Capital Budgeting
frequency of techniques uses
most- IRR, NPV, hurdle rate, payback least- APV least, then PI
CAPITAL BUDGETING VS CAPITAL STRUCTURE
project A- 10%, project B- 5% (would have negative NPV) cost of capital assume= 8% (part of long term debt and equity) cost of capital- avg funding - cost for company financial manager would pick project A bc it has a higher return -if both projects have IRR < cost of capital, both would have negative NPV so reject both
PAYBACK PERIOD advantages
Advantages Easy Disadvantages -Does not take the time value of money . -Requires an arbitrage cutoff point. -Ignore cash flows beyond the cutoff point -No necessary relationship between payback and investor wealth maximization
AVERAGE ACCOUNTING RETURN (AAR)
Concept Average accounting profits over average accounting value Method AAR= average net income / average book value -avg book value depends on how asset is depreciated avg BV= (initial investment + salvage value)/2- [conditions- straight line and zero salvage value] decision rule: if ARR > target benchmark -> accept if ARR < target benchmark -> reject
CAPITAL BUDGETING
Stand-alone project Take-it-or-leave-it decision / go-or-no-go choice Decision on this project will not affect the decisions on other projects Follow simple decision rule. Mutually exclusive projects Can only choose one among multiple projects -require the use of the same limited resource
The scale problem
Suppose I'd like to open a convenience store in Amherst. My 5-year-old nephew claims to have a better business idea: a lemonade stand at UB. Suppose the cost of capital for us is 10%. lemonade stand- higher IRR convenient store- higher NPV Suppose they are mutually exclusive, which one should I invest (???? ask her)
PROFITABILITY INDEX
Concept Value created per dollar invested Method PI= sumt=1 of PV(CFt)/initial investment Decision rule If NPV >0 -> PI>1 -> accept If NPV <0 -> PI<1 -> reject
NPV Advantage
Takes the time value of money into consideration Considers all cash flows (not all methods consider all CF) Not accounting income (CF is the main focus in next chapter) -not all methods incorporate cost of capital Incorporate cost of capital in the discount rate . Easy and intuitive to interpret NPV>0 :Project will increase shareholders value. NPV<0 :Project will decrease shareholders value. Best method. Golden rule.
WHEN NPV AND IRR CONFLICT
The NPV rule: Choose the one with largest NPV The IRR rule: Choose the one with highest IRR When conflicts exist between mutually exclusive projects, use the NPV method.
TRUE OR FALSE
"If a project has non-conventional cash flows and has multiple IRRs, the lowest one (IRR) is incorrect." -FALSE. in this case, either use NPV or MIRR, abandon IRR rule
INTERNAL RATE OF RETURN (IRR) cont
Decision rule of IRR IRR > Cost of capital: Accept the project IRR < Cost of capital: Reject the project Generally, for mutually exclusive projectsIf IRR>cost of capital IRR > Cost of capital -> NPV>0 -> both rules accept If IRR<cost of capital -> NPV<0 -> both rules reject In some occasions*** The two rules have conflicts results When this happens & what will we choose? ***
AVERAGE ACCOUNTING RETURN (AAR) Q's
Does the AAR rule account for the time value of money?- No. AAR ignores time value of money Does the AAR rule account for the risk of the cash flows?- NO. AAR does not consider cash flows or market value. instead, it uses net income and book value Does the AAR rule provide an indication about the increase in value?- No. AAR is not a rate of return w meaningful economic sense
FOR EACH METHOD YOU NEED TO KNOW...
How to calculate it How to interpret it (what is the decision rule?) In stand-alone decisions In mutually exclusive situations What are the advantage(s) and disadvantage(s) of such method Generally, we take NPV method as golden standard.
CAPITAL PROJECTS
Long-term decisions Large expenditures for: -New plant and equipment -Expansion -Replacement of equipment -Research and Development (R&D) -Mergers and acquisitions Difficult/impossible to reverse
FEED YOUR BRAIN
Modified internal rate of return (MIRR) is specifically designed to address the problems associated with unconventional cash flows -MIRR is not a true return pros: MIRR can be used in unconventional CFs. MIRR has only one single solution cons: interpretation not intuitive
AAR advantages
Advantages Easy to calculate. Needed information will usually be available Disadvantages Ignore time value of money. Require an arbitrary benchmark cutoff rate ("a target AAR") Based on accounting number and book value, not cash flows and market value.
PROFITABILITY INDEX advantages
Advantages Easy to communicate. Related to NPV, generally leading to identical decisions Usually used to rank projects if firms have capital rationing (limited set on the amount of money.funds available for investment. may land on suboptimal decision bc of constraints) Disadvantages May lead to conflicting decisions to NPV rule in the mutually exclusive projects.
PAYBACK PERIOD
Concept How many years does it take to get our money back? (to break even) Method Add up the cash flows produced by the project until they equal your initial investment Determine how many years it took to recover the initial investment Compare with the company's cutoff period(prespecified) , the shorter the better
INTERNAL RATE OF RETURN (IRR)
Concept Express the project return in a percentage rate Method IRR is the discount rate that sets NPV equal to zero NPV= CFo + sum(CFt/(1+IRR)^t=0 issue CFo is negative -solve for the rate that makes this equation trye conceptually, IRR is similar to bonds YTM This is also the rate at which the project would break even! Excelfunction:=IRR(CF0,CF1,CF2...[default=10%]
Nonconventional Cash Flows
Create multiple IRRs t=0- CF= (1.60) t=1- CF= 10.00 t=2- CF= (10.00) excel =IRR(B1:B3, 10%) IRR= 25% =IRR(B1:B3, 200%) IRR= 400% -multiple IRR problem (multiple IRRs can make NPV=0) if cost of capital is 10%, NPV is negative based on graph in notes, so reject project Non-conventional cash flows create multiple IRRs Can we prepare for "multiple IRRs"? Yes, based on cash flow pattern! rule: # of change in CF signs= number of IRR solutions ex. -4, 3, 3, 5, -7
INTERNAL RATE OF RETURN
Critical pitfalls with IRR Conventional cash flow-one sign change- [−,+,+,+,...] (capital budgeting- investment decision) or[+,−,−,−,...] (capital structure- financing decision) Nonconventional CFs create multiple IRRs -> This creates problem when making decision.
MUTUALLY EXCLUSIVE PROJECTS WHEN NPV AND IRR CONFLICT
Critical pitfalls with IRR II. What if NPV and IRR produce conflicting conclusion when the projects are mutually exclusive? • The NPV rule: Choose the one with largest NPV • The IRR rule: Choose the one with highest IRR Cause to this pitfall -The scale problem -The timing problem
MODIFIED INTERNAL RATE OF RETURN (MIRR)
Modified internal rate of return (MIRR)- one solution only Can fix multiple IRRs issue. assumption: company can reinvest cash flows at rate of cost of capital (so interest rate used to compound=cost of capital) Method: The Reinvestment Approach (4 cash flows) CFo= (FVCF1 + FVCF2 + FVCF3 + FVCF4)/(1+MIRR)^4 -need to find MIRR- discount interest rate that makes terminal value= CFo
methods
NPV: investment rule- Accept project if NPV is positive.For mutually exclusive projects, choose the one with the highest (positive) NPV. comments-The "gold standard" of investment criteria, Only criterion necessarily consistent with maximizing the value of the firm, Provides appropriate rule for choosing among mutually exclusive investments, Only pitfall involves capital rationing, when one cannot accept all positive NPV projects. IRR: investment rule- Accept project if IRR is greater than cost of capital. comments- If used properly, results in same accept-reject decision as NPV in the absence of project interactions, Beware of the pitfall: IRR cannot rank mutually exclusive projects— the project with higher IRR may have lower NPV, The simple IRR rule cannot be used in cases of multiple IRRs.
NET PRESENT VALUE (NPV)
The present value of the project's all cash flows NPV= CFo + CF1/(1+r)^1 + CF2/(1+r)^2 + CFn/(1+r)^n r- discount rate= cost of capital if benefits of investment> costs to acquire- good investment Decision rule of NPV (stand-alone): if NPV > 0- undertake the project if not- reject Project S Cash Flow $ (1,000) $ 500 $ 400 $ 300 $ 100 (1000) + (500/1.1) + (400/1.1^2) + (300/1.1^3) + (100/1.1^4)= 78.82 Project L Cash Flow $ (1,000) $ 100 $ 300 $ 400 $ 675 NPV= 100.43 Should you accept or reject each project if they are stand-alone? both (both positive) What project should accept if they are mutually exclusive? project L, bigger NPV
AVERAGE ACCOUNTING RETURN (AAR) ex
You're trying to determine whether or not to expand your business by building a new manufacturing plant. The plant has an installation cost of $10.8 million, which will be depreciated straight-line to zero over its four-year life. It the plant has projected net income (in thousands) of $1,293, $1,725, $1,548, and $1,310 over these four years, what is the project's average accounting return(AAR)? avg net income= (1293 + 1725 + 1548 + 1310)/4= 1469 depreciation expenses= (10800[initial investment]-0[salvage value])/4=2700 fixed assets: t=0- BV= 10800 t=1- 10800-2700= 8700 (book value) t=2- 8700-2700= 5400 (BV) t=3- 5400-2700= 2700 t=4- 2700-2700=0 average book value= (10800 + 8700 + 5400 _ 2700 + 0)/5 or (10800 + 0)/2= 5400 [second one conditions- straight line and zero salvage value] AAR= 1469/5400= 27.2% -comparable with target AAR (not cost of capital)
PRACTICEMODIFIED INTERNAL RATE OF RETURN
cost of capital is 10% t=0 CF- (1000), t=1 CF- 500, t=2 CF- 400, t=3 CF- 300, t=4 CF- 100 500(1+10%)^3[3 away from CF4] + 400(1.1)^2 + 300(1.1) + 400= 1579.50 1000[use positive #]= 1579.5/(1+MIRR)^4 MIRR= 12.11%
MUTUALLY EXCLUSIVE PROJECTS WHEN NPV AND IRR CONFLICT cont
cost of capital= 0%, project A= $60, project B= $70- NPV decision- choose project B cost of capital= 5%, project A= $43.13, project B= $47.88- NPV decision- choose project B cost of capital= 10%, project A= $29.06, project B= $29.79- NPV decision- choose project B -first 3 have NPV and IRR result in conflict decision -CC 10% and lower, pick highest NPV- B cost of capital= 15%, project A= $17.18, project B= $14.82- NPV decision- choose project A cost of capital= 20%, project A= $7.06, project B= $2.31- NPV decision- choose project A -somewhere 10-15%, two projects have same NPV (crossover point) -CC 14% and up, pick highest (A) IRR A- 24%, B- 21.03%- pick A -NPV generally decreases as discount rate increases (inverse relationship) -when there are conflicting decisions between NPV and IRR, NPV is golden standard. IRR can be misleading
methods cont
payback period: investment rule- Accept project if payback period is less than specified number of years. comments- A quick and dirty rule of thumb, with several critical pitfalls., Ignores cash flows beyond the acceptable payback period, Ignores discounting (time value of money), Tends to improperly reject long-lived projects. profitability index: investment rule- Accept project if profitability index is greater than 1.In case of capital rationing, accept projects with highest profitability index comments- Results in same accept-reject decision as NPV, Useful for ranking projects in case of capital rationing, but misleading in the presence of interactions, Cannot rank mutually exclusive projects.
EXAMPLE OF CAPITAL RATIONING
project C- NPV=21, PI=3.1 project D- NPV=16, PI=4.2 project E- NPV=12, PI=3.4 budget= 10 A. Which projects will be chosen if these are mutually exclusive projects?- mutually exclusive- use NPV and choose project w largest NPV B. Which projects should the manager choose with capital rationing? 1. rank the projects based on PI 2. select projects w the highest PI until budget is exhausted (D -> E -> C) -project D and E combined create value of 16+12=28 for shareholders (bc 5 [CFD1] + 5 [CFE1] = 10 (budget)) -project C alone can also meet capital budget but create only $21M for SHs project D and E are better choices here even if project C has the highest NPV- may lead to conflicting decisions to NPV rule in mutually exclusive projects
PROFITABILITY INDEX ex
t=0 CF- (1000), t=1 CF- 500, t=2 CF- 400, t=3 CF- 300, t=4 CF- 100 r=10% (-1000) + (500/1.1) + (400/1.1^2) + (300/1.1^3) + (100/1.1^4) NPV (sum of PV)= 78.82 PI= 1078.82/1000= 1.08 -each $ of investment project will create $1.08 or $.08 of NPV if project S PI= 1.08 and project L PI= 1.1 -stand alone, take both (PI>1) -mutually exclusive- take project L (large PI)
payback period example
t=0 CF- (1000), t=1 CF- 500, t=2 CF- 400, t=3 CF- 300m t=4 CF- 100 500-1000= -500 400 -500= -100 300-100=200 (stop when accumulative CF is positive) -project is paid back somewhere between 2nd and 3rd period -project pays back $900 by the end of the second and leaves $100 to be recovered in the third -this $100 is 100/300= .33 of third period -it will take 2+.33= 2.33 years to recover the project 2.33 < 3 (cutoff) so accept project (if PB period is greater than cutoff, reject project)
The timing problem
timing of cash inflows Project A - (100), 50, 40, 40, 30 project B- (100), 20, 40, 50, 60 -observe pattern of cash inflows between two projects -project A pays back faster than B
