will result in a higher ->? 6by /0,GL/.JH7 than would the use of a straight=line depreciation method. 12/+
(6->?7 F .B6=G7 N .06=0B7 N .B6/07 N .0607 N .B6C7 F =C.B N =B. N J. N H. N /.B F C. million. σ->?
F O.B6=G K C70 N .06=0B K C70 N .B6/0 K C70 N .060 K C70 N .B6C K C70PQ F 0C.J00 million.
Chapter 12 Cash Flow Estimation and Risk Analysis
Answers and Solutions
+3
'?
12/4
A0C.J00 =
AC.:
=
G.LGH.
a7 he net cost is /GL,: 'ost of in!estment at t F : Mase price &odi$cation %ncrease in -4' 'ash outlay for new machine
6/H,7 6C,7 6L,7 6/GL,7
b7 he operating cash "ows follow: 9ear / C, 00,HH B0,HH
After=tax sa!ings Depreciation tax sa!ings -et operating cash "ow
9ear 0 C, C,J J,J
9ear C C, /,0 H,0
-otes: /. he after=tax cost sa!ings is B,6/ K 7 F B,6.J7 F C,. 0. he depreciation expense in each year is the depreciable basis, /G,, times the &A'52 allowance percentages of .CC, .HB, and ./B for 9ears /, 0, and C, respecti!ely. Depreciation expense in 9ears /, 0, and C is BJ,/, GJ,B, and 0B,B. he depreciation tax sa!ings is calculated as the tax rate 6HI7 times the depreciation expense in each year. c7 he terminal cash "ow is HL,GJ: 2al!age !alue ax on 2?R 5eturn of -4'
J, 6/E,0H7 L, HL,GJ
Rax on 2? F 6J, K //,E76.H7 F /E,0H. 5emaining M? in 9ear H F /G,6.G7 F //,E. d7 he project has an ->? of 6/E,BHE7. hus, it should not be accepted. 9ear / 0 C
-et 'ash )low 6/GL,7 B0,HH J,J LL,EJ
>? S /0I 6/GL,7 HJ,L0/ HL,C/ JC,C0 ->?F 6 /E,BHE7
Alternati!ely, place the cash "ows on a time line: /0I T =/GL,
+! Answers and Solutions
/ T B0,HH
0 T J,J
C T H,0 HL,GJ
Chapter 12 Cash Flow Estimation and Risk Analysis
LL,EJ ith a $nancial calculator, input the cash "ows into the cash "ow register, %*95 F /0, and then sol!e for ->? F =/E,BHL.JB ≈ =/E,BHE.
12/"
a7 he B, spent last year on exploring the feasibility of the project is a sunk cost and should not be included in the analysis. b7 he net cost is /0J,: >rice 6/L,7 &odi$cation 6/0,B7 %ncrease in -4' 6B,B7 'ash outlay for new machine6/0J,7 c7 he operating cash "ows follow: 9ear / /. After=tax sa!ings 0L,J 0. Depreciation tax sa!ings /C,E/L -et cash "ow H0,B/L
9ear 0 0L,J /L,EGE HG,BGE
9ear C 0L,J J,C0J CH,E0J
-otes: /. he after=tax cost sa!ings is HH,6/ K 7 F HH,6.JB7 F 0L,J. 0. he depreciation expense in each year is the depreciable basis, /0,B, times the &A'52 allowance percentages of .CC, .HB, and ./B for 9ears /, 0, and C, respecti!ely. Depreciation expense in 9ears /, 0, and C is CE,GJB, BH,00B, and /L,GB. he depreciation tax sa!ings is calculated as the tax rate 6CBI7 times the depreciation expense in each year. d7 he terminal cash "ow is B,G0: 2al!age !alue ax on 2?R 5eturn of -4'
JB, 6/E,GEL7 B,B B,G0
Rax on 2? F 6JB, K L,HCB76.CB7 F /E,GEL. M? in 9ear H F /0,B6.G7 F L,HCB. e7 he project has an ->? of /,LH/8 thus, it should be accepted. 9ear / 0 C
-et 'ash )low 6/0J,7 H0,B/L HG,BGE LB,J0L
>? S /0I 6/0J,7 CG,EJC CG,EC J,EHL ->?F /,LH/
Alternati!ely, place the cash "ows on a time line: /0I T =/0J,
/ T H0,B/L
0 T HG,BGE
Chapter 12 Cash Flow Estimation and Risk Analysis
C T CH,E0J Answers and Solutions
++
B,G0 LB,J0L ith a $nancial calculator, input the appropriate cash "ows into the cash "ow register, input %*95 F /0, and then sol!e for ->? F /,LH.B/ ≈ /,LH/.
12/,
a7 (xpected annual cash "ows: >roject A: >robable >robability U 'ash )low F 'ash )low .0 J, /,0 .J J,GB H,B .0 G,B /,B (xpected annual cash "owF J,GB >roject M: >robable >robability U 'ash )low F 'ash )low .0 .J J,GB H,B .0 /L, C,J (xpected annual cash "owF G,JB 'oecient of !ariation:
'? =
σ ->? 2tandardde!iation = (xpected!alue (xpected->?
>roject A: σA
=
6=GB:70 6:.07 + 6:70 6:.J7 + 6GB:70 6:.07 = HGH.CH.
>roject M: σM
=
0 0 6=G,JB:7 6:.07 + 6=E::70 6:.J7 + 6/:,CB:7 6:.07 = B,GEG.L
'?A F HGH.CH*J,GB F .GC. '?M F B,GEG.LH*G,JB F .GBGE. b7 >roject M is the riskier project because it has the greater !ariability in its probable cash "ows, whether measured by the standard de!iation or the coecient of !ariation. roject M is e!aluated at the /0I cost of capital, while >roject A requires only a /I cost of capital. @sing a $nancial calculator, input the appropriate expected annual cash "ows for >roject A into the cash "ow register, input %*95 F /, and sol!e for ->? A F /,CJ.0B. @sing a $nancial calculator, input the appropriate expected annual cash "ows for >roject M into the cash "ow register, input %*95 F /0, and sol!e for ->? M F //,J0H./.
+4 Answers and Solutions
Chapter 12 Cash Flow Estimation and Risk Analysis
>roject M has the higher ->?8 therefore, the $rm should accept >roject M. c7 he portfolio e#ects from >roject M would tend to make it less risky than otherwise. his would tend to reinforce the decision to accept >roject M. Again, if >roject M were negati!ely correlated with the D> 6>roject M is pro$table when the economy is down7, then it is less risky and >roject MVs acceptance is reinforced. 12/5
%f actual life is B years: @sing a time line approach: /I / T T %n!estment outlay 6CJ,7 4perating cash "ows excl. deprec. 6A7 G,0 Depreciation sa!ings 0,LL -et cash "ow 6CJ,7 /,L
0 T G,0 0,LL /,L
C T G,0 0,LL /,L
H T G,0 0,LL /,L
B T G,0 0,LL /,L
->?/I F 0,0//./C. %f actual life is H years: @sing a time line approach: /I / T T %n!estment outlay 6CJ,7 4perating cash "ows excl. deprec. 6A7 G,0 Depreciation sa!ings 0,LL ax sa!ings on loss -et cash "ow 6CJ,7 /,L
0 T
C T
G,0 0,LL
G,0 0,LL
/,L
/,L
H T G,0 0,LL 0,LL /0,EJ
->?/I F =0,L.JL. %f actual life is L years: @sing a time line approach: /I T 6CJ,7
/ T
%n!estment outlay 4perating cash "ows excl. deprec. 6A7 G,0 Depreciation sa!ings 0,LL -et cash "ow 6CJ,7 /,L
B T
• • •
G,0 0,LL /,L
J T
G T
L T
G,0
G,0
G,0
G,0
G,0
G,0
->?/I F /C,C0L.EC. %f the life is as low as H years 6an unlikely e!ent7, the in!estment will not be desirable. Mut, if the in!estment life is longer than H years, the in!estment will be a good one. herefore, the decision will depend on the managersV con$dence in the life of the tractor. i!en the low probability of the tractorVs life being only H years, it is likely that the managers will decide to purchase the tractor. Chapter 12 Cash Flow Estimation and Risk Analysis
Answers and Solutions
+"
+, Answers and Solutions
Chapter 12 Cash Flow Estimation and Risk Analysis
12/1. a7
%nitial in!estment 60B,7 -et oper. ' 60B,7 'ost sa!ings Depreciationa 4per. inc. before taxes axes 6HI7 4per. %nc. 6A7 Add: Depreciation 4per. ')
/
0
E, E, L0,B //0,B G,B 6 00,B7 C, 6E,7 H,B 6 /C,B7 L0,B //0,B LG, EE,
5eturn of -4' 2ale of &achine ax on sale 6HI7 -et cash "ow 60GB,7 LG, EE,
C
H
B
E, CG,B B0,B 0/, C/,B CG,B JE,
E, /G,B G0,B 0E, HC,B /G,B J/,
E, E, CJ, BH, BH,
J/,
0B, 0C, 6E,07 E0,L
JE,
->? F CG,CB./C %55 F /B.CI &%55 F /0.L/I >ayback F C.CC years -otes: a
Depreciation 2chedule, Masis F 0B,
9ear / 0 C H
Meg. Mk. ?alue &A'52 5ate 0B, .CC /JG,B .HB BB, ./B /G,B .G
&A'52 5ate × Masis F Depreciation L0,B //0,B CG,B /G,B 0B,
(nding M? /JG,B BB, /G,B
b7 %f sa!ings increase by 0I, then sa!ings will be 6/.076E,7 F /L,. %f sa!ings decrease by 0I, then sa!ings will be 6.L76E,7 F G0,.
Chapter 12 Cash Flow Estimation and Risk Analysis
Answers and Solutions
+5
6/7
2a!ings increase by 0I:
%nitial in!estment 60B,7 -et oper. ' 60B,7 'ost sa!ings Depreciation 4per. inc. before taxes axes 6HI7 4per. %nc. 6A7 Add: Depreciation 4per. ')
/
/L, L0,B 0B,B /,0 /B,C L0,B EG,L
0
C
/L, /L, //0,B CG,B 6 H,B7 G,B 6/,L7 0L,0 6 0,G7 H0,C //0,B CG,B /E,L GE,L
H
/L, /G,B E,B CJ,0 BH,C /G,B G/,L
B
/L, /L, HC,0 JH,L JH,L
5eturn of -4' 0B, 2ale of &achine 0C, ax on sale 6HI7 6E,07 -et cash "ow 60GB,7 EG,L /E,L GE,L G/,L /C,J ->? F GG,EGB.JC 607
2a!ings decrease by 0I:
%nitial in!estment 60B,7 -et oper. ' 60B,7 'ost sa!ings Depreciation 4per. inc. before taxes axes 6HI7 4per. %nc. 6A7 Add: Depreciation 4per. ')
/
0
G0, G0, L0,B //0,B 6/,B76 H,B7 6H,07 6/J,07 6 J,C76 0H,C7 L0,B //0,B GJ,0 LL,0
5eturn of -4' 2ale of &achine ax on sale 6HI7 -et cash "ow 60GB,7 GJ,0 LL,0
C
H
B
G0, CG,B CH,B /C,L 0,G CG,B BL,0
G0, /G,B BH,B 0/,L C0,G /G,B B,0
G0, G0, 0L,L HC,0 HC,0
B,0
0B, 0C, 6E,07 L0,
BL,0
->? F =C,EB.CG
4. Answers and Solutions
Chapter 12 Cash Flow Estimation and Risk Analysis
c7 orst=case scenario: %nitial in!estment 60B,7 -et oper. ' 6C,7 'ost sa!ings Depreciation 4per. inc. before taxes axes 6HI7 4per. %nc. 6A7 Add: Depreciationa 4per. ')
/
0
G0, G0, L0,B //0,B 6/,B76 H,B7 6H,07 6/J,07 6 J,C76 0H,C7 L0,B //0,B GJ,0 LL,0
5eturn of -4' 2ale of &achine ax on sale 6HI7 -et cash "ow 60L,7 GJ,0 LL,0
C
H
B
G0, CG,B CH,B /C,L 0,G CG,B BL,0
G0, /G,B BH,B 0/,L C0,G /G,B B,0
G0, G0, 0L,L HC,0 HC,0
BL,0
B,0
C, /L, 6G,07 LH,
C
H
B
->? F =G,JJC.B0 Mase=case scenario: his was worked out in part a. ->? F CG,CB./C. Mest=case scenario: %nitial in!estment 60B,7 -et oper. ' 60,7 'ost sa!ings Depreciation 4per. inc. before taxes axes 6HI7 4per. %nc. 6A7 Add: Depreciationa 4per. ')
/
/L, L0,B 0B,B /,0 /B,C L0,B EG,L
0
/L, /L, //0,B CG,B 6 H,B7 G,B 6/,L7 0L,0 6 0,G7 H0,C //0,B CG,B /E,L GE,L
/L, /G,B E,B CJ,0 BH,C /G,B G/,L
/L, /L, HC,0 JH,L JH,L
5eturn of -4' 0, 2ale of &achine 0L, ax on sale 6HI7 6//,07 -et cash "ow 60G,7 EG,L /E,L GE,L G/,L //,J ->? F L/,GCC.GE
orst=case Mase=case Mest=case
σ->?
>rob. .CB .CB .C
->? >rob. × ->? 6 G,JJC.B07 6 0,JL0.0C7 CG,CB./C /0,EJ0.C L/,GCC.GE 0H,B0./H (6->?7CH,L.0/
F O6.CB76=G,JJC.B0 K CH,L.0/70 N 6.CB76CG,CB./C K CH,L.0/70 N 6.C76L/,GCC.GE K CH,L.0/70PQ
Chapter 12 Cash Flow Estimation and Risk Analysis
Answers and Solutions
41
F OJC/,/L,E0G.EC N /,GHL,0C.BE N JJ,L0L,0GE.HEPQ F CB,EJG. LH. '? F CB,EJG.LH*CH,L.0/ F /.C. 12/11 a7 ->? of abandonment after 9ear t: @sing a $nancial calculator, input the following: ') F =00B, ')/ F 0CGB, and %*95 F / to sol!e for ->?/ F =EE.E ≈ =EE. @sing a $nancial calculator, input the following: ') F =00B, ')/ F J0B, ')0 F 00B, and %*95 F / to sol!e for ->?0 F =L0.JH ≈ =LC. @sing a $nancial calculator, input the following: ') F =00B, ')/ F J0B, - j F 0, ')C F /G0B, and %*95 F / to sol!e for ->?C F /,CG.0E ≈ /,CG. @sing a $nancial calculator, input the following: ') F =00B, ')/ F J0B, - j F C, ')H F //0B, and %*95 F / to sol!e for ->?H F G0J.GC ≈ G0G. @sing a $nancial calculator, input the following: ') F =00B, ')/ F J0B, - j F B, and %*95 F / to sol!e for ->?B F /,/E0.H0 ≈ /,/E0. he $rm should operate the truck for C years, ->?C F /,CG. b7 -o. Abandonment possibilities could only raise ->? and %55. he $rm;s !alue is maximized by abandoning the project after 9ear C. 12/12 a7 A''/ F /0I8 A''0 F /0.BI after C,0B, of new capital is raised. 2ince each project is independent and of a!erage risk, all projects whose %55 W A''0 will be accepted. 'onsequently, >rojects A, M, ', D, and ( will be accepted and the optimal capital budget is B,0B,. b7 %f >rojects ' and D are mutually exclusi!e, then only one of these projects can be accepted. he project that should be accepted is the one whose ->? is greater. hus, >roject D should be chosen because its ->? is greater than ->?'. >rojects A, M, D, and ( should be chosen and the optimal capital budget F H,,. c7 >roject A M ' D ( )
2ize GB, /,0B, /,0B, /,0B, GB, GB, GB,
%55
5isk
5isk=Adjusted A''
/H.I /C.B /C.0 /C. /0.G /0.C /0.0
/0.BI N 0I F/H.BI /0.B /0.B /0.B /0.B /0.BI K 0I F/.B /0.BI K 0I F/.B
>rojects M, ', D, (, ), and would be accepted because each has %55 W risk= adjusted A''. he optimal capital budget is J,,.
42 Answers and Solutions
Chapter 12 Cash Flow Estimation and Risk Analysis
Comprehensive8$preadsheet )roblem
Note to Instructors: *he sol#tion to this problem is not provided to st#dents at the back o their te6t7 9nstr#ctors can access the Excel :le on the te6tbook;s
12/13 a7
b7 he C, 5XD costs are sunk costs. herefore, these costs will ha!e no e#ect on ->? and other pro$tability measures. c7 %f the new project will reduce cash "ows from the $rmVs other projects, then this is a negati!e externality and must be considered in the analysis. 'onsequently, these should be considered costs of the new project and would reduce the projectVs ->?. %f the project can be housed in an empty building that the $rm owns and could sell if it were not used for the project, then this is an opportunity cost which should also be considered as a YcostY of this project. he after=tax sales amount for this building will reduce the projectVs ->?. d7 he projectVs cash "ows are likely to be positi!ely correlated with returns on the $rmVs other projects and with the economy. he $rm is in!ol!ed with materials and caulking compound is a building material, so it is a similar product to the $rmVs other products. %n addition, when the economy is booming, housing starts increase Zwhich would mean an increase in sales of the caulking compound. hether a project is positi!ely or negati!ely correlated with the $rmVs other projects impacts the risk of the project and the rele!ant cost of capital at which it should be e!aluated. e7
Chapter 12 Cash Flow Estimation and Risk AnalysisComprehensiveSpreadsheet 43 !roblem
4! ComprehensiveSpreadsheet !roblem Chapter 12 Cash Flow Estimation and Risk Analysis
7
Chapter 12 Cash Flow Estimation and Risk AnalysisComprehensiveSpreadsheet 4+ !roblem
g7 -ote that Ybest=caseY !alues for !ariable costs, $xed costs, A'', and equipment cost are 0I less than base=case !alues, while the Yworst=caseY !alues for !ariable costs, $xed costs, A'', and equipment cost are 0I higher than base=case !alues.
he scenario analysis suggests that the project could be highly pro$table, but also that it is quite risky. here is a 0BI probability that the project would result in a loss of 00G,E0. here is also a 0BI probability that it could produce an ->? of C0H,0HH. he standard de!iation is high, at /EJ,HBL, and the coecient of !ariation is a high G.BC.
44 ComprehensiveSpreadsheet !roblem Chapter 12 Cash Flow Estimation and Risk Analysis
9ntegrated Case
12/1!
Allied Food )rod#cts Capital "udgeting and Cash #low Estimation Allied Food )rod#cts is considering e6panding into the r#it j#ice b#siness with a new resh lemon j#ice prod#ct7 Ass#me that yo# were recently hired as assistant to the director o capital b#dgeting= and yo# m#st eval#ate the new project7 *he lemon j#ice wo#ld be prod#ced in an #n#sed b#ilding adjacent to Allied;s Fort >yers plant? Allied owns the b#ilding= which is #lly depreciated7 *he re@#ired e@#ipment wo#ld cost 2..=...= pl#s an additional !.=... or shipping and installation7 9n addition= inventories wo#ld rise by 2+=...= while acco#nts payable wo#ld increase by +=...7 All o these costs wo#ld be inc#rred at t B .7 y a special r#ling= the machinery co#ld be depreciated #nder the >ACR$ system as 3/year property7 *he applicable depreciation rates are 33D= !+D= 1+D= and "D7 *he project is e6pected to operate or ! years= at which time it will be terminated7 *he cash inows are ass#med to begin 1 year ater the project is #ndertaken= or at t B 1= and to contin#e o#t to t B !7 At the end o the project;s lie -t B !0= the e@#ipment is e6pected to have a salvage val#e o 2+=...7 nit sales are e6pected to total 1..=... #nits per year= and the e6pected sales price is 27.. per #nit7 Cash operating costs or the project -total operating costs less depreciation0 are e6pected to total 4.D o dollar sales7 Allied;s ta6 rate is !.D= and its
Integrated Case
4"
&o# have been asked to eval#ate the project and to make a recommendation as to whether it sho#ld be accepted or rejected7 *o g#ide yo# in yo#r analysis= yo#r boss gave yo# the ollowing set o @#estions7 *able 9C 12/17Allied;s Lemon G#ice )roject -*otal Cost in *ho#sands0 End o &ear 97
.
1
2
3
!
9nvestment O#tlay E@#ipment cost 9nstallation 9ncrease in inventory 9ncrease in acco#nts payable *otal net investment
997
Operating Cash Flows nit sales -tho#sands0 )rice8#nit
1.. 27..
27..
*otal reven#es
2..7 .
Operating costs= e6cl#ding depreciation
12.7 .
%epreciation 347. *otal costs
1557 2
Operating income beore ta6es -E9*0 *a6es on operating income
22,7 . !!7.
.73 Operating income ater ta6es -'O)A*0 %epreciation Operating cash ow 9997
147,
2+73 247!
.7.
"572 "57"
347. +!7"
*erminal &ear Cash Flows Ret#rn o net operating working capital $alvage val#e *a6 on salvage val#e *otal termination cash ows
4,
Integrated Case
Chapter 12 Cash Flow Estimation and Risk Analysis
9H7 H7
)roject Cash Flows )roject cash ow
-24.7. 0
,57"
Res#lts ')H B 9RR B >9RR B )ayback B
Chapter 12 Cash Flow Estimation and Risk Analysis
Integrated Case
45
A7
Allied has a standard orm that is #sed in the capital b#dgeting process? see *able 9C 12/17 )art o the table has been completed= b#t yo# m#st replace the blanks with the missing n#mbers7
Complete the table in the ollowing
steps -10 Fill in the blanks #nder &ear . or the initial investment o#tlay7 Answer I$how
$12/1
thro#gh
$12/+
here7J
*his
answer
is
straightorward7 'ote that acco#nts payable is an oKset to the inventory b#ild#p= so the net operating working capital re@#irement is 2.=...= which will be recovered at the end o the project;s lie7 I$ee completed table in the answer to A-+07J A7
-20 Complete
the table or #nit sales=
sales price= total
reven#es= and operating costs e6cl#ding depreciation7 Answer *his answer re@#ires no e6planation7
$t#dents may note=
tho#gh= that ination is not reected at this point7 9t will be later7
I*he completed table is shown below in the
answer to A-+07J A7
-30 Complete the depreciation data7
Answer I$how
$12/4
here7J
*he
only
thing
that
re@#ires
e6planation here is the #se o the depreciation tables in Appendi6 12A7 (ere are the rates or 3/year property? they are m#ltiplied by the depreciable basis= 2!.=...= to calc#late the ann#al depreciation allowances
".
Integrated Case
Chapter 12 Cash Flow Estimation and Risk Analysis
-%ollars in tho#sands0 &ear &ear &ear &ear
A7
1 2 3 !
.733 .7!+ .71+ .7." 17..
2!. 2!. 2!. 2!.
B "572 B 1.,7. B 347. B 147, 2!.7.
-!0 'ow complete the table down to 'O)A*= and then down to operating cash ows7
Answer I$how $12/" here7J *his is straightorward7 *he only even slightly complicated item is adding back depreciation to calc#late net CF7
I*he completed table is shown below in
the answer to A-+07J A7
-+0 'ow :ll in the blanks #nder &ear ! or the terminal cash ows= and complete the project cash ow line7 working capital7
%isc#ss
machinery were sold or less than its book val#e Answer I$how $12/, here7J
*hese are all straightorward7
'ote
that the net operating working capital re@#irement is recovered at the end o &ear !7 Also= the salvage val#e is #lly ta6able= beca#se the asset has been depreciated to a Mero book val#e7 9 book val#e were something other than Mero= the ta6 eKect co#ld be positive -i the asset were sold or less than book val#e0 or negative7
Chapter 12 Cash Flow Estimation and Risk Analysis
Integrated Case
"1
*able 9C 12/17 Allied;s Lemon G#ice )roject -*otal Cost in *ho#sands0 9np#ts
)rice HC rate
27.. 4.7. D
End o &ear 97
1.D !.D
.
9nvestment o#tlay E@#ipment cost 9nstallation 9ncrease in inventory 9ncrease in acco#nts payable
9n
.7.D
1
2
3
!
1.. 27.. 2..7 .
1.. 27.. 2..7 .
1.. 27.. 2..7 .
1.. 27.. 2..7 .
12.7 .
12.7 . 1.,7 . 22,7 . - 2,7.0 -1172 0 - 147,0 1.,7 . 5172
12.7 .
12.7 .
347. 1+47 . !!7.
147, 1347 , 4372
1"74 247!
2+73 3"75 147 , +!7"
-2..0 -!.0 -2+0 +
*otal net investment -24.0 997
Operating cash ows nit sales -tho#sands0 )rice8#nit *otal reven#es Operating costs= e6cl#ding depreciation %epreciation "572 1557 2 .7,
*otal costs Operating income beore ta6es *a6es on operating income
.73 .7+
Operating income ater ta6es %epreciation Operating cash ow 9997
.7.
"572 "57"
347. 427!
*erminal year cash ows Ret#rn o net operating working capital $alvage val#e
2.7. 2+7. -1.7. 0 3+7.
*a6 on salvage val#e *otal termination cash ows 9H7
"2
)roject cash ows )roject cash ow Integrated Case
-24.7.
Chapter 12 Cash Flow Estimation and Risk Analysis
0
"57"
5172
427!
,57"
-24.7.0
-1,.73 0
-,5710
-247"0
437.
1.471
11.7!
4,74
,57"
C#m#lative cash ow or payback Compo#nded inows or >9RR *erminal val#e o inows
3"!7, H7
Res#lts ')H B 9RR B >9RR B )ayback B
/!7. 573D 574D 373 years
Chapter 12 Cash Flow Estimation and Risk Analysis
Integrated Case
"3
7
-10 Allied #ses debt in its capital str#ct#re= so some o the money #sed to :nance the project will be debt7 Niven this act= sho#ld the projected cash ows be revised to show projected interest charges E6plain7
Answer I$how $12/5 here7J *he projected cash ows in the table sho#ld not be revised to show interest charges7 *he eKects o debt :nancing are reected in the cost o capital= which is #sed to disco#nt the cash ows7
9ncl#ding interest
charges wo#ld constit#te a do#ble co#ntingP o the cost o debt :nancing7 7
-20 $#ppose yo# learned that Allied had spent +.=... to renovate the b#ilding last year= e6pensing these costs7 $ho#ld this cost be reected in the analysis E6plain7
Answer I$how $12/1. here7J *his e6pendit#re is a s#nk cost= hence it wo#ld not aKect the decision and sho#ld not be incl#ded in the analysis7 7
-30 'ow s#ppose yo# learned that Allied co#ld lease its b#ilding to another party and earn 2+=... per year7
$ho#ld that
act be reected in the analysis 9 so= how Answer I$how $12/11 here7J
*he rental payment represents an
opport#nity cost= and as s#ch its ater/ta6 amo#nt= 2+=...-1 Q *0 B 2+=...-.740 B 1+=...= sho#ld be s#btracted rom the cash ows the company wo#ld otherwise have7 7
-!0 'ow ass#me that the lemon j#ice project wo#ld take away pro:table sales rom Allied;s resh orange j#ice b#siness7 $ho#ld that act be reected in yo#r analysis 9 so= how
"!
Integrated Case
Chapter 12 Cash Flow Estimation and Risk Analysis
Answer I$how $12/12 here7J
*he decreased sales rom Allied;s
resh orange j#ice b#siness sho#ld be acco#nted or in the analysis7 *his is an e6ternality to Alliedthe lemon j#ice project will aKect the cash ows to its orange j#ice b#siness7 $ince the lemon j#ice project will take b#siness away rom its orange j#ice b#siness= the reven#es as shown in this analysis are overstated= and th#s they need to be red#ced by the amo#nt o decreased reven#es or the orange j#ice b#siness7 E6ternalities are oten diSc#lt to @#antiy= b#t they need to be considered7 C7
%isregard all the ass#mptions made in part = and ass#me there was no alternative #se or the b#ilding over the ne6t ! years7
'ow calc#late the project;s ')H= 9RR= >9RR= and
payback7
%o these indicators s#ggest that the project
sho#ld be accepted Answer I$how $12/13 here7J
and e6plain how each o the indicators is calc#lated7
2 T 5172
3 T 427!
! T ,57"
')H B /!7.7 ')H is negative? do not accept7 9RR B / A24.
A"57" -1 9RR 0
9RR B 573D7
A5172 1
-1 9RR 0
A427! 2
-1 9RR 0
A,57" 3
-1 9RR 0 !
.7
9RR is less than the cost o capital? do not
accept7 Chapter 12 Cash Flow Estimation and Risk Analysis
Integrated Case
"+
>9RR
. 1.D 1 T T -24.0 "57"
2 T 5172
3 T 427!
! T ,57" 171. 4,74 -171.0 11.7! -171.0 1.471 *erminal val#e -*H0 3"!7, 2
3
)H o *H 24. ')H .
>9RR B 574D
>9RR is less than the cost o capital? do not accept7 )ayback
&ear . 1 2 3 !
Cash Flow -24.7.0 "57" 5172 427! ,57"
C#m#lative Cash Flow -24.7.0 -1,.730 -,5710 -247"0 437.
)ayback B 3 years U 247"8,57" B 373 years7 ased on the analysis to this point= the project sho#ld not be #ndertaken7 (owever= this may not be correct= as we will see shortly7 %7
9 this project had been a replacement rather than an e6pansion project= how wo#ld the analysis have changed *hink abo#t the changes that wo#ld have to occ#r in the cash ow table7
Answer I$how $12/1! here7J
9n a replacement analysis= we m#st
:nd diKerences in cash ows= i7e7= the cash ows that wo#ld e6ist i we take on the project vers#s i we do not7 *h#s= in the table there wo#ld need to be= or each year= a col#mn or no change= a col#mn or the new project= and or the diKerence7 *he diKerence col#mn is the one that wo#ld be #sed to obtain the ')H= 9RR= etc7 "4
Integrated Case
Chapter 12 Cash Flow Estimation and Risk Analysis
E7
-10
Answer I$how $12/1+ thro#gh $12/1, here7J
(ere are the three
types o project risk 17
$tand/alone risk is the projectVs total risk i it were operated independently7 $tand/alone risk ignores both the :rmVs diversi:cation among projects and investorsV diversi:cation
among
:rms7
$tand/alone
risk
is
meas#red either by the projectVs standard deviation 27
0 or its coeScient o variation o ')H -CH ')H07
')H
9t is the
contrib#tion o the project to the :rmVs total risk= and it is a #nction o -a0 the projectVs standard deviation o ')H and -20 the correlation o the projectsV ret#rns with those o the rest o the :rm7
>arket risk is the riskiness o the project to a well/ diversi:ed investor7 *heoretically= it is meas#red by the projectVs beta= and it considers both corporate risk and stockholder diversi:cation7
E7
-20
Answer I$how $12/15 here7J eca#se managementVs primary goal is shareholder wealth ma6imiMation= the most relevant risk or capital projects is market risk7 Chapter 12 Cash Flow Estimation and Risk Analysis
(owever= creditors= Integrated Case
""
c#stomers= s#ppliers= and employees are all aKected by a :rmVs total risk7 $ince these parties in#ence the :rmVs pro:tability= a projectVs within/:rm risk sho#ld not be completely ignored7 E7
-30
Answer I$how $12/2. here7J
y ar the easiest type o risk to
meas#re is a projectVs stand/alone risk7 *h#s= :rms oten oc#s primarily on this type o risk when making capital b#dgeting decisions7 *his oc#s is not theoretically correct= b#t it does not necessarily lead to poor decisions= beca#se most projects that a :rm #ndertakes are in its core b#siness7 E7
-!0 Are the three types o risk generally highly correlated
Answer I$how $12/21 here7J
eca#se most projects that a :rm
#ndertakes are in its core b#siness= a projectVs stand/alone risk is likely to be highly correlated with its corporate risk= which in t#rn is likely to be highly correlated with its market risk7 F7
-10
Answer I$how $12/22 here7J
$ensitivity analysis meas#res the
eKect o changes in a partic#lar variable= say reven#es= on a projectVs ')H7
*o perorm a sensitivity analysis= all
variables are :6ed at their e6pected val#es e6cept one7 *his one variable is then changed= oten by speci:ed percentages= and the res#lting eKect on ')H is noted7 -One co#ld allow more than one variable to change= b#t this then ",
Integrated Case
Chapter 12 Cash Flow Estimation and Risk Analysis
merges sensitivity analysis into scenario analysis70
Chapter 12 Cash Flow Estimation and Risk Analysis
Integrated Case
"5
F7
-20 (ow wo#ld one perorm a sensitivity analysis on the #nit sales= salvage val#e= and
Ass#me
that each o these variables deviates rom its base/case= or e6pected= val#e by pl#s and min#s 1.D= 2.D= and 3.D7 E6plain how yo# wo#ld calc#late the ')H= 9RR= >9RR= and payback or each case= b#t don;t do the analysis #nless yo#r instr#ctor asks yo# to7 Answer *he base case val#e or #nit sales was 1..? thereore= i yo# were to ass#me that this val#e deviated by pl#s and min#s 1.D= 2.D= and 3.D= the #nit sales val#es to be #sed in the sensitivity analysis wo#ld be ".= ,.= 5.= 11.= 12.= and 13. #nits7 &o# wo#ld then go back to the table at the beginning o the problem= insert the appropriate sales #nit n#mber= say ". #nits= and rework the table or the change in sales #nits arriving at diKerent net cash ow val#es or the project7 Once yo# had the net cash ow val#es= yo# wo#ld calc#late the ')H= 9RR= >9RR= and payback as yo# did previo#sly7 -'ote that sensitivity analysis involves making a change to only one variable to see how it impacts other variables70 *hen= yo# wo#ld go back and repeat the same steps or ,. #nitsthis wo#ld be done or each o the #nit sales val#es7 *hen= yo# wo#ld repeat the same proced#re or the sensitivity analysis on salvage val#e and on cost o capital7 -'ote that or the cost o capital analysis= the net cash ows wo#ld remain the same= b#t the cost o capital #sed in the ')H and >9RR calc#lations wo#ld be diKerent70 Excel $ is ideally s#ited or sensitivity analysis7 9n act
we created a spreadsheet to obtain this project;s net cash ows and its ')H= 9RR= >9RR= and payback7 Once a model ,.
Integrated Case
Chapter 12 Cash Flow Estimation and Risk Analysis
has been created= it is very easy to change the val#es o variables and obtain the new res#lts7
*he res#lts o the
sensitivity analysis on the projectVs ')H -or the +D ination case= #sing *able 9C 12/20 ass#ming the pl#s and min#s 1.D= 2.D= and 3.D deviations are shown below7
*he sensitivity lines intersect at .D change and the base case ')H= at appro6imately 1+=...7
$ince all
other variables are set at their base case= or e6pected= val#es= the Mero change sit#ation is the base case7 27
*he plots or #nit sales and salvage val#e are #pward sloping= indicating that higher variable val#es lead to higher
')Hs7
Conversely=
the
plot
or
is
downward sloping= beca#se a higher
*he plot o #nit sales is m#ch steeper than that or salvage val#e7 *his indicates that ')H is more sensitive to changes in #nit sales than to changes in salvage val#e7
!7
$teeper sensitivity lines indicate greater risk7 *h#s= in comparing two projects= the one with the steeper lines is considered to be riskier7
Chapter 12 Cash Flow Estimation and Risk Analysis
Integrated Case
,1
*he sensitivity data are given here in tab#lar orm -in tho#sands o dollars0 Change rom ase Level
Res#lting ')H ater the 9ndicated Change in nit $ales $alvage Hal#e
/3.D /2. /1. . U1. U2. U3. F7
-347!0 -15730 -2710 1+7. 3271 !572 4473
1175 1275 1375 1+7. 147. 1"7. 1,7.
3!71 2"7+ 2171 1+7. 57. 373 -2720
-30
Answer I$how $12/23 here7J
*he two primary disadvantages o
sensitivity analysis are -10 that it does not reect the eKects o diversi:cation and -20 that it does not incorporate any inormation abo#t the possible magnit#des o the orecast errors7 *h#s= a sensitivity analysis might indicate that a projectVs ')H is highly sensitive to the sales orecast=
,2
Integrated Case
Chapter 12 Cash Flow Estimation and Risk Analysis
hence that the project is @#ite risky= b#t i the projectVs sales= hence its reven#es= are :6ed by a long/term contract= then sales variations may act#ally contrib#te little to the projectVs risk7 *hereore= in many sit#ations= sensitivity analysis is not a partic#larly good indicator o risk7
(owever= sensitivity
analysis does identiy those variables that potentially have the
greatest
impact
on
pro:tability=
and
this
helps
management oc#s its attention on those variables that are probably most important7
Ass#me that ination is e6pected to average +D over the ne6t ! years= and this e6pectation is reected in the oreover= ination is e6pected to increase reven#es and variable costs by this same +D7
%oes it appear that
ination has been dealt with properly in the initial analysis to this point 9 not= what sho#ld be done= and how wo#ld the re@#ired adj#stment aKect the decision Answer I$how $12/2! thro#gh $12/24 here7J 9t is apparent rom the data in the previo#s table that ination has not been reected in the calc#lations7 9n partic#lar= the sales price is held constant rather than rising with ination7 *hereore= reven#es and costs -e6cept depreciation0 sho#ld both be increased by +D per year7 $ince reven#es are larger than operating costs= ination will ca#se cash ows to increase7 *his will lead to a higher ')H= 9RR= and >9RR= and to a Chapter 12 Cash Flow Estimation and Risk Analysis
Integrated Case
,3
shorter payback7 *able 9C 12/2 reects the changes= and it shows the new cash ows and the new indicators7
ination is properly acco#nted or the project is seen to be pro:table7
,!
Integrated Case
Chapter 12 Cash Flow Estimation and Risk Analysis
*able 9C 12/27Allied;s Lemon G#ice )roject Considering +D 9nation -*otal Cost in *ho#sands0 9np#ts
)rice HC rate
27.. 4.7. D
End o &ear 97
1.D !.D
.
9nvestment o#tlay E@#ipment cost 9nstallation 9ncrease in inventory 9ncrease in acco#nts payable
9n
+7.D
1
2
3
!
1.. 271. 21.7 .
1.. 272. + 22.7 +
1.. 2731 + 2317 +
1.. 27!3 1 2!37 1
1247 .
1327 3 1.,7 . 2!.7 3 - 157,0 -"75 0 - 11750 1.,7 . 5471
13,7 5
1!+7 5
347. 1"!7 5 +474 227 4 3!7.
147, 1427 " ,.7!
-2..0 -!.0 -2+0 +
*otal net investment -24.0 997
Operating cash ows nit sales -tho#sands0 )rice8#nit *otal reven#es Operating costs= e6cl#ding depreciation %epreciation "572 2.+7 2 !7,
*otal costs Operating income beore ta6es *a6es on operating income
175 275
Operating income ater ta6es %epreciation Operating cash ow 9997
.7.
"572 ,271
*erminal year cash ows Ret#rn o net operating working capital $alvage val#e *a6 on salvage val#e *otal termination cash ows
9H7
347. ".7.
3271 !,73 147 , 4+71 2.7. 2+7. -1.7. 0 3+7.
)roject cash ows
Chapter 12 Cash Flow Estimation and Risk Analysis
Integrated Case
,+
)roject cash ow
-24.7. 0
,271
5471
".7.
1..7 1
-24.7.0
-1""75 0
-,17,0
-117,0
,,73
1.572
11473
""7.
1..71
C#m#lative cash ow or payback Compo#nded inows or >9RR *erminal val#e o inows
!.274 H7
,4
Res#lts ')H B 9RR B >9RR B )ayback B
1+7. 1274D 1174D 371 years
Integrated Case
Chapter 12 Cash Flow Estimation and Risk Analysis
(7
*he e6pected cash ows= considering ination -in tho#sands o dollars0= are given in *able 9C 12/27 Allied;s
9
prod#ct acceptance is poor= sales wo#ld be only "+=... #nits a year= while a strong cons#mer response wo#ld prod#ce sales o 12+=... #nits7 9n either case= cash costs wo#ld still amo#nt to 4.D o reven#es7 &o# believe that there is a 2+D chance o poor acceptance= a 2+D chance o e6cellent acceptance= and a +.D chance o average acceptance -the base case07
)rovide n#mbers only i yo# are #sing a
comp#ter model7 -10
model to develop the scenarios -in tho#sands o dollars0= which are s#mmariMed below Case
)robability .72+ .7+. .72+
')H -...s0 -2"7,0 1+7. +"7,
-20 se the worst= most likely -or base0= and best/case ')Hs= with their probabilities o occ#rrence= to :nd the projectVs e6pected
')H=
standard
deviation=
and
coeScient
o
variation7 Answer I$how $12/25 here7J *he e6pected ')H is 1!=54, -ro#nded to the nearest tho#sand below07 E-')H0 B .72+-/2"7,0 U .7+.-1+7.0 U .72+-+"7,0 B 1+7
Chapter 12 Cash Flow Estimation and Risk Analysis
Integrated Case
,"
*he standard deviation o ')H is 3.73 ')H
B I.72+-/2"7, Q 1+0 2 U .7+.-1+ Q 1+0 2U .72+-+"7, Q
1+02JW B I514JW B 3.73= and the projectVs coeScient o variation is 27. CH')H B
97
')H
A3.73
E-')H0
A1+
27.7
Ass#me that AlliedVs average project has a coeScient o variation -CH0 in the range o 172+ to 17"+7
lemon j#ice project be classi:ed as high risk= average risk= or low risk
*he CH meas#res a
projectVs stand/alone riskit is merely a meas#re o the variability o ret#rns -as meas#red by
0 abo#t the
')H
e6pected ret#rn7 G7
ased on common sense= how highly correlated do yo# think the project wo#ld be with the :rmVs other assets -Nive a correlation coeScient= or range o coeScients= based on yo#r j#dgment70
Answer I$how $12/31 here7J 9t is reasonable to ass#me that i the economy is strong and people are b#ying a lot o lemon j#ice= then sales wo#ld be strong in all o the companyVs lines= so there wo#ld be positive correlation between this project and the rest o the b#siness7 (owever= each line
,,
Integrated Case
Chapter 12 Cash Flow Estimation and Risk Analysis
co#ld be more or less s#ccess#l= so the correlation wo#ld be less than U17.7
A reasonable g#ess might be U.7"= or
within a range o U.7+ to U.757 X7
(ow wo#ld this correlation coeScient and the previo#sly calc#lated
combine to aKect the projectVs contrib#tion to
corporate= or within/:rm= risk E6plain7 Answer I$how $12/32 here7J 9 the projectVs cash ows are likely to be highly correlated with the :rmVs aggregate cash ows= which is generally a reasonable ass#mption= then the project wo#ld have high corporate risk7
(owever= i the
projectVs
to
cash
ows
were
e6pected
be
totally
#ncorrelated with the :rmVs aggregate cash ows= or positively correlated b#t less than perectly positively correlated= then accepting the project wo#ld red#ce the :rmVs total risk= and in that case= the riskiness o the project wo#ld be less than s#ggested by its stand/alone risk7
9 the projectVs cash ows were e6pected to be
negatively correlated with the :rmVs aggregate cash ows= then the project wo#ld red#ce the total risk o the :rm even more7 L7
ased on yo#r j#dgment= what do yo# think the projectVs correlation coeScient wo#ld be with respect to the general economy and th#s with ret#rns on Ythe marketY
(ow
wo#ld correlation with the economy aKect the project;s market risk Answer 9n all
likelihood=
this
project wo#ld
have
a
positive
correlation with ret#rns on other assets in the economy= Chapter 12 Cash Flow Estimation and Risk Analysis
Integrated Case
,5
and speci:cally with the stock market7 Allied Food )rod#cts prod#ces ood items= and s#ch :rms tend to have less risk than the economy as a wholepeople m#st eat regardless o the national economic sit#ation7 (owever= people wo#ld tend to spend more on non/essential types o ood when the economy is good and to c#t back when the economy is weak7 A reasonable g#ess might be U.7"= or within a range o U.7+ to U.757 9 an asset -project= in this case0 has a high correlation with the market= it has a high beta= and hence high market risk7 >7
Allied typically adds or s#btracts 3D to its
Ater adj#sting or risk= sho#ld the lemon j#ice
project be accepted $ho#ld any s#bjective risk actors be considered beore the :nal decision is made E6plain7 Answer I$how $12/33 and $12/3! here7J $ince the project is j#dged to have above/average risk= its diKerential risk/adj#sted= or project= cost o capital wo#ld be 13D7 At this disco#nt rate= its ')H wo#ld be /2=224= so it wo#ld not be acceptable7 9 it were a low/risk project= its cost o capital wo#ld be "D= its ')H wo#ld be 3!=11"= and it wo#ld be a pro:table project on a risk/ adj#sted basis7 (owever= a n#merical analysis s#ch as this one may not capt#re all o the risk actors inherent in the project7 9 the project has a potential or bringing on harm#l laws#its= then it might be riskier than :rst assessed7 Also= i the projectVs assets can be redeployed within the :rm or can be easily sold= then the project may be less risky than the analysis indicates7 '7
9n recent months= Allied;s gro#p has beg#n to oc#s on real option analysis7
5.
Integrated Case
Chapter 12 Cash Flow Estimation and Risk Analysis
